{ "total": 2000, "page": 1, "pagesize": 200, "questions": [ { "tags": [], "question_id":86200, "title": "Start", "body": "

Welcome to the STEP database website

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To find a question, or a year, or a topic, simply type a keyword in the search box, e.g.

88 (year) S2 (STEP II) Q2 (Question 2)

or

Pure (Mech or Stats) Coordinate geometry

Each question entry has access to the pdf and the tex source files (the program these papers are typesetted) for that paper, i.e.

\"pdf\"\"tex\"

1404 questions from 1987-2018 (including 1986 Specimen)

" }, { "tags": ["Inequalities,","Binomial coefficient"], "question_id":86101, "title": "Spec-S1-Q1", "body": "Quadratic functions, partial fractions, coefficient of binomial expansion.

\"q\"

[STEP I Specimen Question 1 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":86102, "title": "Spec-S1-Q2", "body": "Lines, right angle, differentiation, maximum value, optimisation, trigonometry. C1

\"q\"

[STEP I Specimen Question 2 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":86103, "title": "Spec-S1-Q3", "body": "Substitution, initial condition, forced second order equation.

\"q\"

[STEP I Specimen Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":86104, "title": "Spec-S1-Q4", "body": "Trigonometry, trigonometric, integral, arctan.

\"q\"

[STEP I Specimen Question 4 (Pure)]

" }, { "tags": ["Numbers"], "question_id":86105, "title": "Spec-S1-Q5", "body": "Positive integers, digits in base 10, zeros, factorial. C1

\"q\"

[STEP I Specimen Question 5 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":86106, "title": "Spec-S1-Q6", "body": "50p (fifty pence) coin, arc, cross section, diametrically opposite, radius, circle, area. C1

\"q\"

[STEP I Specimen Question 6 (Pure)]

" }, { "tags": ["Complex Numbers"], "question_id":86107, "title": "Spec-S1-Q7", "body": "Modulus and argument, complex exponential, de Moivre's theorem, sum of complex series.

\"q\"

[STEP I Specimen Question 7 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":86108, "title": "Spec-S1-Q8", "body": "Fixed point, curve, rectangle, vertices, area, arc, parabola, integration, finding area.

\"q\"

[STEP I Specimen Question 8 (Pure)]

" }, { "tags": ["Inequality,","Integral"], "question_id":86109, "title": "Spec-S1-Q9", "body": "Modulus function, rational function, surds, trigonometry, trigonometric, integration.

\"q\"

[STEP I Specimen Question 9 (Pure)]

" }, { "tags": ["Work,","Power"], "question_id":86110, "title": "Spec-S1-Q10", "body": "Rate of work, constant force and resistance, speed, distance.

\"q\"

[STEP I Specimen Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":86111, "title": "Spec-S1-Q11", "body": "Limiting friction, uniform cylinder, coefficient of friction, inclined plane ramp, constant force.

\"q\"

[STEP I Specimen Question 11 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":86112, "title": "Spec-S1-Q12", "body": "Uniform disc, coefficient of friction and restitution.

\"q\"

[STEP I Specimen Question 12 (Mechanics)]

" }, { "tags": ["Circular Motion"], "question_id":86113, "title": "Spec-S1-Q13", "body": "String, angular speed, horizontal circle, vertical plane motion.

\"q\"

[STEP I Specimen Question 13 (Mechanics)]

" }, { "tags": ["Discrete random variable,"], "question_id":86114, "title": "Spec-S1-Q14", "body": "Unbiased four-faced dice, expectation.

\"q\"

[STEP I Specimen Question 14 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":86115, "title": "Spec-S1-Q15", "body": "Expectation and variance, integer values.

\"q\"

[STEP I Specimen Question 15 (Probability and Statistics)]

" }, { "tags": ["Probability density function"], "question_id":86116, "title": "Spec-S1-Q16", "body": "Pdf, cumulative distribution function (cdf), expectation, continuous random variable.

\"q\"

[STEP I Specimen Question 16 (Probability and Statistics)]

" }, { "tags": ["Rational Functions"], "question_id":86201, "title": "Spec-S2-Q1", "body": "Algebra, partial fractions, positive integers.

\"q\"

[STEP II Specimen Question 1 (Pure)]

" }, { "tags": ["Simultaneous equations"], "question_id":86202, "title": "Spec-S2-Q2", "body": "Algebra, discriminant, system of equations, three unknowns.

\"q\"

[STEP II Specimen Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":86203, "title": "Spec-S2-Q3", "body": "de Moivre's theorem, system and simultaneous equations, trigonometry.

\"q\"

[STEP II Specimen Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":86204, "title": "Spec-S2-Q4", "body": "Trigonometry, hyperbolic function, inverse functions, principal value, function.

\"q\"

[STEP II Specimen Question 4 (Pure)]

" }, { "tags": ["Analysis"], "question_id":86205, "title": "Spec-S2-Q5", "body": "Approximating integrals with sums, bounds, error.

\"q\"

[STEP II Specimen Question 5 (Pure)]

" }, { "tags": ["Functional equation"], "question_id":86206, "title": "Spec-S2-Q6", "body": "Trigonometry, exponential, logarithm, sine, cosine, differentiation, identity.

\"q\"

[STEP II Specimen Question 6 (Pure)]

" }, { "tags": ["Integral"], "question_id":86207, "title": "Spec-S2-Q7", "body": "Integer part, floor function, curve sketching, exponential function.

\"q\"

[STEP II Specimen Question 7 (Pure)]

" }, { "tags": ["Groups"], "question_id":86208, "title": "Spec-S2-Q8", "body": "Multiplication modulo N, cyclic group, order 12, isomorphism.

\"q\"

[STEP II Specimen Question 8 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":86209, "title": "Spec-S2-Q9", "body": "Intersection of plane and sphere, circle.

\"q\"

[STEP II Specimen Question 9 (Pure)]

" }, { "tags": ["Logic"], "question_id":86210, "title": "Spec-S2-Q10", "body": "Speaking frogs arguing with toads, truth and lies.

\"q\"

[STEP II Specimen Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":86211, "title": "Spec-S2-Q11", "body": "Collision in trajectory, combined particle, coalesce.

\"q\"

[STEP II Specimen Question 11 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":86212, "title": "Spec-S2-Q12", "body": "Simple harmonic oscillation, period, bead on wire, string and springs, small angle approximation, inequality.

\"q\"

[STEP II Specimen Question 12 (Mechanics)]

" }, { "tags": ["Moment of inertia"], "question_id":86213, "title": "Spec-S2-Q13", "body": "Uniform sphere, tension, chocolate orange, centre of mass of segment.

\"q\"

[STEP II Specimen Question 13 (Mechanics)]

" }, { "tags": ["Circular motion,","Friction"], "question_id":86214, "title": "Spec-S2-Q14", "body": "Uniform disc, angular speed, constant frictional force, rate of change.

\"q\"

[STEP II Specimen Question 14 (Mechanics)]

" }, { "tags": ["Mean and variances"], "question_id":86215, "title": "Spec-S2-Q15", "body": "King of Smorgasbrod, Kippers, mean and variances, schemes.

\"q\"

[STEP II Specimen Question 15 (Probability and Statistics)]

" }, { "tags": ["Tree diagram"], "question_id":86216, "title": "Spec-S2-Q16", "body": "Tennis tournament, probability, draw, first, final round.

\"q\"

[STEP II Specimen Question 16 (Probability and Statistics)]

" }, { "tags": ["Proof by Induction"], "question_id":86301, "title": "Spec-S3-Q1", "body": "Product, sum, binomial coefficient.

\"q\"

[STEP III Specimen Question 1 (Pure)]

" }, { "tags": ["Proof,","Numbers"], "question_id":86302, "title": "Spec-S3-Q2", "body": "Binomial expansion, positive integer, inequality, power, Bernoulli inequality.

\"q\"

[STEP III Specimen Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":86303, "title": "Spec-S3-Q3", "body": "Triangle inequality, solution of complex polynomial equation.

\"q\"

[STEP III Specimen Question 3 (Pure)]

" }, { "tags": ["Conic sections"], "question_id":86304, "title": "Spec-S3-Q4", "body": "Coordinate geometry, tangent, parabola, directrix, straight line.

\"q\"

[STEP III Specimen Question 4 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":86305, "title": "Spec-S3-Q5", "body": "Curve sketching, non-zero solutions, small approximations, sine function, interval.

\"q\"

[STEP III Specimen Question 5 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":86306, "title": "Spec-S3-Q6", "body": "Recurrence relation, integral, sech, hyperbolic function.

\"q\"

[STEP III Specimen Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":86307, "title": "Spec-S3-Q7", "body": "Solution by substitution, general solution, second order equation.

\"q\"

[STEP III Specimen Question 7 (Pure)]

" }, { "tags": ["Vectors"], "question_id":86308, "title": "Spec-S3-Q8", "body": "Sum of squares, midpoints on opposite edges, tetrahedron, scalar product, inequality.

\"q\"

[STEP III Specimen Question 8 (Pure)]

" }, { "tags": ["Groups"], "question_id":86309, "title": "Spec-S3-Q9", "body": "Group of matrices under matrix multiplication, associative, subset, integers, identity matrix, commute.

\"q\"

[STEP III Specimen Question 9 (Pure)]

" }, { "tags": ["Number theory"], "question_id":86310, "title": "Spec-S3-Q10", "body": "Odd squares, remainder, even squares, expressable as a sum of three squares, divisibility.

\"q\"

[STEP III Specimen Question 10 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":86311, "title": "Spec-S3-Q11", "body": "Identical snowploughs, constant rate acceleration, first order equation, general solution, time-distance (x-t).

\"q\"

[STEP III Specimen Question 11 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":86312, "title": "Spec-S3-Q12", "body": "Uniform rod, light inextensible string, inclined to the vertical, tension, resolve forces, centre of mass.

\"q\"

[STEP III Specimen Question 12 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":86313, "title": "Spec-S3-Q13", "body": "Bead on a rolling circular hoop, second order differential equation, slip, reaction force.

\"q\"

[STEP III Specimen Question 13 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":86314, "title": "Spec-S3-Q14", "body": "Uniform rod, rotation about midpoint on smooth horizontal table, perfectly elastic collision, angular speed.

\"q\"

[STEP III Specimen Question 14 (Mechanics)]

" }, { "tags": ["Optimisation"], "question_id":86315, "title": "Spec-S3-Q15", "body": "Mountain villages, vertices of tetrahedron, snowfall probability, independence.

\"q\"

[STEP III Specimen Question 15 (Probability and Statistics)]

" }, { "tags": ["Combinatorics"], "question_id":86316, "title": "Spec-S3-Q16", "body": "President of the republic, no children, sons and daughters, expectation.

\"q\"

[STEP III Specimen Question 16 (Probability and Statistics)]

" }, { "tags": ["Curve sketching"], "question_id":87101, "title": "87-S1-Q1", "body": "Trigonometric and exponential functions, stationary points, geometric progression, ratio, differentiation.

\"q\"

[STEP I 1987 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":87102, "title": "87-S1-Q2", "body": "Coordinate geometry, circles, area of region, limit.

\"q\"

[STEP I 1987 Question 2 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":87103, "title": "87-S1-Q3", "body": "Solution by substitution, initial condition, limit, first order equation.

\"q\"

[STEP I 1987 Question 3 (Pure)]

" }, { "tags": ["Series"], "question_id":87104, "title": "87-S1-Q4", "body": "Analysis, sum of infinite series, logarithm, exponential function.

\"q\"

[STEP I 1987 Question 4 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":87105, "title": "87-S1-Q5", "body": "Trigonometry, sine and cosine functions.

\"q\"

[STEP I 1987 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":87106, "title": "87-S1-Q6", "body": "Integral of functions, geometrical argument, inequality, trigonometric and inverse function, differentiation.

\"q\"

[STEP I 1987 Question 6 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":87107, "title": "87-S1-Q7", "body": "Sum, finite sine series, tangent.

\"q\"

[STEP I 1987 Question 7 (Pure)]

" }, { "tags": ["Integral"], "question_id":87108, "title": "87-S1-Q8", "body": "Integration by substitution, equivalent, 1/t, 1/x, trigonometry.

\"q\"

[STEP I 1987 Question 8 (Pure)]

" }, { "tags": ["Vectors"], "question_id":87109, "title": "87-S1-Q9", "body": "Coordinate geometry, triangle in a plane, plane sketching, parametrisation, position vector.

\"q\"

[STEP I 1987 Question 9 (Pure)]

" }, { "tags": ["Hooke's Law"], "question_id":87110, "title": "87-S1-Q10", "body": "Spring, modulus of elasticity, cylinder, equilibrium, stretched spring.

\"q\"

[STEP I 1987 Question 10 (Mechanics)]

" }, { "tags": ["Energy"], "question_id":87111, "title": "87-S1-Q11", "body": "Momentum, sphere, lose contact, energy consideration, particle striking floor.

\"q\"

[STEP I 1987 Question 11 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":87112, "title": "87-S1-Q12", "body": "Bouncing ball down flight of stairs, momentum, coefficient of restitution, middle of step, perpendicular.

\"q\"

[STEP I 1987 Question 12 (Mechanics)]

" }, { "tags": ["Forces"], "question_id":87113, "title": "87-S1-Q13", "body": "Force, non-constant acceleration, first order differential equation, position, x-t graph.

\"q\"

[STEP I 1987 Question 13 (Mechanics)]

" }, { "tags": ["Probability"], "question_id":87114, "title": "87-S1-Q14", "body": "Table tennis tournament, successive, probability, C1.

\"q\"

[STEP I 1987 Question 14 (Probability and Statistics)]

" }, { "tags": ["Uniform distribution"], "question_id":87115, "title": "87-S1-Q15", "body": "Continuous random variable, point on a unit circle, mean and variance.

\"q\"

[STEP I 1987 Question 15 (Probability and Statistics)]

" }, { "tags": ["Normal distribution"], "question_id":87116, "title": "87-S1-Q16", "body": "Parliament of Laputa, progressive and preservative, normal approximation, vote.

\"q\"

[STEP I 1987 Question 16 (Probability and Statistics)]

" }, { "tags": ["Quadratics"], "question_id":87201, "title": "87-S2-Q1", "body": "Algebra, substitution, general case, function, C1.

\"q\"

[STEP II 1987 Question 1 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":87202, "title": "87-S2-Q2", "body": "Sine function, angles, identity, quartic, quadratic.

\"q\"

[STEP II 1987 Question 2 (Pure)]

" }, { "tags": ["Surds"], "question_id":87203, "title": "87-S2-Q3", "body": "Algebra, quadratic function, positive integers.

\"q\"

[STEP II 1987 Question 3 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":87204, "title": "87-S2-Q4", "body": "Argand diagram, geometry, necessary and sufficient, if and only if, vertices of equilateral triangle.

\"q\"

[STEP II 1987 Question 4 (Pure)]

" }, { "tags": ["Functions"], "question_id":87205, "title": "87-S2-Q5", "body": "Lagrange's identity, inverse functions, root of equation, exponential function, derivatives, series, sequences.

\"q\"

[STEP II 1987 Question 5 (Pure)]

" }, { "tags": ["Integral"], "question_id":87206, "title": "87-S2-Q6", "body": "Integration by substitution, trigonometric function, parameter.

\"q\"

[STEP II 1987 Question 6 (Pure)]

" }, { "tags": ["Integration"], "question_id":87207, "title": "87-S2-Q7", "body": "Definite integral, trapezium rule, intervals, logarithm, factorial function, curve sketching, stirling's approximation.

\"q\"

[STEP II 1987 Question 7 (Pure)]

" }, { "tags": ["Vectors"], "question_id":87208, "title": "87-S2-Q8", "body": "Position vector, locus, spheres, planes, algebra, geometrical, equivalent.

\"q\"

[STEP II 1987 Question 8 (Pure)]

" }, { "tags": ["Matrices"], "question_id":87209, "title": "87-S2-Q9", "body": "Square matrix, non-singular, unit, zero matrix, if and only if.

\"q\"

[STEP II 1987 Question 9 (Pure)]

" }, { "tags": ["Groups"], "question_id":87210, "title": "87-S2-Q10", "body": "Binary operation, group axioms, set.

\"q\"

[STEP II 1987 Question 10 (Pure)]

" }, { "tags": ["Friction"], "question_id":87211, "title": "87-S2-Q11", "body": "Ring, inclined plane, uniform rod, pivot, limiting equilibrium.

\"q\"

[STEP II 1987 Question 11 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":87212, "title": "87-S2-Q12", "body": "String, ring, static equilibrium, shortest distance, plane polar coordinates, equation of curve.

\"q\"

[STEP II 1987 Question 12 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":87213, "title": "87-S2-Q13", "body": "Coefficient of restitution, ice snooker, puck, cushions, table, path, ratio.

\"q\"

[STEP II 1987 Question 13 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":87214, "title": "87-S2-Q14", "body": "Second order differential equation, uniform elastic band, modulus of elasticity, circular cone, vertex.

\"q\"

[STEP II 1987 Question 14 (Mechanics)]

" }, { "tags": ["Uniform distribution"], "question_id":87215, "title": "87-S2-Q15", "body": "Train and lorry, level crossing, collision, independent random variables.

\"q\"

[STEP II 1987 Question 15 (Probability and Statistics)]

" }, { "tags": ["Tree diagram"], "question_id":87216, "title": "87-S2-Q16", "body": "Logic, body in fridge, enemy, truth and lies, probability, C1.

\"q\"

[STEP II 1987 Question 16 (Probability and Statistics)]

" }, { "tags": ["Numbers"], "question_id":87301, "title": "87-S3-Q1", "body": "Positive integers, divisibility, factorial function, C1.

\"q\"

[STEP II 1987 Question 1 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":87302, "title": "87-S3-Q2", "body": "Trigonometric function, sine, cosine function, recurrence relation, iteration, odd, even.

\"q\"

[STEP II 1987 Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":87303, "title": "87-S3-Q3", "body": "Inequality, binomial expansion, trigonometric identity, arctan function.

\"q\"

[STEP II 1987 Question 3 (Pure)]

" }, { "tags": ["Functions"], "question_id":87304, "title": "87-S3-Q4", "body": "Rotating curves, funnels, surfaces, inverse hyperbolic function, water tap.

\"q\"

[STEP II 1987 Question 4 (Pure)]

" }, { "tags": ["Modulo arithmetic"], "question_id":87305, "title": "87-S3-Q5", "body": "Numbers, secret message, encoding, decoding, modulo 50.

\"q\"

[STEP II 1987 Question 5 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":87306, "title": "87-S3-Q6", "body": "Forced system of first order equation, explicit solution.

\"q\"

[STEP II 1987 Question 6 (Pure)]

" }, { "tags": ["Analysis"], "question_id":87307, "title": "87-S3-Q7", "body": "Taylor series of arctan function with remainder, inequality, modulus function, series, error approximation.

\"q\"

[STEP II 1987 Question 7 (Pure)]

" }, { "tags": ["Inequalities"], "question_id":87308, "title": "87-S3-Q8", "body": "Inequality, diagonals of a parallelogram, maximum area, set of points, sketching, C1.

\"q\"

[STEP II 1987 Question 8 (Pure)]

" }, { "tags": ["Groups"], "question_id":87309, "title": "87-S3-Q9", "body": "Group multiplication, product group, abelian, if and only if, subgroup, isomorphism, cyclic group.

\"q\"

[STEP II 1987 Question 9 (Pure)]

" }, { "tags": ["Induction"], "question_id":87310, "title": "87-S3-Q10", "body": "Bernoulli polynomial, recurrence relation, differentiation, integration, series, telescoping sequence, sum.

\"q\"

[STEP II 1987 Question 10 (Pure)]

" }, { "tags": ["Time-distance graphs"], "question_id":87311, "title": "87-S3-Q11", "body": "Bank of river, swimming downstream, shortest possible time, stump, sketch, C1.

\"q\"

[STEP II 1987 Question 11 (Mechanics)]

" }, { "tags": ["Variable mass"], "question_id":87312, "title": "87-S3-Q12", "body": "Firework burning, rocket, first order differential equation.

\"q\"

[STEP II 1987 Question 12 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":87313, "title": "87-S3-Q13", "body": "Uniform rod, inclined, coefficient of friction, slide, equilibrium.

\"q\"

[STEP II 1987 Question 13 (Mechanics)]

" }, { "tags": ["Gravitational force"], "question_id":87314, "title": "87-S3-Q14", "body": "Sphere, attraction, first order differential equation, cloud, instantanesous velocity.

\"q\"

[STEP II 1987 Question 14 (Mechanics)]

" }, { "tags": ["Optimisation"], "question_id":87315, "title": "87-S3-Q15", "body": "Expectation, recurrence relation, Steppe syndrome.

\"q\"

[STEP II 1987 Question 15 (Probability and Statistics)]

" }, { "tags": ["Uniform distribution"], "question_id":87316, "title": "87-S3-Q16", "body": "Independent identically distributed random variables (iid), min, max, Lord Copper, lottery.

\"q\"

[STEP II 1987 Question 16 (Probability and Statistics)]

" }, { "tags": ["Curve sketching"], "question_id":88101, "title": "88-S1-Q1", "body": "Logarithm, lnx/x, positive integers, functions, C1.

\"q\"

[STEP I 1988 Question 1 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":88102, "title": "88-S1-Q2", "body": "Trigonometry, stationary point, maxima, minima, derivatives.

\"q\"

[STEP I 1988 Question 2 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":88103, "title": "88-S1-Q3", "body": "Square, C1.

\"q\"

[STEP I 1988 Question 3 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":88104, "title": "88-S1-Q4", "body": "Proof, line segments, midpoint, intersection, C1.

\"q\"

[STEP I 1988 Question 4 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":88105, "title": "88-S1-Q5", "body": "Partial fraction, taylor series, general term.

\"q\"

[STEP I 1988 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":88106, "title": "88-S1-Q6", "body": "Argand diagram, perpendicular, geometry, real part, convex hexagon, distance.

\"q\"

[STEP I 1988 Question 6 (Pure)]

" }, { "tags": ["Quadratic function"], "question_id":88107, "title": "88-S1-Q7", "body": "Differentiation, modulus function, functional equation, inequality, C1.

\"q\"

[STEP I 1988 Question 7 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":88108, "title": "88-S1-Q8", "body": "Skew (non-planar) quadrilaterial, opposite sides, midpoints, diagonals, C1.

\"q\"

[STEP I 1988 Question 8 (Pure)]

" }, { "tags": ["Integral"], "question_id":88109, "title": "88-S1-Q9", "body": "Integration by parts, trigonometry, substitution.

\"q\"

[STEP I 1988 Question 9 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":88110, "title": "88-S1-Q10", "body": "Sniper, bullet, circle.

\"q\"

[STEP I 1988 Question 10 (Mechanics)]

" }, { "tags": ["Centre of mass"], "question_id":88111, "title": "88-S1-Q11", "body": "Uniform circular arc, plane framework, equilibrium.

\"q\"

[STEP I 1988 Question 11 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":88112, "title": "88-S1-Q12", "body": "Skater, force, travelling in a circle, hitting bank.

\"q\"

[STEP I 1988 Question 12 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":88113, "title": "88-S1-Q13", "body": "Nellie the elephant, circus, elasticity, time-distance.

\"q\"

[STEP I 1988 Question 13 (Mechanics)]

" }, { "tags": ["Normal distribution"], "question_id":88114, "title": "88-S1-Q14", "body": "Normal random variable, expectation, pdf, cdf, HOGPo, tourist, vloska.

\"q\"

[STEP I 1988 Question 14 (Probability and Statistics)]

" }, { "tags": ["Probability distribution"], "question_id":88115, "title": "88-S1-Q15", "body": "Fridge football, goals and fouls, probability distribution.

\"q\"

[STEP I 1988 Question 15 (Probability and Statistics)]

" }, { "tags": ["Pdf"], "question_id":88116, "title": "88-S1-Q16", "body": "Wondergoo, cars, rust, conditional probability.

\"q\"

[STEP I 1988 Question 16 (Probability and Statistics)]

" }, { "tags": ["Binomial expansion"], "question_id":88201, "title": "88-S2-Q1", "body": "Laurent series, series.

\"q\"

[STEP II 1988 Question 1 (Pure)]

" }, { "tags": ["Quadratic equation"], "question_id":88202, "title": "88-S2-Q2", "body": "C1.

\"q\"

[STEP II 1988 Question 2 (Pure)]

" }, { "tags": ["Polynomial equations"], "question_id":88203, "title": "88-S2-Q3", "body": "Quadratic equation, roots (complex), cubic equation, real, C1.

\"q\"

[STEP II 1988 Question 3 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":88204, "title": "88-S2-Q4", "body": "Argand diagram, locus.

\"q\"

[STEP II 1988 Question 4 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":88205, "title": "88-S2-Q5", "body": "Complex numbers, de Moivre's theorem, imaginary part, tan, product.

\"q\"

[STEP II 1988 Question 5 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":88206, "title": "88-S2-Q6", "body": "Hyperbolic function, turning point, differentiation, positive function.

\"q\"

[STEP II 1988 Question 6 (Pure)]

" }, { "tags": ["Integral"], "question_id":88207, "title": "88-S2-Q7", "body": "Integration by substitution, trigonometry, monstrously hard.

\"q\"

[STEP II 1988 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":88208, "title": "88-S2-Q8", "body": "System of first order equation, aardvark, buffalo, population dynamic, matrix method, linear combination, equilibrium, stationary point.

\"q\"

[STEP II 1988 Question 8 (Pure)]

" }, { "tags": ["Groups"], "question_id":88209, "title": "88-S2-Q9", "body": "Subgroups.

\"q\"

[STEP II 1988 Question 9 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":88210, "title": "88-S2-Q10", "body": "3d surface, triangle, scalar product, cross product, locus, position vector.

\"q\"

[STEP II 1988 Question 10 (Pure)]

" }, { "tags": ["Circular motion"], "question_id":88211, "title": "88-S2-Q11", "body": "Particle, cartesian axes, first order equation, string.

\"q\"

[STEP II 1988 Question 11 (Mechanics)]

" }, { "tags": ["Inextensible string"], "question_id":88212, "title": "88-S2-Q12", "body": "Hole, surface of table, string.

\"q\"

[STEP II 1988 Question 12 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":88213, "title": "88-S2-Q13", "body": "Librarian, book, coefficient of friction, slip.

\"q\"

[STEP II 1988 Question 13 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":88214, "title": "88-S2-Q14", "body": "Axel, rotating about vertical axis, angular speed, inclined angle.

\"q\"

[STEP II 1988 Question 14 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":88215, "title": "88-S2-Q15", "body": "Examination paper, mark, elementary probability, C1.

\"q\"

[STEP II 1988 Question 15 (Probability and Statistics)]

" }, { "tags": ["Normal distribution"], "question_id":88216, "title": "88-S2-Q16", "body": "Quadratic equation, expectation, variance, normal distribution.

\"q\"

[STEP II 1988 Question 16 (Probability and Statistics)]

" }, { "tags": ["Curve sketching"], "question_id":88301, "title": "88-S3-Q1", "body": "Integral, inequality, exponential function.

\"q\"

[STEP III 1988 Question 1 (Pure)]

" }, { "tags": ["Difference equation"], "question_id":88302, "title": "88-S3-Q2", "body": "Recurrence relation, quadratic equation, proof by induction, C1.

\"q\"

[STEP III 1988 Question 2 (Pure)]

" }, { "tags": ["Complex number"], "question_id":88303, "title": "88-S3-Q3", "body": "Argand diagram, locus, curve sketching.

\"q\"

[STEP III 1988 Question 3 (Pure)]

" }, { "tags": ["Optimisation"], "question_id":88304, "title": "88-S3-Q4", "body": "Kingdom, parabolic hill, minimal, differentiation, rotating curves. C1.

\"q\"

[STEP III 1988 Question 4 (Pure)]

" }, { "tags": ["Geometric sequence"], "question_id":88305, "title": "88-S3-Q5", "body": "Engineers, borrow money, interest, tunnel, C1.

\"q\"

[STEP III 1988 Question 5 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":88306, "title": "88-S3-Q6", "body": "Differentiation, sine and cosine function, approximation.

\"q\"

[STEP III 1988 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":88307, "title": "88-S3-Q7", "body": "Sturm-Liouville, orthogonal functions.

\"q\"

[STEP III 1988 Question 7 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":88308, "title": "88-S3-Q8", "body": "Tangent and normal, parabola, determinant, area, necessary and sufficient, concurrent.

\"q\"

[STEP III 1988 Question 8 (Pure)]

" }, { "tags": ["Groups"], "question_id":88309, "title": "88-S3-Q9", "body": "Order of group, conjugation.

\"q\"

[STEP III 1988 Question 9 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":88310, "title": "88-S3-Q10", "body": "Greyhounds, polar curve, vertices of regular n-gon.

\"q\"

[STEP III 1988 Question 10 (Pure)]

" }, { "tags": ["Friction"], "question_id":88311, "title": "88-S3-Q11", "body": "Coefficient of friction, ladder, minima, inclined plane.

\"q\"

[STEP III 1988 Question 11 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":88312, "title": "88-S3-Q12", "body": "Coefficient of restitution, billiard ball, maximum angle of deflection.

\"q\"

[STEP III 1988 Question 12 (Mechanics)]

" }, { "tags": ["Differential equation"], "question_id":88313, "title": "88-S3-Q13", "body": "Air resistance, first order equation, gravity, goalkeeper, tan.

\"q\"

[STEP III 1988 Question 13 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":88314, "title": "88-S3-Q14", "body": "Quadratic equation, bead on wire, angle, trigonometric function, polar equation.

\"q\"

[STEP III 1988 Question 14 (Mechanics)]

" }, { "tags": ["Difference equation"], "question_id":88315, "title": "88-S3-Q15", "body": "Library book, quadratic equation.

\"q\"

[STEP III 1988 Question 15 (Probability and Statistics)]

" }, { "tags": ["Combinatorics"], "question_id":88316, "title": "88-S3-Q16", "body": "Balls from urns, mean, expectation, variance, sum of random variable, indicator function.

\"q\"

[STEP III 1988 Question 16 (Probability and Statistics)]

" }, { "tags": ["Euclidean geometry"], "question_id":89101, "title": "89-S1-Q1", "body": "Semi circles, parabola, vertex, arc, midpoint, area, C1.

\"q\"

[STEP I 1989 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":89102, "title": "89-S1-Q2", "body": "Logarithm function, approximating area, rectangle, limit.

\"q\"

[STEP I 1989 Question 2 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":89103, "title": "89-S1-Q3", "body": "Scalar product, triangle, line segments, inequality.

\"q\"

[STEP I 1989 Question 3 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":89104, "title": "89-S1-Q4", "body": "Collinear points, line segment, triangle, general position, C1.

\"q\"

[STEP I 1989 Question 4 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":89105, "title": "89-S1-Q5", "body": "Binomial coefficient, sum of.

\"q\"

[STEP I 1989 Question 5 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":89106, "title": "89-S1-Q6", "body": "Normal to curve, differential equation, minimum point, differentiation, exponential function.

\"q\"

[STEP I 1989 Question 6 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":89107, "title": "89-S1-Q7", "body": "Modulus function, rectangle, area, maximimum, implicit, curve, C1.

\"q\"

[STEP I 1989 Question 7 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":89108, "title": "89-S1-Q8", "body": "de Moivre's theorem, trigonometry, roots of polynomial equation.

\"q\"

[STEP I 1989 Question 8 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":89109, "title": "89-S1-Q9", "body": "Cubic equations, polynomial, turning points, differentiation, C1.

\"q\"

[STEP I 1989 Question 9 (Pure)]

" }, { "tags": ["Acceleration"], "question_id":89110, "title": "89-S1-Q10", "body": "Constant acceleration, Time-distance graph, resistive force.

\"q\"

[STEP I 1989 Question 10 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":89111, "title": "89-S1-Q11", "body": "Shot put, horizontal distance, perturbation.

\"q\"

[STEP I 1989 Question 11 (Mechanics)]

" }, { "tags": ["Centre of mass"], "question_id":89112, "title": "89-S1-Q12", "body": "Tetrahedron, elastic string, modulus of elasticity, Hooke's law, equilibrium

\"q\"

[STEP I 1989 Question 12 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":89113, "title": "89-S1-Q13", "body": "Ladder, normal reaction, frictional force, coefficient of friction, equilibrium.

\"q\"

[STEP I 1989 Question 13 (Mechanics)]

" }, { "tags": ["Continuous random variable"], "question_id":89114, "title": "89-S1-Q14", "body": "Enchanted castle, prevailing wind, princess magic seed, expectation, pdf.

\"q\"

[STEP I 1989 Question 14 (Probability and Statistics)]

" }, { "tags": ["Poission distribution"], "question_id":89115, "title": "89-S1-Q15", "body": "Cycling routes, mean, optimisation.

\"q\"

[STEP I 1989 Question 15 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":89116, "title": "89-S1-Q16", "body": "Expectation, probability, long time.

\"q\"

[STEP I 1989 Question 16 (Probability and Statistics)]

" }, { "tags": ["Cubic equation"], "question_id":89201, "title": "89-S2-Q1", "body": "Algebra, polynomial equation, trigonometry, substitution, counterdatabase.

\"q\"

[STEP II 1989 Question 1 (Pure)]

" }, { "tags": ["Series"], "question_id":89202, "title": "89-S2-Q2", "body": "Taylor series for tan and cot, recurrence relation, trigonometric identity

\"q\"

[STEP II 1989 Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":89203, "title": "89-S2-Q3", "body": "Ellipse, hyperbola, intersection, curve sketching.

\"q\"

[STEP II 1989 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":89204, "title": "89-S2-Q4", "body": "Rational function, functional equation, differentiation, inequality, different cases.

\"q\"

[STEP II 1989 Question 4 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":89205, "title": "89-S2-Q5", "body": "Differentiation, mirror, ray of light, reflection, bisect, parabola.

\"q\"

[STEP II 1989 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":89206, "title": "89-S2-Q6", "body": "Integration by substitution, inverse function, geometrical interpretation.

\"q\"

[STEP II 1989 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":89207, "title": "89-S2-Q7", "body": "Substitution, unique solution, second order equation.

