Free resource · Cambridge AS & A Level Mathematics 9709
AS & A Level Mathematics 9709 past paper questions by topic (2022–2025)
Every question from the 140 papers of 2022–2025 — Paper 1 (Pure Mathematics 1), Paper 3 (Pure Mathematics 3), Paper 4 (Mechanics), Paper 5 (Probability & Statistics 1), Paper 6 (Probability & Statistics 2) — sorted into the 32 chapters of our Mathematics notes: 1,306 questions. Pick a chapter, then open the official paper and go straight to the question number. Questions on content that is no longer in the current syllabus are left out.
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- P1 Quadratics (30)
- P1 Functions (50)
- P1 Coordinate Geometry (34)
- P1 Circular Measure (30)
- P1 Trigonometry (38)
- P1 Series (62)
- P1 Differentiation (61)
- P1 Integration (53)
- P3 Algebra (58)
- P3 Logarithmic and Exponential Functions (29)
- P3 Trigonometry (30)
- P3 Differentiation (53)
- P3 Integration (46)
- P3 Numerical Solution of Equations (26)
- P3 Vectors (28)
- P3 Differential Equations (28)
- P3 Complex Numbers (48)
- M1 Forces and Equilibrium (33)
- M1 Kinematics of Motion in a Straight Line (56)
- M1 Momentum (23)
- M1 Newton's Laws of Motion (42)
- M1 Energy, Work and Power (48)
- S1 Representation of Data (35)
- S1 Permutations and Combinations (34)
- S1 Probability (26)
- S1 Discrete Random Variables (61)
- S1 The Normal Distribution (34)
- S2 The Poisson Distribution (43)
- S2 Linear Combinations of Random Variables (28)
- S2 Continuous Random Variables (29)
- S2 Sampling and Estimation (55)
- S2 Hypothesis Tests (55)
Chapter 1: P1 Quadratics
30 past-paper questions
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Paper 1 (Pure Mathematics 1): 30 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q1 | 4 | Discriminant condition for two distinct roots |
| Oct/Nov 2025 · Paper 11 | Q4 (a) | 3 | Completing the square with negative quadratic |
| Oct/Nov 2025 · Paper 12 | Q1 | 5 | Completing the square, no real roots, exact roots |
| Oct/Nov 2025 · Paper 13 | Q10 | 9 | Completing the square, range and root conditions |
| May/June 2025 · Paper 11 | Q6 | 9 | Intersection of curve and line, discriminant |
| May/June 2025 · Paper 12 | Q2 | 4 | Simultaneous curve and line intersection |
| Feb/March 2025 · Paper 12 | Q1 | 4 | Quadratic inequality for no intersection |
| Oct/Nov 2024 · Paper 11 | Q4 | 5 | Line and curve always meet via discriminant |
| Oct/Nov 2024 · Paper 12 | Q9 | 10 | Intersections and non-intersection of line and curve |
| Oct/Nov 2024 · Paper 13 | Q9 (a) | 3 | Intersections of two cubic curves |
| May/June 2024 · Paper 11 | Q1 | 5 | Completing the square then solving quartic |
| Feb/March 2024 · Paper 12 | Q7 | 6 | Tangency of line and curve, discriminant |
| Oct/Nov 2023 · Paper 11 | Q2 | 4 | Comparing intersections using discriminant |
| Oct/Nov 2023 · Paper 11 | Q8 (a) | 4 | Solving equation by substitution for intersections |
| Oct/Nov 2023 · Paper 12 | Q6 (a) | 2 | Minimum point by completing the square |
| Oct/Nov 2023 · Paper 12 | Q9 (a) | 4 | Intersections of two curves with substitution |
| Oct/Nov 2023 · Paper 13 | Q6 | 7 | Tangency of line and curve using discriminant |
| May/June 2023 · Paper 11 | Q5 | 5 | Tangent line to a curve, finding constant |
| May/June 2023 · Paper 12 | Q3 | 3 | Completing square and no real roots |
| May/June 2023 · Paper 12 | Q4 | 3 | Equation quadratic in a power of x |
| May/June 2023 · Paper 13 | Q2 | 4 | Completing square and range inequality |
| Feb/March 2023 · Paper 12 | Q1 | 4 | Showing line and curve always meet using discriminant |
