Σ TMUA Practice

Real questions by topic

All 360 questions from the published TMUA papers, indexed by specification topic. Use it to see what a topic really looks like in the exam, or to find every past question on your weakest area.

360 questions9 series
Indices and surds (3)Quadratic functions (18)Simultaneous equations and inequalities (12)Polynomials, factor and remainder theorems (12)Functions and transformations (11)Sequences and series (24)Binomial expansion (12)Straight lines (7)Circles and circle theorems (13)Triangles, radians and sectors (8)Trigonometric functions and equations (33)Exponentials and logarithms (25)Differentiation (26)Integration (35)Graphs of functions (24)Number, units and estimation (4)Ratio, proportion and percentages (2)GCSE algebra (1)Angles, polygons, congruence and vectors (9)Pythagoras, mensuration and 3D (3)Statistics (3)Probability (3)The logic of arguments (24)Mathematical proof (12)Chains of reasoning (18)Identifying errors in proofs (18)

Indices and surds 3 questions

2022 · Paper 1Question 13surd expression with a and bquestion papersit online
2020 · Paper 1Question 7simultaneous equations in powers of 2question papersit online
2019 · Paper 2Question 19nested surdsquestion papersit online

Quadratic functions 18 questions

2023 · Paper 1Question 2line and parabola do not meet: range of mquestion papersit online
2023 · Paper 2Question 18x^4 + bx^2 + c = 0 has four real roots iffquestion papersit online
2022 · Paper 1Question 12family of quadratics y_kquestion papersit online
2021 · Paper 1Question 8two tangent lines to a parabolaquestion papersit online
2021 · Paper 1Question 12minimum of x^4 - p^2 x^2 is -9question papersit online
2020 · Paper 1Question 5curve y = px^2 + 6x - qquestion papersit online
2020 · Paper 1Question 8maximum of (p - x)(x + 2)question papersit online
2020 · Paper 1Question 9roots alpha, beta of x^2 - 14x + 9question papersit online
2020 · Paper 1Question 11quadratic through (2, 0) and (q, 0)question papersit online
2020 · Paper 2Question 1line crosses or touches a parabolaquestion papersit online
2019 · Paper 1Question 1quadratic through (1, -1) with vertex (-1, 3)question papersit online
2019 · Paper 1Question 2positive for all x: range of kquestion papersit online
2019 · Paper 2Question 16y = px^2 + qx + p: graph of p against rootsquestion papersit online
October 2018 · Paper 1Question 16stationary point closest to the originquestion papersit online
November 2017 · Paper 2Question 14graph of x^2 - 2Bx + c with B > bquestion papersit online
Specimen papers · Paper 1Question 9roots differ by 2question papersit online
Specimen papers · Paper 1Question 17real distinct roots for all non-zero kquestion papersit online
Practice papers · Paper 2Question 15roots differ by between 2 and 4: iff conditionquestion papersit online

Simultaneous equations and inequalities 12 questions

2022 · Paper 2Question 14two modulus inequalitiesquestion papersit online
2021 · Paper 2Question 13region defined by two inequalitiesquestion papersit online
2020 · Paper 1Question 3cubic and quadratic inequalitiesquestion papersit online
2020 · Paper 1Question 19lowest integer with x^2 - 52x - 52 > 0question papersit online
2019 · Paper 2Question 18a|x| + 1 >= |x - 2|question papersit online
October 2018 · Paper 1Question 43x^2 + 2xy = 4, x + y = aquestion papersit online
October 2018 · Paper 1Question 10|2 - x| <= 6, |y + 2| <= 4: max |xy|question papersit online
November 2017 · Paper 1Question 5combine two inequalities into onequestion papersit online
November 2017 · Paper 1Question 19solution set of x^2 + bcx + c^3 < 0question papersit online
Specimen papers · Paper 1Question 1simultaneous equations: sum of solutionsquestion papersit online
Specimen papers · Paper 1Question 4set of values satisfying an inequalityquestion papersit online
Practice papers · Paper 2Question 8region x + y > 6, x - y > -4question papersit online