\"q\"

[STEP II 1989 Question 7 (Pure)]

" }, { "tags": ["Groups"], "question_id":89208, "title": "89-S2-Q8", "body": "Complex numbers, permutation group, Mobius transformation, order of group.

\"q\"

[STEP II 1989 Question 8 (Pure)]

" }, { "tags": ["Matrices"], "question_id":89209, "title": "89-S2-Q9", "body": "Matrix power, series, exponential, differential equation, system, integrating factor.

\"q\"

[STEP II 1989 Question 9 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":89210, "title": "89-S2-Q10", "body": "Line, intersection, system of equation, scalars.

\"q\"

[STEP II 1989 Question 10 (Pure)]

" }, { "tags": ["Collision"], "question_id":89211, "title": "89-S2-Q11", "body": "Pulley, lift, perfectly inelastic, loss of energy.

\"q\"

[STEP II 1989 Question 11 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":89212, "title": "89-S2-Q12", "body": "Uniform rectangular lamina, vertical plane, peg.

\"q\"

[STEP II 1989 Question 12 (Mechanics)]

" }, { "tags": ["Centre of mass"], "question_id":89213, "title": "89-S2-Q13", "body": "Dynamically equivalent, rod, particle, rectangular lamina, moment of inertia.

\"q\"

[STEP II 1989 Question 13 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":89214, "title": "89-S2-Q14", "body": "Light inextensible string, circular motion, reaction force.

\"q\"

[STEP II 1989 Question 14 (Mechanics)]

" }, { "tags": ["Probability density function"], "question_id":89215, "title": "89-S2-Q15", "body": "Continuous random variable, pdf, random points on permieter of semicircle, expectation.

\"q\"

[STEP II 1989 Question 15 (Probability and Statistics)]

" }, { "tags": ["Binomial distribution"], "question_id":89216, "title": "89-S2-Q16", "body": "Widget faults, expectation, probability.

\"q\"

[STEP II 1989 Question 16 (Probability and Statistics)]

" }, { "tags": ["3-D geometry"], "question_id":89301, "title": "89-S3-Q1", "body": "Area of surface, sphere, conic section, tangent, circle.

\"q\"

[STEP III 1989 Question 1 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":89302, "title": "89-S3-Q2", "body": "Coal seam, inclined plane, bearing, trigonometry, bore hole.

\"q\"

[STEP III 1989 Question 2 (Pure)]

" }, { "tags": ["Groups"], "question_id":89303, "title": "89-S3-Q3", "body": "Matrix groups, Cayley-Hamilton, binary operation, group axioms.

\"q\"

[STEP III 1989 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":89304, "title": "89-S3-Q4", "body": "Asymptotes, turning points, roots of equations, C1.

\"q\"

[STEP III 1989 Question 4 (Pure)]

" }, { "tags": ["Hyperbolic functions"], "question_id":89305, "title": "89-S3-Q5", "body": "Sum, series, polynomial, Chebyshev's polynomial (hyperbolic).

\"q\"

[STEP III 1989 Question 5 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":89306, "title": "89-S3-Q6", "body": "Conic section, tangent, intersection, bisection.

\"q\"

[STEP III 1989 Question 6 (Pure)]

" }, { "tags": ["Transformation"], "question_id":89307, "title": "89-S3-Q7", "body": "Linear transformation, matrix, necessary ans sufficient, commute.

\"q\"

[STEP III 1989 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":89308, "title": "89-S3-Q8", "body": "System of first order equation, exponential function.

\"q\"

[STEP III 1989 Question 8 (Pure)]

" }, { "tags": ["Infinite series"], "question_id":89309, "title": "89-S3-Q9", "body": "Sum, sequences, infinite.

\"q\"

[STEP III 1989 Question 9 (Pure)]

" }, { "tags": ["Riemann integration"], "question_id":89310, "title": "89-S3-Q10", "body": "Sum of powers, inequality, limit, increasing function, rigorous proof of integration of polynomials.

\"q\"

[STEP III 1989 Question 10 (Pure)]

" }, { "tags": ["Collision"], "question_id":89311, "title": "89-S3-Q11", "body": "Coefficient of restitution, spheres, strike, rigid rod.

\"q\"

[STEP III 1989 Question 11 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":89312, "title": "89-S3-Q12", "body": "Vertical axis.

\"q\"

[STEP III 1989 Question 12 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":89313, "title": "89-S3-Q13", "body": "Elastic strings, modulus of elasticity, Hooke's law, simple harmonic motion, equilibrium.

\"q\"

[STEP III 1989 Question 13 (Mechanics)]

" }, { "tags": ["Moment of inertia"], "question_id":89314, "title": "89-S3-Q14", "body": "Circular disc, minelastic string, pulley.

\"q\"

[STEP III 1989 Question 14 (Mechanics)]

" }, { "tags": ["Uniform distribution"], "question_id":89315, "title": "89-S3-Q15", "body": "Continuous random variable, independent, probability density function, pdf, median, integration, expectation, variance.

\"q\"

[STEP III 1989 Question 15 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":89316, "title": "89-S3-Q16", "body": "Ruritania, tree diagram, C1.

\"q\"

[STEP III 1989 Question 16 (Probability and Statistics)]

" }, { "tags": ["Euclidean geometry"], "question_id":90101, "title": "90-S1-Q1", "body": "Semicircle, quadrilateral, blind, maximum area, C1.

\"q\"

[STEP I 1990 Question 1 (Pure)]

" }, { "tags": ["Binomial coefficient"], "question_id":90102, "title": "90-S1-Q2", "body": "Complex numbers, modulus and argument, roots of unity, binomial expansion, sum.

\"q\"

[STEP I 1990 Question 2 (Pure)]

" }, { "tags": ["Curves"], "question_id":90103, "title": "90-S1-Q3", "body": "Push-off, normal, position vector, gradient.

\"q\"

[STEP I 1990 Question 3 (Pure)]

" }, { "tags": ["Progressions"], "question_id":90104, "title": "90-S1-Q4", "body": "Arithmetic, double arithmetic, factorial progression, sequence, sum, C1.

\"q\"

[STEP I 1990 Question 4 (Pure)]

" }, { "tags": ["Integral,","Curve sketching"], "question_id":90105, "title": "90-S1-Q5", "body": "Integration by substitution, curve sketching, polynomial, distinct roots, inequality.

\"q\"

[STEP I 1990 Question 5 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":90106, "title": "90-S1-Q6", "body": "Parallelogram, area of rectangle, projection, diagonals.

\"q\"

[STEP I 1990 Question 6 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":90107, "title": "90-S1-Q7", "body": "Substitution, first order equation.

\"q\"

[STEP I 1990 Question 7 (Pure)]

" }, { "tags": ["Infinite product"], "question_id":90108, "title": "90-S1-Q8", "body": "Trigonometry, sine, cosine function.

\"q\"

[STEP I 1990 Question 8 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":90109, "title": "90-S1-Q9", "body": "Curve, intersection, projection, area of quadrilaterals, inequality, C1.

\"q\"

[STEP I 1990 Question 9 (Pure)]

" }, { "tags": ["Time-distance"], "question_id":90110, "title": "90-S1-Q10", "body": "Work, energy and power, relative velocity.

\"q\"

[STEP I 1990 Question 10 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":90111, "title": "90-S1-Q11", "body": "Superman, shell, downward velocity.

\"q\"

[STEP I 1990 Question 11 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":90112, "title": "90-S1-Q12", "body": "Spring, modulus of elasticity, equilibrium, potential energy.

\"q\"

[STEP I 1990 Question 12 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":90113, "title": "90-S1-Q13", "body": "Cylinder, coefficient of friction, inequality, normal reaction, smooth rail.

\"q\"

[STEP I 1990 Question 13 (Mechanics)]

" }, { "tags": ["Expectation"], "question_id":90114, "title": "90-S1-Q14", "body": "Bag of balls, Blackball, expectation, strategy.

\"q\"

[STEP I 1990 Question 14 (Probability and Statistics)]

" }, { "tags": ["Coin toss"], "question_id":90115, "title": "90-S1-Q15", "body": "Binomial coefficient, combinatorics, probability, tosses, C1.

\"q\"

[STEP I 1990 Question 15 (Probability and Statistics)]

" }, { "tags": ["Pdf"], "question_id":90116, "title": "90-S1-Q16", "body": "Probability density function, Poisson distribution, bus, stop.

\"q\"

[STEP I 1990 Question 16 (Probability and Statistics)]

" }, { "tags": ["Polynomial equation"], "question_id":90201, "title": "90-S2-Q1", "body": "Algebra, roots of equations, ineqlaity, non-negative, C1.

\"q\"

[STEP II 1990 Question 1 (Pure)]

" }, { "tags": ["Polynomial equation"], "question_id":90201, "title": "90-S2-Q1", "body": "Algebra, roots of equations, ineqlaity, non-negative, C1.

\"q\"

[STEP II 1990 Question 1 (Pure)]

" }, { "tags": ["Polynomial equation"], "question_id":90201, "title": "90-S2-Q1", "body": "Algebra, roots of equations, ineqlaity, non-negative, C1.

\"q\"

[STEP II 1990 Question 1 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":90202, "title": "90-S2-Q2", "body": "Sine function, circle, geometry.

\"q\"

[STEP II 1990 Question 2 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":90203, "title": "90-S2-Q3", "body": "Cubic equation, cases, inequality, C1.

\"q\"

[STEP II 1990 Question 3 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":90204, "title": "90-S2-Q4", "body": "Proof by induction, plane, lines, intersection, line segments, C1.

\"q\"

[STEP II 1990 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":90205, "title": "90-S2-Q5", "body": "Geometry, circle, argand diagram, position.

\"q\"

[STEP II 1990 Question 5 (Pure)]

" }, { "tags": ["Inequality"], "question_id":90206, "title": "90-S2-Q6", "body": "Positive integers, fractions, C1.

\"q\"

[STEP II 1990 Question 6 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":90207, "title": "90-S2-Q7", "body": "Damped system with feedback, exponential function, curve sketching, root of equations, first order equation.

\"q\"

[STEP II 1990 Question 7 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":90208, "title": "90-S2-Q8", "body": "Identity.

\"q\"

[STEP II 1990 Question 8 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":90209, "title": "90-S2-Q9", "body": "Curve sketching, cardioid, length of curve.

\"q\"

[STEP II 1990 Question 9 (Pure)]

" }, { "tags": ["Matrices"], "question_id":90210, "title": "90-S2-Q10", "body": "Determinants, Cayley-Hamilton theorem, necessary and sufficient, counterexamples.

\"q\"

[STEP II 1990 Question 10 (Pure)]

" }, { "tags": ["Circular motion"], "question_id":90211, "title": "90-S2-Q11", "body": "Disc spinning about vertical axis, moment of inertia, first order equation, integration by substitution.

\"q\"

[STEP II 1990 Question 11 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":90212, "title": "90-S2-Q12", "body": "Coefficient of restitution, straight staircase, edge.

\"q\"

[STEP II 1990 Question 12 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":90213, "title": "90-S2-Q13", "body": "Centre of gravity, non-uniform rod, light inextensible string.

\"q\"

[STEP II 1990 Question 13 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":90214, "title": "90-S2-Q14", "body": "Kinetic energy, identical smooth marbles.

\"q\"

[STEP II 1990 Question 14 (Mechanics)]

" }, { "tags": ["Pdf"], "question_id":90215, "title": "90-S2-Q15", "body": "Probability density function, expectation, taget, shot, marksman.

\"q\"

[STEP II 1990 Question 15 (Probability and Statistics)]

" }, { "tags": ["Tree diagram"], "question_id":90216, "title": "90-S2-Q16", "body": "Trousers, ties and compromising photographs, elementary probability, C1.

\"q\"

[STEP II 1990 Question 16 (Probability and Statistics)]

" }, { "tags": ["Complex numbers"], "question_id":90301, "title": "90-S3-Q1", "body": "de Moivre's theorem, trigonometry, roots of equation, tangent function.

\"q\"

[STEP III 1990 Question 1 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":90302, "title": "90-S3-Q2", "body": "3-dimensional space, line, intersection, angle, C1.

\"q\"

[STEP III 1990 Question 2 (Pure)]

" }, { "tags": ["Groups"], "question_id":90303, "title": "90-S3-Q3", "body": "Binary operation, order 2, commute, conjugate elements.

\"q\"

[STEP III 1990 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":90304, "title": "90-S3-Q4", "body": "Sum of trigonometric functions, cosine, binomial coefficient.

\"q\"

[STEP III 1990 Question 4 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":90305, "title": "90-S3-Q5", "body": "Binomial coefficient, differential equations, arcsin function, Leibniz's rule.

\"q\"

[STEP III 1990 Question 5 (Pure)]

" }, { "tags": ["Transformation"], "question_id":90306, "title": "90-S3-Q6", "body": "Vectors, matrices, eigenvectors, area, equation of tangent, circle.

\"q\"

[STEP III 1990 Question 6 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":90307, "title": "90-S3-Q7", "body": "Taylor series, curve sketching, inequality, asymptote.

\"q\"

[STEP III 1990 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":90308, "title": "90-S3-Q8", "body": "Second order equation, integrating factor.

\"q\"

[STEP III 1990 Question 8 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":90309, "title": "90-S3-Q9", "body": "Polar differential equations, hyperbolic and trigonometric functions.

\"q\"

[STEP III 1990 Question 9 (Pure)]

" }, { "tags": ["Roots of equations"], "question_id":90310, "title": "90-S3-Q10", "body": "Curve sketching, interval, inequality, estimation, approximation, C1.

\"q\"

[STEP III 1990 Question 10 (Pure)]

" }, { "tags": ["Equilibrium"], "question_id":90311, "title": "90-S3-Q11", "body": "Uniform square lamina, revolution about axis, rotation.

\"q\"

[STEP III 1990 Question 11 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":90312, "title": "90-S3-Q12", "body": "Smooth wedge, particle, elastic collision.

\"q\"

[STEP III 1990 Question 12 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":90313, "title": "90-S3-Q13", "body": "Projection from sphere, strike surface.

\"q\"

[STEP III 1990 Question 13 (Mechanics)]

" }, { "tags": ["Work done"], "question_id":90314, "title": "90-S3-Q14", "body": "Rigid cube, moment, force.

\"q\"

[STEP III 1990 Question 14 (Mechanics)]

" }, { "tags": ["Discrete random variables"], "question_id":90315, "title": "90-S3-Q15", "body": "Marginal distribution, mean, expectation, probability, unbiased 12-sided die, dice.

\"q\"

[STEP III 1990 Question 15 (Probability and Statistics)]

" }, { "tags": ["Normal and Uniform distribution"], "question_id":90316, "title": "90-S3-Q16", "body": "Rod cut into pieces, conditional probability, triangle formed, bivariate distribution, construction possible, obtuse angle.

\"q\"

[STEP III 1990 Question 16 (Probability and Statistics)]

" }, { "tags": ["Trigonometry"], "question_id":91101, "title": "91-S1-Q1", "body": "Cubic equation.

\"q\"

[STEP I 1991 Question 1 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":91102, "title": "91-S1-Q2", "body": "Frosty the snowman, melting, ratio of volume, surface area, maximum value, C1.

\"q\"

[STEP I 1991 Question 2 (Pure)]

" }, { "tags": ["Complex number"], "question_id":91103, "title": "91-S1-Q3", "body": "Argand diagram, path.

\"q\"

[STEP I 1991 Question 3 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":91104, "title": "91-S1-Q4", "body": "Prison compound, square, Black Tower, distance, area, maximum value, C1.

\"q\"

[STEP I 1991 Question 4 (Pure)]

" }, { "tags": ["Vectors"], "question_id":91105, "title": "91-S1-Q5", "body": "Regular vectors, centroid.

\"q\"

[STEP I 1991 Question 5 (Pure)]

" }, { "tags": ["Proof"], "question_id":91106, "title": "91-S1-Q6", "body": "Differentiation, integration, criticise argument, maximum, minimum, C1.

\"q\"

[STEP I 1991 Question 6 (Pure)]

" }, { "tags": ["Geometric progression"], "question_id":91107, "title": "91-S1-Q7", "body": "Slakan Treasury, Economics, continuous variable, vloskan, interest, sequence, inequality, C1.

\"q\"

[STEP I 1991 Question 7 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":91108, "title": "91-S1-Q8", "body": "Trigonometric integral, sin substitution, arcsin function.

\"q\"

[STEP I 1991 Question 8 (Pure)]

" }, { "tags": ["Analysis"], "question_id":92010, "title": "91-S1-Q9", "body": "Sum, inequality, approximation, analysis, C1.

\"q\"

[STEP I 1991 Question 9 (Pure)]

" }, { "tags": ["Equilibrium"], "question_id":91110, "title": "91-S1-Q10", "body": "Suspension bridge, flexible chains, weight, tension, parabola.

\"q\"

[STEP I 1991 Question 10 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":91111, "title": "91-S1-Q11", "body": "Piledriver, acceleration, collision, geometric progression, inelastic.

\"q\"

[STEP I 1991 Question 11 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":91112, "title": "91-S1-Q12", "body": "Makeshift stepladder, coefficient of friction.

\"q\"

[STEP I 1991 Question 12 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":91113, "title": "91-S1-Q13", "body": "Lamina, slide, semicircle, speed.

\"q\"

[STEP I 1991 Question 13 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":91114, "title": "91-S1-Q14", "body": "Rod, triangle, non-degenerate, without replacement, C1.

\"q\"

[STEP I 1991 Question 14 (Probability and Statistics)]

" }, { "tags": ["Coin toss"], "question_id":91115, "title": "91-S1-Q15", "body": "Binomial distribution, probability, mean and variance.

\"q\"

[STEP I 1991 Question 15 (Probability and Statistics)]

" }, { "tags": ["Probability"], "question_id":91116, "title": "91-S1-Q16", "body": "Toad and frog cross the road, probability.

\"q\"

[STEP I 1991 Question 16 (Probability and Statistics)]

" }, { "tags": ["Quadratic equations"], "question_id":91201, "title": "91-S2-Q1", "body": "Linear combination, algebra, C1.

\"q\"

[STEP II 1991 Question 1 (Pure)]

" }, { "tags": ["Conic sections"], "question_id":91202, "title": "91-S2-Q2", "body": "Hyperbola, curves, differentiation, equation of tangent, asymptote, bisect angles.

\"q\"

[STEP II 1991 Question 2 (Pure)]

" }, { "tags": ["Functions"], "question_id":91203, "title": "91-S2-Q3", "body": "Algebraic manipulation, C1.

\"q\"

[STEP II 1991 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":91204, "title": "91-S2-Q4", "body": "Sum, quadratic equation, cosine function.

\"q\"

[STEP II 1991 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":91205, "title": "91-S2-Q5", "body": "Analysis, curve sketching, tangent function, sum, logarithm function.

\"q\"

[STEP II 1991 Question 5 (Pure)]

" }, { "tags": ["Inequality"], "question_id":91206, "title": "91-S2-Q6", "body": "Integration, approximation, Taylor series.

\"q\"

[STEP II 1991 Question 6 (Pure)]

" }, { "tags": ["Functions"], "question_id":91207, "title": "91-S2-Q7", "body": "Differentiation, logarithmic function, functional equations.

\"q\"

[STEP II 1991 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":91208, "title": "91-S2-Q8", "body": "Quadratic equations, hyperbolic functions, substitution.

\"q\"

[STEP II 1991 Question 8 (Pure)]

" }, { "tags": ["Groups"], "question_id":91209, "title": "91-S2-Q9", "body": "Groups under matrix multiplication, commute, subgroup.

\"q\"

[STEP II 1991 Question 9 (Pure)]

" }, { "tags": ["Spherical polar coordinates"], "question_id":91210, "title": "91-S2-Q10", "body": "Straight stick, shadow, displacement vector.

\"q\"

[STEP II 1991 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":91211, "title": "91-S2-Q11", "body": "Ruritanian army, shells, maximum height, angle of elevation.

\"q\"

[STEP II 1991 Question 11 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":91212, "title": "91-S2-Q12", "body": "String, second order differential equation, necessary and sufficient.

\"q\"

[STEP II 1991 Question 12 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":91213, "title": "91-S2-Q13", "body": "Uniform rod, moment of inertia, coefficient of friction.

\"q\"

[STEP II 1991 Question 13 (Mechanics)]

" }, { "tags": ["Velocity"], "question_id":91214, "title": "91-S2-Q14", "body": "Current in a river, vector, first order differential equation, hyperbolic, exponential functions.

\"q\"

[STEP II 1991 Question 14 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":91215, "title": "91-S2-Q15", "body": "Expectation, combinatorics, desk, examination hall, invigilator.

\"q\"

[STEP II 1991 Question 15 (Probability and Statistics)]

" }, { "tags": ["Uniform distribution"], "question_id":91216, "title": "91-S2-Q16", "body": "Cabbibo dam, rain, approximation.

\"q\"

[STEP II 1991 Question 16 (Probability and Statistics)]

" }, { "tags": ["Taylor series"], "question_id":91301, "title": "91-S3-Q1", "body": "Sum, logarithm, exponential function.

\"q\"

[STEP III 1991 Question 1 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":91302, "title": "91-S3-Q2", "body": "Argand diagram, triangles, rotation, deterinant of matrix, similar triangles, centroid, equilateral, geometry.

\"q\"

[STEP III 1991 Question 2 (Pure)]

" }, { "tags": ["Modulus function"], "question_id":91303, "title": "91-S3-Q3", "body": "Differentiation, stationary, inflection points, continuous and differentiable, inverse function, C1.

\"q\"

[STEP III 1991 Question 3 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":91304, "title": "91-S3-Q4", "body": "3-dimensional space, position vector, equation of path.

\"q\"

[STEP III 1991 Question 4 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":91305, "title": "91-S3-Q5", "body": "Polar coordinates, integration, closed loop, area of region.

\"q\"

[STEP III 1991 Question 5 (Pure)]

" }, { "tags": ["Transformation"], "question_id":91306, "title": "91-S3-Q6", "body": "Equation of lines, hyperbolic functions, necessary and sufficient.

\"q\"

[STEP III 1991 Question 6 (Pure)]

" }, { "tags": ["Integration"], "question_id":91307, "title": "91-S3-Q7", "body": "Logarithm, trigonometry, analysis, inequality, limits.

\"q\"

[STEP III 1991 Question 7 (Pure)]

" }, { "tags": ["Sum"], "question_id":91308, "title": "91-S3-Q8", "body": "Integration by parts, reccurence formula, binomial coefficient.

\"q\"

[STEP III 1991 Question 8 (Pure)]

" }, { "tags": ["Conic sections"], "question_id":91309, "title": "91-S3-Q9", "body": "Parametric equations, ellipse, polar equation, perimeter, integration.

\"q\"

[STEP III 1991 Question 9 (Pure)]

" }, { "tags": ["Roots of polynomials"], "question_id":91310, "title": "91-S3-Q10", "body": "Sum of roots, proof by induction.

\"q\"

[STEP III 1991 Question 10 (Pure)]

" }, { "tags": ["Friction"], "question_id":91311, "title": "91-S3-Q11", "body": "Uniform circular cylinder on inclined plane, coefficient of friction.

\"q\"

[STEP III 1991 Question 11 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":91312, "title": "91-S3-Q12", "body": "Elliptic tube, acceleration, polar coordinates.

\"q\"

[STEP III 1991 Question 12 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":91313, "title": "91-S3-Q13", "body": "Ceiling, perfectly inelastic collision.

\"q\"

[STEP III 1991 Question 13 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":91314, "title": "91-S3-Q14", "body": "Modulus of elasticity, spring, reaction force.

\"q\"

[STEP III 1991 Question 14 (Mechanics)]

" }, { "tags": ["Combinatorics"], "question_id":91315, "title": "91-S3-Q15", "body": "Pack of cards, without replacement, identical, elementary probabliity.

\"q\"

[STEP III 1991 Question 15 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":91316, "title": "91-S3-Q16", "body": "Joint probability distribution, marginal probability, expectation.

\"q\"

[STEP III 1991 Question 16 (Probability and Statistics)]

" }, { "tags": ["Counting"], "question_id":92101, "title": "92-S1-Q1", "body": "Date of the week, methodical, C1.

\"q\"

[STEP I 1992 Question 1 (Pure)]

" }, { "tags": ["Magic square"], "question_id":92102, "title": "92-S1-Q2", "body": "C1.

\"q\"

[STEP I 1992 Question 2 (Pure)]

" }, { "tags": ["Integral"], "question_id":92103, "title": "92-S1-Q3", "body": "Sine and modulus function, integration by parts.

\"q\"

[STEP I 1992 Question 3 (Pure)]

" }, { "tags": ["Complex number"], "question_id":92104, "title": "92-S1-Q4", "body": "Argand diagram, locus.

\"q\"

[STEP I 1992 Question 4 (Pure)]

" }, { "tags": ["Polynomial factors"], "question_id":92105, "title": "92-S1-Q5", "body": "Differentiation, C1.

\"q\"

[STEP I 1992 Question 5 (Pure)]

" }, { "tags": ["Approximation"], "question_id":92106, "title": "92-S1-Q6", "body": "Small angle approximation, C1.

\"q\"

[STEP I 1992 Question 6 (Pure)]

" }, { "tags": ["Functions"], "question_id":92107, "title": "92-S1-Q7", "body": "Quadratic equation, functional equation, integer, C1.

\"q\"

[STEP I 1992 Question 7 (Pure)]

" }, { "tags": ["Derivative of an integral"], "question_id":92108, "title": "92-S1-Q8", "body": "Differentiation, integration, exponential function.

\"q\"

[STEP I 1992 Question 8 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":92109, "title": "92-S1-Q9", "body": "Coffee filter, cone, height of water, C1.

\"q\"

[STEP I 1992 Question 9 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":92110, "title": "92-S1-Q10", "body": "Toy cannon, force exerted on projectile.

\"q\"

[STEP I 1992 Question 10 (Mechanics)]

" }, { "tags": ["Elastic strings"], "question_id":92111, "title": "92-S1-Q11", "body": "Modulus of elasticity.

\"q\"

[STEP I 1992 Question 11 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":92112, "title": "92-S1-Q12", "body": "Stepladder, coefficient of friction, equilibrium.

\"q\"

[STEP I 1992 Question 12 (Mechanics)]

" }, { "tags": ["Gravitational attraction"], "question_id":92113, "title": "92-S1-Q13", "body": "Inverse square law, comet, escape velocity.

\"q\"

[STEP I 1992 Question 13 (Mechanics)]

" }, { "tags": ["Statistics"], "question_id":92114, "title": "92-S1-Q14", "body": "Pedestrains, Poldavia, newspaper headlines, C1.

\"q\"

[STEP I 1992 Question 14 (Probability and Statistics)]

" }, { "tags": ["Graphical probability"], "question_id":92115, "title": "92-S1-Q15", "body": "Trains, London, Barchester, C1.

\"q\"

[STEP I 1992 Question 15 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":92116, "title": "92-S1-Q16", "body": "Closure of roads, binomial distribution, C1.

\"q\"

[STEP I 1992 Question 16 (Probability and Statistics)]

" }, { "tags": ["Limits"], "question_id":92201, "title": "92-S2-Q1", "body": "Functions, trigonometry, square roots.

\"q\"

[STEP II 1992 Question 1 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":92202, "title": "92-S2-Q2", "body": "Second order equation, differentiation, hyperbolic functions.

\"q\"

[STEP II 1992 Question 2 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":92203, "title": "92-S2-Q3", "body": "Curve sketching, integration, area of region.

\"q\"

[STEP II 1992 Question 3 (Pure)]

" }, { "tags": ["Diamond derivative"], "question_id":92204, "title": "92-S2-Q4", "body": "Functional equation, differentiation, polynomial, C1.

\"q\"

[STEP II 1992 Question 4 (Pure)]

" }, { "tags": ["Groups"], "question_id":92205, "title": "92-S2-Q5", "body": "Order of an element, SL2(R), inverse, matrix multiplication.

\"q\"

[STEP II 1992 Question 5 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":92206, "title": "92-S2-Q6", "body": "Trigonometry, logarithm, root of equation, approximation.

\"q\"

[STEP II 1992 Question 6 (Pure)]

" }, { "tags": ["Cubic equation"], "question_id":92207, "title": "92-S2-Q7", "body": "Differentiation, logarithmic function, functional equations.

\"q\"

[STEP II 1992 Question 7 (Pure)]

" }, { "tags": ["Integrals"], "question_id":92208, "title": "92-S2-Q8", "body": "Integration by substitution, trigonometry, hyperbolic function.

\"q\"

[STEP II 1992 Question 8 (Pure)]

" }, { "tags": ["Vectors"], "question_id":92209, "title": "92-S2-Q9", "body": "Locus, scalar product, vector identity, vector triple product.

\"q\"

[STEP II 1992 Question 9 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":92210, "title": "92-S2-Q10", "body": "Locus, argand diagram, real part, points on a circle.

\"q\"

[STEP II 1992 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":92211, "title": "92-S2-Q11", "body": "Throwing wallet up a cliff?! inequality.

\"q\"

[STEP II 1992 Question 11 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":92212, "title": "92-S2-Q12", "body": "Two wheels, modulus of elasticity, equilibrium positions.

\"q\"

[STEP II 1992 Question 12 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":92213, "title": "92-S2-Q13", "body": "Coefficient of friction, coefficient of restitution, inequality, bounce, particles on table.

\"q\"

[STEP II 1992 Question 13 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":92214, "title": "92-S2-Q14", "body": "Tensions in string, tension, equilibrium.

\"q\"

[STEP II 1992 Question 14 (Mechanics)]

" }, { "tags": ["Random walk"], "question_id":92215, "title": "92-S2-Q15", "body": "Binomial coefficient, differentiation.

\"q\"

[STEP II 1992 Question 15 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":92216, "title": "92-S2-Q16", "body": "Taxi driver, tofees and mint.

\"q\"

[STEP II 1992 Question 16 (Probability and Statistics)]

" }, { "tags": ["Taylor series"], "question_id":92301, "title": "92-S3-Q1", "body": "Logarithm, differentiation, hyperbolic function, exponential function.

\"q\"

[STEP III 1992 Question 1 (Pure)]

" }, { "tags": ["Matrices"], "question_id":92302, "title": "92-S3-Q2", "body": "Proof by induction, matrix multiplication.

\"q\"

[STEP III 1992 Question 2 (Pure)]

" }, { "tags": ["Parametric equations"], "question_id":92303, "title": "92-S3-Q3", "body": "Curve sketching, quadratic equations, intersection of curves.

\"q\"

[STEP III 1992 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":92304, "title": "92-S3-Q4", "body": "Family of curves, rational functions, first order differential equation, intersection of curve.

\"q\"

[STEP III 1992 Question 4 (Pure)]

" }, { "tags": ["Vectors"], "question_id":92305, "title": "92-S3-Q5", "body": "Coordinate geometry, tetrahedron, midpoint, sphere, intersections.

\"q\"

[STEP III 1992 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":92306, "title": "92-S3-Q6", "body": "Integration by parts, recurrence relation, reduction formula, curve sketching, area under curve.

\"q\"

[STEP III 1992 Question 6 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":92307, "title": "92-S3-Q7", "body": "Parallelogram, meet in a point.

\"q\"

[STEP III 1992 Question 7 (Pure)]

" }, { "tags": ["Sum"], "question_id":92308, "title": "92-S3-Q8", "body": "Trigonometry, binomial coefficients, sum.

\"q\"

[STEP III 1992 Question 8 (Pure)]

" }, { "tags": ["Conic sections"], "question_id":92309, "title": "92-S3-Q9", "body": "Straight line, bosect angle, ellipse, focus, polar coordinates, pole, tangent, first order differential equation.

\"q\"

[STEP III 1992 Question 9 (Pure)]

" }, { "tags": ["Parametric equation,","Polar coordinates"], "question_id":92310, "title": "92-S3-Q10", "body": "Curve sketching, perimeter, area of region, integration.

\"q\"

[STEP III 1992 Question 10 (Pure)]

" }, { "tags": ["Collision"], "question_id":92311, "title": "92-S3-Q11", "body": "Barrier, wall, rebound, coefficient of restitution.

\"q\"

[STEP III 1992 Question 11 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":92312, "title": "92-S3-Q12", "body": "Hemispherical bowl, slide, first order differential equation, velocity.

\"q\"

[STEP III 1992 Question 12 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":92313, "title": "92-S3-Q13", "body": "Modulus of elasticity, circular disc, string, reaction force, turn about fixed horizontal axis.

\"q\"

[STEP III 1992 Question 13 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":92314, "title": "92-S3-Q14", "body": "Motion in polar coordinates, friction, tension, acceleration, second order differential equation.

\"q\"

[STEP III 1992 Question 14 (Mechanics)]

" }, { "tags": ["Continuous random variable"], "question_id":92315, "title": "92-S3-Q15", "body": "Goat, probability density function, pdf, median, conditional probability.

\"q\"

[STEP III 1992 Question 15 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":92316, "title": "92-S3-Q16", "body": "Misprint in newspapper, probability.

\"q\"

[STEP III 1992 Question 16 (Probability and Statistics)]

" }, { "tags": ["Combinatorics"], "question_id":93101, "title": "93-S1-Q1", "body": "Dice, colors, number of ways, C1.

\"q\"

[STEP I 1993 Question 1 (Pure)]

" }, { "tags": ["Geometric progression"], "question_id":93102, "title": "93-S1-Q2", "body": "Series, limit, sequence, C1.

\"q\"

[STEP I 1993 Question 2 (Pure)]

" }, { "tags": ["Solution of equation"], "question_id":93103, "title": "93-S1-Q3", "body": "Inequality, algebra, reciprocal function, inverse, integer solution, inequality, C1.

\"q\"

[STEP I 1993 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":93104, "title": "93-S1-Q4", "body": "Trigonometry, sine function.

\"q\"

[STEP I 1993 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":93105, "title": "93-S1-Q5", "body": "Modulus, triangle inequality, roots of equation.

\"q\"

[STEP I 1993 Question 5 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":93106, "title": "93-S1-Q6", "body": "Bump, rational functions, sine function, C1.

\"q\"

[STEP I 1993 Question 6 (Pure)]

" }, { "tags": ["Cubic equation"], "question_id":93107, "title": "93-S1-Q7", "body": "Curve sketching, roots of equation, inequality, C1.