| Oct/Nov 2022 · Paper 11 | Q1 | 3 | Forming and solving a quadratic from a fraction |
| Oct/Nov 2022 · Paper 12 | Q3 (a) | 2 | Discriminant for no real roots |
| Oct/Nov 2022 · Paper 12 | Q6 | 9 | Completing the square, solving and sketching quadratic |
| May/June 2022 · Paper 11 | Q1 | 4 | Completing the square and solving exactly |
| May/June 2022 · Paper 11 | Q7 (a) | 4 | Intersection of curve and line |
| May/June 2022 · Paper 12 | Q5 | 9 | Line and curve intersection and tangency |
| Feb/March 2022 · Paper 12 | Q2 | 5 | Discriminant for line and curve meeting twice |
| Feb/March 2022 · Paper 12 | Q5 (a) | 2 | Completing the square for a quadratic |
Chapter 2: P1 Functions
50 past-paper questions
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Paper 1 (Pure Mathematics 1): 50 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q4 (b) | 3 | Reflection and translation from quadratic form |
| Oct/Nov 2025 · Paper 11 | Q6 | 7 | Range, inverse and composite function equation |
| Oct/Nov 2025 · Paper 12 | Q3 | 5 | Describing combined graph transformations |
| Oct/Nov 2025 · Paper 12 | Q9 (b)–(d) | 4 | Inverse existence, range and composite condition |
| Oct/Nov 2025 · Paper 13 | Q6 | 8 | Sequence of transformations of cubic curve |
| Oct/Nov 2025 · Paper 13 | Q7 | 4 | Inverse function and self-inverse check |
| May/June 2025 · Paper 11 | Q10 | 12 | Describing transformations, inverse and composite functions |
| May/June 2025 · Paper 12 | Q1 | 4 | Describing two transformations from graphs |
| May/June 2025 · Paper 12 | Q11 | 9 | Completing square, inverse and composite inverse |
| May/June 2025 · Paper 13 | Q10 (c) | 4 | Translation and reflection of curve |
| May/June 2025 · Paper 13 | Q11 | 10 | Range of quadratic and inverse composition |
| Feb/March 2025 · Paper 12 | Q11 | 10 | Composite function, transformations and range |
| Oct/Nov 2024 · Paper 11 | Q11 | 11 | Completing square, transformations and inverse function |
| Oct/Nov 2024 · Paper 12 | Q5 | 10 | Inverse and composite function, graph of inverse |
| Oct/Nov 2024 · Paper 13 | Q5 | 8 | Sequence of transformations from graph and function form |
| Oct/Nov 2024 · Paper 13 | Q8 | 9 | Completing square, restricted domain, inverse and composite |
| May/June 2024 · Paper 11 | Q2 | 6 | Trig graph transformations and function rule |
| May/June 2024 · Paper 11 | Q6 | 7 | Inverse function graph, expression and solving |
| May/June 2024 · Paper 12 | Q2 | 5 | Sequence of transformations from quadratic to another |
| May/June 2024 · Paper 12 | Q4 | 7 | Inverse, range and composite function equation |
| May/June 2024 · Paper 13 | Q6 (b) | 3 | Stretch and translation of a curve |
| May/June 2024 · Paper 13 | Q11 | 9 | Range by completing square and inverse composite |
| Feb/March 2024 · Paper 12 | Q2 | 4 | Sine graph and transformations |
| Feb/March 2024 · Paper 12 | Q9 | 9 | Range of composite function and inverse |
| Oct/Nov 2023 · Paper 11 | Q4 | 6 | Order of reflection and translation |
| Oct/Nov 2023 · Paper 11 | Q9 | 9 | Completing the square, composite and inverse functions |
| Oct/Nov 2023 · Paper 12 | Q6 (b)–(c) | 6 | Stretch and translation of a curve |
| Oct/Nov 2023 · Paper 12 | Q8 | 8 | Inverse, domain, range and composite equation |
| Oct/Nov 2023 · Paper 13 | Q7 | 7 | Range, inverse, domain and composite function |
| Oct/Nov 2023 · Paper 13 | Q8 (b) | 3 | Transformed stationary point |
| May/June 2023 · Paper 11 | Q3 | 4 | Describing two graph transformations |
| May/June 2023 · Paper 11 | Q8 | 8 | Composite function constants, domain and inverse |
| May/June 2023 · Paper 12 | Q8 | 12 | Inverse function graph and expression |