Polynomials, factor and remainder theorems 12 questions

2023 · Paper 1Question 7polynomials P(x) and Q(x)question papersit online
2023 · Paper 2Question 19roots of f(x) and x f(x)question papersit online
2020 · Paper 1Question 2factors of 2x^3 + px^2 + qquestion papersit online
2020 · Paper 1Question 20(x - a)(x^2 - x + a) = 0: exactly two rootsquestion papersit online
2020 · Paper 2Question 18f - g > 0 for cubicsquestion papersit online
2019 · Paper 2Question 2factors of 2x^3 + px^2 + qquestion papersit online
October 2018 · Paper 1Question 5cubic with coefficients 1, 2, 3 in some orderquestion papersit online
November 2017 · Paper 1Question 4remainder theorem with (px - 1)question papersit online
Practice papers · Paper 1Question 2factorise a cubic with factor (x + 2)question papersit online
Specimen papers · Paper 1Question 6(x - 2) is a factor: sum of possible valuesquestion papersit online
Specimen papers · Paper 1Question 11sum of roots of a factorised quarticquestion papersit online
Specimen papers · Paper 2Question 12deductions from p(1) = 2question papersit online

Functions and transformations 11 questions

2023 · Paper 1Question 11f(kx) and f(x - c) with the same minimumquestion papersit online
2023 · Paper 1Question 20graph of f with given max and minquestion papersit online
2022 · Paper 1Question 10translations of y = x^3question papersit online
2022 · Paper 2Question 20compositions of cos and sinquestion papersit online
2021 · Paper 1Question 5multiplicative function f(mn)question papersit online
2021 · Paper 1Question 15g built from f(2^r x)question papersit online
2021 · Paper 2Question 20f(n+1)(x) = |f(n)(x) + x|question papersit online
2020 · Paper 1Question 10sequence of transformations of 4x^2question papersit online
2019 · Paper 2Question 20reflect then translate the graph of fquestion papersit online
October 2018 · Paper 2Question 10symmetry conditions f(a - x) = f(a + x)question papersit online
Specimen papers · Paper 1Question 10cos x reflected then translatedquestion papersit online

Sequences and series 24 questions

2023 · Paper 1Question 18geometric series in kquestion papersit online
2023 · Paper 2Question 16recurrence with u1 = a, u2 = bquestion papersit online
2022 · Paper 1Question 5recurrence x(n+1) = x(n) + p x(n) + qquestion papersit online
2022 · Paper 1Question 8geometric series: S30 - S20 = k S10question papersit online
2021 · Paper 1Question 3arithmetic and convergent geometric progressionsquestion papersit online
2021 · Paper 2Question 10sequence 15, 21, ...question papersit online
2020 · Paper 1Question 4GP terms in an AP; sum to infinity 12question papersit online
2020 · Paper 2Question 14sum of first 4 terms = sum of first 8 termsquestion papersit online
2019 · Paper 1Question 4sequence x(n+1) = sqrt(x(n))question papersit online
2019 · Paper 1Question 5S6 = 9 S3, seventh term 360question papersit online
2019 · Paper 2Question 11integer arithmetic series summing to 20question papersit online
October 2018 · Paper 1Question 2S5 = S8 in an arithmetic progressionquestion papersit online
October 2018 · Paper 1Question 8sum to infinity of squares and cubesquestion papersit online
October 2018 · Paper 2Question 7numbers in both arithmetic progressionsquestion papersit online
October 2018 · Paper 2Question 16median of an integer arithmetic progressionquestion papersit online
November 2017 · Paper 1Question 7p, q, p^2 arithmetic and p, p^2, q geometricquestion papersit online
November 2017 · Paper 1Question 11recurrence x(n+1) = (23x(n) - 53)/(5x(n) + 1)question papersit online
November 2017 · Paper 2Question 3sum to infinity from the first and fourth termsquestion papersit online
November 2017 · Paper 2Question 15Collatz-style recurrencequestion papersit online
Practice papers · Paper 1Question 4sum of (-1)^n termsquestion papersit online
Practice papers · Paper 1Question 14sum of two geometric seriesquestion papersit online
Specimen papers · Paper 1Question 19geometric series terms forming an arithmetic seriesquestion papersit online
Practice papers · Paper 2Question 12S8 > 3S6: signs of a and dquestion papersit online
Specimen papers · Paper 2Question 16sequence with (-1)^n termsquestion papersit online