\"q\"

[STEP I 1993 Question 7 (Pure)]

" }, { "tags": ["3-D geometry"], "question_id":93108, "title": "93-S1-Q8", "body": "Intersection of surface with spheres, Little Fitton.

\"q\"

[STEP I 1993 Question 8 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":93109, "title": "93-S1-Q9", "body": "Handmade ice-cream, first order differential equation.

\"q\"

[STEP I 1993 Question 9 (Pure)]

" }, { "tags": ["Springs and strings"], "question_id":93110, "title": "93-S1-Q10", "body": "Modulus of elasticity, lamp, equilibrium, rotate.

\"q\"

[STEP I 1993 Question 10 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":93111, "title": "93-S1-Q11", "body": "Centre of mass, uniform square wire.

\"q\"

[STEP I 1993 Question 11 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":93112, "title": "93-S1-Q12", "body": "Clay pigeon, rifle, inequality, range.

\"q\"

[STEP I 1993 Question 12 (Mechanics)]

" }, { "tags": ["Work and power"], "question_id":93113, "title": "93-S1-Q13", "body": "Train, tractive force, engine, time-distance.

\"q\"

[STEP I 1993 Question 13 (Mechanics)]

" }, { "tags": ["Continuous random variable"], "question_id":93114, "title": "93-S1-Q14", "body": "Mr Toad, probability density function, probability, limit, traffic light, Wild Wood.

\"q\"

[STEP I 1993 Question 14 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":93115, "title": "93-S1-Q15", "body": "Captain Spalding, Gambriced, Frodox, truth, logic, native, probability.

\"q\"

[STEP I 1993 Question 15 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":93116, "title": "93-S1-Q16", "body": "Integration by substitution, uniform distribution, pins on lines.

\"q\"

[STEP I 1993 Question 16 (Probability and Statistics)]

" }, { "tags": ["Colonel Blotto"], "question_id":93201, "title": "93-S2-Q1", "body": "C1.

\"q\"

[STEP II 1993 Question 1 (Pure)]

" }, { "tags": ["Integrals"], "question_id":93202, "title": "93-S2-Q2", "body": "Substitution, trigonometry.

\"q\"

[STEP II 1993 Question 2 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":93203, "title": "93-S2-Q3", "body": "Substitution, first order equation.

\"q\"

[STEP II 1993 Question 3 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":93204, "title": "93-S2-Q4", "body": "3D, non-parallel lines, shortest distance.

\"q\"

[STEP II 1993 Question 4 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":93205, "title": "93-S2-Q5", "body": "Curve sketching, equiangular spiral, plane geometry, arc length of curve.

\"q\"

[STEP II 1993 Question 5 (Pure)]

" }, { "tags": ["Matrices"], "question_id":93206, "title": "93-S2-Q6", "body": "Proofs and counterexamples, determinant, quadratic, matrix multiplication, linear algebra.

\"q\"

[STEP II 1993 Question 6 (Pure)]

" }, { "tags": ["Modulo arithmetic"], "question_id":93207, "title": "Roots of equation", "body": "Divisibility, solution of equation.

\"q\"

[STEP II 1993 Question 7 (Pure)]

" }, { "tags": ["Inequalities"], "question_id":93208, "title": "93-S2-Q8", "body": "AM-GM inequality, proof by induction, C1.

\"q\"

[STEP II 1993 Question 8 (Pure)]

" }, { "tags": ["Complex number"], "question_id":93209, "title": "93-S2-Q9", "body": "Argument, imaginary part, inequality, proof.

\"q\"

[STEP II 1993 Question 9 (Pure)]

" }, { "tags": ["Matrices"], "question_id":93210, "title": "93-S2-Q10", "body": "Diagonal matrix, transformation, change of basis.

\"q\"

[STEP II 1993 Question 10 (Pure)]

" }, { "tags": ["Fluid dynamics"], "question_id":93211, "title": "93-S2-Q11", "body": "Immersed body into liquid, buoyancy and drag, equilibrium.

\"q\"

[STEP II 1993 Question 11 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":93212, "title": "93-S2-Q12", "body": "Sphere on inclined plane, rolling not slipping.

\"q\"

[STEP II 1993 Question 12 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":93213, "title": "93-S2-Q13", "body": "Simple harmonic motion, repulsive force, electrical charge, perturbation, period of motion, binomial approximation.

\"q\"

[STEP II 1993 Question 13 (Mechanics)]

" }, { "tags": ["Energy"], "question_id":93214, "title": "93-S2-Q14", "body": "Hooke's law, restitution, kinetic energy, ball thrown from floor.

\"q\"

[STEP II 1993 Question 14 (Mechanics)]

" }, { "tags": ["Uniform distribution"], "question_id":93215, "title": "93-S2-Q15", "body": "LEP, VOZ, computer programs, fractional part, magnitude of error.

\"q\"

[STEP II 1993 Question 15 (Probability and Statistics)]

" }, { "tags": ["Poisson process"], "question_id":93216, "title": "93-S2-Q16", "body": "Bus arriving.

\"q\"

[STEP II 1993 Question 16 (Probability and Statistics)]

" }, { "tags": ["Parametric equations"], "question_id":93301, "title": "93-S3-Q1", "body": "Curve sketching, parabola, length of curve, volume of revolution.

\"q\"

[STEP III 1993 Question 1 (Pure)]

" }, { "tags": ["Implicit equation"], "question_id":93302, "title": "93-S3-Q2", "body": "Implicit differentiation, polar coordinates, area of curve.

\"q\"

[STEP III 1993 Question 2 (Pure)]

" }, { "tags": ["Matrices"], "question_id":93303, "title": "93-S3-Q3", "body": "System of equations, unique solution, inverse.

\"q\"

[STEP III 1993 Question 3 (Pure)]

" }, { "tags": ["Sum of series"], "question_id":93304, "title": "93-S3-Q4", "body": "Sequences.

\"q\"

[STEP III 1993 Question 4 (Pure)]

" }, { "tags": ["Groups"], "question_id":93305, "title": "93-S3-Q5", "body": "Set of complex numbers, binary operation, associative and commutative, identity, isomorphism, matrix groups.

\"q\"

[STEP III 1993 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":93306, "title": "93-S3-Q6", "body": "Argand diagram, circle, locus, Mobius transformation, position.

\"q\"

[STEP III 1993 Question 6 (Pure)]

" }, { "tags": ["Hyperbolic functions"], "question_id":93307, "title": "93-S3-Q7", "body": "Simultaneous equations, root of equation, iterative root finding.

\"q\"

[STEP III 1993 Question 7 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":93308, "title": "93-S3-Q8", "body": "Square pyramid, vectors, quadrilateral, parallelogram.

\"q\"

[STEP III 1993 Question 8 (Pure)]

" }, { "tags": ["Inequality"], "question_id":93309, "title": "93-S3-Q9", "body": "Proof, sum over pairs, sum of squares.

\"q\"

[STEP III 1993 Question 9 (Pure)]

" }, { "tags": ["Linear transformation"], "question_id":93310, "title": "93-S3-Q10", "body": "Parallelogram, lines, gradients, matrix transformation, area, determinant.

\"q\"

[STEP III 1993 Question 10 (Pure)]

" }, { "tags": ["Moment of inertia"], "question_id":93311, "title": "93-S3-Q11", "body": "Force along lines, direction of rotation, parallel axis theorem, angular acceleration.

\"q\"

[STEP III 1993 Question 11 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":93312, "title": "93-S3-Q12", "body": "Modulus of elasticity, equilibrium, string, tension.

\"q\"

[STEP III 1993 Question 12 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":93313, "title": "93-S3-Q13", "body": "Energy, variable mass, circular disc.

\"q\"

[STEP III 1993 Question 13 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":93314, "title": "93-S3-Q14", "body": "Coefficient of restitution, strike, rebound.

\"q\"

[STEP III 1993 Question 14 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":93315, "title": "93-S3-Q15", "body": "Elementary probability, expectation, binomial distribution, C1ish.

\"q\"

[STEP III 1993 Question 15 (Probability and Statistics)]

" }, { "tags": ["Truncated normal distribution"], "question_id":93316, "title": "93-S3-Q16", "body": "Pdf, probability density function, mean, curve sketching, setting questions.

\"q\"

[STEP III 1993 Question 16 (Probability and Statistics)]

" }, { "tags": ["Volume and Surface area"], "question_id":94101, "title": "94-S1-Q1", "body": "Attic, rectangular base, C1.

\"q\"

[STEP I 1994 Question 1 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":94102, "title": "94-S1-Q2", "body": "Derivatives of powers.

\"q\"

[STEP I 1994 Question 2 (Pure)]

" }, { "tags": ["Binomial coefficient"], "question_id":94103, "title": "94-S1-Q3", "body": "Binomail expansion, coefficient, sum, even and odd.

\"q\"

[STEP I 1994 Question 3 (Pure)]

" }, { "tags": ["Integration"], "question_id":94104, "title": "94-S1-Q4", "body": "Trigonometry identity, arctan.

\"q\"

[STEP I 1994 Question 4 (Pure)]

" }, { "tags": ["Sketching"], "question_id":94105, "title": "94-S1-Q5", "body": "Locus, parabola, tangents.

\"q\"

[STEP I 1994 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":94106, "title": "94-S1-Q6", "body": "Mobius transformation, real and imaginary part, conjugate, composition of functions.

\"q\"

[STEP I 1994 Question 6 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":94107, "title": "94-S1-Q7", "body": "Pattern, cubes of integers, sum.

\"q\"

[STEP I 1994 Question 7 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":94108, "title": "94-S1-Q8", "body": "Logarithmic, trigonometric functions, change of variables, phase.

\"q\"

[STEP I 1994 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":94109, "title": "94-S1-Q9", "body": "Cannon ball, equation of motion, range, inequality, angle of firing.

\"q\"

[STEP I 1994 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":94110, "title": "94-S1-Q10", "body": "Modulus of elasticity, horizontal circle, inequality, angular velocity.

\"q\"

[STEP I 1994 Question 10 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":94111, "title": "94-S1-Q11", "body": "Railway wagon, equilibrium, collide, incline.

\"q\"

[STEP I 1994 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":94112, "title": "94-S1-Q12", "body": "Female colleges of Cambridge, Newnham, New Hall, C1.

\"q\"

[STEP I 1994 Question 12 (Probability and Statistics)]

" }, { "tags": ["Indicator function"], "question_id":94113, "title": "94-S1-Q13", "body": "Without replacement, expectation, binomial coefficients.

\"q\"

[STEP I 1994 Question 13 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":94114, "title": "94-S1-Q14", "body": "Handing essays, mean and variance, probability density functino, pdf.

\"q\"

[STEP I 1994 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":94201, "title": "94-S2-Q1", "body": "Digits, C1.

\"q\"

[STEP II 1994 Question 1 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":94202, "title": "94-S2-Q2", "body": "Polynomials, nth derivatives, degree of polynomials.

\"q\"

[STEP II 1994 Question 2 (Pure)]

" }, { "tags": ["Functions"], "question_id":94203, "title": "94-S2-Q3", "body": "Functional equation, non-constnat function, C1.

\"q\"

[STEP II 1994 Question 3 (Pure)]

" }, { "tags": ["Integration"], "question_id":94204, "title": "94-S2-Q4", "body": "Area of circles and ellipses, intersection.

\"q\"

[STEP II 1994 Question 4 (Pure)]

" }, { "tags": ["Roots of equations"], "question_id":94205, "title": "94-S2-Q5", "body": "Modulus function, curve sketching, C1.

\"q\"

[STEP II 1994 Question 5 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":94206, "title": "94-S2-Q6", "body": "Trigonometric series.

\"q\"

[STEP II 1994 Question 6 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":94207, "title": "94-S2-Q7", "body": "Ruritanian Infantry division, flagpoles, cartesian equations, straight lines, C1.

\"q\"

[STEP II 1994 Question 7 (Pure)]

" }, { "tags": ["Financial mathematics"], "question_id":94208, "title": "94-S2-Q8", "body": "24 Hour Spares, continuous function, profits, inequality, C1.

\"q\"

[STEP II 1994 Question 8 (Pure)]

" }, { "tags": ["Equilibrium"], "question_id":94209, "title": "94-S2-Q9", "body": "Particle attached to rod, angle with horizontal.

\"q\"

[STEP II 1994 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":94210, "title": "94-S2-Q10", "body": "Modulus of elasticity, rope, truk towing a trailer, taut.

\"q\"

[STEP II 1994 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":94211, "title": "94-S2-Q11", "body": "Upwards projectile, inequality, fragments, split into fragments, conservation of momentum.

\"q\"

[STEP II 1994 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":94212, "title": "94-S2-Q12", "body": "Calamity Jane, Buffalo Bill, craps, fair dice, C1.

\"q\"

[STEP II 1994 Question 12 (Probability and Statistics)]

" }, { "tags": ["Exponential distribution"], "question_id":94213, "title": "94-S2-Q13", "body": "Cruncho, cards of mathematicians, expectation.

\"q\"

[STEP II 1994 Question 13 (Mechanics)]

" }, { "tags": ["Geometrical probability"], "question_id":94214, "title": "94-S2-Q14", "body": "Septimus Moneybags, dart board, uniform distribution, variance, charity fete, minimise expected loss.

\"q\"

[STEP II 1994 Question 14 (Mechanics)]

" }, { "tags": ["Integration by parts"], "question_id":94301, "title": "94-S3-Q1", "body": "Reduction formula, hyperbolica functions.

\"q\"

[STEP III 1994 Question 1 (Pure)]

" }, { "tags": ["Polynomial equations"], "question_id":94302, "title": "94-S3-Q2", "body": "Substitution, algebra, quartic equations, C1.

\"q\"

[STEP III 1994 Question 2 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":94303, "title": "94-S3-Q3", "body": "Intersection of plane with sphere, simultaneous equations, circle.

\"q\"

[STEP III 1994 Question 3 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":94304, "title": "94-S3-Q4", "body": "Solution curves, curve sketching, tangent.

\"q\"

[STEP III 1994 Question 4 (Pure)]

" }, { "tags": ["Taylor series"], "question_id":94305, "title": "94-S3-Q5", "body": "Proof by induction, derivatives, logarithmic function, Maclaurin series, coefficient, power series.

\"q\"

[STEP III 1994 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":94306, "title": "94-S3-Q6", "body": "Argand diagram, rotation, necessary and sufficient.

\"q\"

[STEP III 1994 Question 6 (Pure)]

" }, { "tags": ["Groups"], "question_id":94307, "title": "94-S3-Q7", "body": "Permutation, isomorphism, roots of unity, complex multiplication.

\"q\"

[STEP III 1994 Question 7 (Pure)]

" }, { "tags": ["Matrices"], "question_id":94308, "title": "94-S3-Q8", "body": "Matrix product, determinant, complex numbers, sum of squares.

\"q\"

[STEP III 1994 Question 8 (Pure)]

" }, { "tags": ["Collision"], "question_id":94309, "title": "94-S3-Q9", "body": "Coefficient of restitution, symmetrical bowl, first order differential equation.

\"q\"

[STEP III 1994 Question 9 (Mechanics)]

" }, { "tags": ["Time-distance"], "question_id":94310, "title": "94-S3-Q10", "body": "Gammaland, pilot constant wind, C1.

\"q\"

[STEP III 1994 Question 10 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":94311, "title": "94-S3-Q11", "body": "Stepladder, modulus of elasticity, rope.

\"q\"

[STEP III 1994 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":94312, "title": "94-S3-Q12", "body": "Tennis match, winning match.

\"q\"

[STEP III 1994 Question 12 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":94313, "title": "94-S3-Q13", "body": "Trapeze artist, probability density function, hyperbolic function, rope failure.

\"q\"

[STEP III 1994 Question 13 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":94314, "title": "94-S3-Q14", "body": "Points on perimeter of circle, form triangle, probability.

\"q\"

[STEP III 1994 Question 14 (Probability and Statistics)]

" }, { "tags": ["Inequalities"], "question_id":95101, "title": "95-S1-Q1", "body": "Curve sketching, region, lines, C1.

\"q\"

[STEP I 1995 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":95102, "title": "95-S1-Q2", "body": "Trigonometric substitution.

\"q\"

[STEP I 1995 Question 2 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":95103, "title": "95-S1-Q3", "body": "Telescoping sum, sum of cubes.

\"q\"

[STEP I 1995 Question 3 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":95104, "title": "95-S1-Q4", "body": "de Moivre's theorem, binomial theorem, real and imaginary parts.

\"q\"

[STEP I 1995 Question 4 (Pure)]

" }, { "tags": ["Analysis"], "question_id":95105, "title": "95-S1-Q5", "body": "Binomial coefficient, differentiation, integral, harmonic sum.

\"q\"

[STEP I 1995 Question 5 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":95106, "title": "95-S1-Q6", "body": "Substitution.

\"q\"

[STEP I 1995 Question 6 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":95107, "title": "95-S1-Q7", "body": "Centroid, midpoint, altitudes of triangle.

\"q\"

[STEP I 1995 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":95108, "title": "95-S1-Q8", "body": "Second order equation, substitution.

\"q\"

[STEP I 1995 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":95109, "title": "95-S1-Q9", "body": "Angle of projection, parabola, assumptions.

\"q\"

[STEP I 1995 Question 9 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":95110, "title": "95-S1-Q10", "body": "Equilibrium, modulus of elasticity, restitution.

\"q\"

[STEP I 1995 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":95111, "title": "95-S1-Q11", "body": "Cylinder, surface in contact, coefficient of friction.

\"q\"

[STEP I 1995 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":95112, "title": "95-S1-Q12", "body": "Combinatorics, hockey, C1.

\"q\"

[STEP I 1995 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":95113, "title": "95-S1-Q13", "body": "Cancerous cells, expectation, probability.

\"q\"

[STEP I 1995 Question 13 (Probability and Statistics)]

" }, { "tags": ["Normal distribution"], "question_id":95114, "title": "95-S1-Q14", "body": "Proportion, maximum value, differentiation.

\"q\"

[STEP I 1995 Question 14 (Probability and Statistics)]

" }, { "tags": ["Sum"], "question_id":95201, "title": "95-S2-Q1", "body": "Geometric series, differentiation, sum of squares.

\"q\"

[STEP II 1995 Question 1 (Pure)]

" }, { "tags": ["Combinatorics"], "question_id":95202, "title": "95-S2-Q2", "body": "Recurrence relation, proof by induction.

\"q\"

[STEP II 1995 Question 2 (Pure)]

" }, { "tags": ["Tour de Clochemerle"], "question_id":95203, "title": "95-S2-Q3", "body": "C1.

\"q\"

[STEP II 1995 Question 3 (Pure)]

" }, { "tags": ["Analysis"], "question_id":95204, "title": "95-S2-Q4", "body": "Integration by parts, recurrence relation, curve sketching, trigonometry, inequality, limit.

\"q\"

[STEP II 1995 Question 4 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":95205, "title": "95-S2-Q5", "body": "Birkhoff Maclane, C1.

\"q\"

[STEP II 1995 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":95206, "title": "95-S2-Q6", "body": "Roots of quadratics, roots of unity.

\"q\"

[STEP II 1995 Question 6 (Pure)]

" }, { "tags": ["Heron's formula"], "question_id":95207, "title": "95-S2-Q7", "body": "Circle, triangle, coordinate geometry, C1.

\"q\"

[STEP II 1995 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":95208, "title": "95-S2-Q8", "body": "Bacteria in nutrient medium, limit, first order equation.

\"q\"

[STEP II 1995 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":95209, "title": "95-S2-Q9", "body": "Equilibrium, inclined plane.

\"q\"

[STEP II 1995 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":95210, "title": "95-S2-Q10", "body": "Coefficient of restitution, spheres.

\"q\"

[STEP II 1995 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":95211, "title": "95-S2-Q11", "body": "Mass under gravity, distance apart of two particles.

\"q\"

[STEP II 1995 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":95212, "title": "95-S2-Q12", "body": "Bread roll throwing duel Drones' club, probability, C1.

\"q\"

[STEP II 1995 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":95213, "title": "95-S2-Q13", "body": "Fly By Night Airline, expectation, maximum.

\"q\"

[STEP II 1995 Question 13 (Mechanics)]

" }, { "tags": ["Normal distribution"], "question_id":95214, "title": "95-S2-Q14", "body": "Scientist, probability density, hypothesis testing.

\"q\"

[STEP II 1995 Question 14 (Mechanics)]

" }, { "tags": ["Simultaneous equations"], "question_id":95301, "title": "95-S3-Q1", "body": "Linear systems, C1.

\"q\"

[STEP III 1995 Question 1 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":95302, "title": "95-S3-Q2", "body": "Recurrence formula.

\"q\"

[STEP III 1995 Question 2 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":95303, "title": "95-S3-Q3", "body": "Simple harmonic motion, SHM, damped, maximum, second order equations.

\"q\"

[STEP III 1995 Question 3 (Pure)]

" }, { "tags": ["Analysis"], "question_id":95304, "title": "95-S3-Q4", "body": "Trigonometric series, inequality.

\"q\"

[STEP III 1995 Question 4 (Pure)]

" }, { "tags": ["Taylor series"], "question_id":95305, "title": "95-S3-Q5", "body": "Maclaurin series, coefficient, power series, differentiation, trigonometric functions, proof by induction.

\"q\"

[STEP III 1995 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":95306, "title": "95-S3-Q6", "body": "Argand diagram, inverse function.

\"q\"

[STEP III 1995 Question 6 (Pure)]

" }, { "tags": ["Groups"], "question_id":95307, "title": "95-S3-Q7", "body": "Set, isomorphism.

\"q\"

[STEP III 1995 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":95308, "title": "95-S3-Q8", "body": "3D, perpendicular distance, plane, surface, scalar product, geometrical interpretation, circles.

\"q\"

[STEP III 1995 Question 8 (Pure)]

" }, { "tags": ["Circular motion"], "question_id":95309, "title": "95-S3-Q9", "body": "Circular disc, stable equilibrium, moment of inertia, maximum.

\"q\"

[STEP III 1995 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":95310, "title": "95-S3-Q10", "body": "Cannon ball, angle of firing, range.

\"q\"

[STEP III 1995 Question 10 (Mechanics)]

" }, { "tags": ["Time-distance"], "question_id":95311, "title": "95-S3-Q11", "body": "Ship sailing, wind, C1.

\"q\"

[STEP III 1995 Question 11 (Mechanics)]

" }, { "tags": ["Probability density function"], "question_id":95312, "title": "95-S3-Q12", "body": "Joint pdf, normal distribution, radially symmetric.

\"q\"

[STEP III 1995 Question 12 (Probability and Statistics)]

" }, { "tags": ["Coding and Cryptography"], "question_id":95313, "title": "95-S3-Q13", "body": "C1.

\"q\"

[STEP III 1995 Question 13 (Probability and Statistics)]

" }, { "tags": ["Moment generating function"], "question_id":95314, "title": "95-S3-Q14", "body": "Probability density function, pdf, candidate, examination.

\"q\"

[STEP III 1995 Question 14 (Probability and Statistics)]

" }, { "tags": ["Differentiation"], "question_id":96101, "title": "96-S1-Q1", "body": "Surface area, minimum, sphere, cylinder, C1.

\"q\"

[STEP I 1996 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":96102, "title": "96-S1-Q2", "body": "Polynomial, binomial coefficient.

\"q\"

[STEP I 1996 Question 2 (Pure)]

" }, { "tags": ["Number theory"], "question_id":96103, "title": "96-S1-Q3", "body": "Divisibility, factorisation, modulo arithmetic, C1.

\"q\"

[STEP I 1996 Question 3 (Pure)]

" }, { "tags": ["Integral"], "question_id":96104, "title": "96-S1-Q4", "body": "Arctan, logarithmic integration, substitution.

\"q\"

[STEP I 1996 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":96105, "title": "96-S1-Q5", "body": "Quadratic equations, rational numbers.

\"q\"

[STEP I 1996 Question 5 (Pure)]

" }, { "tags": ["Analysis"], "question_id":96106, "title": "96-S1-Q6", "body": "Telescoping sum, trigonometry, integration.

\"q\"

[STEP I 1996 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":96107, "title": "96-S1-Q7", "body": "Water tank, power law, steady rate, first order equation.

\"q\"

[STEP I 1996 Question 7 (Pure)]

" }, { "tags": ["Decimal expansions"], "question_id":96108, "title": "96-S1-Q8", "body": "Geometric series, positive integer, rational numbers, C1.

\"q\"

[STEP I 1996 Question 8 (Pure)]

" }, { "tags": ["Hooke's law"], "question_id":96109, "title": "96-S1-Q9", "body": "Bungee jumping, ravine, modulus of elasticity, maximum speed.

\"q\"

[STEP I 1996 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":96110, "title": "96-S1-Q10", "body": "Kinetic energy, spaceship, relative speed, explosion.

\"q\"

[STEP I 1996 Question 10 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":96111, "title": "96-S1-Q11", "body": "Angle of projection, speed of projection.

\"q\"

[STEP I 1996 Question 11 (Mechanics)]

" }, { "tags": ["Combinatorics"], "question_id":96112, "title": "96-S1-Q12", "body": "Binomial coefficients, exam scripts, expectation, C1.

\"q\"

[STEP I 1996 Question 12 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":96113, "title": "96-S1-Q13", "body": "Expectation and variance, Penny Black stamp.

\"q\"

[STEP I 1996 Question 13 (Probability and Statistics)]

" }, { "tags": ["Coin toss"], "question_id":96114, "title": "96-S1-Q14", "body": "Biased coin, successive, conditional probability, C1.

\"q\"

[STEP I 1996 Question 14 (Probability and Statistics)]

" }, { "tags": ["Binomial expansion"], "question_id":96201, "title": "96-S2-Q1", "body": "Binomial coefficients.

\"q\"

[STEP II 1996 Question 1 (Pure)]

" }, { "tags": ["Simultaneous equations"], "question_id":96202, "title": "96-S2-Q2", "body": "Linear system, C1.

\"q\"

[STEP II 1996 Question 2 (Pure)]

" }, { "tags": ["Fibonacci number"], "question_id":96203, "title": "96-S2-Q3", "body": "General formula, proof by induction.

\"q\"

[STEP II 1996 Question 3 (Pure)]

" }, { "tags": ["Integral"], "question_id":96204, "title": "96-S2-Q4", "body": "Change of variable, trigonometry, cosine, integral.

\"q\"

[STEP II 1996 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":96205, "title": "96-S2-Q5", "body": "Quartic equations, root of unity.

\"q\"

[STEP II 1996 Question 5 (Pure)]

" }, { "tags": ["Number theory"], "question_id":96206, "title": "96-S2-Q6", "body": "Proper factor, prime factorisation, C1.

\"q\"

[STEP II 1996 Question 6 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":96207, "title": "96-S2-Q7", "body": "Square, perpendicular distance, straight line, circle, solutions.

\"q\"

[STEP II 1996 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":96208, "title": "96-S2-Q8", "body": "Functional equation, trigonometry, initial condition.

\"q\"

[STEP II 1996 Question 8 (Pure)]

" }, { "tags": ["Centre of mass"], "question_id":96209, "title": "96-S2-Q9", "body": "Child's toy, hemisphere, surface, equilibrium, centre of gravity.

\"q\"

[STEP II 1996 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":96210, "title": "96-S2-Q10", "body": "Rhode Island Red and the Henhouse of Doom, fairground wheel, maximum.

\"q\"

[STEP II 1996 Question 10 (Pure)]

" }, { "tags": ["SHM"], "question_id":96211, "title": "96-S2-Q11", "body": "Simple harmonic motion, ceiling, second order equation, amplitude of oscillation

\"q\"

[STEP II 1996 Question 11 (Mechanics)]

" }, { "tags": ["Pdf"], "question_id":96212, "title": "96-S2-Q12", "body": "Probabiltiy density function, uniform distribution, variance, expectation, exponential distribution.

\"q\"

[STEP II 1996 Question 12 (Probability and Statistics)]

" }, { "tags": ["Binomial distribution"], "question_id":96213, "title": "96-S2-Q13", "body": "Binomial coefficients, sum, Triposville, elementary probability, conditional probability.

\"q\"

[STEP II 1996 Question 13 (Mechanics)]

" }, { "tags": ["Continuous random variable"], "question_id":96214, "title": "96-S2-Q14", "body": "Uniform distribution, expectation, moments, inequality, approximation.

\"q\"

[STEP II 1996 Question 14 (Mechanics)]

" }, { "tags": ["Hyperbolic functions"], "question_id":96301, "title": "96-S3-Q1", "body": "Sum, identity, definition.

\"q\"

[STEP III 1996 Question 1 (Pure)]

" }, { "tags": ["Simultaneous equations"], "question_id":96302, "title": "96-S3-Q2", "body": "Linear system, proof, C1.

\"q\"

[STEP III 1996 Question 2 (Pure)]

" }, { "tags": ["Integral"], "question_id":96303, "title": "96-S3-Q3", "body": "Integration by substitution, arctan, trigonometry.

\"q\"

[STEP III 1996 Question 3 (Pure)]

" }, { "tags": ["Number theory"], "question_id":96304, "title": "96-S3-Q4", "body": "Inequality, sum, largest product, proof, C1.

\"q\"

[STEP III 1996 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":96305, "title": "96-S3-Q5", "body": "de Moivre's theorem, tangent identity, sum, cubic equation, roots of unity.

\"q\"

[STEP III 1996 Question 5 (Pure)]

" }, { "tags": ["Groups"], "question_id":96306, "title": "96-S3-Q6", "body": "Group of matrices, singular matrix, determinant.

\"q\"

[STEP III 1996 Question 6 (Pure)]

" }, { "tags": ["Area and perimeters"], "question_id":96307, "title": "96-S3-Q7", "body": "Simultaneous equations, roots of polynomials, area of triangle, semi-perimeter, heron, cubic equation, C1.

\"q\"

[STEP III 1996 Question 7 (Pure)]

" }, { "tags": ["Transformation"], "question_id":96308, "title": "96-S3-Q8", "body": "Mobius transformation, inverse operation, composition, identity, C1.

\"q\"

[STEP III 1996 Question 8 (Pure)]

" }, { "tags": ["Centre of mass"], "question_id":96309, "title": "96-S3-Q9", "body": "Sphere, small displacement, perturbation.

\"q\"

[STEP III 1996 Question 9 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":96310, "title": "96-S3-Q10", "body": "Circular cylinders, coefficient of friction, equilibrium, inequalities.

\"q\"

[STEP III 1996 Question 10 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":96311, "title": "96-S3-Q11", "body": "Simple harmonic motion, circular wire, second order equation, equilibrium, period of oscillation, displacement.

\"q\"

[STEP III 1996 Question 11 (Mechanics)]

" }, { "tags": ["Markov chains"], "question_id":96312, "title": "96-S3-Q12", "body": "Professor Ecks, proving theorem, matrices.

\"q\"

[STEP III 1996 Question 12 (Probability and Statistics)]

" }, { "tags": ["Chebyshev's inequality"], "question_id":96313, "title": "96-S3-Q13", "body": "Random variables, expectation and variance, linearity, inequalities.

\"q\"

[STEP III 1996 Question 13 (Probability and Statistics)]

" }, { "tags": ["Differential equation"], "question_id":96314, "title": "96-S3-Q14", "body": "Bike, puncture, first order equation, approximation.

\"q\"

[STEP III 1996 Question 14 (Probability and Statistics)]

" }, { "tags": ["Combinatorics"], "question_id":97101, "title": "97-S1-Q1", "body": "10 and 20 pence coins, number of ways, C1.

\"q\"

[STEP I 1997 Question 1 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":97102, "title": "97-S1-Q2", "body": "Trigonometry, identity, chain rule, implicit differentiation.

\"q\"

[STEP I 1997 Question 2 (Pure)]

" }, { "tags": ["Sequences"], "question_id":97103, "title": "97-S1-Q3", "body": "Recurrence relation, decimal places, digit, numbers, C1.

\"q\"

[STEP I 1997 Question 3 (Pure)]

" }, { "tags": ["Modulus function"], "question_id":97104, "title": "97-S1-Q4", "body": "Roots of equations, C1.

\"q\"

[STEP I 1997 Question 4 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":97105, "title": "97-S1-Q5", "body": "Quadrilateral, midpoints, constant, vertices, C1.

\"q\"

[STEP I 1997 Question 5 (Pure)]

" }, { "tags": ["Analysis"], "question_id":97106, "title": "97-S1-Q6", "body": "Factorisation, algebraic manipulation, integration, inequality, C1.

\"q\"

[STEP I 1997 Question 6 (Pure)]

" }, { "tags": ["Cubic polynomial"], "question_id":97107, "title": "97-S1-Q7", "body": "Integration.

\"q\"

[STEP I 1997 Question 7 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":97108, "title": "97-S1-Q8", "body": "Roots of equation, logarithmic function.

\"q\"

[STEP I 1997 Question 8 (Pure)]

" }, { "tags": ["How does a chicken cross the road?"], "question_id":97109, "title": "97-S1-Q9", "body": "Successive car width, chicken, inequality, time-distance, C1.

\"q\"

[STEP I 1997 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":97110, "title": "97-S1-Q10", "body": "Horizontal circle, tension in string.

\"q\"

[STEP I 1997 Question 10 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":97111, "title": "97-S1-Q11", "body": "First order differential equation, maximum height, velocity.

\"q\"

[STEP I 1997 Question 11 (Mechanics)]

" }, { "tags": ["Uniform distribution"], "question_id":97112, "title": "97-S1-Q12", "body": "Root of quadratic, expectation and variance, sum of random variable, probability.

\"q\"

[STEP I 1997 Question 12 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":97113, "title": "97-S1-Q13", "body": "Bond, assasin, tree diagram, C1.

\"q\"

[STEP I 1997 Question 13 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":97114, "title": "97-S1-Q14", "body": "Maximum flood, cost, expected cost, logarithm function.

\"q\"

[STEP I 1997 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":97201, "title": "97-S2-Q1", "body": "Sum of numbers, digits, product of primes, C1.

\"q\"

[STEP II 1997 Question 1 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":97202, "title": "97-S2-Q2", "body": "Iteration, proof.