| May/June 2023 · Paper 13 | Q1 | 4 | Transformation effect on a line graph |
| May/June 2023 · Paper 13 | Q7 | 8 | Range, inverse and composite function |
| Feb/March 2023 · Paper 12 | Q2 | 4 | Sequence of graph transformations on a function |
| Feb/March 2023 · Paper 12 | Q9 | 9 | Range, inverse and composite function equation |
| Oct/Nov 2022 · Paper 11 | Q8 | 8 | Increasing test, inverse and self-inverse function |
| Oct/Nov 2022 · Paper 11 | Q9 | 8 | Completing the square and linking transformations |
| Oct/Nov 2022 · Paper 12 | Q5 | 5 | Stretch and translation of a graph |
| Oct/Nov 2022 · Paper 12 | Q9 | 8 | Composite functions, inverse existence and domain |
| Oct/Nov 2022 · Paper 13 | Q2 | 6 | Completing the square, range and inverse |
| Oct/Nov 2022 · Paper 13 | Q5 | 6 | Reading transformations of a circle from graph |
| May/June 2022 · Paper 11 | Q6 | 8 | Inverse, range and composite function existence |
| May/June 2022 · Paper 11 | Q8 (a) | 5 | Describing combined graph transformations |
| May/June 2022 · Paper 12 | Q10 (a)–(d) | 7 | Inverse, composite and domain of functions |
| May/June 2022 · Paper 13 | Q4 | 5 | Translation and single stretch of a curve |
| May/June 2022 · Paper 13 | Q6 | 8 | Completing the square, range, inverse and composite |
| Feb/March 2022 · Paper 12 | Q5 (b) | 4 | Describing a sequence of graph transformations |
| Feb/March 2022 · Paper 12 | Q9 | 8 | Composite functions and solving with surds |
Chapter 3: P1 Coordinate Geometry
34 past-paper questions
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Paper 1 (Pure Mathematics 1): 34 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q10 | 7 | Circle and line intersection, triangle area |
| Oct/Nov 2025 · Paper 12 | Q7 | 11 | Circle on diameter, tangents and intersection |
| Oct/Nov 2025 · Paper 13 | Q8 | 8 | Circle on diameter and parallel tangents |
| May/June 2025 · Paper 11 | Q8 | 8 | Triangle from tangents and chord of a circle |
| May/June 2025 · Paper 12 | Q8 | 9 | Circle and line intersection, angle and segment area |
| May/June 2025 · Paper 13 | Q9 | 9 | Perpendicular lines, circle through three points, tangent |
| Feb/March 2025 · Paper 12 | Q6 | 6 | Circle tangent to axes, distance, tangent gradient |
| Oct/Nov 2024 · Paper 11 | Q6 | 7 | Distance between circles and extreme distances |
| Oct/Nov 2024 · Paper 12 | Q8 | 10 | Circle equation, normal and tangent conditions |
| Oct/Nov 2024 · Paper 13 | Q10 | 9 | Circle through two points with given radius |
| May/June 2024 · Paper 11 | Q10 | 8 | Tangent lines to a circle through external point |
| May/June 2024 · Paper 12 | Q7 | 8 | Tangent to a circle and perpendicular diameter |
| May/June 2024 · Paper 12 | Q10 (b) | 6 | Perpendicular bisector of a chord |
| May/June 2024 · Paper 13 | Q8 | 8 | Tangents to a circle meeting at a point |
| Feb/March 2024 · Paper 12 | Q10 (a)–(b) | 5 | Tangent and equation of a circle |
| Oct/Nov 2023 · Paper 11 | Q11 | 9 | Parallel tangents and chord of a circle |
| Oct/Nov 2023 · Paper 12 | Q11 | 10 | Perpendicular lines, circle through points, tangent |
| Oct/Nov 2023 · Paper 13 | Q2 | 4 | Circle meeting axis, circle on diameter |
| May/June 2023 · Paper 11 | Q12 | 9 | Circle equations, tangent and intersections |
| May/June 2023 · Paper 12 | Q10 | 13 | Tangent to a circle, normal and parallel tangents |
| May/June 2023 · Paper 13 | Q5 | 7 | Circle and line intersections, circle on diameter |
| May/June 2023 · Paper 13 | Q10 (b) | 3 | Verifying a normal line |
| Feb/March 2023 · Paper 12 | Q5 | 6 | Circle and chord, finding second intersection |