Binomial expansion 12 questions

2023 · Paper 1Question 6coefficients of (2 + 3x)^12 divisible by 12question papersit online
2022 · Paper 2Question 2coefficient of x^5 in (1 + x)^5 times a sumquestion papersit online
2021 · Paper 1Question 16third term of (a + bx)^n is 105x^2question papersit online
2020 · Paper 1Question 13coefficient of x^2 y^4 in (1 + x + y^2)^7question papersit online
2019 · Paper 1Question 3coefficient of x in a sum of (1 + x)^nquestion papersit online
2019 · Paper 2Question 1coefficient of x^4 in (x^2/2 + x)^6question papersit online
October 2018 · Paper 1Question 7equal coefficients of x^6question papersit online
October 2018 · Paper 2Question 2constant term in (x - 2/x^2)^12question papersit online
November 2017 · Paper 1Question 13coefficient of x^4 is 8 times coefficient of x^2question papersit online
Practice papers · Paper 1Question 1expansion of (ax + b)^3question papersit online
Practice papers · Paper 1Question 19coefficients in (1 + 2x + 3x^2)^6 and (1 - ax^2)^5question papersit online
Specimen papers · Paper 1Question 20coefficient in an expansionquestion papersit online

Straight lines 7 questions

2023 · Paper 1Question 16right-angled triangle from coordinatesquestion papersit online
2023 · Paper 2Question 14three lines ax + by + c = 0 ...question papersit online
2021 · Paper 2Question 2diagonal of a squarequestion papersit online
2021 · Paper 2Question 7line bisecting a circle and a squarequestion papersit online
November 2017 · Paper 1Question 3area enclosed by two perpendicular lines and the x-axisquestion papersit online
November 2017 · Paper 2Question 2rectangle PQRS from two verticesquestion papersit online
Specimen papers · Paper 1Question 3perpendicular bisector meets an axisquestion papersit online

Circles and circle theorems 13 questions

2023 · Paper 1Question 13maximum distance between points on two circlesquestion papersit online
2023 · Paper 1Question 17family of circles x^2 + y^2 = 2n(x + y)question papersit online
2022 · Paper 1Question 2when x^2 - 2px + y^2 - 6y ... is a circlequestion papersit online
2022 · Paper 1Question 19two circles: C1 radius 5, C2 radius 4question papersit online
2021 · Paper 1Question 1two circles of equal radiusquestion papersit online
2021 · Paper 2Question 15x^2 + ax + y^2 + by + c = 0question papersit online
2020 · Paper 1Question 16common tangent to two circlesquestion papersit online
2019 · Paper 1Question 6two circles touchingquestion papersit online
October 2018 · Paper 1Question 3shortest distance between two circlesquestion papersit online
November 2017 · Paper 1Question 6tangent to x^2 + y^2 = 144 through (20, 0)question papersit online
November 2017 · Paper 1Question 9regular hexagon inscribed in a circlequestion papersit online
Practice papers · Paper 1Question 9circle translated, reflected and enlargedquestion papersit online
Specimen papers · Paper 2Question 1radius of x^2 + y^2 - 8x + 12y + 15 = 0question papersit online

Triangles, radians and sectors 8 questions

2023 · Paper 1Question 8'fun' triangles: sine rule ambiguous casequestion papersit online
2022 · Paper 1Question 4similar sectors: arc, area and perimeterquestion papersit online
2022 · Paper 1Question 14triangle in a circle of radius 6question papersit online
2022 · Paper 1Question 17two non-congruent triangles: the ambiguous case with sides x - 1 and sqrt(-x^2 + 6x - 5)question papersit online
2021 · Paper 2Question 18can the triangle be drawn?question papersit online
October 2018 · Paper 1Question 19two possible triangles: the larger onequestion papersit online
October 2018 · Paper 2Question 14values of p that determine PQ uniquelyquestion papersit online
November 2017 · Paper 1Question 20range of an angle in a triangle with sides a, a + d, a + 2dquestion papersit online