\"q\"

[STEP II 1997 Question 2 (Pure)]

" }, { "tags": ["Integral"], "question_id":97203, "title": "97-S2-Q3", "body": "Integration by partial fractions, arctan, logarithm.

\"q\"

[STEP II 1997 Question 3 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":97204, "title": "97-S2-Q4", "body": "Factors of polynomials, divisibility, degree, C1.

\"q\"

[STEP II 1997 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":97205, "title": "97-S2-Q5", "body": "Locus, subset, regions of Argand diagram.

\"q\"

[STEP II 1997 Question 5 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":97206, "title": "97-S2-Q6", "body": "Trigonometric identity, solution of equations, rational, inequality.

\"q\"

[STEP II 1997 Question 6 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":97207, "title": "97-S2-Q7", "body": "Differentiation, maximum, minimum, C1.

\"q\"

[STEP II 1997 Question 7 (Pure)]

" }, { "tags": ["Inequalities"], "question_id":97208, "title": "97-S2-Q8", "body": "Integration.

\"q\"

[STEP II 1997 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":97209, "title": "97-S2-Q9", "body": "Coefficient of friction, solid sphere, no slip, horizontal force.

\"q\"

[STEP II 1997 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":97210, "title": "97-S2-Q10", "body": "Coefficient of restitution, elastic collision, coalesce, energy, explosion.

\"q\"

[STEP II 1997 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":97211, "title": "97-S2-Q11", "body": "Tennis player, angle and velocity, lower bound for serve.

\"q\"

[STEP II 1997 Question 11 (Mechanics)]

" }, { "tags": ["Binomial expansion"], "question_id":97212, "title": "97-S2-Q12", "body": "Cambridge Whispers, elementary probability.

\"q\"

[STEP II 1997 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":97213, "title": "97-S2-Q13", "body": "Buffon's needle, continuous random variable, cumulative distribution function, lines.

\"q\"

[STEP II 1997 Question 13 (Mechanics)]

" }, { "tags": ["Poisson distribution"], "question_id":97214, "title": "97-S2-Q14", "body": "Traffic, tunnel, expectation.

\"q\"

[STEP II 1997 Question 14 (Mechanics)]

" }, { "tags": ["Taylor series"], "question_id":97301, "title": "97-S3-Q1", "body": "Exponential function, Maclaurin series.

\"q\"

[STEP III 1997 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":97302, "title": "97-S3-Q2", "body": "Logarithmic and exponential function, maximum, differentiation, root of equation, C1.

\"q\"

[STEP III 1997 Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":97303, "title": "97-S3-Q3", "body": "Roots of unity, points around a circle, coordinate geometry.

\"q\"

[STEP III 1997 Question 3 (Pure)]

" }, { "tags": ["AM-GM inequality"], "question_id":97304, "title": "97-S3-Q4", "body": "Roots of cubic equations, coefficient, differentiation, C1.

\"q\"

[STEP III 1997 Question 4 (Pure)]

" }, { "tags": ["Surface of revolution"], "question_id":97305, "title": "97-S3-Q5", "body": "Ratio, distance of wheel rolling, integration.

\"q\"

[STEP III 1997 Question 5 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":97306, "title": "97-S3-Q6", "body": "Harmonic oscillator, second order equation, recurrence relation, difference equation.

\"q\"

[STEP III 1997 Question 6 (Pure)]

" }, { "tags": ["e is irrational"], "question_id":97307, "title": "97-S3-Q7", "body": "Proof, integer parts, inequality, C1.

\"q\"

[STEP III 1997 Question 7 (Pure)]

" }, { "tags": ["Transformations"], "question_id":97308, "title": "97-S3-Q8", "body": "Diagonal matrix, matrix of rotation, ellipse, diagonalise.

\"q\"

[STEP III 1997 Question 8 (Pure)]

" }, { "tags": ["Hooke's law"], "question_id":97309, "title": "97-S3-Q9", "body": "Ratio of stretched and unstretched springs.

\"q\"

[STEP III 1997 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":97310, "title": "97-S3-Q10", "body": "Friction, spherical marble on horizontal table.

\"q\"

[STEP III 1997 Question 10 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":97311, "title": "97-S3-Q11", "body": "Symmetrical bell and clapper, angle vith vertical.

\"q\"

[STEP III 1997 Question 11 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":97312, "title": "97-S3-Q12", "body": "Biased coin, probability generating function, pgf, expectation and variance, sample cards, normal approximation, harmonic series.

\"q\"

[STEP III 1997 Question 12 (Probability and Statistics)]

" }, { "tags": ["Pdf,","Mgf"], "question_id":97313, "title": "97-S3-Q13", "body": "Probability density and moment generating functions, expectation, normal distribution.

\"q\"

[STEP III 1997 Question 13 (Probability and Statistics)]

" }, { "tags": ["Independence"], "question_id":97314, "title": "97-S3-Q14", "body": "Mean and variance, industrial process, standard deviation, area and perimeter.

\"q\"

[STEP III 1997 Question 14 (Probability and Statistics)]

" }, { "tags": ["Numbers"], "question_id":98101, "title": "98-S1-Q1", "body": "Integers, digits, number of, C1.

\"q\"

[STEP I 1998 Question 1 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":98102, "title": "98-S1-Q2", "body": "

\"q\"

[STEP I 1998 Question 2 (Pure)]

" }, { "tags": ["Proof"], "question_id":98103, "title": "98-S1-Q3", "body": "Statements, proof, polynomials, trigonometry, inequality, logarithmic functions.

\"q\"

[STEP I 1998 Question 3 (Pure)]

" }, { "tags": ["Optimisation"], "question_id":98104, "title": "98-S1-Q4", "body": "Differentiation, rectangle inscribed in circle, greatest, maximum, perimeter, sum of lengths, proof, C1.

\"q\"

[STEP I 1998 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":98105, "title": "98-S1-Q5", "body": "Argand diagram, six-sided polygon.

\"q\"

[STEP I 1998 Question 5 (Pure)]

" }, { "tags": ["Recurrence relation"], "question_id":98106, "title": "98-S1-Q6", "body": "Difference equation, trigonometry.

\"q\"

[STEP I 1998 Question 6 (Pure)]

" }, { "tags": ["Geometric sequences"], "question_id":98107, "title": "98-S1-Q7", "body": "Bank, interest, deposit, financial, C1.

\"q\"

[STEP I 1998 Question 7 (Pure)]

" }, { "tags": ["Fluid dynamics"], "question_id":98108, "title": "98-S1-Q8", "body": "Differential equations, volume flux, second order equation.

\"q\"

[STEP I 1998 Question 8 (Pure)]

" }, { "tags": ["Collision"], "question_id":98109, "title": "98-S1-Q9", "body": "Coefficient of resitution, spheres.

\"q\"

[STEP I 1998 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":98110, "title": "98-S1-Q10", "body": "Shell, greatest height, maximum, distance.

\"q\"

[STEP I 1998 Question 10 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":98111, "title": "98-S1-Q11", "body": "Hank's Gold mine, maximum, differentiation.

\"q\"

[STEP I 1998 Question 11 (Mechanics)]

" }, { "tags": ["Algebraic probability"], "question_id":98112, "title": "98-S1-Q12", "body": "Independence, solution to equation, divisibility.

\"q\"

[STEP I 1998 Question 12 (Probability and Statistics)]

" }, { "tags": ["Sampling with replacement"], "question_id":98113, "title": "98-S1-Q13", "body": "Elementary probability, C1.

\"q\"

[STEP I 1998 Question 13 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":98114, "title": "98-S1-Q14", "body": "Geometrical probability, Genland, Slihing, tax on yaks, expectation.

\"q\"

[STEP I 1998 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":98201, "title": "98-S2-Q1", "body": "Cubic equation, factors, integer solution to equation, C1.

\"q\"

[STEP II 1998 Question 1 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":98202, "title": "98-S2-Q2", "body": "Approximation to square roots.

\"q\"

[STEP II 1998 Question 2 (Pure)]

" }, { "tags": ["Analysis"], "question_id":98203, "title": "98-S2-Q3", "body": "Telescoping sum, limit, ratio of terms.

\"q\"

[STEP II 1998 Question 3 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":98204, "title": "98-S2-Q4", "body": "Recurrence formula, trigonometric integral.

\"q\"

[STEP II 1998 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":98205, "title": "98-S2-Q5", "body": "Triangle inequality, induction, roots of equation, geometry.

\"q\"

[STEP II 1998 Question 5 (Pure)]

" }, { "tags": ["Parametric equations"], "question_id":98206, "title": "98-S2-Q6", "body": "Curve sketching, normal and tangent.

\"q\"

[STEP II 1998 Question 6 (Pure)]

" }, { "tags": ["Functions"], "question_id":98207, "title": "98-S2-Q7", "body": "Differentiation, maximum, minimum, inequality, trigonometric functions.

\"q\"

[STEP II 1998 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":98208, "title": "98-S2-Q8", "body": "3D, triangle, plane, midpoint, line meet plane.

\"q\"

[STEP II 1998 Question 8 (Pure)]

" }, { "tags": ["Centre of mass"], "question_id":98209, "title": "98-S2-Q9", "body": "Equilibrium, planar hexagon framework, suspended, diagram.

\"q\"

[STEP II 1998 Question 9 (Mechanics)]

" }, { "tags": ["Wedge"], "question_id":98210, "title": "98-S2-Q10", "body": "CConservation of momentum and energy, inclined surface, differential equation, mechanical principles.

\"q\"

[STEP II 1998 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":98211, "title": "98-S2-Q11", "body": "Cricket, fielder, batsman, constant angle.

\"q\"

[STEP II 1998 Question 11 (Mechanics)]

" }, { "tags": ["Mathematitis"], "question_id":98212, "title": "98-S2-Q12", "body": "AL, STEP, tree diagram, sufferer C1.

\"q\"

[STEP II 1998 Question 12 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":98213, "title": "98-S2-Q13", "body": "Conditional probability, serve customer, independent.

\"q\"

[STEP II 1998 Question 13 (Mechanics)]

" }, { "tags": ["Poisson distribution"], "question_id":98214, "title": "98-S2-Q14", "body": "Catastrophe college, Dr Doom, inequality.

\"q\"

[STEP II 1998 Question 14 (Mechanics)]

" }, { "tags": ["Curve sketching"], "question_id":98301, "title": "98-S3-Q1", "body": "Trigonometry, differentiation, stationary points.

\"q\"

[STEP III 1998 Question 1 (Pure)]

" }, { "tags": ["Integral"], "question_id":98302, "title": "98-S3-Q2", "body": "Beta function, integration by parts, recurrence formula.

\"q\"

[STEP III 1998 Question 2 (Pure)]

" }, { "tags": ["Difference equation"], "question_id":98303, "title": "98-S3-Q3", "body": "Bank bond, power law solution substitution, limit, C1.

\"q\"

[STEP III 1998 Question 3 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":98304, "title": "98-S3-Q4", "body": "Curve sketching, circles, area enclosed by curve, integration.

\"q\"

[STEP III 1998 Question 4 (Pure)]

" }, { "tags": ["Matrices"], "question_id":98305, "title": "98-S3-Q5", "body": "Exponential of square matrix, geometry.

\"q\"

[STEP III 1998 Question 5 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":98306, "title": "98-S3-Q6", "body": "Cube, tetrahedron, polyhedra, octahedron, vertices, faces, volume, edges, C1.

\"q\"

[STEP III 1998 Question 6 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":98307, "title": "98-S3-Q7", "body": "Differentiation, stationary points, statistical physics, integral.

\"q\"

[STEP III 1998 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":98308, "title": "98-S3-Q8", "body": "Line intersecting spheres, inequality, minimum distance.

\"q\"

[STEP III 1998 Question 8 (Pure)]

" }, { "tags": ["SHM"], "question_id":98309, "title": "98-S3-Q9", "body": "Period of simple harmonic motion, moment of inertia, circular cone.

\"q\"

[STEP III 1998 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":98310, "title": "98-S3-Q10", "body": "Conservation of momentum and energy, coeffcient of restitution.

\"q\"

[STEP III 1998 Question 10 (Mechanics)]

" }, { "tags": ["Real pendulum"], "question_id":98311, "title": "98-S3-Q11", "body": "Binomial expansion, equation of motion, period, integration by substitution.

\"q\"

[STEP III 1998 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":98312, "title": "98-S3-Q12", "body": "Mountain villages, tetrahedron, snowfall, C1.

\"q\"

[STEP III 1998 Question 12 (Probability and Statistics)]

" }, { "tags": ["MLE"], "question_id":98313, "title": "98-S3-Q13", "body": "Maximum likelihood estimator, coin toss, C1.

\"q\"

[STEP III 1998 Question 13 (Probability and Statistics)]

" }, { "tags": ["Uniform distribution"], "question_id":98314, "title": "98-S3-Q14", "body": "Submarines, max, sum of random variables, estimator, expectation and variances.

\"q\"

[STEP III 1998 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":99101, "title": "99-S1-Q1", "body": "Divisibility, average value, C1.

\"q\"

[STEP I 1999 Question 1 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":99102, "title": "99-S1-Q2", "body": "Sum of squares, centroid, C1

\"q\"

[STEP I 1999 Question 2 (Pure)]

" }, { "tags": ["Recurrence relation"], "question_id":99103, "title": "99-S1-Q3", "body": "Proof, inequality, C1.

\"q\"

[STEP I 1999 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":99104, "title": "99-S1-Q4", "body": "Modulus function, inequality, C1.

\"q\"

[STEP I 1999 Question 4 (Pure)]

" }, { "tags": ["Approximation"], "question_id":99105, "title": "99-S1-Q5", "body": "Small angle approximation, cartesian coordinates, satellites, general relativity, earth, C1.

\"q\"

[STEP I 1999 Question 5 (Pure)]

" }, { "tags": ["Inequality"], "question_id":99106, "title": "99-S1-Q6", "body": "Maximum and minimum, quadratic equation, C1.

\"q\"

[STEP I 1999 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":99107, "title": "99-S1-Q7", "body": "Trigonometry, second order equation.

\"q\"

[STEP I 1999 Question 7 (Pure)]

" }, { "tags": ["Analysis"], "question_id":99108, "title": "99-S1-Q8", "body": "Inequality, integral, logarithm function, harmonic series, sum, limit.

\"q\"

[STEP I 1999 Question 8 (Pure)]

" }, { "tags": ["Time-distance"], "question_id":99109, "title": "99-S1-Q9", "body": "Tortoise, hare, C1.

\"q\"

[STEP I 1999 Question 9 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":99110, "title": "99-S1-Q10", "body": "Simple harmonic motion, period.

\"q\"

[STEP I 1999 Question 10 (Mechanics)]

" }, { "tags": ["Gravitational attraction"], "question_id":99111, "title": "99-S1-Q11", "body": "Inverse square law, Krypton, starmaker, centre of mass.

\"q\"

[STEP I 1999 Question 11 (Mechanics)]

" }, { "tags": ["Die"], "question_id":99112, "title": "99-S1-Q12", "body": "Sum of dice, probability, inequality, C1.

\"q\"

[STEP I 1999 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":99113, "title": "99-S1-Q13", "body": "Bar magnets, expectation and variance, continuous random variable.

\"q\"

[STEP I 1999 Question 13 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":99114, "title": "99-S1-Q14", "body": "Dart throwing, expectation, total score, probability, density function.

\"q\"

[STEP I 1999 Question 14 (Probability and Statistics)]

" }, { "tags": ["Binomial expansion"], "question_id":99201, "title": "99-S2-Q1", "body": "Stirling's formula, factorial, logarithm, exponentials, magnitude, C1-ish.

\"q\"

[STEP II 1999 Question 1 (Pure)]

" }, { "tags": ["Quadratic equation"], "question_id":99202, "title": "99-S2-Q2", "body": "Inequality, real roots, C1.

\"q\"

[STEP II 1999 Question 2 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":99203, "title": "99-S2-Q3", "body": "Hermite polynomial, differentiation, exponential function, coefficient.

\"q\"

[STEP II 1999 Question 3 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":99204, "title": "99-S2-Q4", "body": "Sum of binomial coefficients, identity.

\"q\"

[STEP II 1999 Question 4 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":99205, "title": "99-S2-Q5", "body": "Solutions of trigonometric equation, inequality.

\"q\"

[STEP II 1999 Question 5 (Pure)]

" }, { "tags": ["Integral"], "question_id":99206, "title": "99-S2-Q6", "body": "Substitution of Mobius form, logarithm, nice trick.

\"q\"

[STEP II 1999 Question 6 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":99207, "title": "99-S2-Q7", "body": "Differentiation, stationary points, C1.

\"q\"

[STEP II 1999 Question 7 (Pure)]

" }, { "tags": ["Analysis"], "question_id":99208, "title": "99-S2-Q8", "body": "Differentiation, trigonometry, approximation, small angle.

\"q\"

[STEP II 1999 Question 8 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":99209, "title": "99-S2-Q9", "body": "Acceleration, fragment, star, Z-universe.

\"q\"

[STEP II 1999 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":99210, "title": "99-S2-Q10", "body": "Coefficient of restitution, impact, velocity, loss of kinetic energy.

\"q\"

[STEP II 1999 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":99211, "title": "99-S2-Q11", "body": "Automated mobile dummy target for gunnery practice, circle, distance, shell.

\"q\"

[STEP II 1999 Question 11 (Mechanics)]

" }, { "tags": ["Micro-chip"], "question_id":99212, "title": "99-S2-Q12", "body": "Conditional probability, C1.

\"q\"

[STEP II 1999 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":99213, "title": "99-S2-Q13", "body": "Stick, broken, pieces, expectation and variance, pdf, probability density function.

\"q\"

[STEP II 1999 Question 13 (Mechanics)]

" }, { "tags": ["Die"], "question_id":99214, "title": "99-S2-Q14", "body": "Six-sided fair dice, strategy, maximise, expectation, C1.

\"q\"

[STEP II 1999 Question 14 (Mechanics)]

" }, { "tags": ["Cubic equation"], "question_id":99301, "title": "99-S3-Q1", "body": "Roots of equation, geometric progression, polynomial, C1.

\"q\"

[STEP III 1999 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":99302, "title": "99-S3-Q2", "body": "Transcendental equation, inequality, roots of equation, differentiation.

\"q\"

[STEP III 1999 Question 2 (Pure)]

" }, { "tags": ["Limit"], "question_id":99303, "title": "99-S3-Q3", "body": "Integration, sum, limit.

\"q\"

[STEP III 1999 Question 3 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":99304, "title": "99-S3-Q4", "body": "Euler's formula, polyhedron, edge, vertices, faces, regular, Euclidean, C1.

\"q\"

[STEP III 1999 Question 4 (Pure)]

" }, { "tags": ["Difference equation"], "question_id":99305, "title": "99-S3-Q5", "body": "Proof by induction.

\"q\"

[STEP III 1999 Question 5 (Pure)]

" }, { "tags": ["Parametric equation"], "question_id":99306, "title": "99-S3-Q6", "body": "Integration, curve sketching, area.

\"q\"

[STEP III 1999 Question 6 (Pure)]

" }, { "tags": ["Groups"], "question_id":99307, "title": "99-S3-Q7", "body": "Binary operation, associative, subgroup.

\"q\"

[STEP III 1999 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":99308, "title": "99-S3-Q8", "body": "Harmonic oscillator, sum, tirgonometry, integration, zeta function.

\"q\"

[STEP III 1999 Question 8 (Pure)]

" }, { "tags": ["Gravitational force"], "question_id":99309, "title": "99-S3-Q9", "body": "Shell, circular ring, attraction.

\"q\"

[STEP III 1999 Question 9 (Mechanics)]

" }, { "tags": ["Impulse"], "question_id":99310, "title": "99-S3-Q10", "body": "Momentum, integral.

\"q\"

[STEP III 1999 Question 10 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":99311, "title": "99-S3-Q11", "body": "Moment of inertia, circular hoop, contact, table.

\"q\"

[STEP III 1999 Question 11 (Mechanics)]

" }, { "tags": ["Discrete random variable"], "question_id":99312, "title": "99-S3-Q12", "body": "Increasing function, solution of equation, expectation.

\"q\"

[STEP III 1999 Question 12 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":99313, "title": "99-S3-Q13", "body": "Cake in canteen, expectation.

\"q\"

[STEP III 1999 Question 13 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":99314, "title": "99-S3-Q14", "body": "Horizons, expected winnings.

\"q\"

[STEP III 1999 Question 14 (Probability and Statistics)]

" }, { "tags": ["Logarithms"], "question_id":2000101, "title": "00-S1-Q1", "body": "Inequality, number, digit, C1-ish.

\"q\"

[STEP I 2000 Question 1 (Pure)]

" }, { "tags": ["Binomial coefficient"], "question_id":2000102, "title": "00-S1-Q2", "body": "Binomial expansion

\"q\"

[STEP I 2000 Question 2 (Pure)]

" }, { "tags": ["Integration"], "question_id":2000103, "title": "00-S1-Q3", "body": "Integer part, floor function, exponential and logarithm, curve sketching.

\"q\"

[STEP I 2000 Question 3 (Pure)]

" }, { "tags": ["Integration"], "question_id":2000104, "title": "00-S1-Q4", "body": "Inequality, maximum, quotient rule, differentiation, C1.

\"q\"

[STEP I 2000 Question 4 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2000105, "title": "00-S1-Q5", "body": "Trigonometry, steepest line, inclined plane, C1.

\"q\"

[STEP I 2000 Question 5 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2000106, "title": "00-S1-Q6", "body": "Factorisation, inequality, coordinate geometry, circles and lines, C1.

\"q\"

[STEP I 2000 Question 6 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":2000107, "title": "00-S1-Q7", "body": "Quotient rule, derivative, C1.

\"q\"

[STEP I 2000 Question 7 (Pure)]

" }, { "tags": ["Integral"], "question_id":2000108, "title": "00-S1-Q8", "body": "Modulus function, absolute value, trigonometric function, curve sketching.

\"q\"

[STEP I 2000 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2000109, "title": "00-S1-Q9", "body": "Toy cannon in railway carriage, maximum range.

\"q\"

[STEP I 2000 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2000110, "title": "00-S1-Q10", "body": "Energy of system, coefficients of restitution.

\"q\"

[STEP I 2000 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2000111, "title": "00-S1-Q11", "body": "Rod inclined against wall, ladder, coefficient of friction, limiting.

\"q\"

[STEP I 2000 Question 11 (Mechanics)]

" }, { "tags": ["Sampling with/out replacement"], "question_id":2000112, "title": "00-S1-Q12", "body": "Key, front door, elementary probability, combinatorics, C1.

\"q\"

[STEP I 2000 Question 12 (Probability and Statistics)]

" }, { "tags": ["Tree diagram"], "question_id":2000113, "title": "00-S1-Q13", "body": "Gene, elementary probability, C1.

\"q\"

[STEP I 2000 Question 13 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":2000114, "title": "00-S1-Q14", "body": "Uniform distribution, expectation, moments, variance.

\"q\"

[STEP I 2000 Question 14 (Probability and Statistics)]

" }, { "tags": ["Unit fraction"], "question_id":2000201, "title": "00-S2-Q1", "body": "Egyption fractions, prime, factors, number theory, C1.

\"q\"

[STEP II 2000 Question 1 (Pure)]

" }, { "tags": ["Factors of polynomials"], "question_id":2000202, "title": "00-S2-Q2", "body": "Proof, factorisation, C1.

\"q\"

[STEP II 2000 Question 2 (Pure)]

" }, { "tags": ["Approximation"], "question_id":2000203, "title": "00-S2-Q3", "body": "Error estimation, perturbation, range, inequality, length of triangle, C1.

\"q\"

[STEP II 2000 Question 3 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2000204, "title": "00-S2-Q4", "body": "de Moivre's theorem, trigonometric identities, arctan, induction.

\"q\"

[STEP II 2000 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":2000205, "title": "00-S2-Q5", "body": "Approximation by linear functions, residual error, trigonometric functions, small angle approximation.

\"q\"

[STEP II 2000 Question 5 (Pure)]

" }, { "tags": ["Integral"], "question_id":2000206, "title": "00-S2-Q6", "body": "t-substitution, tan half angle substitution, trigonometry.

\"q\"

[STEP II 2000 Question 6 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2000207, "title": "00-S2-Q7", "body": "Equation of a line and plane, interection, circle, line through origin.

\"q\"

[STEP II 2000 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2000208, "title": "00-S2-Q8", "body": "Separable, integration, limit, small angle approximation.

\"q\"

[STEP II 2000 Question 8 (Pure)]

" }, { "tags": ["Free-fall"], "question_id":2000209, "title": "00-S2-Q9", "body": "Acceleration, equilibrium, air resistance, differential equation, parachute.

\"q\"

[STEP II 2000 Question 9 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":2000210, "title": "00-S2-Q10", "body": "Equilibrium, acceleration.

\"q\"

[STEP II 2000 Question 10 (Pure)]

" }, { "tags": ["Hooke's law"], "question_id":2000211, "title": "00-S2-Q11", "body": "Modulus of elasticity, ceiling, simple harmonic motion, SHM.

\"q\"

[STEP II 2000 Question 11 (Mechanics)]

" }, { "tags": ["Normal distribution"], "question_id":2000212, "title": "00-S2-Q12", "body": "Henry the commuter, Cambridge to King's Cross, Liverpool street, train, inequality, expectation.

\"q\"

[STEP II 2000 Question 12 (Probability and Statistics)]

" }, { "tags": ["Microtus agrestis"], "question_id":2000213, "title": "00-S2-Q13", "body": "Biologists, voles, combinatorics, binomial coefficients, sampling with/out replacement, C1.

\"q\"

[STEP II 2000 Question 13 (Mechanics)]

" }, { "tags": ["Uniform distribution"], "question_id":2000214, "title": "00-S2-Q14", "body": "Independent, medium, probability density function, pdf, expectation and variance, inequality, normal distribution, central limit theorem.

\"q\"

[STEP II 2000 Question 14 (Mechanics)]

" }, { "tags": ["Curve sketching"], "question_id":2000301, "title": "00-S3-Q1", "body": "Reciprocal and hyperbola functions, tangent, square, coordinate geometry, C1.

\"q\"

[STEP III 2000 Question 1 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2000302, "title": "00-S3-Q2", "body": "Substitution by trigonometric functions.

\"q\"

[STEP III 2000 Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2000303, "title": "00-S3-Q3", "body": "Roots of unity, Argand diagram, equilateral triangle, geometry.

\"q\"

[STEP III 2000 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2000304, "title": "00-S3-Q4", "body": "Rational function, algebraic, intersection, oblique asymptote, C1-ish.

\"q\"

[STEP III 2000 Question 4 (Pure)]

" }, { "tags": ["2d Vector product"], "question_id":2000305, "title": "00-S3-Q5", "body": "Matrix, vector cyclic triple product, transformation.

\"q\"

[STEP III 2000 Question 5 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":2000306, "title": "00-S3-Q6", "body": "Roots of cubic equation, factorisation, quartic equations, C1-ish.

\"q\"

[STEP III 2000 Question 6 (Pure)]

" }, { "tags": ["Analysis"], "question_id":2000307, "title": "00-S3-Q7", "body": "AM-GM inequality, e, binomial theorem, limit, product, exponential function, C1-ish.

\"q\"

[STEP III 2000 Question 7 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":2000308, "title": "00-S3-Q8", "body": "Recurrence relation, difference equation.

\"q\"

[STEP III 2000 Question 8 (Pure)]

" }, { "tags": ["Collision"], "question_id":2000309, "title": "00-S3-Q9", "body": "Disc, kineic energy, cosine of angle, inequality.

\"q\"

[STEP III 2000 Question 9 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2000310, "title": "00-S3-Q10", "body": "Coefficient of friction, sphere, slipping.

\"q\"

[STEP III 2000 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2000311, "title": "00-S3-Q11", "body": "Beam, limiting friction, slipping.

\"q\"

[STEP III 2000 Question 11 (Mechanics)]

" }, { "tags": ["Lottery"], "question_id":2000312, "title": "00-S3-Q12", "body": "Combinatorics, binomial approximation, exponential function, expectation, C1-ish.

\"q\"

[STEP III 2000 Question 12 (Probability and Statistics)]

" }, { "tags": ["Pgf"], "question_id":2000313, "title": "00-S3-Q13", "body": "Probability generating function, dice, six, expectation.

\"q\"

[STEP III 2000 Question 13 (Probability and Statistics)]

" }, { "tags": ["Joint distribution"], "question_id":2000314, "title": "00-S3-Q14", "body": "Independence, expectation algebra.

\"q\"

[STEP III 2000 Question 14 (Probability and Statistics)]

" }, { "tags": ["Euclidean geometry"], "question_id":2001101, "title": "01-S1-Q1", "body": "Triangle, length, C1.

\"q\"

[STEP I 2001 Question 1 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2001102, "title": "01-S1-Q2", "body": "Square root, quadratic function, C1

\"q\"

[STEP I 2001 Question 2 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":2001103, "title": "01-S1-Q3", "body": "Differentiation, stationary points, factors, inequality, cubic, quadratic, sufficient and necessary conditions, C1.

\"q\"

[STEP I 2001 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2001104, "title": "01-S1-Q4", "body": "Solution of equations.

\"q\"

[STEP I 2001 Question 4 (Pure)]

" }, { "tags": ["Integral"], "question_id":2001105, "title": "01-S1-Q5", "body": "Derivatives.

\"q\"

[STEP I 2001 Question 5 (Pure)]

" }, { "tags": ["Area/Volume of revolution"], "question_id":2001106, "title": "01-S1-Q6", "body": "Spherical loaf of bread, slices, integration.

\"q\"

[STEP I 2001 Question 6 (Pure)]

" }, { "tags": ["Hubble's constant"], "question_id":2001107, "title": "01-S1-Q7", "body": "Cosmology, curve sketching, inequality, C1.

\"q\"

[STEP I 2001 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2001108, "title": "01-S1-Q8", "body": "Substitution, trigonometry, second order equation.

\"q\"

[STEP I 2001 Question 8 (Pure)]

" }, { "tags": ["Time-distance"], "question_id":2002010, "title": "01-S1-Q9", "body": "Ship, tugboat, C1.

\"q\"

[STEP I 2001 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2001110, "title": "01-S1-Q10", "body": "Gun shell, equation of motion.

\"q\"

[STEP I 2001 Question 10 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":2001111, "title": "01-S1-Q11", "body": "Cylinder, circular motion, modulus of elasticity.

\"q\"

[STEP I 2001 Question 11 (Mechanics)]

" }, { "tags": ["Tree diagram"], "question_id":2001112, "title": "01-S1-Q12", "body": "Gossip, rumour, C1.

\"q\"

[STEP I 2001 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":2001113, "title": "01-S1-Q13", "body": "Breaking plates.

\"q\"

[STEP I 2001 Question 13 (Probability and Statistics)]

" }, { "tags": ["Combintorics"], "question_id":2001114, "title": "01-S1-Q14", "body": "Interview, candidates, elementary probability.

\"q\"

[STEP I 2001 Question 14 (Probability and Statistics)]

" }, { "tags": ["Binomial approximation"], "question_id":2001201, "title": "01-S2-Q1", "body": "Approximation to square roots, error, C1-ish.

\"q\"

[STEP II 2001 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2001202, "title": "01-S2-Q2", "body": "Integer part, floor function, sum, limit, C1-ish.

\"q\"

[STEP II 2001 Question 2 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2001203, "title": "01-S2-Q3", "body": "Cuboid, ratio of volume to surface area, inequality, C1.

\"q\"

[STEP II 2001 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2001204, "title": "01-S2-Q4", "body": "Roots of equation, identity.

\"q\"

[STEP II 2001 Question 4 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2001205, "title": "01-S2-Q5", "body": "Curve sketching, maximum and minimum, stationary point, C1.

\"q\"

[STEP II 2001 Question 5 (Pure)]

" }, { "tags": ["Integral"], "question_id":2001206, "title": "01-S2-Q6", "body": "Arctan, integration by substitution.

\"q\"

[STEP II 2001 Question 6 (Pure)]

" }, { "tags": ["Complex number"], "question_id":2001207, "title": "01-S2-Q7", "body": "Argand diagram, 12-gon, rotation.

\"q\"

[STEP II 2001 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2001208, "title": "01-S2-Q8", "body": "Functional equation, integer, limit.

\"q\"

[STEP II 2001 Question 8 (Pure)]

" }, { "tags": ["Air resistance"], "question_id":2001209, "title": "01-S2-Q9", "body": "Upward projection, energy, gravity.

\"q\"

[STEP II 2001 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2001210, "title": "01-S2-Q10", "body": "Coefficient of restitution, kinetic energy, rebound.

\"q\"

[STEP II 2001 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2001211, "title": "01-S2-Q11", "body": "Two-stage missile, fragments at highest point, range, inequality.

\"q\"

[STEP II 2001 Question 11 (Mechanics)]

" }, { "tags": ["Lottery"], "question_id":2001212, "title": "01-S2-Q12", "body": "Ruritania, integer, combinatorics, expectation, C1.

\"q\"

[STEP II 2001 Question 12 (Probability and Statistics)]

" }, { "tags": ["Pdf"], "question_id":2001213, "title": "01-S2-Q13", "body": "Probability density function, median, light bulbs, independent, identically distributed, iid, fail.

\"q\"

[STEP II 2001 Question 13 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":2001214, "title": "01-S2-Q14", "body": "Random variable, expectation, minimum, variance, cumulative distribution function, cdf, mean.

\"q\"

[STEP II 2001 Question 14 (Mechanics)]

" }, { "tags": ["Maclaurin series"], "question_id":2001301, "title": "01-S3-Q1", "body": "Taylor series, differentiation, induction, differential equation.

\"q\"

[STEP III 2001 Question 1 (Pure)]

" }, { "tags": ["Area by integration"], "question_id":2001302, "title": "01-S3-Q2", "body": "Hyperbolic function, area, inequality.

\"q\"

[STEP III 2001 Question 2 (Pure)]

" }, { "tags": ["Quadratic equations"], "question_id":2001303, "title": "01-S3-Q3", "body": "Regions, inequality, roots.

\"q\"

[STEP III 2001 Question 3 (Pure)]

" }, { "tags": ["Functions"], "question_id":2001304, "title": "01-S3-Q4", "body": "Range, curve sketching, trigonometric, rational functions, arctan, sine.