| Feb/March 2023 · Paper 12 | Q11 (a) | 2 | Equation of a chord |
| Oct/Nov 2022 · Paper 11 | Q11 | 10 | Tangents from external point to circle |
| Oct/Nov 2022 · Paper 12 | Q1 | 6 | Perpendicular bisector and circle through a point |
| Oct/Nov 2022 · Paper 13 | Q10 (a) | 4 | Intersection of line and circle |
| Oct/Nov 2022 · Paper 13 | Q11 | 11 | Equal-length condition and circle through three points |
| May/June 2022 · Paper 11 | Q9 | 10 | Circle centre, lowest point, line intersection |
| May/June 2022 · Paper 12 | Q8 | 8 | Circle through two points and tangent |
| May/June 2022 · Paper 13 | Q7 | 7 | Equation of a line and point on circle |
| May/June 2022 · Paper 13 | Q11 | 10 | Tangent line to a curve and normal intersection |
| Feb/March 2022 · Paper 12 | Q6 | 8 | Circle and line intersection, tangent circle |
| Feb/March 2022 · Paper 12 | Q8 (a) | 3 | Chord of a circle meeting axis |
Chapter 4: P1 Circular Measure
30 past-paper questions
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Paper 1 (Pure Mathematics 1): 28 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q7 (a) | 2 | Segment area of a sector |
| Oct/Nov 2025 · Paper 12 | Q10 | 9 | Area of region between two circles |
| Oct/Nov 2025 · Paper 13 | Q5 | 5 | Exact angle and segment area |
| May/June 2025 · Paper 11 | Q9 | 8 | Area of segment using triangle and sector |
| May/June 2025 · Paper 13 | Q8 | 8 | Perimeter and area of shape with arc |
| Feb/March 2025 · Paper 12 | Q4 | 6 | Perimeter and area of region with sectors |
| Oct/Nov 2024 · Paper 11 | Q3 | 5 | Perimeter and area of shape from sectors |
| Oct/Nov 2024 · Paper 12 | Q6 | 6 | Perimeter and area of plate of sectors |
| Oct/Nov 2024 · Paper 13 | Q7 | 10 | Plate area and perimeter from sectors |
| May/June 2024 · Paper 11 | Q7 | 8 | Perimeter and area of composite sector shape |
| May/June 2024 · Paper 12 | Q8 | 10 | Perimeter and area of plate of sectors |
| May/June 2024 · Paper 13 | Q3 | 6 | Reflex sector perimeter and triangle area |
| Feb/March 2024 · Paper 12 | Q10 (c)–(d) | 7 | Angle, arc length and segment area |
| Oct/Nov 2023 · Paper 11 | Q6 | 7 | Perimeter and area of a motif from arcs |
| Oct/Nov 2023 · Paper 12 | Q4 | 6 | Perimeter and area of arc-bounded coin shape |
| Oct/Nov 2023 · Paper 13 | Q10 | 9 | Region between two arcs of circles |
| May/June 2023 · Paper 11 | Q4 | 4 | Perimeter of segment of a circle |
| May/June 2023 · Paper 12 | Q6 | 6 | Arc length and area with triangle in sector |
| May/June 2023 · Paper 13 | Q6 | 7 | Area and perimeter of region in a sector |
| Feb/March 2023 · Paper 12 | Q8 | 8 | Perimeter and area of shaded region with sector |
| Oct/Nov 2022 · Paper 11 | Q5 | 6 | Perimeter and area of a circle segment |
| Oct/Nov 2022 · Paper 12 | Q10 | 8 | Perimeter and area of aircraft cross-section |
| Oct/Nov 2022 · Paper 13 | Q8 | 7 | Perimeter and area of overlapping circles region |
| Oct/Nov 2022 · Paper 13 | Q10 (c) | 2 | Exact perimeter including arc |
| May/June 2022 · Paper 11 | Q5 | 7 | Triangle area and perimeter within a sector |
| May/June 2022 · Paper 12 | Q7 | 6 | Sector angle and region area |
| May/June 2022 · Paper 13 | Q9 | 8 | Perimeter and area of a shaded sector region |
| Feb/March 2022 · Paper 12 | Q10 | 8 | Perimeter and area of region between two circles |
Paper 3 (Pure Mathematics 3): 2 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Feb/March 2023 · Paper 32 | Q7 (a) | 4 | Sector and segment area relationship |
| Oct/Nov 2022 · Paper 32 | Q9 (a) | 4 | Segment area relationship in semicircle |
Chapter 5: P1 Trigonometry
38 past-paper questions