Trigonometric functions and equations 33 questions

2023 · Paper 1Question 4sum of sinesquestion papersit online
2023 · Paper 1Question 9count solutions of (1 + 3cos 3x)^2 = 4question papersit online
2023 · Paper 1Question 12solutions of 2tan^2 x sin 2x = 1question papersit online
2023 · Paper 1Question 15max minus min of a cos xquestion papersit online
2023 · Paper 2Question 12number of solutions of sin x cos^2 x = p^2 sin xquestion papersit online
2022 · Paper 1Question 12cos^4 - 5cos^2 + 3 = 0: number of solutionsquestion papersit online
2022 · Paper 1Question 9f - g = 2 sin x, fg = cos^2 x: minimum of fquestion papersit online
2022 · Paper 1Question 167x^4 - 6x^2 + 1 = 0 with cos to sinquestion papersit online
2021 · Paper 1Question 6max minus min of a trig functionquestion papersit online
2021 · Paper 1Question 14(x + 1)(3 - x) = 2(1 - cos x)question papersit online
2021 · Paper 1Question 19equation with exactly three solutionsquestion papersit online
2021 · Paper 2Question 19how many angles make an expression zeroquestion papersit online
2020 · Paper 1Question 123cos x = x: number of solutionsquestion papersit online
2020 · Paper 1Question 181 - 2cos^2 x = |cos x|question papersit online
2020 · Paper 2Question 2tan = 2 in the fourth quadrantquestion papersit online
2020 · Paper 2Question 9evaluating x sin x with a degrees calculatorquestion papersit online
2020 · Paper 2Question 15necessary and sufficient condition involving sinquestion papersit online
2019 · Paper 1Question 14simultaneous trig equationsquestion papersit online
2019 · Paper 1Question 17fraction of an interval satisfying a trig inequalityquestion papersit online
2019 · Paper 1Question 19sum of sin(10 + 90k)question papersit online
October 2018 · Paper 1Question 6x sin 2x = cos 2x: number of solutionsquestion papersit online
October 2018 · Paper 1Question 18line of symmetry of sin(2x - 4pi/3)question papersit online
October 2018 · Paper 1Question 20sum of sin^2 0 to sin^2 90question papersit online
October 2018 · Paper 2Question 4cos x = c has two solutions: cos^2 2x = c^2question papersit online
November 2017 · Paper 1Question 8(1 - 2 sin x) cos x >= 0question papersit online
November 2017 · Paper 2Question 12graphs of sin 2x and cos 2xquestion papersit online
Specimen papers · Paper 1Question 2sin 3x = cos 3x on [0, 4pi]question papersit online
Practice papers · Paper 1Question 8cos^2 2x + sqrt3 sin 2x - 7/4 = 0question papersit online
Practice papers · Paper 1Question 17where (1 + 2cos x)cos 2x is negativequestion papersit online
Specimen papers · Paper 1Question 18total length of intervals: tan and sin conditionsquestion papersit online
Practice papers · Paper 2Question 38 sin^2 x + 4 cos^2 x = 7question papersit online
Specimen papers · Paper 2Question 11which value is largest (radians)question papersit online
Practice papers · Paper 2Question 17y = 3 sin x + 2 and y = x + cquestion papersit online

Exponentials and logarithms 25 questions

2023 · Paper 2Question 6a^x = x: same number of solutionsquestion papersit online
2022 · Paper 1Question 6integral between log2 5 and log2 20question papersit online
2022 · Paper 1Question 11sum of logs from 1 to 100question papersit online
2022 · Paper 2Question 15log_x y = z and log_y z = xquestion papersit online
2021 · Paper 1Question 4minimum of 2^2x - 2^(x+3) + 4question papersit online
2021 · Paper 1Question 20length of a curve given by a log equationquestion papersit online
2021 · Paper 2Question 14simultaneous equations with log2 yquestion papersit online
2021 · Paper 2Question 17log2 log2 x and its squarequestion papersit online
2020 · Paper 1Question 6maximum of an expression in 5^xquestion papersit online
2020 · Paper 1Question 15quartic in log2 xquestion papersit online
2019 · Paper 1Question 11simultaneous log equationsquestion papersit online
2019 · Paper 1Question 13maximum of 4^sin x - 4 . 2^sin x + 417question papersit online
2019 · Paper 1Question 152(9^x) + 8(3^x) = 4question papersit online
2019 · Paper 2Question 15log(ab^2 c) = 7 and similarquestion papersit online
October 2018 · Paper 1Question 14line through (3, log2 p) and (log2 p, 4)question papersit online
October 2018 · Paper 1Question 153^x - sqrt(3)^(x+4) + 20 = 0question papersit online
October 2018 · Paper 2Question 19inequalities in 2^x, 5^x, 7^xquestion papersit online
November 2017 · Paper 1Question 14simultaneous equations in 2^x and 2^yquestion papersit online
November 2017 · Paper 1Question 18translation of log10 x as a stretchquestion papersit online
November 2017 · Paper 2Question 8which number is smallestquestion papersit online
Specimen papers · Paper 1Question 5log equation: express in terms of ...question papersit online
Specimen papers · Paper 1Question 8positive reals and a log relationshipquestion papersit online
Practice papers · Paper 1Question 114^2x + 12 = 2^(2x+3)question papersit online
Practice papers · Paper 1Question 16simultaneous log10 equationsquestion papersit online
Specimen papers · Paper 2Question 5approximating log 2 from 2^10 ~ 10^3question papersit online