\"q\"

[STEP III 2001 Question 4 (Pure)]

" }, { "tags": ["Parabola"], "question_id":2001305, "title": "01-S3-Q5", "body": "Cubic equation, normal and tangents, cartesian equation, locus, curve sketching.

\"q\"

[STEP III 2001 Question 5 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2001306, "title": "01-S3-Q6", "body": "Ellipsoid, plane, orthocentre, circumcentre, triangle, centroid, triangle, line segment, ratio.

\"q\"

[STEP III 2001 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2001307, "title": "01-S3-Q7", "body": "Curve sketching, logarithm function, separable equation, parabola, orthogonal intersection.

\"q\"

[STEP III 2001 Question 7 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2001308, "title": "01-S3-Q8", "body": "Equations of locus, arcs, circles, lines arguments, sketching.

\"q\"

[STEP III 2001 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":2001309, "title": "01-S3-Q9", "body": "Horizontal beams, coefficient of friction, slip, limiting equilibrium, centre of gravity.

\"q\"

[STEP III 2001 Question 9 (Mechanics)]

" }, { "tags": ["Vector velocity"], "question_id":2001310, "title": "01-S3-Q10", "body": "Ships, velocities, magnitude, dot scalar product.

\"q\"

[STEP III 2001 Question 10 (Mechanics)]

" }, { "tags": ["Moment of inertia"], "question_id":2001311, "title": "01-S3-Q11", "body": "Angular velocity, cylinder, rotation.

\"q\"

[STEP III 2001 Question 11 (Mechanics)]

" }, { "tags": ["Sampling with/out replacement"], "question_id":2001312, "title": "01-S3-Q12", "body": "A bag of balls, combinatorics, C1.

\"q\"

[STEP III 2001 Question 12 (Probability and Statistics)]

" }, { "tags": ["Coin toss"], "question_id":2001313, "title": "01-S3-Q13", "body": "Elementary probability, conditional probability, C1-ish.

\"q\"

[STEP III 2001 Question 13 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":2001314, "title": "01-S3-Q14", "body": "Uniform distribution, variance, estimators.

\"q\"

[STEP III 2001 Question 14 (Probability and Statistics)]

" }, { "tags": ["Simultaneous equations"], "question_id":2002101, "title": "02-S1-Q1", "body": "Ellipse, circle, intersection, C1.

\"q\"

[STEP I 2002 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2002102, "title": "02-S1-Q2", "body": "Differentiation, stationary point, maximum, minimum, C1

\"q\"

[STEP I 2002 Question 2 (Pure)]

" }, { "tags": ["Inequalities"], "question_id":2002103, "title": "02-S1-Q3", "body": "Differentiation, trigonometric functions, maximum and minimum, C1.

\"q\"

[STEP I 2002 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2002104, "title": "02-S1-Q4", "body": "Intersection with line, area under curve, integration, volume of revolution.

\"q\"

[STEP I 2002 Question 4 (Pure)]

" }, { "tags": ["Roots of polynomials"], "question_id":2002105, "title": "02-S1-Q5", "body": "Factorisation, product, quartic equations, integer, C1.

\"q\"

[STEP I 2002 Question 5 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2002106, "title": "02-S1-Q6", "body": "Pyramid, equilateral triangle, volume, C1.

\"q\"

[STEP I 2002 Question 6 (Pure)]

" }, { "tags": ["Integral"], "question_id":2002107, "title": "02-S1-Q7", "body": "Trickery, trigonometric functions.

\"q\"

[STEP I 2002 Question 7 (Pure)]

" }, { "tags": ["Geometric series"], "question_id":2002108, "title": "02-S1-Q8", "body": "Sequences, interest, financial maths, C1-ish.

\"q\"

[STEP I 2002 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":2002109, "title": "02-S1-Q9", "body": "Lorry on inclined plane, centre of gravity, inequality.

\"q\"

[STEP I 2002 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2002110, "title": "02-S1-Q10", "body": "Bicycle pump, speed.

\"q\"

[STEP I 2002 Question 10 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2002111, "title": "02-S1-Q11", "body": "Particles, sin, angle, conservation of energy.

\"q\"

[STEP I 2002 Question 11 (Mechanics)]

" }, { "tags": ["Harry the Calculating Horse"], "question_id":2002112, "title": "02-S1-Q12", "body": "Elementary probability, expectation, C1.

\"q\"

[STEP I 2002 Question 12 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":2002113, "title": "02-S1-Q13", "body": "Roots of quadratic, expectation, cubic equation.

\"q\"

[STEP I 2002 Question 13 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":2002114, "title": "02-S1-Q14", "body": "Cash dispenser, police.

\"q\"

[STEP I 2002 Question 14 (Probability and Statistics)]

" }, { "tags": ["Integral"], "question_id":2002201, "title": "02-S2-Q1", "body": "Integration by substitution, sine, trigonometry.

\"q\"

[STEP II 2002 Question 1 (Pure)]

" }, { "tags": ["Polynomial equation"], "question_id":2002202, "title": "02-S2-Q2", "body": "Substitution, quartic, quadratic equations, algebra, C1.

\"q\"

[STEP II 2002 Question 2 (Pure)]

" }, { "tags": ["Fermat number"], "question_id":2002203, "title": "02-S2-Q3", "body": "Number theory, prime, induction, C1.

\"q\"

[STEP II 2002 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2002204, "title": "02-S2-Q4", "body": "Quadratic equation, sine, inequality, determinant, logarithmic function.

\"q\"

[STEP II 2002 Question 4 (Pure)]

" }, { "tags": ["Logistic map"], "question_id":2002205, "title": "02-S2-Q5", "body": "Recurrence relation, difference equation, quartic equation, C1.

\"q\"

[STEP II 2002 Question 5 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2002206, "title": "02-S2-Q6", "body": "Inclined plane, rotate, angle.

\"q\"

[STEP II 2002 Question 6 (Pure)]

" }, { "tags": ["3-D geometry"], "question_id":2002207, "title": "02-S2-Q7", "body": "3-dimensional, vector geometry, lines, distance, perpendicular.

\"q\"

[STEP II 2002 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2002208, "title": "02-S2-Q8", "body": "Continuity, modulus function, limit.

\"q\"

[STEP II 2002 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2002209, "title": "02-S2-Q9", "body": "Range, equation of motion, small perturbation, small angle approximation, trigonometry, inequality.

\"q\"

[STEP II 2002 Question 9 (Mechanics)]

" }, { "tags": ["Time-distance"], "question_id":2002210, "title": "02-S2-Q10", "body": "Marathon, C1.

\"q\"

[STEP II 2002 Question 10 (Pure)]

" }, { "tags": ["Friction"], "question_id":2002211, "title": "02-S2-Q11", "body": "Beam, centre of mass, ladder, limiting equilibrium.

\"q\"

[STEP II 2002 Question 11 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":2002212, "title": "02-S2-Q12", "body": "Binomial expansion, normal approximation.

\"q\"

[STEP II 2002 Question 12 (Probability and Statistics)]

" }, { "tags": ["Cdf"], "question_id":2002213, "title": "02-S2-Q13", "body": "Cumulative distribution function, inequality, expectation and variance.

\"q\"

[STEP II 2002 Question 13 (Mechanics)]

" }, { "tags": ["Geometric probability"], "question_id":2002214, "title": "02-S2-Q14", "body": "Circular island, concentric regions.

\"q\"

[STEP II 2002 Question 14 (Mechanics)]

" }, { "tags": ["Volume of revolution"], "question_id":2002301, "title": "02-S3-Q1", "body": "Integration, limit, lograithm function.

\"q\"

[STEP III 2002 Question 1 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2002302, "title": "02-S3-Q2", "body": "Sum, arctan, identity.

\"q\"

[STEP III 2002 Question 2 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2002303, "title": "02-S3-Q3", "body": "Square root function, inequality, roots.

\"q\"

[STEP III 2002 Question 3 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2002304, "title": "02-S3-Q4", "body": "Number theory, positive integer, difference of cubes, sum of square, C1.

\"q\"

[STEP III 2002 Question 4 (Pure)]

" }, { "tags": ["Quartic equation"], "question_id":2002305, "title": "02-S3-Q5", "body": "Quadratic equation, factorisation, C1.

\"q\"

[STEP III 2002 Question 5 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2002306, "title": "02-S3-Q6", "body": "Solution curve, curve sketching.

\"q\"

[STEP III 2002 Question 6 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2002307, "title": "02-S3-Q7", "body": "Trigonometry, coordinate geometry, algebraic manipulation, C1-ish.

\"q\"

[STEP III 2002 Question 7 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2002308, "title": "02-S3-Q8", "body": "Modulus and argument, modulus, identity.

\"q\"

[STEP III 2002 Question 8 (Pure)]

" }, { "tags": ["Inclined plane"], "question_id":2002309, "title": "02-S3-Q9", "body": "Equilibrium, fluid, topple, centre of mass.

\"q\"

[STEP III 2002 Question 9 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2002310, "title": "02-S3-Q10", "body": "Cylinder, trigonometry, second order differential equation, slip.

\"q\"

[STEP III 2002 Question 10 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2002311, "title": "02-S3-Q11", "body": "Coefficient of restitution, triangular horizontal surface.

\"q\"

[STEP III 2002 Question 11 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":2002312, "title": "02-S3-Q12", "body": "Expectation, C1.

\"q\"

[STEP III 2002 Question 12 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":2002313, "title": "02-S3-Q13", "body": "Exponential distribution, bus route, median.

\"q\"

[STEP III 2002 Question 13 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":2002314, "title": "02-S3-Q14", "body": "Variance, covariance, binomial distribution, RSS.

\"q\"

[STEP III 2002 Question 14 (Probability and Statistics)]

" }, { "tags": ["Sum"], "question_id":2003101, "title": "03-S1-Q1", "body": "Simultaneous equations, sum of squares and cubes.

\"q\"

[STEP I 2003 Question 1 (Pure)]

" }, { "tags": ["Solution to equations"], "question_id":2003102, "title": "03-S1-Q2", "body": "Examination paper, candidate, reciprocal functions, if and only if, C1

\"q\"

[STEP I 2003 Question 2 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2003103, "title": "03-S1-Q3", "body": "If and only if, general solution to trigonometric equations.

\"q\"

[STEP I 2003 Question 3 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2003104, "title": "03-S1-Q4", "body": "Trigonometry.

\"q\"

[STEP I 2003 Question 4 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":2003105, "title": "03-S1-Q5", "body": "Binomial coefficient, algebraic manipulation.

\"q\"

[STEP I 2003 Question 5 (Pure)]

" }, { "tags": ["Integrals"], "question_id":2003106, "title": "03-S1-Q6", "body": "Integration by substitution.

\"q\"

[STEP I 2003 Question 6 (Pure)]

" }, { "tags": ["Number theory"], "question_id":2003107, "title": "03-S1-Q7", "body": "Inequality, divisibility, sum of digits, C1.

\"q\"

[STEP I 2003 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2003108, "title": "03-S1-Q8", "body": "Chemicals, rate of change, first order equation.

\"q\"

[STEP I 2003 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2003109, "title": "03-S1-Q9", "body": "Angle of projection, range equation.

\"q\"

[STEP I 2003 Question 9 (Mechanics)]

" }, { "tags": ["Centre of gravity"], "question_id":2003110, "title": "03-S1-Q10", "body": "Rectangular lamina, triangle, trapezium, equilibrium.

\"q\"

[STEP I 2003 Question 10 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2003111, "title": "03-S1-Q11", "body": "Inclined plane, coefficient of restitution, kinetic energy.

\"q\"

[STEP I 2003 Question 11 (Mechanics)]

" }, { "tags": ["Sampling with/out replacement"], "question_id":2003112, "title": "03-S1-Q12", "body": "Balls out of bag, expectation, sum of squares, C1-ish.

\"q\"

[STEP I 2003 Question 12 (Probability and Statistics)]

" }, { "tags": ["Binomial distribution"], "question_id":2003113, "title": "03-S1-Q13", "body": "Football, penalty shootout, expectation, elementary probability.

\"q\"

[STEP I 2003 Question 13 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":2003114, "title": "03-S1-Q14", "body": "Phone calls, average.

\"q\"

[STEP I 2003 Question 14 (Probability and Statistics)]

" }, { "tags": ["Simultaneous equations"], "question_id":2003201, "title": "03-S2-Q1", "body": "Linear system, solution, inequality, C1.

\"q\"

[STEP II 2003 Question 1 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2003202, "title": "03-S2-Q2", "body": "Identity, inverse trigonometric functions.

\"q\"

[STEP II 2003 Question 2 (Pure)]

" }, { "tags": ["Irrational number"], "question_id":2003203, "title": "03-S2-Q3", "body": "Number theory, cube root, proof by induction, sequence, converge, C1-ish.

\"q\"

[STEP II 2003 Question 3 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2003204, "title": "03-S2-Q4", "body": "Lines and circles, intersection, segment, C1.

\"q\"

[STEP II 2003 Question 4 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2003205, "title": "03-S2-Q5", "body": "Position vector, intersection, midpoint.

\"q\"

[STEP II 2003 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":2003206, "title": "03-S2-Q6", "body": "Curve sketching, modulus function, composition of function, trigonometric function.

\"q\"

[STEP II 2003 Question 6 (Pure)]

" }, { "tags": ["Analysis"], "question_id":2003207, "title": "03-S2-Q7", "body": "Integration by parts, logarithmic function, limit, inequality, sum of inverse squares.

\"q\"

[STEP II 2003 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2003208, "title": "03-S2-Q8", "body": "Stationary value, first order equation, curve sketching, limit.

\"q\"

[STEP II 2003 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":2003209, "title": "03-S2-Q9", "body": "Rod, cylinder, coefficient of friction, limiting equilibrium.

\"q\"

[STEP II 2003 Question 9 (Mechanics)]

" }, { "tags": ["Acceleration"], "question_id":2003210, "title": "03-S2-Q10", "body": "Equilibrium, triangle, reaction, normal force.

\"q\"

[STEP II 2003 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2003211, "title": "03-S2-Q11", "body": "Angle of elevation, equation of range.

\"q\"

[STEP II 2003 Question 11 (Mechanics)]

" }, { "tags": ["Elementary particles"], "question_id":2003212, "title": "03-S2-Q12", "body": "Binomial distribution, conditional probability, expectation algebra, limit.

\"q\"

[STEP II 2003 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":2003213, "title": "03-S2-Q13", "body": "Normal approximatino, mean, inequality, discrete random variable.

\"q\"

[STEP II 2003 Question 13 (Mechanics)]

" }, { "tags": ["Hypothesis testing"], "question_id":2003214, "title": "03-S2-Q14", "body": "Coin toss, biased die, statistical test, alternative hypothesis, curve sketching.

\"q\"

[STEP II 2003 Question 14 (Mechanics)]

" }, { "tags": ["Integration"], "question_id":2003301, "title": "03-S3-Q1", "body": "Inverse differentiation, inverse trigonometric and hyperbolic functions.

\"q\"

[STEP III 2003 Question 1 (Pure)]

" }, { "tags": ["Binomial series"], "question_id":2003302, "title": "03-S3-Q2", "body": "Binomial coefficient, sum.

\"q\"

[STEP III 2003 Question 2 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2003303, "title": "03-S3-Q3", "body": "Reciprocal function, differentiation, C1.

\"q\"

[STEP III 2003 Question 3 (Pure)]

" }, { "tags": ["Parametric equation"], "question_id":2003304, "title": "03-S3-Q4", "body": "Tangent, sequence of points meet the curve.

\"q\"

[STEP III 2003 Question 4 (Pure)]

" }, { "tags": ["Cubic equations"], "question_id":2003305, "title": "03-S3-Q5", "body": "Quadratic equations, curve sketching, necessary and sufficient conditions, turning points, C1-ish.

\"q\"

[STEP III 2003 Question 5 (Pure)]

" }, { "tags": ["Trigonometric series"], "question_id":2003306, "title": "03-S3-Q6", "body": "Solution to trigonometric equations, product to sum formula.

\"q\"

[STEP III 2003 Question 6 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2003307, "title": "03-S3-Q7", "body": "Feet of the perpendicular, geometrical interpretation, collinear.

\"q\"

[STEP III 2003 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2003308, "title": "03-S3-Q8", "body": "Implicit differentiation, general solution.

\"q\"

[STEP III 2003 Question 8 (Pure)]

" }, { "tags": ["SHM"], "question_id":2003309, "title": "03-S3-Q9", "body": "Simple harmonic motion, Hooke's law, modulus of elasticity, equilibrium, small displacement, perturbation.

\"q\"

[STEP III 2003 Question 9 (Mechanics)]

" }, { "tags": ["Acceleration"], "question_id":2003310, "title": "03-S3-Q10", "body": "Time-distance, limit, C1.

\"q\"

[STEP III 2003 Question 10 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2003311, "title": "03-S3-Q11", "body": "Direction of projection, inequality, velocity equation, distance.

\"q\"

[STEP III 2003 Question 11 (Mechanics)]

" }, { "tags": ["Poisson distribution"], "question_id":2003312, "title": "03-S3-Q12", "body": "Interruptions to work, expectation.

\"q\"

[STEP III 2003 Question 12 (Probability and Statistics)]

" }, { "tags": ["Rabbit warren"], "question_id":2003313, "title": "03-S3-Q13", "body": "Elementary probability, conditional probability.

\"q\"

[STEP III 2003 Question 13 (Probability and Statistics)]

" }, { "tags": ["Dice roll"], "question_id":2003314, "title": "03-S3-Q14", "body": "Probability generating function, pgf.

\"q\"

[STEP III 2003 Question 14 (Probability and Statistics)]

" }, { "tags": ["Surds and polynomials"], "question_id":2004101, "title": "04-S1-Q1", "body": "Square roots, cube roots, solutions to polynomial equations, C1.

\"q\"

[STEP I 2004 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2004102, "title": "04-S1-Q2", "body": "Integration, integer part, floor function, square root, sum.

\"q\"

[STEP I 2004 Question 2 (Pure)]

" }, { "tags": ["Factors of polynomials"], "question_id":2004103, "title": "04-S1-Q3", "body": "Factorisation, linear factors, C1.

\"q\"

[STEP I 2004 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2004104, "title": "04-S1-Q4", "body": "Differentiation, trigonometric substitution.

\"q\"

[STEP I 2004 Question 4 (Pure)]

" }, { "tags": ["Number theory"], "question_id":2004105, "title": "04-S1-Q5", "body": "Arithmetic progression, square, solution, C1.

\"q\"

[STEP I 2004 Question 5 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2004106, "title": "04-S1-Q6", "body": "Intersections, midpoint, line, right angle, C1.

\"q\"

[STEP I 2004 Question 6 (Pure)]

" }, { "tags": ["Recurrence relation"], "question_id":2004107, "title": "04-S1-Q7", "body": "Difference equations, algebraic fractions, C1.

\"q\"

[STEP I 2004 Question 7 (Pure)]

" }, { "tags": ["Recurrence relations"], "question_id":2004108, "title": "04-S1-Q8", "body": "Sequence, strictly increasing, inequality, proof, C1.

\"q\"

[STEP I 2004 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2004109, "title": "04-S1-Q9", "body": "Maximum height, inequality.

\"q\"

[STEP I 2004 Question 9 (Mechanics)]

" }, { "tags": ["Time-distance"], "question_id":2004110, "title": "04-S1-Q10", "body": "Acceleration, magnitude, inequality, C1.

\"q\"

[STEP I 2004 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2004111, "title": "04-S1-Q11", "body": "Two ladders, coefficient of friction, slip.

\"q\"

[STEP I 2004 Question 11 (Mechanics)]

" }, { "tags": ["Microships"], "question_id":2004112, "title": "04-S1-Q12", "body": "Large random sample, C1-ish.

\"q\"

[STEP I 2004 Question 12 (Probability and Statistics)]

" }, { "tags": ["Hypothesis testing"], "question_id":2004113, "title": "04-S1-Q13", "body": "Continuous rectangular distribution, null and alternative hypothesis.

\"q\"

[STEP I 2004 Question 13 (Probability and Statistics)]

" }, { "tags": ["Pirates"], "question_id":2004114, "title": "04-S1-Q14", "body": "Elementary probability, tree diagram, C1.

\"q\"

[STEP I 2004 Question 14 (Probability and Statistics)]

" }, { "tags": ["Surds"], "question_id":2004201, "title": "04-S2-Q1", "body": "Solution of equations, square root function, C1.

\"q\"

[STEP II 2004 Question 1 (Pure)]

" }, { "tags": ["Quadratic function"], "question_id":2004202, "title": "04-S2-Q2", "body": "Curve sketching, proof, modulus function, inequality, C1.

\"q\"

[STEP II 2004 Question 2 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2004203, "title": "04-S2-Q3", "body": "Nature of stationary point, differentiation, C1.

\"q\"

[STEP II 2004 Question 3 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2004204, "title": "04-S2-Q4", "body": "Move rod from corridor, inequality, trigonometry, table-top, C1.

\"q\"

[STEP II 2004 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":2004205, "title": "04-S2-Q5", "body": "Trigonometric integrals, equating coefficients.

\"q\"

[STEP II 2004 Question 5 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2004206, "title": "04-S2-Q6", "body": "Planes, perpendicular, parallel, scalar product.

\"q\"

[STEP II 2004 Question 6 (Pure)]

" }, { "tags": ["Interval bisection"], "question_id":2004207, "title": "04-S2-Q7", "body": "Trigonometric equation, sequence of intervals, approximations, C1-ish.

\"q\"

[STEP II 2004 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2004208, "title": "04-S2-Q8", "body": "First order equation, curve sketching, inequality.

\"q\"

[STEP II 2004 Question 8 (Pure)]

" }, { "tags": ["Centre of gravity"], "question_id":2004209, "title": "04-S2-Q9", "body": "Equilibrium, non-uniform solid hemisphere.

\"q\"

[STEP II 2004 Question 9 (Mechanics)]

" }, { "tags": ["Inclined plane"], "question_id":2004210, "title": "04-S2-Q10", "body": "Friction, projection, collision, loss of energy.

\"q\"

[STEP II 2004 Question 10 (Pure)]

" }, { "tags": ["Work and power"], "question_id":2004211, "title": "04-S2-Q11", "body": "Train and engines, velocities, conservation of energy.

\"q\"

[STEP II 2004 Question 11 (Mechanics)]

" }, { "tags": ["Pdf"], "question_id":2004212, "title": "04-S2-Q12", "body": "Probability density function, mode, median, inequality, conditional probability, curve sketching, gaussian.

\"q\"

[STEP II 2004 Question 12 (Probability and Statistics)]

" }, { "tags": ["Balls from bags"], "question_id":2004213, "title": "04-S2-Q13", "body": "Expectation, maximise, integer part, C1.

\"q\"

[STEP II 2004 Question 13 (Mechanics)]

" }, { "tags": ["Probability with sets"], "question_id":2004214, "title": "04-S2-Q14", "body": "Union of three events, plum pudding, Christmas, sixpences, C1.

\"q\"

[STEP II 2004 Question 14 (Mechanics)]

" }, { "tags": ["Integration by substitution"], "question_id":2004301, "title": "04-S3-Q1", "body": "Hyperbolic functions, exponential and logarithms, partial fractions.

\"q\"

[STEP III 2004 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2004302, "title": "04-S3-Q2", "body": "Vertical and oblique asymptotes, tangent, double root.

\"q\"

[STEP III 2004 Question 2 (Pure)]

" }, { "tags": ["Analysis"], "question_id":2004303, "title": "04-S3-Q3", "body": "Approximating an integral, inequalities, sum, inverse square, bounds.

\"q\"

[STEP III 2004 Question 3 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2004304, "title": "04-S3-Q4", "body": "Isoceles triangle, tangent to circles, ratio of radii, area, C1.

\"q\"

[STEP III 2004 Question 4 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2004305, "title": "04-S3-Q5", "body": "Identities, proof, counterexample, general solutions to trigonometric equations.

\"q\"

[STEP III 2004 Question 5 (Pure)]

" }, { "tags": ["Recurrence relations"], "question_id":2004306, "title": "04-S3-Q6", "body": "Difference equations, sequence, proof, period of sequences, C1-ish.

\"q\"

[STEP III 2004 Question 6 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":2004307, "title": "04-S3-Q7", "body": "Recurrence formula, greatest value, inequality, logarithm.

\"q\"

[STEP III 2004 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2004308, "title": "04-S3-Q8", "body": "Substitution, curve sketching.

\"q\"

[STEP III 2004 Question 8 (Pure)]

" }, { "tags": ["Circular motion"], "question_id":2004309, "title": "04-S3-Q9", "body": "Hoop, equilibrium, mouse, friction.

\"q\"

[STEP III 2004 Question 9 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":2004310, "title": "04-S3-Q10", "body": "Modulus of elasticity, string, acceleration, inequality.

\"q\"

[STEP III 2004 Question 10 (Mechanics)]

" }, { "tags": ["Repulsive force"], "question_id":2004311, "title": "04-S3-Q11", "body": "Second order differential equations.

\"q\"

[STEP III 2004 Question 11 (Mechanics)]

" }, { "tags": ["Approximations"], "question_id":2004312, "title": "04-S3-Q12", "body": "Expectation, variance and covariances, sum of random variables, Normal and Poisson approximations, relative error.

\"q\"

[STEP III 2004 Question 12 (Probability and Statistics)]

" }, { "tags": ["Tree diagram"], "question_id":2004313, "title": "04-S3-Q13", "body": "Endurance competition, rounds, elementary probability, C1.

\"q\"

[STEP III 2004 Question 13 (Probability and Statistics)]

" }, { "tags": ["Hypothesis testing"], "question_id":2004314, "title": "04-S3-Q14", "body": "Normal distribution, null and alternative hypothesis, approximations.

\"q\"

[STEP III 2004 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":2005101, "title": "05-S1-Q1", "body": "Sum of digits, C1.

\"q\"

[STEP I 2005 Question 1 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2005102, "title": "05-S1-Q2", "body": "Parabola, intersection, tangent, quadrilateral, C1.

\"q\"

[STEP I 2005 Question 2 (Pure)]

" }, { "tags": ["Solutions of equation"], "question_id":2005103, "title": "05-S1-Q3", "body": "If and only if, C1.

\"q\"

[STEP I 2005 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2005104, "title": "05-S1-Q4", "body": "Trigonometric identity, general solution of trig equations.

\"q\"

[STEP I 2005 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":2005105, "title": "05-S1-Q5", "body": "Approximation, logarithm.

\"q\"

[STEP I 2005 Question 5 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2005106, "title": "05-S1-Q6", "body": "Cartesian equation, circle, locus, ratio, C1.

\"q\"

[STEP I 2005 Question 6 (Pure)]

" }, { "tags": ["Product"], "question_id":2005107, "title": "05-S1-Q7", "body": "Manipulation of product sign, trigonometric identity.

\"q\"

[STEP I 2005 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2005108, "title": "05-S1-Q8", "body": "Implicity differentiation, geometrical interpretation, logarithm.

\"q\"

[STEP I 2005 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":2005109, "title": "05-S1-Q9", "body": "Equilibrium, slip prevention, tension.

\"q\"

[STEP I 2005 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2005110, "title": "05-S1-Q10", "body": "Collinear, coefficient of resititution.

\"q\"

[STEP I 2005 Question 10 (Mechanics)]

" }, { "tags": ["Time-distance"], "question_id":2005111, "title": "05-S1-Q11", "body": "Curve sketching, trigonometry, parameteric, velocity.

\"q\"

[STEP I 2005 Question 11 (Mechanics)]

" }, { "tags": ["Hobbit and Wizard"], "question_id":2005112, "title": "05-S1-Q12", "body": "Elementary probability, Lord the Rings, conditional probability.

\"q\"

[STEP I 2005 Question 12 (Probability and Statistics)]

" }, { "tags": ["Normal distribution"], "question_id":2005113, "title": "05-S1-Q13", "body": "Continuous random variable, supermarket, milk, estimate, inequality, conditional probability.

\"q\"

[STEP I 2005 Question 13 (Probability and Statistics)]

" }, { "tags": ["Discrete random variable"], "question_id":2005114, "title": "05-S1-Q14", "body": "Expectation, median, gaussian, variance.

\"q\"

[STEP I 2005 Question 14 (Probability and Statistics)]

" }, { "tags": ["Polynomials"], "question_id":2005201, "title": "05-S2-Q1", "body": "Differentiation, exponential function.

\"q\"

[STEP II 2005 Question 1 (Pure)]

" }, { "tags": ["Number theory"], "question_id":2005202, "title": "05-S2-Q2", "body": "Euler totient function, prime factors, proof, counterexample, C1.

\"q\"

[STEP II 2005 Question 2 (Pure)]

" }, { "tags": ["Integration"], "question_id":2005203, "title": "05-S2-Q3", "body": "Curve sketching, trigonometry, inequality.

\"q\"

[STEP II 2005 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2005204, "title": "05-S2-Q4", "body": "Tan identity, proof, simultaneous equations.

\"q\"

[STEP II 2005 Question 4 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2005205, "title": "05-S2-Q5", "body": "Ratio of area, tangent to circle, triangle, inequality.

\"q\"

[STEP II 2005 Question 5 (Pure)]

" }, { "tags": ["Sum"], "question_id":2005206, "title": "05-S2-Q6", "body": "Differentiation, binomial expansion, general term, series.

\"q\"

[STEP II 2005 Question 6 (Pure)]

" }, { "tags": ["Vectors"], "question_id":2005207, "title": "05-S2-Q7", "body": "Position vectors, geometrical interpretation, angle, time.

\"q\"

[STEP II 2005 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2005208, "title": "05-S2-Q8", "body": "First order equation, curve sketching, approximation.

\"q\"

[STEP II 2005 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":2005209, "title": "05-S2-Q9", "body": "Equilibrium, inclined plane, connected particles, slip.

\"q\"

[STEP II 2005 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2005210, "title": "05-S2-Q10", "body": "Missile, anti-missile, collision.

\"q\"

[STEP II 2005 Question 10 (Pure)]

" }, { "tags": ["Inclined plane"], "question_id":2005211, "title": "05-S2-Q11", "body": "Acceleration, string breaks, maximum point.

\"q\"

[STEP II 2005 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":2005212, "title": "05-S2-Q12", "body": "Coin toss, truth and lies, C1.

\"q\"

[STEP II 2005 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":2005213, "title": "05-S2-Q13", "body": "Independence, errors, approximation, conditional probability, maximisation.

\"q\"

[STEP II 2005 Question 13 (Mechanics)]

" }, { "tags": ["Pdf"], "question_id":2005214, "title": "05-S2-Q14", "body": "Probability density function, normal distribution, standard deviation, expectation, cumulative distribution function, cdf.

\"q\"

[STEP II 2005 Question 14 (Mechanics)]

" }, { "tags": ["Curve sketching"], "question_id":2005301, "title": "05-S3-Q1", "body": "Trigonometric, modulus functions, solution to equations, general solution.

\"q\"

[STEP III 2005 Question 1 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2005302, "title": "05-S3-Q2", "body": "General solution, curve sketching, least distance.

\"q\"

[STEP III 2005 Question 2 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":2005303, "title": "05-S3-Q3", "body": "Quadratic, quartic equations, necessary and sufficient, if and only if.

\"q\"

[STEP III 2005 Question 3 (Pure)]

" }, { "tags": ["Recurrence relations"], "question_id":2005304, "title": "05-S3-Q4", "body": "Difference equations, proof by induction, geometric progression, period of sequences.

\"q\"

[STEP III 2005 Question 4 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2005305, "title": "05-S3-Q5", "body": "Lines, tangent, quadratic equations, common tangents, C1.

\"q\"

[STEP III 2005 Question 5 (Pure)]

" }, { "tags": ["Hyperbolic functions"], "question_id":2005306, "title": "05-S3-Q6", "body": "Complex numbers, roots of equation, cubic equations.

\"q\"

[STEP III 2005 Question 6 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2005307, "title": "05-S3-Q7", "body": "Polynomial substitution.

\"q\"

[STEP III 2005 Question 7 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2005308, "title": "05-S3-Q8", "body": "Argand diagram, triangle, circle, tangent.

\"q\"

[STEP III 2005 Question 8 (Pure)]

" }, { "tags": ["Collision"], "question_id":2005309, "title": "05-S3-Q9", "body": "Coefficient of restitution, rebound.

\"q\"

[STEP III 2005 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2005310, "title": "05-S3-Q10", "body": "Friction, kinetic energy, inequality.

\"q\"

[STEP III 2005 Question 10 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":2005311, "title": "05-S3-Q11", "body": "Energy of system in (stable) equilibrium, angular velocity.

\"q\"

[STEP III 2005 Question 11 (Mechanics)]

" }, { "tags": ["Sum of random variables"], "question_id":2005312, "title": "05-S3-Q12", "body": "Independent, runners, continuous random variable, interval estimation.

\"q\"

[STEP III 2005 Question 12 (Probability and Statistics)]

" }, { "tags": ["Pack of cards"], "question_id":2005313, "title": "05-S3-Q13", "body": "Expectation.

\"q\"

[STEP III 2005 Question 13 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":2005314, "title": "05-S3-Q14", "body": "Integration by substitution, density function, median, expectation, gas molecule.

\"q\"

[STEP III 2005 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":2006101, "title": "06-S1-Q1", "body": "Perfect square, inequality, factors, C1.

\"q\"

[STEP I 2006 Question 1 (Pure)]

" }, { "tags": ["Optimisation"], "question_id":2006102, "title": "06-S1-Q2", "body": "Goat, rope, barn, differentiation, C1.

\"q\"

[STEP I 2006 Question 2 (Pure)]

" }, { "tags": ["Quadratic equations"], "question_id":2006103, "title": "06-S1-Q3", "body": "Roots, determinant, necessary and sufficient, cubic equations, C1.

\"q\"

[STEP I 2006 Question 3 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":2006104, "title": "06-S1-Q4", "body": "Area and perimeter of polygon, curve sketching, trigonometry, mainimisation, differentiation, C1-ish.

\"q\"

[STEP I 2006 Question 4 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2006105, "title": "06-S1-Q5", "body": "Polynomial substitution, exponential and logarithms.