Differentiation 26 questions

2023 · Paper 1Question 14cubic with three distinct real rootsquestion papersit online
2022 · Paper 1Question 15largest rectangle between two parabolasquestion papersit online
2022 · Paper 2Question 1stationary points of 3x^4 + 4x^3 + 6x^2 - 5question papersit online
2021 · Paper 1Question 11fraction of an interval where f decreasesquestion papersit online
2021 · Paper 2Question 8exists c with p'(c) = 0question papersit online
2020 · Paper 1Question 1derivative of (x^3 - 5x^2) / (2x sqrt x)question papersit online
2019 · Paper 1Question 7gradient at x = -1 as a function of qquestion papersit online
2019 · Paper 1Question 18shortest distance from a parabola to a linequestion papersit online
2019 · Paper 2Question 14statements p(a), p(b), p'(a), p'(b)question papersit online
October 2018 · Paper 1Question 92x^3 - 3x^2 - 12x + c: three real rootsquestion papersit online
October 2018 · Paper 1Question 11normal to y = 10 - x^2question papersit online
October 2018 · Paper 1Question 13graph of f': which point is a local minimum of fquestion papersit online
October 2018 · Paper 2Question 1f(x) = (x^3 - 4x)/... for x > 0question papersit online
October 2018 · Paper 2Question 15x^3 + 3qx^2 + 2 with three distinct rootsquestion papersit online
November 2017 · Paper 1Question 2f''(1) for (2/x - 1/(2x^2))^2question papersit online
November 2017 · Paper 1Question 10greatest gradient of a normal as p variesquestion papersit online
November 2017 · Paper 1Question 16one function increasing, the other decreasingquestion papersit online
November 2017 · Paper 2Question 1derivative of (1 - 3x)^2 / (2x^(3/2))question papersit online
Practice papers · Paper 1Question 3normal to y = 2/x^2: length PQquestion papersit online
Practice papers · Paper 1Question 12largest cylinder inside a spherequestion papersit online
Practice papers · Paper 1Question 15least gradient at x = 1 as a variesquestion papersit online
Specimen papers · Paper 1Question 15smallest possible value as x variesquestion papersit online
Practice papers · Paper 1Question 18where (1 - x)/x^(2/3) decreasesquestion papersit online
Practice papers · Paper 2Question 2derivative of (x^2 + 5)(2x)/x^(3/4)question papersit online
Specimen papers · Paper 2Question 2gradient at x = 2question papersit online
Practice papers · Paper 2Question 6sequence f(n+1) = x f(n)'question papersit online

Integration 35 questions

2023 · Paper 1Question 1definite integrals of ax + b fix a and bquestion papersit online
2023 · Paper 1Question 3combining integrals over adjacent rangesquestion papersit online
2023 · Paper 1Question 10trapezium rule error for sqrt(4 - x^2)question papersit online
2023 · Paper 1Question 19dy/dx = |-6x|question papersit online
2023 · Paper 2Question 2difference of two definite integralsquestion papersit online
2023 · Paper 2Question 17integral of the ceiling functionquestion papersit online
2023 · Paper 2Question 20statements about I(p, q)question papersit online
2022 · Paper 1Question 3f'(x) <= a with an integral conditionquestion papersit online
2022 · Paper 1Question 7area enclosed by y = x^2 - 4|x| - 12question papersit online
2022 · Paper 2Question 12ordering three integralsquestion papersit online
2021 · Paper 1Question 2integral between turning points of a cubicquestion papersit online
2021 · Paper 1Question 7x f(x) > 0 and an integralquestion papersit online
2021 · Paper 1Question 10trapezium rule for log10 xquestion papersit online
2021 · Paper 1Question 13integrals over unit intervalsquestion papersit online
2021 · Paper 2Question 1definite integral of a rational expressionquestion papersit online
2021 · Paper 2Question 12statements about f <= g and integrals/derivativesquestion papersit online
2020 · Paper 1Question 14area between y = mx and y = x^3 is 6question papersit online
2020 · Paper 2Question 12when the trapezium rule overestimatesquestion papersit online
2020 · Paper 2Question 13function identity involving integralsquestion papersit online
2019 · Paper 1Question 8trapezium rule underestimatequestion papersit online
2019 · Paper 1Question 9area between y = px and x = pyquestion papersit online
2019 · Paper 1Question 10integral of |x|(1 - x)question papersit online
2019 · Paper 1Question 12dV/dt = 24(t - 1)question papersit online
2019 · Paper 1Question 16combining integrals with unknown fquestion papersit online
2019 · Paper 2Question 13trapezium rule for sin^2 x overestimatequestion papersit online
October 2018 · Paper 1Question 1integral of |3 - 2x|question papersit online
November 2017 · Paper 1Question 1find y from dy/dx = 3x^2 - (2 - 3x)/x^3question papersit online
November 2017 · Paper 1Question 12integral of f(x + 2) + 1question papersit online
November 2017 · Paper 1Question 15trapezium rule over/under for three related curvesquestion papersit online
November 2017 · Paper 1Question 17F(n) as an integral, G(n) as a sumquestion papersit online
November 2017 · Paper 2Question 6sequence defined by integralsquestion papersit online
November 2017 · Paper 2Question 11area under an increasing f between a and bquestion papersit online
Practice papers · Paper 1Question 5area between y = x^2 - 1 and the x-axisquestion papersit online
Practice papers · Paper 2Question 1integral of (x^2 - 4/x^2)^2question papersit online
Practice papers · Paper 2Question 18counterexample about integrals of f^2 and fquestion papersit online

Graphs of functions 24 questions

2022 · Paper 1Question 18f(x) = x^2(x - 1)^2(x - 2) and g(x)question papersit online
2022 · Paper 1Question 20intersections of y = |x^2 - a^2| and y = a^2 |x - 1|question papersit online
2022 · Paper 2Question 18identify graphs of (cos x)^cos x etc.question papersit online
2021 · Paper 1Question 9area enclosed by |x| + |y| = 1question papersit online
2021 · Paper 1Question 17sketch of sin(x^2 + y^2) = 1question papersit online
2021 · Paper 1Question 18parabola rotated 90 degreesquestion papersit online
2021 · Paper 2Question 9statements about a cubicquestion papersit online
2021 · Paper 2Question 16x|x| = px + q: number of solutionsquestion papersit online
2020 · Paper 1Question 17y = mx + c meets y = sqrt(x) twicequestion papersit online
2020 · Paper 2Question 5graph of 2^x / (1 + 2^x)question papersit online
2019 · Paper 1Question 20range of k for curves to intersectquestion papersit online
October 2018 · Paper 1Question 12quartic x(x - p)(x - q)(r - x)question papersit online
October 2018 · Paper 2Question 112^x = mx + c statementsquestion papersit online
October 2018 · Paper 2Question 20|x + p| + |x| = p has a solutionquestion papersit online
November 2017 · Paper 2Question 7graphs of a^x and f(x)question papersit online
Practice papers · Paper 1Question 10x tan x = 1: number of solutionsquestion papersit online
Practice papers · Paper 1Question 13real roots of 3x^5 - 10x^3 - 120x + 30question papersit online
Specimen papers · Paper 1Question 13number of real roots of a quarticquestion papersit online
Specimen papers · Paper 2Question 7sketch of (x + y)(x - y + 1) = ...question papersit online
Specimen papers · Paper 2Question 10sketch of log x for x > 1question papersit online
Practice papers · Paper 2Question 11polynomial with roots at -p and pquestion papersit online
Practice papers · Paper 2Question 14quartic: numbers of solutions of f(x) = kquestion papersit online
Specimen papers · Paper 2Question 14sketch of a degree-5 polynomialquestion papersit online
Specimen papers · Paper 2Question 19equation with three real roots, one positivequestion papersit online

Number, units and estimation 4 questions

2023 · Paper 2Question 15binary fractionsquestion papersit online
November 2017 · Paper 2Question 13standard form additionquestion papersit online
Specimen papers · Paper 1Question 16when an expression is an integerquestion papersit online
Specimen papers · Paper 2Question 6bounds: area and width of a rectanglequestion papersit online