\"q\"

[STEP I 2006 Question 5 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2006106, "title": "06-S1-Q6", "body": "Hyperbolas, curve, postive integers, C1.

\"q\"

[STEP I 2006 Question 6 (Pure)]

" }, { "tags": ["Integration"], "question_id":2006107, "title": "06-S1-Q7", "body": "Trigonometry, modulus, exponential function, curve sketching, roots of equation.

\"q\"

[STEP I 2006 Question 7 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2006108, "title": "06-S1-Q8", "body": "Tetrahedron, volume, triangle, C1.

\"q\"

[STEP I 2006 Question 8 (Pure)]

" }, { "tags": ["Pulley"], "question_id":2006109, "title": "06-S1-Q9", "body": "Equilibrium.

\"q\"

[STEP I 2006 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2006110, "title": "06-S1-Q10", "body": "Equation of trajectory, trigonometry, slide along a rail.

\"q\"

[STEP I 2006 Question 10 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2006111, "title": "06-S1-Q11", "body": "Conservation of energy and momentum.

\"q\"

[STEP I 2006 Question 11 (Mechanics)]

" }, { "tags": ["Oxtown and Camville"], "question_id":2006112, "title": "06-S1-Q12", "body": "Elementary probability, road blocks, limit, conditional probability, C1.

\"q\"

[STEP I 2006 Question 12 (Probability and Statistics)]

" }, { "tags": ["Dice roll"], "question_id":2006113, "title": "06-S1-Q13", "body": "Diamond in chocolate bars, expectation, binomial expansion.

\"q\"

[STEP I 2006 Question 13 (Probability and Statistics)]

" }, { "tags": ["Sampling with/out replacement"], "question_id":2006114, "title": "06-S1-Q14", "body": "Bag of sweet, maximisation, C1.

\"q\"

[STEP I 2006 Question 14 (Probability and Statistics)]

" }, { "tags": ["Difference equation"], "question_id":2006201, "title": "06-S2-Q1", "body": "Recurrence relations, period of sequences, limit, convergence.

\"q\"

[STEP II 2006 Question 1 (Pure)]

" }, { "tags": ["Analysis"], "question_id":2006202, "title": "06-S2-Q2", "body": "Curve sketching, turning points, differentiation, exponential function, inequality.

\"q\"

[STEP II 2006 Question 2 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2006203, "title": "06-S2-Q3", "body": "Surds, square root functions, binomial expansion, approximation, C1-ish.

\"q\"

[STEP II 2006 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2006204, "title": "06-S2-Q4", "body": "Trigonometry, modulus function, change of period.

\"q\"

[STEP II 2006 Question 4 (Pure)]

" }, { "tags": ["Floor function"], "question_id":2006205, "title": "06-S2-Q5", "body": "Curve sketching, quadratics, area under curve, integer part, C1.

\"q\"

[STEP II 2006 Question 5 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2006206, "title": "06-S2-Q6", "body": "Proof, simultaneous equations, C1.

\"q\"

[STEP II 2006 Question 6 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2006207, "title": "06-S2-Q7", "body": "Curve sketching, ellipse, tangent.

\"q\"

[STEP II 2006 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2006208, "title": "06-S2-Q8", "body": "Equation of line, position vectors, trapezium, ratio.

\"q\"

[STEP II 2006 Question 8 (Pure)]

" }, { "tags": ["Ladder"], "question_id":2006209, "title": "06-S2-Q9", "body": "Friction, slip.

\"q\"

[STEP II 2006 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2006210, "title": "06-S2-Q10", "body": "Coefficient of restitution, second time.

\"q\"

[STEP II 2006 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2006211, "title": "06-S2-Q11", "body": "Horizontal force, blow back, maximisation.

\"q\"

[STEP II 2006 Question 11 (Mechanics)]

" }, { "tags": ["Binomial distribution"], "question_id":2006212, "title": "06-S2-Q12", "body": "Approximation, cricket.

\"q\"

[STEP II 2006 Question 12 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":2006213, "title": "06-S2-Q13", "body": "Strategy, C1.

\"q\"

[STEP II 2006 Question 13 (Mechanics)]

" }, { "tags": ["Continuous random variable"], "question_id":2006214, "title": "06-S2-Q14", "body": "Probability density function, curve sketching, pdf.

\"q\"

[STEP II 2006 Question 14 (Mechanics)]

" }, { "tags": ["Curve sketching"], "question_id":2006301, "title": "06-S3-Q1", "body": "Vertical and oblique asymptotes, roots of equations, C1.

\"q\"

[STEP III 2006 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":2006302, "title": "06-S3-Q2", "body": "Trigonometry, substitution.

\"q\"

[STEP III 2006 Question 2 (Pure)]

" }, { "tags": ["Series"], "question_id":2006303, "title": "06-S3-Q3", "body": "Maclaurin, taylor series for trigonometric functions, recurrence, difference equations, comparing coefficients, identity.

\"q\"

[STEP III 2006 Question 3 (Pure)]

" }, { "tags": ["Functional equations"], "question_id":2006304, "title": "06-S3-Q4", "body": "Logarithm, exponential and trigonometric functions, Maclaurin series.

\"q\"

[STEP III 2006 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2006305, "title": "06-S3-Q5", "body": "Roots of unity, equilateral triangle, transformation.

\"q\"

[STEP III 2006 Question 5 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":2006306, "title": "06-S3-Q6", "body": "Gradient, implicit differentiation, mirror, incident and reflected ray.

\"q\"

[STEP III 2006 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2006307, "title": "06-S3-Q7", "body": "Hyperbolic functions, asymptotes.

\"q\"

[STEP III 2006 Question 7 (Pure)]

" }, { "tags": ["Diamond derivatives"], "question_id":2006308, "title": "06-S3-Q8", "body": "Differentiation, proof, first principle, polynomial, C1.

\"q\"

[STEP III 2006 Question 8 (Pure)]

" }, { "tags": ["Energy"], "question_id":2006309, "title": "06-S3-Q9", "body": "Bead on wire, projection, first order differential equation.

\"q\"

[STEP III 2006 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":2006310, "title": "06-S3-Q10", "body": "Angular velocity, substitution, hyperbolic function, differential equation.

\"q\"

[STEP III 2006 Question 10 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2006311, "title": "06-S3-Q11", "body": "Coefficient of restitution, pulley, loss of energy of impact, lift.

\"q\"

[STEP III 2006 Question 11 (Mechanics)]

" }, { "tags": ["Normal distributions"], "question_id":2006312, "title": "06-S3-Q12", "body": "Cruise liner, approximation, cdf.

\"q\"

[STEP III 2006 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":2006313, "title": "06-S3-Q13", "body": "Points on permieter of semicircle, independent, expectation, area of triangle.

\"q\"

[STEP III 2006 Question 13 (Probability and Statistics)]

" }, { "tags": ["Independence"], "question_id":2006314, "title": "06-S3-Q14", "body": "Industrial process, expectation algebra, variance, standard deviation.

\"q\"

[STEP III 2006 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":2007101, "title": "07-S1-Q1", "body": "Balanced number, sum of digits, C1.

\"q\"

[STEP I 2007 Question 1 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2007102, "title": "07-S1-Q2", "body": "Identity, arctan, highest common factor, hcf.

\"q\"

[STEP I 2007 Question 2 (Pure)]

" }, { "tags": ["Integration"], "question_id":2007103, "title": "07-S1-Q3", "body": "Trigonometry, identity.

\"q\"

[STEP I 2007 Question 3 (Pure)]

" }, { "tags": ["Cubic equations"], "question_id":2007104, "title": "07-S1-Q4", "body": "Quadratic equations, factor, perfect square, root, C1.

\"q\"

[STEP I 2007 Question 4 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":2007105, "title": "07-S1-Q5", "body": "Octahedron, polyhedron, equilateral triangle, volume, faces, vertices, ratio, C1.

\"q\"

[STEP I 2007 Question 5 (Pure)]

" }, { "tags": ["Numbers"], "question_id":2007106, "title": "07-S1-Q6", "body": "Quadratic equations, square roots, cubic, factorisation, positive integers, C1.

\"q\"

[STEP I 2007 Question 6 (Pure)]

" }, { "tags": ["Vectors"], "question_id":2007107, "title": "07-S1-Q7", "body": "Equation of line, minimum distance.

\"q\"

[STEP I 2007 Question 7 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":2007108, "title": "07-S1-Q8", "body": "Cubic equations, intersection, C1.

\"q\"

[STEP I 2007 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":2007109, "title": "07-S1-Q9", "body": "Inclined plane, inequality.

\"q\"

[STEP I 2007 Question 9 (Mechanics)]

" }, { "tags": ["Norman army"], "question_id":2007110, "title": "07-S1-Q10", "body": "Time-distance, horsemen, Saxon army, inequality, C1.

\"q\"

[STEP I 2007 Question 10 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2007111, "title": "07-S1-Q11", "body": "Distance equation, differentiation.

\"q\"

[STEP I 2007 Question 11 (Mechanics)]

" }, { "tags": ["Coin and sweets"], "question_id":2007112, "title": "07-S1-Q12", "body": "Elementary probability, C1.

\"q\"

[STEP I 2007 Question 12 (Probability and Statistics)]

" }, { "tags": ["Sampling with/out replacement"], "question_id":2007113, "title": "07-S1-Q13", "body": "Discs, conditional probability, C1.

\"q\"

[STEP I 2007 Question 13 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":2007114, "title": "07-S1-Q14", "body": "Curve sketching, discrete random variable.

\"q\"

[STEP I 2007 Question 14 (Probability and Statistics)]

" }, { "tags": ["Binomial approximations"], "question_id":2007201, "title": "07-S2-Q1", "body": "Binomial expansion, square roots, decimal places.

\"q\"

[STEP II 2007 Question 1 (Pure)]

" }, { "tags": ["Cubic equation"], "question_id":2007202, "title": "07-S2-Q2", "body": "Curve sketching, turning points, differentiation, area enclosed, symmetry, C1.

\"q\"

[STEP II 2007 Question 2 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2007203, "title": "07-S2-Q3", "body": "tan half angle substitution, t-sub, arctan, trigonometry.

\"q\"

[STEP II 2007 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2007204, "title": "07-S2-Q4", "body": "Identity manipulation, solution to equations.

\"q\"

[STEP II 2007 Question 4 (Pure)]

" }, { "tags": ["Functions"], "question_id":2007205, "title": "07-S2-Q5", "body": "Composition of functions, trigonometry, periodicity, C1.

\"q\"

[STEP II 2007 Question 5 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2007206, "title": "07-S2-Q6", "body": "Differentiation, logarithm function, quadratic equation.

\"q\"

[STEP II 2007 Question 6 (Pure)]

" }, { "tags": ["Jensen's inequality"], "question_id":2007207, "title": "07-S2-Q7", "body": "Concave functions, inequalities, minimum value, C1.

\"q\"

[STEP II 2007 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2007208, "title": "07-S2-Q8", "body": "Position vector, locus, ratio, intersection.

\"q\"

[STEP II 2007 Question 8 (Pure)]

" }, { "tags": ["Collision"], "question_id":2007209, "title": "07-S2-Q9", "body": "Coefficient of restitution, circulr cone, impact, greatest value.

\"q\"

[STEP II 2007 Question 9 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2007210, "title": "07-S2-Q10", "body": "Coefficient of restitution, solid cylinder, hemisphere, equilibrium.

\"q\"

[STEP II 2007 Question 10 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2007211, "title": "07-S2-Q11", "body": "vector, maximum height, bullet.

\"q\"

[STEP II 2007 Question 11 (Mechanics)]

" }, { "tags": ["Dice"], "question_id":2007212, "title": "07-S2-Q12", "body": "Binomial distribution, expectation, large approximation.

\"q\"

[STEP II 2007 Question 12 (Probability and Statistics)]

" }, { "tags": ["Birthday problem"], "question_id":2007213, "title": "07-S2-Q13", "body": "Elementary probability, same birthday, C1.

\"q\"

[STEP II 2007 Question 13 (Mechanics)]

" }, { "tags": ["Pdf"], "question_id":2007214, "title": "07-S2-Q14", "body": "Probability density function, curve sketching, median.

\"q\"

[STEP II 2007 Question 14 (Mechanics)]

" }, { "tags": ["Trigonometry"], "question_id":2007301, "title": "07-S3-Q1", "body": "tan, identities, quartic equations.

\"q\"

[STEP III 2007 Question 1 (Pure)]

" }, { "tags": ["Sum"], "question_id":2007302, "title": "07-S3-Q2", "body": "Product, binomial expansion, differentiation.

\"q\"

[STEP III 2007 Question 2 (Pure)]

" }, { "tags": ["Fibonacci numbers"], "question_id":2007303, "title": "07-S3-Q3", "body": "Number theory, proof by induction, divisibility.

\"q\"

[STEP III 2007 Question 3 (Pure)]

" }, { "tags": ["Parametric equations"], "question_id":2007304, "title": "07-S3-Q4", "body": "Curve sketching, tangent to curve, radius of curvature, normal, parallel.

\"q\"

[STEP III 2007 Question 4 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2007305, "title": "07-S3-Q5", "body": "Polar coordinates, logarithmic and hyperbolic functions, proof.

\"q\"

[STEP III 2007 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2007306, "title": "07-S3-Q6", "body": "Argand diagram, circle, geometry.

\"q\"

[STEP III 2007 Question 6 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2007307, "title": "07-S3-Q7", "body": "Trigonometry.

\"q\"

[STEP III 2007 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":2007308, "title": "07-S3-Q8", "body": "Substitution, transform, general solution, linearity.

\"q\"

[STEP III 2007 Question 8 (Pure)]

" }, { "tags": ["SHM"], "question_id":2007309, "title": "07-S3-Q9", "body": "Period of simple harmonic motion, energy in spring.

\"q\"

[STEP III 2007 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2007310, "title": "07-S3-Q10", "body": "Inclined plane, range, maximisation.

\"q\"

[STEP III 2007 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2007311, "title": "07-S3-Q11", "body": "Beads rolling, circular hoop, slip.

\"q\"

[STEP III 2007 Question 11 (Mechanics)]

" }, { "tags": ["Discrete random variables"], "question_id":2007312, "title": "07-S3-Q12", "body": "Expectation, variance and covariances, sum of random variables.

\"q\"

[STEP III 2007 Question 12 (Probability and Statistics)]

" }, { "tags": ["Random walk"], "question_id":2007313, "title": "07-S3-Q13", "body": "Frog jumping towards pond, Markov chain.

\"q\"

[STEP III 2007 Question 13 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":2007314, "title": "07-S3-Q14", "body": "Dartboard, circles, expectation.

\"q\"

[STEP III 2007 Question 14 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":2008101, "title": "08-S1-Q1", "body": "Irrationality, proof by contradiction, C1.

\"q\"

[STEP I 2008 Question 1 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":2008102, "title": "08-S1-Q2", "body": "Integration.

\"q\"

[STEP I 2008 Question 2 (Pure)]

" }, { "tags": ["Inequalities"], "question_id":2008103, "title": "08-S1-Q3", "body": "Squares, sum of squares, C1.

\"q\"

[STEP I 2008 Question 3 (Pure)]

" }, { "tags": ["Convex functions"], "question_id":2008104, "title": "08-S1-Q4", "body": "Curve sketching, exponential and trigonometric functions, differentiation.

\"q\"

[STEP I 2008 Question 4 (Pure)]

" }, { "tags": ["Chebyshev's theorem"], "question_id":2008105, "title": "08-S1-Q5", "body": "Analysis, polynomials, turning point, C1.

\"q\"

[STEP I 2008 Question 5 (Pure)]

" }, { "tags": ["Inverse functions"], "question_id":2008106, "title": "08-S1-Q6", "body": "Curve sketching, integration.

\"q\"

[STEP I 2008 Question 6 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":2008107, "title": "08-S1-Q7", "body": "Rotation, equilateral triangle, C1.

\"q\"

[STEP I 2008 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2008108, "title": "08-S1-Q8", "body": "Line, circle, parabola.

\"q\"

[STEP I 2008 Question 8 (Pure)]

" }, { "tags": ["Kinetic energy"], "question_id":2008109, "title": "08-S1-Q9", "body": "Rolling hoop.

\"q\"

[STEP I 2008 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":2008110, "title": "08-S1-Q10", "body": "Zog, trajectory sketching, range.

\"q\"

[STEP I 2008 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":2008111, "title": "08-S1-Q11", "body": "Limiting equilibrium, coefficient of friction, geometry.

\"q\"

[STEP I 2008 Question 11 (Mechanics)]

" }, { "tags": ["Discrete random variables"], "question_id":2008112, "title": "08-S1-Q12", "body": "Expectation, median.

\"q\"

[STEP I 2008 Question 12 (Probability and Statistics)]

" }, { "tags": ["Combinatorics"], "question_id":2008113, "title": "08-S1-Q13", "body": "Married couples sitting at a table, elementary probability, C1.

\"q\"

[STEP I 2008 Question 13 (Probability and Statistics)]

" }, { "tags": ["Sequences"], "question_id":2008201, "title": "08-S2-Q1", "body": "Difference equations, recurrence, period of sequences, C1.

\"q\"

[STEP II 2008 Question 1 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":2008202, "title": "08-S2-Q2", "body": "Binomial coefficient, partial fractions.

\"q\"

[STEP II 2008 Question 2 (Pure)]

" }, { "tags": ["Cubic equations"], "question_id":2008203, "title": "08-S2-Q3", "body": "Proof by contradiction, inequality, curve sketching, C1.

\"q\"

[STEP II 2008 Question 3 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":2008204, "title": "08-S2-Q4", "body": "Implicit differentiation, tangent and normals.

\"q\"

[STEP II 2008 Question 4 (Pure)]

" }, { "tags": ["Integrals"], "question_id":2008205, "title": "08-S2-Q5", "body": "Approximation using binomial expansion, trigonometry.

\"q\"

[STEP II 2008 Question 5 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2008206, "title": "08-S2-Q6", "body": "Period of function.

\"q\"

[STEP II 2008 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2008207, "title": "08-S2-Q7", "body": "Substitution, general solution, conjecture.

\"q\"

[STEP II 2008 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2008208, "title": "08-S2-Q8", "body": "Ratio, position vector, bisection.

\"q\"

[STEP II 2008 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2008209, "title": "08-S2-Q9", "body": "Cricket bowler, small angle approximation.

\"q\"

[STEP II 2008 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":2008210, "title": "08-S2-Q10", "body": "Billards table, coefficient of restitution, kinetic energy.

\"q\"

[STEP II 2008 Question 10 (Pure)]

" }, { "tags": ["Friction"], "question_id":2008211, "title": "08-S2-Q11", "body": "Wedge, acceleration.

\"q\"

[STEP II 2008 Question 11 (Mechanics)]

" }, { "tags": ["Court of Farnia"], "question_id":2008212, "title": "08-S2-Q12", "body": "Discrete random variable, elementary probability, expectation, conditional probability.

\"q\"

[STEP II 2008 Question 12 (Probability and Statistics)]

" }, { "tags": ["Sampling with/out replacement"], "question_id":2008213, "title": "08-S2-Q13", "body": "Elementary probability, bag and counters, maximisation, C1.

\"q\"

[STEP II 2008 Question 13 (Mechanics)]

" }, { "tags": ["Simultaneous equations"], "question_id":2008301, "title": "08-S3-Q1", "body": "Linear systems, C1.

\"q\"

[STEP III 2008 Question 1 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":2008302, "title": "08-S3-Q2", "body": "Binomial coefficients, sum of powers, degrees of polynomial, sum of coefficients.

\"q\"

[STEP III 2008 Question 2 (Pure)]

" }, { "tags": ["Conic sections"], "question_id":2008303, "title": "08-S3-Q3", "body": "Ellipse, focus, circle, intersection, geometry.

\"q\"

[STEP III 2008 Question 3 (Pure)]

" }, { "tags": ["Inequality"], "question_id":2008304, "title": "08-S3-Q4", "body": "Functions, inverse hyperbolic functions, integration, curve sketching.

\"q\"

[STEP III 2008 Question 4 (Pure)]

" }, { "tags": ["Chebyshev's polynomial"], "question_id":2008305, "title": "08-S3-Q5", "body": "Recurrence relation, proof by induction.

\"q\"

[STEP III 2008 Question 5 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":2008306, "title": "08-S3-Q6", "body": "Implicit differentiation, substitution.

\"q\"

[STEP III 2008 Question 6 (Pure)]

" }, { "tags": ["Complex number"], "question_id":2008307, "title": "08-S3-Q7", "body": "Argand diagram, equilateral triangle, rotation, centroid.

\"q\"

[STEP III 2008 Question 7 (Pure)]

" }, { "tags": ["Infinite series"], "question_id":2008308, "title": "08-S3-Q8", "body": "Recurrence relations, coefficients, partial fractions.

\"q\"

[STEP III 2008 Question 8 (Pure)]

" }, { "tags": ["Time-distance"], "question_id":2008309, "title": "08-S3-Q9", "body": "Acceleration, sinusoidal force, curve sketching.

\"q\"

[STEP III 2008 Question 9 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":2008310, "title": "08-S3-Q10", "body": "Modulus of elasticity, elastic energy, tension.

\"q\"

[STEP III 2008 Question 10 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":2008311, "title": "08-S3-Q11", "body": "Moment of inertia, angular velocity, couple.

\"q\"

[STEP III 2008 Question 11 (Mechanics)]

" }, { "tags": ["Laplace distribution"], "question_id":2008312, "title": "08-S3-Q12", "body": "Moment generating function, variance, curve sketching, frog, sum of random variables, normal distribution.

\"q\"

[STEP III 2008 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":2008313, "title": "08-S3-Q13", "body": "Box, strings, rings, expecttion, harmonic sum, variance.

\"q\"

[STEP III 2008 Question 13 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":2009101, "title": "09-S1-Q1", "body": "Proper factor, integer, prime factors, C1.

\"q\"

[STEP I 2009 Question 1 (Pure)]

" }, { "tags": ["Cubic equations"], "question_id":2009102, "title": "09-S1-Q2", "body": "Curve, tangent, positive integers, C1.

\"q\"

[STEP I 2009 Question 2 (Pure)]

" }, { "tags": ["Quadratic equations"], "question_id":2009103, "title": "09-S1-Q3", "body": "Square and cube roots, distinct real solutions to equations, C1.

\"q\"

[STEP I 2009 Question 3 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2009104, "title": "09-S1-Q4", "body": "Sides of triangles, cosine rule, ratio, C1.

\"q\"

[STEP I 2009 Question 4 (Pure)]

" }, { "tags": ["Optimisation"], "question_id":2009105, "title": "09-S1-Q5", "body": "Circular cone, differentiation, stationary value, C1.

\"q\"

[STEP I 2009 Question 5 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":2009106, "title": "09-S1-Q6", "body": "Polynomial substitution.

\"q\"

[STEP I 2009 Question 6 (Pure)]

" }, { "tags": ["Integration by parts"], "question_id":2009107, "title": "09-S1-Q7", "body": "Trigonometric and exponential functions, sum to product formula.

\"q\"

[STEP I 2009 Question 7 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":2009108, "title": "09-S1-Q8", "body": "Equation of circle, angle, incircle, C1.

\"q\"

[STEP I 2009 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2009109, "title": "09-S1-Q9", "body": "Simultaneous projection, collision, trigonometry, range equation, inequality.

\"q\"

[STEP I 2009 Question 9 (Mechanics)]

" }, { "tags": ["Wedge"], "question_id":2009110, "title": "09-S1-Q10", "body": "Pulley, acceleration, maximisation.

\"q\"

[STEP I 2009 Question 10 (Pure)]

" }, { "tags": ["Collision"], "question_id":2009111, "title": "09-S1-Q11", "body": "Coefficient of restitution, kinetic energy.

\"q\"

[STEP I 2009 Question 11 (Mechanics)]

" }, { "tags": ["Sampling without replacement"], "question_id":2009112, "title": "09-S1-Q12", "body": "Elementary probability, inequality, sweets from bag, C1.

\"q\"

[STEP I 2009 Question 12 (Probability and Statistics)]

" }, { "tags": ["Combinatorics"], "question_id":2009113, "title": "09-S1-Q13", "body": "Ordering, expectation, boys and girls in line, C1.

\"q\"

[STEP I 2009 Question 13 (Mechanics)]

" },{ "tags": ["Coordinate geometry"], "question_id":2009201, "title": "09-S2-Q1", "body": "Curve sketching, lines of symmetry, intersection, area of quadrilateral, C1.

\"q\"

[STEP II 2009 Question 1 (Pure)]

" }, { "tags": ["Functions"], "question_id":2009202, "title": "09-S2-Q2", "body": "Curve sketching, trigonometry, exponential function, stationary points, differentiation, approximation, integration, area under curve.

\"q\"

[STEP II 2009 Question 2 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":2009203, "title": "09-S2-Q3", "body": "Identity proof, tan, surds.

\"q\"

[STEP II 2009 Question 3 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":2009204, "title": "09-S2-Q4", "body": "Degree of polynomial, divisibility, C1.

\"q\"

[STEP II 2009 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":2009205, "title": "09-S2-Q5", "body": "Area under curve, surds.

\"q\"

[STEP II 2009 Question 5 (Pure)]

" }, { "tags": ["Fibonacci numbers"], "question_id":2009206, "title": "09-S2-Q6", "body": "Sum, inequality, sequences, C1.

\"q\"

[STEP II 2009 Question 6 (Pure)]

" }, { "tags": ["Integration"], "question_id":2009207, "title": "09-S2-Q7", "body": "Integration as inverse differentiation, polynomial, exponential, product rule.

\"q\"

[STEP II 2009 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":2009208, "title": "09-S2-Q8", "body": "Equation of line, quadrilateral, position vector.

\"q\"

[STEP II 2009 Question 8 (Pure)]

" }, { "tags": ["Centre of mass"], "question_id":2009209, "title": "09-S2-Q9", "body": "Uniform lamina, trapezium, tank with liquid.

\"q\"

[STEP II 2009 Question 9 (Pure)]

" }, { "tags": ["Collision"], "question_id":2009210, "title": "09-S2-Q10", "body": "Coefficient of restitution, equidistant particles.

\"q\"

[STEP II 2009 Question 10 (Mechanics)]

" }, { "tags": ["Work and Power"], "question_id":2009211, "title": "09-S2-Q11", "body": "Train engine and trucks, inequality, approximation.

\"q\"

[STEP II 2009 Question 11 (Pure)]

" }, { "tags": ["Continuous random variable"], "question_id":2009212, "title": "09-S2-Q12", "body": "Probability density function, pdf, curve sketching, expectation and variance, statistical tables, median.

\"q\"

[STEP II 2009 Question 12 (Mechanics)]

" }, { "tags": ["Andover and Basingstoke Rockets"], "question_id":2009213, "title": "09-S2-Q13", "body": "Expectation.

\"q\"

[STEP II 2009 Question 13 (Probability and Statistics)]

" }, { "tags": ["Coordinate geometry"], "question_id":2009301, "title": "09-S3-Q1", "body": "Quadratic equation, circle, C1.

\"q\"

[STEP III 2009 Question 1 (Mechanics)]

" }, { "tags": ["Series solutions"], "question_id":2009302, "title": "09-S3-Q2", "body": "Comparing coefficients, recurrence relations, differential equations, trigonometric functions.

\"q\"

[STEP III 2009 Question 2 (Pure)]

" }, { "tags": ["Functions"], "question_id":2009303, "title": "09-S3-Q3", "body": "Curve sketching, taylor series, limits, differentiation, even function.

\"q\"

[STEP III 2009 Question 3 (Pure)]

" }, { "tags": ["Laplace transform"], "question_id":2009304, "title": "09-S3-Q4", "body": "Integration, inverse Laplace transform.

\"q\"

[STEP III 2009 Question 4 (Pure)]

" }, { "tags": ["Simultaneous equations"], "question_id":2009305, "title": "09-S3-Q5", "body": "Symmetry, recurrence relations, C1.

\"q\"

[STEP III 2009 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":2009306, "title": "09-S3-Q6", "body": "Modulus and argument, Euler's formula, trigonometry, geometry, cyclic quadrilaterals.

\"q\"

[STEP III 2009 Question 6 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":2009307, "title": "09-S3-Q7", "body": "Reurrence relations, differential equation, degrees of polynomial.

\"q\"

[STEP III 2009 Question 7 (Pure)]

" }, { "tags": ["Infinite series"], "question_id":2009308, "title": "09-S3-Q8", "body": "Limits, exponential functions, recurrence formula of integrals.

\"q\"

[STEP III 2009 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":2009309, "title": "09-S3-Q9", "body": "Second trajectory, trigonometry.

\"q\"

[STEP III 2009 Question 9 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":2009310, "title": "09-S3-Q10", "body": "Simple harmonic motion, second order differential equation, springs, Hooke's law.

\"q\"

[STEP III 2009 Question 10 (Mechanics)]

" }, { "tags": ["Differential equation"], "question_id":2009311, "title": "09-S3-Q11", "body": "Newton's second law, gravitational force, variable mass.

\"q\"

[STEP III 2009 Question 11 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":2009312, "title": "09-S3-Q12", "body": "Conditional expectation, sum of random variables, probability generating function, pgf, expectation and variance.

\"q\"

[STEP III 2009 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometrical probability"], "question_id":2009313, "title": "09-S3-Q13", "body": "Independence, correlation, point on the circumference of a circle, uniform distribution.

\"q\"

[STEP III 2009 Question 13 (Probability and Statistics)]

" }, { "tags": ["Simultaneous equations"], "question_id":10101, "title": "10-S1-Q1", "body": "Factorisation of quadratic polynomials, C1.

\"q\"

[STEP I 2010 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":10102, "title": "10-S1-Q2", "body": "Differentiation, stationary points, vertical asymptote, exponential function

\"q\"

[STEP I 2010 Question 2 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":10103, "title": "10-S1-Q3", "body": "Sum to product formulae, sine, cosine, coordinate geometry, parallel lines.

\"q\"

[STEP I 2010 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":10104, "title": "10-S1-Q4", "body": "Logarithmic and square root function, Volume of revolution.

\"q\"

[STEP I 2010 Question 4 (Pure)]

" }, { "tags": ["Binomial coefficients"], "question_id":10105, "title": "10-S1-Q5", "body": "Sum of binomial coefficients, differentiation.

\"q\"

[STEP I 2010 Question 5 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":10106, "title": "10-S1-Q6", "body": "Eigenfunction substitution, exponential function, linearity.

\"q\"

[STEP I 2010 Question 6 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":10107, "title": "10-S1-Q7", "body": "Position vector, equation of lines, intersection.

\"q\"

[STEP I 2010 Question 7 (Pure)]

" }, { "tags": ["Number theory"], "question_id":10108, "title": "10-S1-Q8", "body": "Divisibility, integer solution to equations, C1.

\"q\"

[STEP I 2010 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":10109, "title": "10-S1-Q9", "body": "Uniform rectangular lamina, centre of mass, coefficient of friction, trigonometry.

\"q\"

[STEP I 2010 Question 9 (Mechanics)]

" }, { "tags": ["Time-displacement"], "question_id":10110, "title": "10-S1-Q10", "body": "Exponential and trigonometric functions, velocity of particles, acceleration.

\"q\"

[STEP I 2010 Question 10 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":10111, "title": "10-S1-Q11", "body": "Coefficient of restitution, changing direction.

\"q\"

[STEP I 2010 Question 11 (Mechanics)]

" }, { "tags": ["Discrete random variables"], "question_id":10112, "title": "10-S1-Q12", "body": "Expectation algebra, toy penguins from cereal boxes.

\"q\"

[STEP I 2010 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":10113, "title": "10-S1-Q13", "body": "Receiving texts, sum of random variables.

\"q\"

[STEP I 2010 Question 13 (Probability and Statistics)]

" }, { "tags": ["Osculating circle"], "question_id":10201, "title": "10-S2-Q1", "body": "Coordinate geometry, differentiation, rate of change, gradient, equation of tangent.

\"q\"

[STEP II 2010 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":10202, "title": "10-S2-Q2", "body": "Trigonometric identities, useless Eustace.

\"q\"

[STEP II 2010 Question 2 (Pure)]

" }, { "tags": ["Fibonacci numbers"], "question_id":10203, "title": "10-S2-Q3", "body": "Recurrence relation, general solution, sum.

\"q\"

[STEP II 2010 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":10204, "title": "10-S2-Q4", "body": "Logarithmic and trigonometric functions.

\"q\"

[STEP II 2010 Question 4 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":10205, "title": "10-S2-Q5", "body": "Position vectors, inclined plane, angle bisector.

\"q\"

[STEP II 2010 Question 5 (Pure)]

" }, { "tags": ["Elementary geometry"], "question_id":10206, "title": "10-S2-Q6", "body": "Tetrahedron, edge, cosine, inscribed sphere, C1.

\"q\"

[STEP II 2010 Question 6 (Pure)]

" }, { "tags": ["Quadratic equation"], "question_id":10207, "title": "10-S2-Q7", "body": "Turning points, cubic equations, relation between roots, C1.

\"q\"

[STEP II 2010 Question 7 (Pure)]

" }, { "tags": ["Integration"], "question_id":10208, "title": "10-S2-Q8", "body": "Curve sketching, trigonometry, exponential function, area under curve, sum.

\"q\"

[STEP II 2010 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":10209, "title": "10-S2-Q9", "body": "Simultaneous projection, inequalities, maximum height, collision.

\"q\"

[STEP II 2010 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":10210, "title": "10-S2-Q10", "body": "Coefficient of restitution, perfectly elastic, approximation.

\"q\"

[STEP II 2010 Question 10 (Pure)]

" }, { "tags": ["Equilibrium"], "question_id":10211, "title": "10-S2-Q11", "body": "Inclined at angle, ladder, trigonometry.

\"q\"

[STEP II 2010 Question 11 (Mechanics)]

" }, { "tags": ["Continuous random variable"], "question_id":10212, "title": "10-S2-Q12", "body": "Expectation, median, inequality.

\"q\"

[STEP II 2010 Question 12 (Probability and Statistics)]

" }, { "tags": ["Elementary probability"], "question_id":10213, "title": "10-S2-Q13", "body": "Stepney Chess club, strategies, C1.