Ratio, proportion and percentages 2 questions

Practice papers · Paper 1Question 6mixing paintsquestion papersit online
Specimen papers · Paper 1Question 14related positive variablesquestion papersit online

GCSE algebra 1 questions

2023 · Paper 2Question 1solve an equation with algebraic fractionsquestion papersit online

Angles, polygons, congruence and vectors 9 questions

2023 · Paper 1Question 5shape with two lines of symmetryquestion papersit online
2022 · Paper 2Question 11kite: necessary and sufficient for a right anglequestion papersit online
2022 · Paper 2Question 19polygon inscribed in a circlequestion papersit online
2020 · Paper 2Question 7conditions on a parallelogramquestion papersit online
2019 · Paper 2Question 10necessary but not sufficient for a parallelogramquestion papersit online
October 2018 · Paper 2Question 5quadrilateral with perpendicular diagonalsquestion papersit online
Practice papers · Paper 2Question 9conditions implying congruent trianglesquestion papersit online
Practice papers · Paper 2Question 16line through the diagonals' intersection of a trapeziumquestion papersit online
Practice papers · Paper 2Question 20interior angles of regular polygons in ratio 3 : 4question papersit online

Pythagoras, mensuration and 3D 3 questions

Specimen papers · Paper 1Question 12triangular prism: surface area and volumequestion papersit online
Practice papers · Paper 1Question 20shortest path on a pyramidquestion papersit online
Practice papers · Paper 2Question 19plans and elevations: counting cubesquestion papersit online

Statistics 3 questions

2020 · Paper 2Question 17means and medians of split setsquestion papersit online
October 2018 · Paper 1Question 17exchanging data between two setsquestion papersit online
Specimen papers · Paper 2Question 18five numbers with mean 0 and range 20question papersit online

Probability 3 questions

2019 · Paper 2Question 12three probabilities for chosen studentsquestion papersit online
Practice papers · Paper 1Question 7sports club: women who play tennisquestion papersit online
Specimen papers · Paper 1Question 7two balls without replacementquestion papersit online

The logic of arguments 24 questions

2023 · Paper 2Question 5necessary/sufficient: k and an integral of sin 2xquestion papersit online
2023 · Paper 2Question 7necessary but not sufficient: line with positive gradient and interceptquestion papersit online
2023 · Paper 2Question 9pentagon statement, converse and contrapositivequestion papersit online
2023 · Paper 2Question 11if 2^k + 1 is prime then k is a power of 2question papersit online
2023 · Paper 2Question 13sufficient condition for three of four statementsquestion papersit online
2022 · Paper 2Question 4sufficient information to find a distance to a circle centrequestion papersit online
2022 · Paper 2Question 5line through (1, 2): statement, converse, contrapositivequestion papersit online
2022 · Paper 2Question 6n odd vs median is in the listquestion papersit online
2022 · Paper 2Question 9for all x, if x < k then x^2 < kquestion papersit online
2022 · Paper 2Question 10quantifier statements about real x and integer nquestion papersit online
2021 · Paper 2Question 3necessary conditions for a probabilityquestion papersit online
2021 · Paper 2Question 6three roots vs two stationary pointsquestion papersit online
2020 · Paper 2Question 6necessary conditions for an integral to be zeroquestion papersit online
2020 · Paper 2Question 20exactly one statement is truequestion papersit online
2019 · Paper 2Question 3ab = ac: what must be truequestion papersit online
2019 · Paper 2Question 5ab divisible by n: necessary/sufficientquestion papersit online
2019 · Paper 2Question 17multiple-choice options about a statementquestion papersit online
October 2018 · Paper 2Question 18necessary condition for f(a) + f(b) >= f((a + b)/2)question papersit online
November 2017 · Paper 2Question 10sufficient condition for an integral to be zeroquestion papersit online
November 2017 · Paper 2Question 16if f(x) integer for integer x then f'(x) ...question papersit online
November 2017 · Paper 2Question 19sufficient condition for exactly one real rootquestion papersit online
Specimen papers · Paper 2Question 4cards with letters and numbers: counterexamplequestion papersit online
Specimen papers · Paper 2Question 9negating 'every day next week'question papersit online
Practice papers · Paper 2Question 10sufficient to conclude x < yquestion papersit online

Mathematical proof 12 questions

2023 · Paper 2Question 3claim about sqrt(xy) = sqrt(x)sqrt(y)question papersit online
2022 · Paper 2Question 3counterexample: n prime, n^2 + 2 not primequestion papersit online
2021 · Paper 2Question 4counterexample: a divides bcquestion papersit online
2020 · Paper 2Question 4N > 6 as a sum of two non-primesquestion papersit online
2019 · Paper 2Question 4conjecture about 10...01 being primequestion papersit online
2019 · Paper 2Question 7counterexample from 12^2 + 16^2 = 20^2question papersit online
October 2018 · Paper 2Question 6counterexample: f' > 0 but f not positivequestion papersit online
October 2018 · Paper 2Question 12N(Km + 1) - 1 is never primequestion papersit online
November 2017 · Paper 2Question 591 = 7 x 13 as a counterexamplequestion papersit online
Practice papers · Paper 2Question 5counting counterexamples to a primality claimquestion papersit online
Practice papers · Paper 2Question 7ordering the lines of a logarithm proofquestion papersit online
Specimen papers · Paper 2Question 8sum of four consecutive integers is a multiple of 6question papersit online

Chains of reasoning 18 questions

2023 · Paper 2Question 8lines dividing a triangle into right-angled trianglesquestion papersit online
2022 · Paper 2Question 8pigeonhole in 1, 4, 7, ..., 70question papersit online
2022 · Paper 2Question 13exists y with x - xy + y negativequestion papersit online
2022 · Paper 2Question 16min and max of sequences a = b + cquestion papersit online
2020 · Paper 2Question 10inequalities in a, b, c, dquestion papersit online
2020 · Paper 2Question 11spiral line on a gridquestion papersit online
2020 · Paper 2Question 19nine people on a 3 by 3 gridquestion papersit online
2019 · Paper 2Question 8a < b < c < 0 inequalitiesquestion papersit online
2019 · Paper 2Question 940 chairs round a tablequestion papersit online
October 2018 · Paper 2Question 8mountain profiles: countingquestion papersit online
October 2018 · Paper 2Question 17squaresum numbersquestion papersit online
November 2017 · Paper 2Question 17'stapled' sets of whole numbersquestion papersit online
November 2017 · Paper 2Question 20forgotten password puzzlequestion papersit online
Practice papers · Paper 2Question 4five urns, exactly one true statementquestion papersit online
Specimen papers · Paper 2Question 13five runners: who beat whomquestion papersit online
Specimen papers · Paper 2Question 15three statements about real numbersquestion papersit online
Specimen papers · Paper 2Question 17S-numbersquestion papersit online
Specimen papers · Paper 2Question 20five logiciansquestion papersit online

Identifying errors in proofs 18 questions

2023 · Paper 2Question 4student's attempt: consecutive odd primesquestion papersit online
2023 · Paper 2Question 10solving x^4 - 2x^2 - 3 < 0 by completing the squarequestion papersit online
2022 · Paper 2Question 7difference of consecutive cubes is always primequestion papersit online
2022 · Paper 2Question 17student proves the converse (cubic roots)question papersit online
2021 · Paper 2Question 5first error: cos x = sqrt(1 - sin^2 x)question papersit online
2021 · Paper 2Question 11student's attempt: a^2 - 4b^3question papersit online
2020 · Paper 2Question 3divisibility argument with 9^n and 3^nquestion papersit online
2020 · Paper 2Question 8proof about |a + b| < |a| + |b|question papersit online
2020 · Paper 2Question 16student uses the FTC wronglyquestion papersit online
2019 · Paper 2Question 6student solves cos x + sin x tan x = 2 sin x - 1question papersit online
October 2018 · Paper 2Question 3average speed of a two-part journeyquestion papersit online
October 2018 · Paper 2Question 9attempt to solve 4x sqrt(2x - 1) = 10x - 5question papersit online
October 2018 · Paper 2Question 13attempted proof: tan > 0 implies sin + cos > 1question papersit online
November 2017 · Paper 2Question 4student finds sin 2x from tan x = 3question papersit online
November 2017 · Paper 2Question 9attempted proof of a^3 + b^3 = c^3 having no solutionsquestion papersit online
November 2017 · Paper 2Question 18solving (1/2)^n < 1/10 with logsquestion papersit online
Specimen papers · Paper 2Question 3attempt to solve sqrt(x + 5) = x + 3question papersit online
Practice papers · Paper 2Question 13attempted proof about a dividing bcquestion papersit online