\"q\"

[STEP II 2010 Question 13 (Mechanics)]

" }, { "tags": ["Sum"], "question_id":10301, "title": "10-S3-Q1", "body": "Sum of squares, algebraic manipulation, inequalities.

\"q\"

[STEP III 2010 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":10302, "title": "10-S3-Q2", "body": "Hyperbolic functions, substitution.

\"q\"

[STEP III 2010 Question 2 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":10303, "title": "10-S3-Q3", "body": "Roots of unity, primitive, polynomials, factorisation, prime.

\"q\"

[STEP III 2010 Question 3 (Pure)]

" }, { "tags": ["Quadratic equations"], "question_id":10304, "title": "10-S3-Q4", "body": "Roots of quadratic equations, common root, proof, cubic, C1.

\"q\"

[STEP III 2010 Question 4 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":10305, "title": "10-S3-Q5", "body": "Line produced, construction using straight-edge, square, C1.

\"q\"

[STEP III 2010 Question 5 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":10306, "title": "10-S3-Q6", "body": "Sphere, rotation, trigonometry, vector.

\"q\"

[STEP III 2010 Question 6 (Pure)]

" }, { "tags": ["Maclaurin series"], "question_id":10307, "title": "10-S3-Q7", "body": "Proof by induction, Chebyshev polynomial, differential equation, polynomial, degree.

\"q\"

[STEP III 2010 Question 7 (Pure)]

" }, { "tags": ["Integrating factors"], "question_id":10308, "title": "10-S3-Q8", "body": "Differential equation, general solution.

\"q\"

[STEP III 2010 Question 8 (Pure)]

" }, { "tags": ["Equilibrium"], "question_id":10309, "title": "10-S3-Q9", "body": "String, normal reaction, inequality.

\"q\"

[STEP III 2010 Question 9 (Mechanics)]

" }, { "tags": ["SHM"], "question_id":10310, "title": "10-S3-Q10", "body": "Period of simple harmonic motion, modulus of elasticity, equation of motion.

\"q\"

[STEP III 2010 Question 10 (Mechanics)]

" }, { "tags": ["Friction force"], "question_id":10311, "title": "10-S3-Q11", "body": "Acceleration, bullet, distance.

\"q\"

[STEP III 2010 Question 11 (Mechanics)]

" }, { "tags": ["Expectation"], "question_id":10312, "title": "10-S3-Q12", "body": "Infinite series, target.

\"q\"

[STEP III 2010 Question 12 (Probability and Statistics)]

" }, { "tags": ["Corr"], "question_id":10313, "title": "10-S3-Q13", "body": "Product moment correlation coefficient, independent random variables, variance, expectation.

\"q\"

[STEP III 2010 Question 13 (Probability and Statistics)]

" }, { "tags": ["Differentiation"], "question_id":11101, "title": "11-S1-Q1", "body": "Normal, gradient, lines and curve, C1.

\"q\"

[STEP I 2011 Question 1 (Pure)]

" }, { "tags": ["Integrals"], "question_id":11102, "title": "11-S1-Q2", "body": "Integration by parts

\"q\"

[STEP I 2011 Question 2 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":11103, "title": "11-S1-Q3", "body": "Differentiation, identity.

\"q\"

[STEP I 2011 Question 3 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":11104, "title": "11-S1-Q4", "body": "Parabola, tangents, bisection, C1.

\"q\"

[STEP I 2011 Question 4 (Pure)]

" }, { "tags": ["Analysis"], "question_id":11105, "title": "11-S1-Q5", "body": "Curve sketching, trigonometry, integration, modulus function, differentiation, stationary, minimum, optimisation.

\"q\"

[STEP I 2011 Question 5 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":11106, "title": "11-S1-Q6", "body": "Binomial series, coefficient, infinite sum.

\"q\"

[STEP I 2011 Question 6 (Pure)]

" }, { "tags": ["Fluid dynamics"], "question_id":11107, "title": "11-S1-Q7", "body": "Differential equation, water leaking out of tank, logarithm function.

\"q\"

[STEP I 2011 Question 7 (Pure)]

" }, { "tags": ["Number theory"], "question_id":11108, "title": "11-S1-Q8", "body": "Cubes and squares, inequality, integer solution to equations, C1.

\"q\"

[STEP I 2011 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":11109, "title": "11-S1-Q9", "body": "Collision, perfectly elastic.

\"q\"

[STEP I 2011 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":11110, "title": "11-S1-Q10", "body": "Perfect elastic, particles dropped from height, horizontal plane.

\"q\"

[STEP I 2011 Question 10 (Mechanics)]

" }, { "tags": ["Equilibrium"], "question_id":11111, "title": "11-S1-Q11", "body": "Trigonometry, pulley.

\"q\"

[STEP I 2011 Question 11 (Mechanics)]

" }, { "tags": ["Raffle tickets"], "question_id":11112, "title": "11-S1-Q12", "body": "Lottery, expectation, combinatorics, C1.

\"q\"

[STEP I 2011 Question 12 (Probability and Statistics)]

" }, { "tags": ["Continuous random variable"], "question_id":11113, "title": "11-S1-Q13", "body": "Integration.

\"q\"

[STEP I 2011 Question 13 (Probability and Statistics)]

" }, { "tags": ["Square roots"], "question_id":11201, "title": "11-S2-Q1", "body": "Curve sketching, graphical solution to equations, C1.

\"q\"

[STEP II 2011 Question 1 (Pure)]

" }, { "tags": ["Number theory"], "question_id":11202, "title": "11-S2-Q2", "body": "Perfect squres, cubes, solution to equations, C1.

\"q\"

[STEP II 2011 Question 2 (Pure)]

" }, { "tags": ["Functions"], "question_id":11203, "title": "11-S2-Q3", "body": "Trigonometry, differentiation, increasing, proof.

\"q\"

[STEP II 2011 Question 3 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":11204, "title": "11-S2-Q4", "body": "Identities, general solution, rational numbers.

\"q\"

[STEP II 2011 Question 4 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":11205, "title": "11-S2-Q5", "body": "Reflection line, position vector.

\"q\"

[STEP II 2011 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":11206, "title": "11-S2-Q6", "body": "Parts, trigonometry.

\"q\"

[STEP II 2011 Question 6 (Pure)]

" }, { "tags": ["Recurrence relations"], "question_id":11207, "title": "11-S2-Q7", "body": "Summation.

\"q\"

[STEP II 2011 Question 7 (Pure)]

" }, { "tags": ["Parametric equation"], "question_id":11208, "title": "11-S2-Q8", "body": "Curve sketching, area integral, integration, maximum value.

\"q\"

[STEP II 2011 Question 8 (Pure)]

" }, { "tags": ["Collision"], "question_id":11209, "title": "11-S2-Q9", "body": "Coefficient of restitution, second collision.

\"q\"

[STEP II 2011 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":11210, "title": "11-S2-Q10", "body": "Horizontal projectile, time, tan equation.

\"q\"

[STEP II 2011 Question 10 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":11211, "title": "11-S2-Q11", "body": "Equilibrium, resolve forces, trigonometry, vectors.

\"q\"

[STEP II 2011 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":11212, "title": "11-S2-Q12", "body": "Expectation.

\"q\"

[STEP II 2011 Question 12 (Probability and Statistics)]

" }, { "tags": ["Skewness"], "question_id":11213, "title": "11-S2-Q13", "body": "Statistics, measure of skewness, decile and Pearson skewness, cdf (cumulative distribution function), continuous random variable.

\"q\"

[STEP II 2011 Question 13 (Mechanics)]

" }, { "tags": ["Differential equation"], "question_id":11301, "title": "11-S3-Q1", "body": "Substitution, general solution.

\"q\"

[STEP III 2011 Question 1 (Pure)]

" }, { "tags": ["Number theory"], "question_id":11302, "title": "11-S3-Q2", "body": "Polynomial, common factor, irrational, nth root, cubic equations.

\"q\"

[STEP III 2011 Question 2 (Pure)]

" }, { "tags": ["Factorisation"], "question_id":11303, "title": "11-S3-Q3", "body": "Cubic and quadratic poynomial, roots, complex numbers.

\"q\"

[STEP III 2011 Question 3 (Pure)]

" }, { "tags": ["Inequalities"], "question_id":11304, "title": "11-S3-Q4", "body": "Theorem, curve sketching, Young's inequality, graphical solution, functions, trigonometric functions.

\"q\"

[STEP III 2011 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":11305, "title": "11-S3-Q5", "body": "Area integral, parametric equation, coordinate geometry.

\"q\"

[STEP III 2011 Question 5 (Pure)]

" }, { "tags": ["Integrals"], "question_id":11306, "title": "11-S3-Q6", "body": "Integration by substitution, hyperbolic and logarithmic functions.

\"q\"

[STEP III 2011 Question 6 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":11307, "title": "11-S3-Q7", "body": "Square root, general forms.

\"q\"

[STEP III 2011 Question 7 (Pure)]

" }, { "tags": ["Mobius map"], "question_id":11308, "title": "11-S3-Q8", "body": "Complex numbers, locus, circle, line segment, real and imaginary parts.

\"q\"

[STEP III 2011 Question 8 (Pure)]

" }, { "tags": ["Equilibrium"], "question_id":11309, "title": "11-S3-Q9", "body": "First order differential equation, contact, cylinder.

\"q\"

[STEP III 2011 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":11310, "title": "11-S3-Q10", "body": "Hooke's law, impulse.

\"q\"

[STEP III 2011 Question 10 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":11311, "title": "11-S3-Q11", "body": "String, couple, angular speed of simple harmonic motion (SHM).

\"q\"

[STEP III 2011 Question 11 (Mechanics)]

" }, { "tags": ["Pgf"], "question_id":11312, "title": "11-S3-Q12", "body": "Probability generating function, sum of independent random variables, expectation and variance algebra, coin toss.

\"q\"

[STEP III 2011 Question 12 (Probability and Statistics)]

" }, { "tags": ["Integer part"], "question_id":11313, "title": "11-S3-Q13", "body": "Sampling with replacement, combinatorics, probability, floor function, C1.

\"q\"

[STEP III 2011 Question 13 (Probability and Statistics)]

" }, { "tags": ["Coordinate geometry"], "question_id":12101, "title": "12-S1-Q1", "body": "Equation of lines, intersection, sum of distance, minimisation, differentiation, C1.

\"q\"

[STEP I 2012 Question 1 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":12102, "title": "12-S1-Q2", "body": "Quartic equations, roots, differentiation, stationary points, C1

\"q\"

[STEP I 2012 Question 2 (Pure)]

" }, { "tags": ["Inequality"], "question_id":12103, "title": "12-S1-Q3", "body": "Integration, curve sketching, tangent, exponential function.

\"q\"

[STEP I 2012 Question 3 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":12104, "title": "12-S1-Q4", "body": "Hyperbola, tangent, intersection, distances, C1.

\"q\"

[STEP I 2012 Question 4 (Pure)]

" }, { "tags": ["Integration"], "question_id":12105, "title": "12-S1-Q5", "body": "Trigonometric and logarithmic functions, parts, substitution.

\"q\"

[STEP I 2012 Question 5 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":12106, "title": "12-S1-Q6", "body": "Trigonometry, inequality.

\"q\"

[STEP I 2012 Question 6 (Pure)]

" }, { "tags": ["Sequences"], "question_id":12107, "title": "12-S1-Q7", "body": "Recurrence relations, factorisation, cubics.

\"q\"

[STEP I 2012 Question 7 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":12108, "title": "12-S1-Q8", "body": "Substitution, general solution.

\"q\"

[STEP I 2012 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":12109, "title": "12-S1-Q9", "body": "Shot putter, distance equation, trigonometry.

\"q\"

[STEP I 2012 Question 9 (Mechanics)]

" }, { "tags": ["Time-distance"], "question_id":12110, "title": "12-S1-Q10", "body": "Stone dropped from well, time.

\"q\"

[STEP I 2012 Question 10 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":12111, "title": "12-S1-Q11", "body": "Coefficient of friction, equilibrium, acceleration.

\"q\"

[STEP I 2012 Question 11 (Mechanics)]

" }, { "tags": ["Pdf"], "question_id":12112, "title": "12-S1-Q12", "body": "Fire extinguishers, continuous probability density function.

\"q\"

[STEP I 2012 Question 12 (Probability and Statistics)]

" }, { "tags": ["Random integer"], "question_id":12113, "title": "12-S1-Q13", "body": "Combinatorics, digits, expectation.

\"q\"

[STEP I 2012 Question 13 (Probability and Statistics)]

" }, { "tags": ["Binomial expansion"], "question_id":12201, "title": "12-S2-Q1", "body": "Coefficients.

\"q\"

[STEP II 2012 Question 1 (Pure)]

" }, { "tags": ["Polynomials"], "question_id":12202, "title": "12-S2-Q2", "body": "Degree of polynomials, C1.

\"q\"

[STEP II 2012 Question 2 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":12203, "title": "12-S2-Q3", "body": "Tan substitution.

\"q\"

[STEP II 2012 Question 3 (Pure)]

" }, { "tags": ["Analysis"], "question_id":12204, "title": "12-S2-Q4", "body": "Logarithm function, infinite series, inequalities, exponential function, limits.

\"q\"

[STEP II 2012 Question 4 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":12205, "title": "12-S2-Q5", "body": "Differentiation, stationary points, C1.

\"q\"

[STEP II 2012 Question 5 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":12206, "title": "12-S2-Q6", "body": "Cyclic quadrilateral, area of triangle, sides, Heron, C1.

\"q\"

[STEP II 2012 Question 6 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":12207, "title": "12-S2-Q7", "body": "Position vectors, centroid, equation of plane and line.

\"q\"

[STEP II 2012 Question 7 (Pure)]

" }, { "tags": ["Difference equaetions"], "question_id":12208, "title": "12-S2-Q8", "body": "Recurrence relations, sequences, proof, strictly increasing.

\"q\"

[STEP II 2012 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":12209, "title": "12-S2-Q9", "body": "Tennis ball, inequality, over net, distance, trigonometry.

\"q\"

[STEP II 2012 Question 9 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":12210, "title": "12-S2-Q10", "body": "Equilibrium, cylinder.

\"q\"

[STEP II 2012 Question 10 (Pure)]

" }, { "tags": ["Collision"], "question_id":12211, "title": "12-S2-Q11", "body": "Kinetic energy lost, particles embedded in block.

\"q\"

[STEP II 2012 Question 11 (Mechanics)]

" }, { "tags": ["Elementary probability"], "question_id":12212, "title": "12-S2-Q12", "body": "Tree diagram, conditional probability, C1.

\"q\"

[STEP II 2012 Question 12 (Probability and Statistics)]

" }, { "tags": ["Geometric probability"], "question_id":12213, "title": "12-S2-Q13", "body": "Poisson random variable, supermarkets, expectation and variance, integration, pdf.

\"q\"

[STEP II 2012 Question 13 (Mechanics)]

" }, { "tags": ["Differential equation"], "question_id":12301, "title": "12-S3-Q1", "body": "Substitution, general solution, forced first order equation.

\"q\"

[STEP III 2012 Question 1 (Pure)]

" }, { "tags": ["Infinite series"], "question_id":12302, "title": "12-S3-Q2", "body": "Expansions of logarithmic, rational functions.

\"q\"

[STEP III 2012 Question 2 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":12303, "title": "12-S3-Q3", "body": "Quadratic and quartic equations, intersection, C1.

\"q\"

[STEP III 2012 Question 3 (Pure)]

" }, { "tags": ["Sum"], "question_id":12304, "title": "12-S3-Q4", "body": "Differentiation, summation sign manipulation, infinite series, logarithms.

\"q\"

[STEP III 2012 Question 4 (Pure)]

" }, { "tags": ["Ratinoal points"], "question_id":12305, "title": "12-S3-Q5", "body": "Integer rational points, circle, number theory, hyperbola, C1.

\"q\"

[STEP III 2012 Question 5 (Pure)]

" }, { "tags": ["Complex number"], "question_id":12306, "title": "12-S3-Q6", "body": "Quadtratic equation, parametesr, root locus, Argand diagram.

\"q\"

[STEP III 2012 Question 6 (Pure)]

" }, { "tags": ["Differential equation"], "question_id":12307, "title": "12-S3-Q7", "body": "Pain-killing drug modelling, brain, system of first order equations.

\"q\"

[STEP III 2012 Question 7 (Pure)]

" }, { "tags": ["Fibonacci sequence"], "question_id":12308, "title": "12-S3-Q8", "body": "Arctan identity, infinite sum, proof by induction.

\"q\"

[STEP III 2012 Question 8 (Pure)]

" }, { "tags": ["Pulley"], "question_id":12309, "title": "12-S3-Q9", "body": "FMoment of inertia, rotation, axle.

\"q\"

[STEP III 2012 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":12310, "title": "12-S3-Q10", "body": "Ring and hoop, equilibrium, reaction force.

\"q\"

[STEP III 2012 Question 10 (Mechanics)]

" }, { "tags": ["Acceleration"], "question_id":12311, "title": "12-S3-Q11", "body": "Rope, energy conservation.

\"q\"

[STEP III 20121 Question 11 (Mechanics)]

" }, { "tags": ["Geometric probability"], "question_id":12312, "title": "12-S3-Q12", "body": "Area of triangle, perpendicular distance, minimum, pdf, expectation, tetrahedron, distance from point to closest face.

\"q\"

[STEP III 2012 Question 12 (Probability and Statistics)]

" }, { "tags": ["Normal distribution"], "question_id":12313, "title": "12-S3-Q13", "body": "Cdf, conditional expectation.

\"q\"

[STEP III 2012 Question 13 (Probability and Statistics)]

" }, { "tags": ["Square roots"], "question_id":13101, "title": "13-S1-Q1", "body": "Substitution, root of equation, C1.

\"q\"

[STEP I 2013 Question 1 (Pure)]

" }, { "tags": ["Integer part"], "question_id":13102, "title": "13-S1-Q2", "body": "Floor function, curve sketching, roots of equation, inequalities, C1

\"q\"

[STEP I 2013 Question 2 (Pure)]

" }, { "tags": ["Vectors"], "question_id":13103, "title": "13-S1-Q3", "body": "Position vectors, associativity, ratio, line segment.

\"q\"

[STEP I 2013 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":13104, "title": "13-S1-Q4", "body": "Trigonometry.

\"q\"

[STEP I 2013 Question 4 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":13105, "title": "13-S1-Q5", "body": "Locus, quadratic, factorisation, circles, coordinate geometry, symmetry, C1.

\"q\"

[STEP I 2013 Question 5 (Pure)]

" }, { "tags": ["Binomial coefficients"], "question_id":13106, "title": "13-S1-Q6", "body": "Sequences, sum, recurrence relation, Fibonacci numbers.

\"q\"

[STEP I 2013 Question 6 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":13107, "title": "13-S1-Q7", "body": "Substitution, logarithmic function.

\"q\"

[STEP I 2013 Question 7 (Pure)]

" }, { "tags": ["Functions"], "question_id":13108, "title": "13-S1-Q8", "body": "Range and domain of logarithmic, polynomial, square root, quadratic functions, composition, curve sketching, asymptotes.

\"q\"

[STEP I 2013 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":13109, "title": "13-S1-Q9", "body": "Simultaneous projection, collide.

\"q\"

[STEP I 2013 Question 9 (Mechanics)]

" }, { "tags": ["Collision and Friction"], "question_id":13110, "title": "13-S1-Q10", "body": "Ice puck, coefficient of restitution and friction.

\"q\"

[STEP I 2013 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":13111, "title": "13-S1-Q11", "body": "Block, weight, coefficient of friction, trigonometry.

\"q\"

[STEP I 2013 Question 11 (Mechanics)]

" }, { "tags": ["Stirling's approximation"], "question_id":13112, "title": "13-S1-Q12", "body": "Medicine tablets, combinatorics, C1.

\"q\"

[STEP I 2013 Question 12 (Probability and Statistics)]

" }, { "tags": ["Discrete random distribution"], "question_id":13113, "title": "13-S1-Q13", "body": "Random numbers, probability distribution, expectation.

\"q\"

[STEP I 2013 Question 13 (Probability and Statistics)]

" }, { "tags": ["Curve sketching"], "question_id":13201, "title": "13-S2-Q1", "body": "Lines and logarithms, inequality.

\"q\"

[STEP II 2013 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":13202, "title": "13-S2-Q2", "body": "Substitution and by parts, recurrence formula.

\"q\"

[STEP II 2013 Question 2 (Pure)]

" }, { "tags": ["Cubic equation"], "question_id":13203, "title": "13-S2-Q3", "body": "Curve sketching, roots of equations, turning points, C1.

\"q\"

[STEP II 2013 Question 3 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":13204, "title": "13-S2-Q4", "body": "Midpoint of chord, line segment, locus, unit circle, C1.

\"q\"

[STEP II 2013 Question 4 (Pure)]

" }, { "tags": ["Functions"], "question_id":13205, "title": "13-S2-Q5", "body": "Functional relations, differentiation, stationary points, inequality, range, C1.

\"q\"

[STEP II 2013 Question 5 (Pure)]

" }, { "tags": ["Sequences"], "question_id":13206, "title": "13-S2-Q6", "body": "Difference equations, proof by induction, convergence to limit.

\"q\"

[STEP II 2013 Question 6 (Pure)]

" }, { "tags": ["Number theory"], "question_id":13207, "title": "13-S2-Q7", "body": "Integer solutions to equations, prime, C1.

\"q\"

[STEP II 2013 Question 7 (Pure)]

" }, { "tags": ["Functions"], "question_id":13208, "title": "13-S2-Q8", "body": "Inequality, strictly decreasing, functional equations, differentiation.

\"q\"

[STEP II 2013 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":13209, "title": "13-S2-Q9", "body": "Discs, normal reaction, equilibrium.

\"q\"

[STEP II 2013 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":13210, "title": "13-S2-Q10", "body": "Trigonometry, trajectory, angle of elevation.

\"q\"

[STEP II 2013 Question 10 (Pure)]

" }, { "tags": ["Collision"], "question_id":13211, "title": "13-S2-Q11", "body": "Coefficient of restitution, identical particles.

\"q\"

[STEP II 2013 Question 11 (Mechanics)]

" }, { "tags": ["Poisson distributions"], "question_id":13212, "title": "13-S2-Q12", "body": "Discrete random variables, expectation and variance.

\"q\"

[STEP II 2013 Question 12 (Probability and Statistics)]

" }, { "tags": ["Coin toss"], "question_id":13213, "title": "13-S2-Q13", "body": "Elementary probability, straight and alternating runs.

\"q\"

[STEP II 2013 Question 13 (Mechanics)]

" }, { "tags": ["Integration"], "question_id":13301, "title": "13-S3-Q1", "body": "Tan half angle substitution, t-sub, differentiation, trigonometry, recurrence formula.

\"q\"

[STEP III 2013 Question 1 (Pure)]

" }, { "tags": ["Infinite series"], "question_id":13302, "title": "13-S3-Q2", "body": "Differential equations, proof by induction, Maclaurin series.

\"q\"

[STEP III 2013 Question 2 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":13303, "title": "13-S3-Q3", "body": "Surface of the sphere, position vector.

\"q\"

[STEP III 2013 Question 3 (Pure)]

" }, { "tags": ["Complex sum"], "question_id":13304, "title": "13-S3-Q4", "body": "Roots of unity, trigonometric sum.

\"q\"

[STEP III 2013 Question 4 (Pure)]

" }, { "tags": ["Number theory"], "question_id":13305, "title": "13-S3-Q5", "body": "Coprime, powers of prime, rational, C1.

\"q\"

[STEP III 2013 Question 5 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":13306, "title": "13-S3-Q6", "body": "Argand diagram, modulus functions, inequality.

\"q\"

[STEP III 2013 Question 6 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":13307, "title": "13-S3-Q7", "body": "Hyperbolic functions.

\"q\"

[STEP III 2013 Question 7 (Pure)]

" }, { "tags": ["Conic sections"], "question_id":13308, "title": "13-S3-Q8", "body": "Complex number, chords, geometry, sum.

\"q\"

[STEP III 2013 Question 8 (Pure)]

" }, { "tags": ["SHM"], "question_id":13309, "title": "13-S3-Q9", "body": "Simple harmonic motion, sphere, displaced liquid, equiibrium, second order differential equation.

\"q\"

[STEP III 2013 Question 9 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":13310, "title": "13-S3-Q10", "body": "Moment of inertia, coefficient of restitution, collision.

\"q\"

[STEP III 2013 Question 10 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":13311, "title": "13-S3-Q11", "body": "Equilateral triangle, modulus of elasticity, equilibrium.

\"q\"

[STEP III 20131 Question 11 (Mechanics)]

" }, { "tags": ["Discrete random variable"], "question_id":13312, "title": "13-S3-Q12", "body": "Expectation, ordering of letters, sum, variance.

\"q\"

[STEP III 2013 Question 12 (Probability and Statistics)]

" }, { "tags": ["Cdf"], "question_id":13313, "title": "13-S3-Q13", "body": "Continuous random variables, pdf, integration, inequalities.

\"q\"

[STEP III 2013 Question 13 (Probability and Statistics)]

" }, { "tags": ["Number theory"], "question_id":14101, "title": "14-S1-Q1", "body": "Difference of squares, odd, even, C1.

\"q\"

[STEP I 2014 Question 1 (Pure)]

" }, { "tags": ["Integration"], "question_id":14102, "title": "14-S1-Q2", "body": "Area under curve, modulus and logarithmic functions.

\"q\"

[STEP I 2014 Question 2 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":14103, "title": "14-S1-Q3", "body": "Integration, cubic.

\"q\"

[STEP I 2014 Question 3 (Pure)]

" }, { "tags": ["Clock"], "question_id":14104, "title": "14-S1-Q4", "body": "Rate of increase, differentiation.

\"q\"

[STEP I 2014 Question 4 (Pure)]

" }, { "tags": ["Cubic equations"], "question_id":14105, "title": "14-S1-Q5", "body": "Factorisation, curve sketching, differentiation, inequality, C1.

\"q\"

[STEP I 2014 Question 5 (Pure)]

" }, { "tags": ["Sequences"], "question_id":14106, "title": "14-S1-Q6", "body": "Substitution, conjecture, proof, difference equation.

\"q\"

[STEP I 2014 Question 6 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":14107, "title": "14-S1-Q7", "body": "Triangle, ratio, intersection, vectors.

\"q\"

[STEP I 2014 Question 7 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":14108, "title": "14-S1-Q8", "body": "Equation of lines, point of intersection, limit, tangent, C1.

\"q\"

[STEP I 2014 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":14109, "title": "14-S1-Q9", "body": "Greatest height, trajectory sketching, inequality.

\"q\"

[STEP I 2014 Question 9 (Mechanics)]

" }, { "tags": ["Collision"], "question_id":14110, "title": "14-S1-Q10", "body": "Uniform spherical ball, coefficient of restitution.

\"q\"

[STEP I 2014 Question 10 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":14111, "title": "14-S1-Q11", "body": "Acceleration and tension.

\"q\"

[STEP I 2014 Question 11 (Mechanics)]

" }, { "tags": ["Gambling"], "question_id":14112, "title": "14-S1-Q12", "body": "Expectation, discrete random variable, strategy, C1.

\"q\"

[STEP I 2014 Question 12 (Probability and Statistics)]

" }, { "tags": ["Triangular distribution"], "question_id":14113, "title": "14-S1-Q13", "body": "Continuous random variable, pdf, mean and median.

\"q\"

[STEP I 2014 Question 13 (Probability and Statistics)]

" }, { "tags": ["Euclidean geometry"], "question_id":14201, "title": "14-S2-Q1", "body": "Triangle, trigonometry, lines produced, C1.

\"q\"

[STEP II 2014 Question 1 (Pure)]

" }, { "tags": ["Inequality"], "question_id":14202, "title": "14-S2-Q2", "body": "Integration, counterexamples, trigonometric and quadratic equations.

\"q\"

[STEP II 2014 Question 2 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":14203, "title": "14-S2-Q3", "body": "Shortest distance, lines and curves, tangent, differential equation.

\"q\"

[STEP II 2014 Question 3 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":14204, "title": "14-S2-Q4", "body": "Logarithmic and arctan integral, substitution of 1/x.

\"q\"

[STEP II 2014 Question 4 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":14205, "title": "14-S2-Q5", "body": "Substitution, first order equation, solution curves, quadratic.

\"q\"

[STEP II 2014 Question 5 (Pure)]

" }, { "tags": ["Trigonometric series"], "question_id":14206, "title": "14-S2-Q6", "body": "Sum to product formula, sum, stationary point, differentiation, curve sketching, inequalities, analysis.

\"q\"

[STEP II 2014 Question 6 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":14207, "title": "14-S2-Q7", "body": "Modulus function, C1.

\"q\"

[STEP II 2014 Question 7 (Pure)]

" }, { "tags": ["Binomial expansion"], "question_id":14208, "title": "14-S2-Q8", "body": "Coefficient, inequality.

\"q\"

[STEP II 2014 Question 8 (Pure)]

" }, { "tags": ["Friction"], "question_id":14209, "title": "14-S2-Q9", "body": "Rectangular lamin, equilibrium.

\"q\"

[STEP II 2014 Question 9 (Mechanics)]

" }, { "tags": ["Projectile motion"], "question_id":14210, "title": "14-S2-Q10", "body": "Trajectory sketching, furthest range.

\"q\"

[STEP II 2014 Question 10 (Pure)]

" }, { "tags": ["Circular motion"], "question_id":14211, "title": "14-S2-Q11", "body": "Second order differential equations, tension, smooth ring, sketch.

\"q\"

[STEP II 2014 Question 11 (Mechanics)]

" }, { "tags": ["Hazard function"], "question_id":14212, "title": "14-S2-Q12", "body": "Cdf (cumulative distribution function), pdf (probability density function).

\"q\"

[STEP II 2014 Question 12 (Probability and Statistics)]

" }, { "tags": ["Discrete random variables"], "question_id":14213, "title": "14-S2-Q13", "body": "Sum of series, expectation.

\"q\"

[STEP II 2014 Question 13 (Mechanics)]

" }, { "tags": ["Series"], "question_id":14301, "title": "14-S3-Q1", "body": "Series expansion, logarithm, coefficients, counterexamples and proof.

\"q\"

[STEP III 2014 Question 1 (Pure)]

" }, { "tags": ["Integration by substitution"], "question_id":14302, "title": "14-S3-Q2", "body": "Hyperbolic functions.

\"q\"

[STEP III 2014 Question 2 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":14303, "title": "14-S3-Q3", "body": "Shortest distance of a line and a parabola, parametric equations.

\"q\"

[STEP III 2014 Question 3 (Pure)]

" }, { "tags": ["Variational principle"], "question_id":14304, "title": "14-S3-Q4", "body": "Integration by parts.

\"q\"

[STEP III 2014 Question 4 (Pure)]

" }, { "tags": ["Complex numbers"], "question_id":14305, "title": "14-S3-Q5", "body": "Quadrilateral, parallelogram, square.

\"q\"

[STEP III 2014 Question 5 (Pure)]

" }, { "tags": ["Analysis"], "question_id":14306, "title": "14-S3-Q6", "body": "Differentiation, increasing and decreasing functions, inequality.

\"q\"

[STEP III 2014 Question 6 (Pure)]

" }, { "tags": ["Vectors"], "question_id":14307, "title": "14-S3-Q7", "body": "Triangles, sum, intersection.

\"q\"

[STEP III 2014 Question 7 (Pure)]

" }, { "tags": ["Analysis"], "question_id":14308, "title": "14-S3-Q8", "body": "Inequalities, sum, positive integers, nubmer theory, decimal representation, sum of reciprocals.

\"q\"

[STEP III 2014 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":14309, "title": "14-S3-Q9", "body": "Resistive force, equation of motion, range equation.

\"q\"

[STEP III 2014 Question 9 (Mechanics)]

" }, { "tags": ["Hooke's law"], "question_id":14310, "title": "14-S3-Q10", "body": "SHM (Simple harmonic motion), second order differential equation, modulus of elasticity.

\"q\"

[STEP III 2014 Question 10 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":14311, "title": "14-S3-Q11", "body": "Tension, strings, bounds.

\"q\"

[STEP III 20141 Question 11 (Mechanics)]

" }, { "tags": ["Normal distribution"], "question_id":14312, "title": "14-S3-Q12", "body": "Median, pdf, expectation, cumulative distribution function (cdf).

\"q\"

[STEP III 2014 Question 12 (Probability and Statistics)]

" }, { "tags": ["Pgf"], "question_id":14313, "title": "14-S3-Q13", "body": "Strategy, probability generating function.

\"q\"

[STEP III 2014 Question 13 (Probability and Statistics)]

" }, { "tags": ["Curve sketching"], "question_id":15101, "title": "15-S1-Q1", "body": "Exponential function, polynomial, curve sketching, limits.

\"q\"

[STEP I 2015 Question 1 (Pure)]

" }, { "tags": ["Trigonometry"], "question_id":15102, "title": "15-S1-Q2", "body": "Cosine and sine function, root of equation, surds.

\"q\"

[STEP I 2015 Question 2 (Pure)]

" }, { "tags": ["Optimisation"], "question_id":15103, "title": "15-S1-Q3", "body": "Prison guard, square, perimeter, maximise, C1.

\"q\"

[STEP I 2015 Question 3 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":15104, "title": "15-S1-Q4", "body": "Locus of points, trigonometry, tangent function, area of curve, integration.

\"q\"

[STEP I 2015 Question 4 (Pure)]

" }, { "tags": ["Curve sketeching"], "question_id":15105, "title": "15-S1-Q5", "body": "Integration, curve sketching.

\"q\"

[STEP I 2015 Question 5 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":15106, "title": "15-S1-Q6", "body": "Quadrilateral, position vectors, optimisation, square, C1.

\"q\"

[STEP I 2015 Question 6 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":15107, "title": "15-S1-Q7", "body": "Optimisation, interval, greatest value, polynomial, cubic function, C1.

\"q\"

[STEP I 2015 Question 7 (Pure)]

" }, { "tags": ["Number theory"], "question_id":15108, "title": "15-S1-Q8", "body": "Sum, divisibility, series, proof, C1.

\"q\"

[STEP I 2015 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":15109, "title": "15-S1-Q9", "body": "Angle of elevation, bullet, range, short-barrelled machine gun.

\"q\"

[STEP I 2015 Question 9 (Mechanics)]

" }, { "tags": ["Bus and rain"], "question_id":15110, "title": "15-S1-Q10", "body": "Inclined plane, rain, bus, constant speed, cuboid, C1-ish.

\"q\"

[STEP I 2015 Question 10 (Mechanics)]

" }, { "tags": ["Friction"], "question_id":15111, "title": "15-S1-Q11", "body": "Acceleration, coefficient of friction, circular cylinders, inclined plane.

\"q\"

[STEP I 2015 Question 11 (Mechanics)]

" }, { "tags": ["Poisson distribution"], "question_id":15112, "title": "15-S1-Q12", "body": "Casualties at hospital, mean and probability, poisson distribution.

\"q\"

[STEP I 2015 Question 12 (Probability and Statistics)]

" }, { "tags": ["Dice"], "question_id":15113, "title": "15-S1-Q13", "body": "Fair die, elementary probability, binomial expansion, C1.

\"q\"

[STEP I 2015 Question 13 (Probability and Statistics)]

" }, { "tags": ["Analysis"], "question_id":15201, "title": "15-S2-Q1", "body": "Differentiation, infinite series, sum, inequality, logarithm function.

\"q\"

[STEP II 2015 Question 1 (Pure)]

" }, { "tags": ["Euclidean geometry"], "question_id":15202, "title": "15-S2-Q2", "body": "Trigonometry, sine function, midpoint, perpendicular, bisector, trisection, C1.

\"q\"

[STEP II 2015 Question 2 (Pure)]

" }, { "tags": ["Proof by induction"], "question_id":15203, "title": "15-S2-Q3", "body": "Triangle, induction, degenerate, cases.

\"q\"

[STEP II 2015 Question 3 (Pure)]

" }, { "tags": ["Curve sketching"], "question_id":15204, "title": "15-S2-Q4", "body": "Tangent function, continuous, range, differentiation, stationary point, asymptote, curve sketching.

\"q\"

[STEP II 2015 Question 4 (Pure)]

" }, { "tags": ["Arctan sum"], "question_id":15205, "title": "15-S2-Q5", "body": "Proof, induction, infinite sum, right-angled triangle.

\"q\"

[STEP II 2015 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":15206, "title": "15-S2-Q6", "body": "Integration by substitution, differentiation.

\"q\"

[STEP II 2015 Question 6 (Pure)]

" }, { "tags": ["Coordinate geometry"], "question_id":15207, "title": "15-S2-Q7", "body": "Bisection, circle, diametrically opposite, inequality, C1.

\"q\"

[STEP II 2015 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":15208, "title": "15-S2-Q8", "body": "Non-overlapping circles, tangent, intersection, position vectors, lines.

\"q\"

[STEP II 2015 Question 8 (Pure)]

" }, { "tags": ["Rotating rods"], "question_id":15209, "title": "15-S2-Q9", "body": "Equilateral triangle, light rods, rotate, equilibrium, impulse.

\"q\"

[STEP II 2015 Question 9 (Mechanics)]

" }, { "tags": ["Pulley"], "question_id":15210, "title": "15-S2-Q10", "body": "Tension, pulley, motion, equilibrium.

\"q\"

[STEP II 2015 Question 10 (Pure)]

" }, { "tags": ["Collisions"], "question_id":15211, "title": "15-S2-Q11", "body": "Impulse, elastic collision, kinematics, differential equations, impulse, inextensible string.

\"q\"

[STEP II 2015 Question 11 (Mechanics)]

" }, { "tags": ["Coin toss"], "question_id":15212, "title": "15-S2-Q12", "body": "Coin-tossing game, sequence, elementary probability, C1

\"q\"

[STEP II 2015 Question 12 (Probability and Statistics)]

" }, { "tags": ["Random variable"], "question_id":15213, "title": "15-S2-Q13", "body": "Probability density function (pdf), flood, cost, expectation and variance.

\"q\"

[STEP II 2015 Question 13 (Mechanics)]

" }, { "tags": ["Integration"], "question_id":15301, "title": "15-S3-Q1", "body": "Recurrence relation, integration by substitution.

\"q\"

[STEP III 2015 Question 1 (Pure)]

" }, { "tags": ["Analysis"], "question_id":15302, "title": "15-S3-Q2", "body": "Sequences, proof, counter-example.

\"q\"

[STEP III 2015 Question 2 (Pure)]

" }, { "tags": ["Polar coordinates"], "question_id":15303, "title": "15-S3-Q3", "body": "Conchoid of Nicomedes, polar coordinates, secant function, trigonometry, integration, area of loop.

\"q\"

[STEP III 2015 Question 3 (Pure)]

" }, { "tags": ["Roots of polynomials"], "question_id":15304, "title": "15-S3-Q4", "body": "Cubic function, real root, algebra, trigonometry, sine function.

\"q\"

[STEP III 2015 Question 4 (Pure)]

" }, { "tags": ["Number theory"], "question_id":15305, "title": "15-S3-Q5", "body": "Proof by contradiction, irrationality of square root 2, rational, C1.

\"q\"

[STEP III 2015 Question 5 (Pure)]

" }, { "tags": ["Complex system"], "question_id":15306, "title": "15-S3-Q6", "body": "System of equation, proof, real and complex values.

\"q\"

[STEP III 2015 Question 6 (Pure)]

" }, { "tags": ["Differentiation"], "question_id":15307, "title": "15-S3-Q7", "body": "Operators, polynomial, divisibility, sum, identity, positive integers, order of polynomials, proof.

\"q\"

[STEP III 2015 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":15308, "title": "15-S3-Q8", "body": "Curve sketching, polar coordinate, differential equations.

\"q\"

[STEP III 2015 Question 8 (Pure)]

" }, { "tags": ["Elastic string"], "question_id":15309, "title": "15-S3-Q9", "body": "Impulse, acceleration, period of motion, integral.

\"q\"

[STEP III 2015 Question 9 (Mechanics)]

" }, { "tags": ["Kinematics"], "question_id":15310, "title": "15-S3-Q10", "body": "Differential equations, rod.

\"q\"

[STEP III 2015 Question 10 (Mechanics)]

" }, { "tags": ["Circular motion"], "question_id":15311, "title": "15-S3-Q11", "body": "Horizontal disc, rotation, moment.

\"q\"

[STEP III 20151 Question 11 (Mechanics)]

" }, { "tags": ["Dice"], "question_id":15312, "title": "15-S3-Q12", "body": "Fair die, random variable, independent, probability generating function (pgf) probability, divisibility, remainder.

\"q\"

[STEP III 2015 Question 12 (Probability and Statistics)]

" }, { "tags": ["Uniform distribution"], "question_id":15313, "title": "15-S3-Q13", "body": "Independent random variable, normal distribution, cumulative function, probability density function (pdf), expectation.

\"q\"

[STEP III 2015 Question 13 (Probability and Statistics)]

" }, { "tags": ["Polynomials"], "question_id":16101, "title": "16-S1-Q1", "body": "factorising, powers of 7.

\"q\"

[STEP I 2016 Question 1 (Pure Mathematics)]

" }, { "tags": ["Anti-differentiation"], "question_id":16102, "title": "16-S1-Q1", "body": "differentiation, integration, anti-derivative.

\"q\"

[STEP I 2016 Question 2 (Pure Mathematics)]

" }, { "tags": ["Graphs of floor functions"], "question_id":16103, "title": "16-S1-Q1", "body": "graphs, floor function, integer part, discontinuity.

\"q\"

[STEP I 2016 Question 3 (Pure Mathematics)]

" }, { "tags": ["Touching circles"], "question_id":16104, "title": "16-S1-Q4", "body": "geometry, circles, touching circles, common tangent, radius.

\"q\"

[STEP I 2016 Question 4 (Pure Mathematics)]

" }, { "tags": ["Curvature"], "question_id":16105, "title": "16-S1-Q5", "body": "differentiation, curvature, radius of curvature.

\"q\"

[STEP I 2016 Question 5 (Pure Mathematics)]

" }, { "tags": ["Vector geometry"], "question_id":16106, "title": "16-S1-Q6", "body": "vectors, vector geometry,quadrilateral, diagonal.

\"q\"

[STEP I 2016 Question 6 (Pure Mathematics)]

" }, { "tags": ["Integer sets"], "question_id":16107, "title": "16-S1-Q7", "body": "sets, integers, prime numbers, mod 4,base 4.

\"q\"

[STEP I 2016 Question 7 (Pure Mathematics)]

" }, { "tags": ["Generating functions"], "question_id":16108, "title": "16-S1-Q8", "body": "sequences, generating functions, recurrence relations, difference equation.

\"q\"

[STEP I 2016 Question 8 (Pure Mathematics)]

" }, { "tags": ["Static equilibrium: wall and rod"], "question_id":16109, "title": "16-S1-Q9", "body": "statics, equilibrium, friction, wall, rod, rail.

\"q\"

[STEP I 2016 Question 9 (Mechanics)]

" }, { "tags": ["Particle collisions"], "question_id":16110, "title": "16-S1-Q10", "body": "particles, coefficient of restitution, collisions.

\"q\"

[STEP I 2016 Question 10 (Mechanics)]

" }, { "tags": ["Projectile and tower"], "question_id":16111, "title": "16-S1-Q11", "body": "projectile, tower, greatest distance.

\"q\"

[STEP I 2016 Question 11 (Mechanics)]

" }, { "tags": ["Coin tossing"], "question_id":16112, "title": "16-S1-Q12", "body": "coins, tossing, Bob, Alice .

\"q\"

[STEP I 2016 Question 12 (Probability and Statistics)]

" }, { "tags": ["Internet tester"], "question_id":16113, "title": "16-S1-Q13", "body": "arrival times, exponential distribution, expectation.

\"q\"

[STEP I 2016 Question 13 (Probability and Statistics)]

" }, { "tags": ["Coordinate geometry"], "question_id":16201, "title": "16-S2-Q1", "body": "coordinate geometry, parametric equation, tangent, parabola.

\"q\"

[STEP II 2016 Question 1 (Pure Mathematics)]

" }, { "tags": ["Factor theorem"], "question_id":16202, "title": "16-S2-Q2", "body": "factor theorem, cubic equation.

\"q\"

[STEP II 2016 Question 2 (Pure Mathematics)]

" }, { "tags": ["Roots of polynomial"], "question_id":16203, "title": "16-S2-Q3", "body": "polynommial, roots, exponential series.

\"q\"

[STEP II 2016 Question 3 (Pure Mathematics)]

" }, { "tags": ["Inequalities for rational function "], "question_id":16204, "title": "16-S2-Q4", "body": "inequality, rational function, quadratic ratio.

\"q\"

[STEP II 2016 Question 4 (Pure Mathematics)]

" }, { "tags": ["Binomial identities"], "question_id":16205, "title": "16-S2-Q5", "body": "binomial coefficient, negative binomial expansion,chu, vandermonde identity.

\"q\"

[STEP II 2016 Question 5 (Pure Mathematics)]

" }, { "tags": ["Quadratic differential equation"], "question_id":16206, "title": "16-S2-Q6", "body": "differential equation, Legendre equation, Legendre polynomials.

\"q\"

[STEP II 2016 Question 6 (Pure Mathematics)]

" }, { "tags": ["Trigonometric integrals"], "question_id":16207, "title": "16-S2-Q7", "body": "integral, substitution, change of variable, trigonometric functions.

\"q\"

[STEP II 2016 Question 7 (Pure Mathematics)]

" }, { "tags": ["Approximating sums using integrals"], "question_id":16208, "title": "16-S2-Q8", "body": "integral, sums, approximations, zeta function.

\"q\"

[STEP II 2016 Question 8 (Pure Mathematics)]

" }, { "tags": ["Bullet fired into block"], "question_id":16209, "title": "16-S2-Q9", "body": "bullet, resistence, block of wood, momentum conservation.

\"q\"

[STEP II 2016 Question 9 (Mechanics)]

" }, { "tags": ["Hanging triangle"], "question_id":16210, "title": "16-S2-Q10", "body": "statics, equilibrium, triangle, friction, coefficient of friction.

\"q\"

[STEP II 2016 Question 10 (Mechanics)]

" }, { "tags": ["Projectile and target"], "question_id":16211, "title": "16-S2-Q11", "body": "projectile, target, collision.

\"q\"

[STEP II 2016 Question 11 (Mechanics)]

" }, { "tags": ["Old hat probability problem"], "question_id":16212, "title": "16-S2-Q12", "body": "probability, inclusion-exclusion, hats, playing cards.

\"q\"

[STEP II 2016 Question 12 (Probability and Statistics)]

" }, { "tags": ["Binomial distribution approximations"], "question_id":16213, "title": "16-S2-Q13", "body": "Binomial distribution, Normal approximation, Poission approximation, n! estimate, Stirling's approximation.

\"q\"

[STEP II 2016 Question 13 (Probability and Statistics)]

" }, { "tags": ["Integral reduction"], "question_id":16301, "title": "16-S3-Q1", "body": "Integral, infinite integral, reduction formula, induction.

\"q\"

[STEP III 2016 Question 1 (Pure Mathematics)]

" }, { "tags": ["Parabola normals"], "question_id":16302, "title": "16-S3-Q2", "body": "Coordinate geometry, parabola, normals, intersecting normals.

\"q\"

[STEP III 2016 Question 2 (Pure Mathematics)]

" }, { "tags": ["Integration"], "question_id":16303, "title": "16-S3-Q3", "body": "Integration, exponential, rational function, polynomial.

\"q\"

[STEP III 2016 Question 3 (Pure Mathematics)]

" }, { "tags": ["Telescoping sums"], "question_id":16304, "title": "16-S3-Q4", "body": "Sum, telescoping sum, hyperbolic functions.

\"q\"

[STEP III 2016 Question 4 (Pure Mathematics)]

" }, { "tags": ["Prime number distribution"], "question_id":16305, "title": "16-S3-Q5", "body": "Binomial coefficients, inequalities, prime numbers, distribution of primes.

\"q\"

[STEP III 2016 Question 5 (Pure Mathematics)]

" }, { "tags": ["Intersecting curves number"], "question_id":16306, "title": "16-S3-Q6", "body": "Hyperbolic functions, conditions for intersection, intersection, amplitude phase.

\"q\"

[STEP III 2016 Question 6 (Pure Mathematics)]

" }, { "tags": ["Argand geometry"], "question_id":16307, "title": "16-S3-Q7", "body": "roots of unity, polygon, argand diagram, complex numbers, side lengths.

\"q\"

[STEP III 2016 Question 7 (Pure Mathematics)]

" }, { "tags": ["Functional equations"], "question_id":16308, "title": "16-S3-Q8", "body": "functional equations, simultaneous functional equations.

\"q\"

[STEP III 2016 Question 8 (Pure Mathematics)]

" }, { "tags": ["Simple harmonic motion"], "question_id":16309, "title": "16-S3-Q9", "body": "simple harmonic motion, equilibrium, triangle, springs, modulus of elasticity.

\"q\"

[STEP III 2016 Question 9 (Mechanics)]

" }, { "tags": ["Motion on a plane"], "question_id":16310, "title": "16-S3-Q10", "body": "plane, string, impulse.

\"q\"

[STEP III 2016 Question 10 (Mechanics)]

" }, { "tags": ["Accelerating car"], "question_id":16311, "title": "16-S3-Q11", "body": "car, work, work rate, resistance.

\"q\"

[STEP III 2016 Question 11 (Mechanics)]

" }, { "tags": ["Chebyshev's inequality"], "question_id":16312, "title": "16-S3-Q12", "body": "Chebyshev, inequality, coin tossing.

\"q\"

[STEP III 2016 Question 12 (Probability and Statistics)]

" }, { "tags": ["Kurtosis"], "question_id":16313, "title": "16-S3-Q13", "body": "expectation, random variable,Normal distribution.

\"q\"

[STEP III 2016 Question 13 (Probability and Statistics)]

" }, { "tags": ["Integration by substitution"], "question_id":17101, "title": "17-S1-Q1", "body": "Integration, substitution, trigonometry.

\"q\"

[STEP I 2017 Question 1 (Pure)]

" }, { "tags": ["Inequlaities"], "question_id":17102, "title": "17-S1-Q2", "body": "Inequalities, integration, logarithm.

\"q\"

[STEP I 2017 Question 2 (Pure)]

" }, { "tags": ["Parabola"], "question_id":17103, "title": "17-S1-Q3", "body": "Parabola, tangents, intersection, area.

\"q\"

[STEP I 2017 Question 3 (Pure)]

" }, { "tags": ["Geometric progression"], "question_id":17104, "title": "17-S1-Q4", "body": "Geometric progression, sum, sum of first three terms.

\"q\"

[STEP I 2017 Question 4 (Pure)]

" }, { "tags": ["Area of rectangle in circle segment"], "question_id":17105, "title": "17-S1-Q5", "body": "Circle, segment, rectangle, greatest area, maximisation.

\"q\"

[STEP I 2017 Question 5 (Pure)]

" }, { "tags": ["Integration"], "question_id":17106, "title": "17-S1-Q6", "body": "Integration, moments.

\"q\"

[STEP I 2017 Question 6 (Pure)]

" }, { "tags": ["Triangles"], "question_id":17107, "title": "17-S1-Q7", "body": "Triangles, equilateral triangles, cosine rule, areas.

\"q\"

[STEP I 2017 Question 7 (Pure)]

" }, { "tags": ["Sequence"], "question_id":17108, "title": "17-S1-Q8", "body": "Sequences, double sequences, induction, approximation for root two, rational approximation.

\"q\"

[STEP I 2017 Question 8 (Pure)]

" }, { "tags": ["Projectile motion"], "question_id":17109, "title": "17-S1-Q9", "body": "Projectile, angle of projection, minimum angle of projection.

\"q\"

[STEP I 2017 Question 9 (Mechanics)]

" }, { "tags": ["Colliding particles"], "question_id":17110, "title": "17-S1-Q10", "body": "Particles, collisions, coefficient of restitution, kinetic energy.

\"q\"

[STEP I 2017 Question 10 (Mechanics)]

" }, { "tags": ["Box on inclined plane"], "question_id":17111, "title": "17-S1-Q11", "body": "Box, inclined plane, friction, slipping, limiting equilibrium.

\"q\"

[STEP I 2017 Question 11 (Mechanics)]

" }, { "tags": ["Lottery"], "question_id":17112, "title": "17-S1-Q12", "body": "Lottery, random numbers, expected profit, expected loss, popular numbers.

\"q\"

[STEP I 2017 Question 12 (Probability and Statistics)]

" }, { "tags": ["Sliced loaf"], "question_id":17113, "title": "17-S1-Q13", "body": "Bread, slices, toast, sandwich, recurrence relations.

\"q\"

[STEP I 2017 Question 13 (Probability and Statistics)]

" }, { "tags": ["arctan integral"], "question_id":17201, "title": "17-S2-Q1", "body": "integration, arctan, recurrence, induction.

\"q\"

[STEP II 2017 Question 1 (Pure)]

" }, { "tags": ["Periodic sequences"], "question_id":17202, "title": "17-S2-Q2", "body": "Sequence, period, period 2, period 4.

\"q\"

[STEP II 2017 Question 2 (Pure)]

" }, { "tags": ["Trigonometric equations"], "question_id":17203, "title": "17-S2-Q3", "body": "Trigonometric equations, sin, arcsin, sin graph, curve sketching.

\"q\"

[STEP II 2017 Question 3 (Pure)]

" }, { "tags": ["Schwarz inequality"], "question_id":17204, "title": "17-S2-Q4", "body": "Inequalities, integral inequalities, Schwarz inequality, sin, exponential, gaussian integral .

\"q\"

[STEP II 2017 Question 4 (Pure)]

" }, { "tags": ["Parabola and circle"], "question_id":17205, "title": "17-S2-Q5", "body": "Parabola, parametric equations, normal, chord length, circle, minimum diameter.

\"q\"

[STEP II 2017 Question 5 (Pure)]

" }, { "tags": ["Inverse square root series"], "question_id":17206, "title": "17-S2-Q6", "body": "Series, square root, induction, inequalities.

\"q\"

[STEP II 2017 Question 6 (Pure)]

" }, { "tags": ["x to the power x to the power x"], "question_id":17207, "title": "17-S2-Q7", "body": "Inequlaities, limits, x to the power x, curve sketching, logarithms.

\"q\"

[STEP II 2017 Question 7 (Pure)]

" }, { "tags": ["Vector geometry"], "question_id":17208, "title": "17-S2-Q8", "body": "Vectors, position vectors, vector geometry, triangle, vector equation of line, altitudes.

\"q\"

[STEP II 2017 Question 8 (Pure)]

" }, { "tags": ["Plank on cylinders"], "question_id":17209, "title": "17-S2-Q9", "body": "Equilibrium, friction, limiting friction, cylinders, plank, normal reaction, inequalities.

\"q\"

[STEP II 2017 Question 9 (Mechanics)]

" }, { "tags": ["Car with air and rolling resistance"], "question_id":17210, "title": "17-S2-Q10", "body": "Car, journey, air resistance, rolling resistance, acceleration, driving force, work.

\"q\"

[STEP II 2017 Question 10 (Pure)]

" }, { "tags": ["Projectile"], "question_id":17211, "title": "17-S2-Q11", "body": "Projectile, walls.

\"q\"

[STEP II 2017 Question 11 (Mechanics)]

" }, { "tags": ["Fishing"], "question_id":17212, "title": "17-S2-Q12", "body": "Fishing, Adam, Eve, Poisson, binomial, expected time, Poisson process.

\"q\"

[STEP II 2017 Question 12 (Probability and Statistics)]

" }, { "tags": ["Game show"], "question_id":17213, "title": "17-S2-Q13", "body": "Game show, keys, door, random, binomial expansion.

\"q\"

[STEP II 2017 Question 13 (Mechanics)]

" }, { "tags": ["Inverse cube series"], "question_id":17301, "title": "17-S3-Q1", "body": "Series, inverse cube, binomial coefficients, inequalities, sum of series, infinite sum.

\"q\"

[STEP III 2017 Question 1 (Pure)]

" }, { "tags": ["Transformations"], "question_id":17302, "title": "17-S3-Q2", "body": "Transformations, rotations, complex numbers, Argand diagram, compound transformations.

\"q\"

[STEP III 2017 Question 2 (Pure)]

" }, { "tags": ["Quartic equation"], "question_id":17303, "title": "17-S3-Q3", "body": "Quartic equation, roots, cubic equation.

\"q\"

[STEP III 2017 Question 3 (Pure)]

" }, { "tags": ["Geomtric mean"], "question_id":17304, "title": "17-S3-Q4", "body": "Geometric mean, exponential, integration.

\"q\"

[STEP III 2017 Question 4 (Pure)]

" }, { "tags": ["Polar equations"], "question_id":17305, "title": "17-S3-Q5", "body": "Polar equations, perpendicular curves, orthogonal families of curves, cardioid, families of curves.

\"q\"

[STEP III 2017 Question 5 (Pure)]

" }, { "tags": ["Arctan"], "question_id":17306, "title": "17-S3-Q6", "body": "Integration, Arctan, integral definition.

\"q\"

[STEP III 2017 Question 6 (Pure)]

" }, { "tags": ["Ellipse"], "question_id":17307, "title": "17-S3-Q7", "body": "Ellipse, tangent, intersecting tangents.

\"q\"

[STEP III 2017 Question 7 (Pure)]

" }, { "tags": ["Trigonometric sums"], "question_id":17308, "title": "17-S3-Q8", "body": "Summation by parts, trigonometric sums, sine sum, cosine sum.

\"q\"

[STEP III 2017 Question 8 (Pure)]

" }, { "tags": ["Particles connected by spring"], "question_id":17309, "title": "17-S3-Q9", "body": "Spring, particles, modulus of elasticity, gravity, table, energy conservation.

\"q\"

[STEP III 2017 Question 9 (Mechanics)]

" }, { "tags": ["Hinged rod"], "question_id":17310, "title": "17-S3-Q10", "body": "Rod, hinge, normal reaction, particle, friction, coefficient of friction.

\"q\"

[STEP III 2017 Question 10 (Mechanics)]

" }, { "tags": ["Gun carriage"], "question_id":17311, "title": "17-S3-Q11", "body": "Gun, projectile, truck, kinetic energy, momentum.

\"q\"

[STEP III 2017 Question 11 (Mechanics)]

" }, { "tags": ["Discrete random variable"], "question_id":17312, "title": "17-S3-Q12", "body": "Discrete random variable, joint probability distribution, independence, covariance.

\"q\"

[STEP III 2017 Question 12 (Probability and Statistics)]

" }, { "tags": ["Variance"], "question_id":17313, "title": "17-S3-Q13", "body": "Random variable, expectation, variance, uniform distribution.

\"q\"

[STEP III 2017 Question 13 (Probability and Statistics)]

" }, { "tags": ["Area between curve and line"], "question_id":18101, "title": "18-S1-Q1", "body": "Integration, area, tangent, triangle, inequality.

\"q\"

[STEP I 2018 Question 1 (Pure)]

" }, { "tags": ["Logarithms"], "question_id":18102, "title": "18-S1-Q2", "body": "Logarithm, pi, Euler, inequalities, bounds, approximation.

\"q\"

[STEP I 2018 Question 2 (Pure)]

" }, { "tags": ["Hyperbola"], "question_id":18103, "title": "18-S1-Q3", "body": "Hyperbola, angles.

\"q\"

[STEP I 2018 Question 3 (Pure)]

" }, { "tags": ["Sketching an integral function"], "question_id":18104, "title": "18-S1-Q4", "body": "Integration, by substitution, curve sketching.

\"q\"

[STEP I 2018 Question 4 (Pure)]

" }, { "tags": ["Polynomials at integer points"], "question_id":18105, "title": "18-S1-Q5", "body": "Polynomials, integers, polynomial degree.

\"q\"

[STEP I 2018 Question 5 (Pure)]

" }, { "tags": ["Numerical integration"], "question_id":18106, "title": "18-S1-Q6", "body": "Numerical integration, trigonometry, trapezium rule, midpoint rule.

\"q\"

[STEP I 2018 Question 6 (Pure)]

" }, { "tags": ["Solving the cubic"], "question_id":18107, "title": "18-S1-Q7", "body": "Cubic, Mobius, roots.

\"q\"

[STEP I 2018 Question 7 (Pure)]

" }, { "tags": ["Coupled differential equations"], "question_id":18108, "title": "18-S1-Q8", "body": "Integral, differential equation, generalised trigonometric functions.

\"q\"

[STEP I 2018 Question 8 (Pure)]

" }, { "tags": ["Motion on two inclined roads"], "question_id":18109, "title": "18-S1-Q9", "body": "Road, go-kart, traffic lights, inclined plane, energy, two roads.

\"q\"

[STEP I 2018 Question 9 (Mechanics)]

" }, { "tags": ["Tension in train coupling"], "question_id":18110, "title": "18-S1-Q10", "body": "Train, tension, carriages, engine, compression.

\"q\"

[STEP I 2018 Question 10 (Mechanics)]

" }, { "tags": ["Pulley and rough inclined plane"], "question_id":18111, "title": "18-S1-Q11", "body": "Inelastic string, pulley, equilibrium, coeffcient of friction, bound, inclined plane, friction.

\"q\"

[STEP I 2018 Question 11 (Mechanics)]

" }, { "tags": ["Coin tosses"], "question_id":18112, "title": "18-S1-Q12", "body": "Coins, bag, coin toss, expectation, variance.

\"q\"

[STEP I 2018 Question 12 (Probability and Statistics)]

" }, { "tags": ["Multiple choice questions"], "question_id":18113, "title": "18-S1-Q13", "body": "Multiple choice, test, MCQ, probability, random answers.

\"q\"

[STEP I 2018 Question 13 (Probability and Statistics)]

" }, { "tags": ["Quartic repeated roots"], "question_id":18201, "title": "18-S2-Q1", "body": "Quartic, roots, repeated roots, symmetric polynomial.

\"q\"

[STEP II 2018 Question 1 (Pure)]

" }, { "tags": ["Concave functions"], "question_id":18202, "title": "18-S2-Q2", "body": "Concave, Jensen, inequalities, triangles, mean.

\"q\"

[STEP II 2018 Question 2 (Pure)]

" }, { "tags": ["Tan integral"], "question_id":18203, "title": "18-S2-Q3", "body": "Range, domain, integral, trigonometric functions, symmetry, odd function, tan.

\"q\"

[STEP II 2018 Question 3 (Pure)]

" }, { "tags": ["Trigonometric equations"], "question_id":18204, "title": "18-S2-Q4", "body": "Trigonometric equations, angle addition, roots.

\"q\"

[STEP II 2018 Question 4 (Pure)]

" }, { "tags": ["Integration of series"], "question_id":18205, "title": "18-S2-Q5", "body": "Series, Taylor, integration, binomial expansion.

\"q\"

[STEP II 2018 Question 5 (Pure)]

" }, { "tags": ["Factorial equations"], "question_id":18206, "title": "18-S2-Q6", "body": "Number theory, primes, factorial, integers, diophantine.

\"q\"

[STEP II 2018 Question 6 (Pure)]

" }, { "tags": ["Triangle intersection"], "question_id":18207, "title": "18-S2-Q7", "body": "Triangle, intersection, ratio, lengths, Euclidean geometry.

\"q\"

[STEP II 2018 Question 7 (Pure)]

" }, { "tags": ["Differential equations"], "question_id":18208, "title": "18-S2-Q8", "body": "Differential equation, square root, curve sketching, substitution.

\"q\"

[STEP II 2018 Question 8 (Pure)]

" }, { "tags": ["Beads on wire"], "question_id":18209, "title": "18-S2-Q9", "body": "Beads, wire, collisions, coefficient of restitution, bounce.

\"q\"

[STEP II 2018 Question 9 (Mechanics)]

" }, { "tags": ["Ant on elastic string"], "question_id":18210, "title": "18-S2-Q10", "body": "Elastic string, ant, equation of motion.

\"q\"

[STEP II 2018 Question 10 (Pure)]

" }, { "tags": ["Motorbike slipping"], "question_id":18211, "title": "18-S2-Q11", "body": "Motorbike, wheelie, moments, slipping, maximum, acceleration.

\"q\"

[STEP II 2018 Question 11 (Mechanics)]

" }, { "tags": ["Coin toss game"], "question_id":18212, "title": "18-S2-Q12", "body": "Coin, toss, game, probability, expectation, winnings.

\"q\"

[STEP II 2018 Question 12 (Probability and Statistics)]

" }, { "tags": ["Pass the parcel"], "question_id":18213, "title": "18-S2-Q13", "body": "pass the parcel, probability, Markov, recurrence.

\"q\"

[STEP II 2018 Question 13 (Mechanics)]

" }, { "tags": ["Quadratic roots inequalities"], "question_id":18301, "title": "18-S3-Q1", "body": "Curve sketcing, inequalities, Vieta, roots, quadratics, stationary points, maximum.

\"q\"

[STEP III 2018 Question 1 (Pure)]

" }, { "tags": ["Hermite polynomials"], "question_id":18302, "title": "18-S3-Q2", "body": "Hermite, differentiation, recurrence, Fibonacci, polynomials.

\"q\"

[STEP III 2018 Question 2 (Pure)]

" }, { "tags": ["Second order differential equation"], "question_id":18303, "title": "18-S3-Q3", "body": "Sturm-Liouville, second order, 2nd order, differential equation.

\"q\"

[STEP III 2018 Question 3 (Pure)]

" }, { "tags": ["Tangent to hyperbola"], "question_id":18304, "title": "18-S3-Q4", "body": "Hyperbola, tangent, geometry, coordinate geometry, conic sections.

\"q\"

[STEP III 2018 Question 4 (Pure)]

" }, { "tags": ["Arithmetic mean - geometric mean"], "question_id":18305, "title": "18-S3-Q5", "body": "arithmetic mean, geometric mean, inequality, induction.

\"q\"

[STEP III 2018 Question 5 (Pure)]

" }, { "tags": ["Complex geometry"], "question_id":18306, "title": "18-S3-Q6", "body": "Complex numbers, Argand, geometry, circle, intersecting lines, intersection.

\"q\"

[STEP III 2018 Question 6 (Pure)]

" }, { "tags": ["Basel series"], "question_id":18307, "title": "18-S3-Q7", "body": "Complex numbers, De Moivre, binomial expansion, cotangent.

\"q\"

[STEP III 2018 Question 7 (Pure)]

" }, { "tags": ["Integrating fractional part"], "question_id":18308, "title": "18-S3-Q8", "body": "Integration, by substitution, periodic, fractional part.

\"q\"

[STEP III 2018 Question 8 (Pure)]

" }, { "tags": ["Particle bouncing"], "question_id":18309, "title": "18-S3-Q9", "body": "Collisions, particle, coefficient of restitution, recurrence relation, wall.

\"q\"

[STEP III 2018 Question 9 (Mechanics)]

" }, { "tags": ["Oscillating disc with point mass"], "question_id":18310, "title": "18-S3-Q10", "body": "Moment, inertia, disc, particle, mass, rotation, rotate, oscillation, energy, equation of motion, linearised equation.

\"q\"

[STEP III 2018 Question 10 (Mechanics)]

" }, { "tags": ["Slack pendulum"], "question_id":18311, "title": "18-S3-Q11", "body": "Circular motion, string, particle, mass, inextensible string, taut, tension, instantaneous, instantaneously, rest.

\"q\"

[STEP III 2018 Question 11 (Mechanics)]

" }, { "tags": ["Ordering samples"], "question_id":18312, "title": "18-S3-Q12", "body": "Random variable, uniform distribution, minimum, smallest, binomial expansion, probability density function, order, samples.

\"q\"

[STEP III 2018 Question 12 (Probability and Statistics)]

" }, { "tags": ["Poisson distribution"], "question_id":18313, "title": "18-S3-Q13", "body": "PGF, probability generating functino, Poisson distribution, expectation, inequality, discrete random variable.

\"q\"

[STEP III 2018 Question 13 (Probability and Statistics)]

" } ] }