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Paper 1 (Pure Mathematics 1): 38 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q5 | 7 | Proving identity and solving trig equation |
| Oct/Nov 2025 · Paper 12 | Q6 | 9 | Sine graph, solution counts, trig equation |
| Oct/Nov 2025 · Paper 13 | Q2 | 6 | Inverse trig equation and trig equation |
| May/June 2025 · Paper 11 | Q1 | 4 | Trig equation reduced to quadratic in sine |
| May/June 2025 · Paper 12 | Q5 | 5 | Greatest, least values and sketch of cosine curve |
| May/June 2025 · Paper 12 | Q7 | 7 | Proving identity and solving trig equation |
| May/June 2025 · Paper 13 | Q5 | 6 | Trig equation reduced to quadratic in cosine |
| Feb/March 2025 · Paper 12 | Q7 | 7 | Proving identity and solving trig equation |
| Oct/Nov 2024 · Paper 11 | Q8 | 8 | Trig expression from a sine value, solving equation |
| Oct/Nov 2024 · Paper 12 | Q1 | 5 | Reading sine graph parameters and solution counts |
| Oct/Nov 2024 · Paper 13 | Q2 | 2 | Exact solution with inverse trig functions |
| Oct/Nov 2024 · Paper 13 | Q4 | 4 | Trig equation reduced to quadratic in sine |
| May/June 2024 · Paper 11 | Q5 | 6 | Proving trig identity and solving |
| May/June 2024 · Paper 12 | Q3 | 6 | Trig equation reduced to quadratic in sine |
| May/June 2024 · Paper 13 | Q2 | 5 | Trig graph coordinates and extreme point |
| May/June 2024 · Paper 13 | Q4 | 6 | Trig equation reduced to quadratic in sine |
| Feb/March 2024 · Paper 12 | Q4 | 6 | Proving a trig identity and solving |
| Oct/Nov 2023 · Paper 11 | Q5 | 6 | Trig equation reduced to quadratic in cosine |
| Oct/Nov 2023 · Paper 12 | Q2 | 2 | Exact solution with inverse trig functions |
| Oct/Nov 2023 · Paper 12 | Q7 | 9 | Identity checks and solving trig equation |
| Oct/Nov 2023 · Paper 13 | Q3 | 7 | Trig equation reduced to quadratic in cosine |
| Oct/Nov 2023 · Paper 13 | Q8 (a) | 2 | Reading sine graph parameters |
| May/June 2023 · Paper 11 | Q1 | 3 | Solving trig equation with tan and sin |
| May/June 2023 · Paper 11 | Q7 | 5 | Extremes, sketch and solutions of sine curve |
| May/June 2023 · Paper 12 | Q7 | 11 | Squaring identity, proving and solving |
| May/June 2023 · Paper 13 | Q4 | 7 | Trig equation reduced to quadratic in cosine |
| Feb/March 2023 · Paper 12 | Q7 | 8 | Solving trig equation via quadratic, proving identity |
| Oct/Nov 2022 · Paper 11 | Q6 | 6 | Identity reduced to quadratic in sine |
| Oct/Nov 2022 · Paper 12 | Q3 (b) | 3 | Trig equation reduced to quadratic in cosine |
| Oct/Nov 2022 · Paper 12 | Q7 | 7 | Proving identity and solving trig equation |
| Oct/Nov 2022 · Paper 13 | Q1 | 3 | Trig equation reduced to quadratic in cosine |
| Oct/Nov 2022 · Paper 13 | Q6 | 5 | Exact trig value from inverse cosine |
| May/June 2022 · Paper 11 | Q4 | 6 | Proving trig identity and solving |
| May/June 2022 · Paper 11 | Q8 (b) | 3 | Exact solution of a trig equation |
| May/June 2022 · Paper 12 | Q11 | 10 | Quadratic in cosine and discriminant condition |
| May/June 2022 · Paper 13 | Q2 | 3 | Amplitude, period and shift from trig graph |
| May/June 2022 · Paper 13 | Q5 | 7 | Substitution to reduce a trig equation to quadratic |
| Feb/March 2022 · Paper 12 | Q7 | 7 | Proving a trig identity and solving |
Chapter 6: P1 Series
62 past-paper questions
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Paper 1 (Pure Mathematics 1): 62 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q2 | 5 | Geometric progression with trig ratio |
| Oct/Nov 2025 · Paper 11 | Q3 | 5 | Binomial expansion with coefficient condition |
| Oct/Nov 2025 · Paper 11 | Q9 | 8 | Arithmetic progression with sums condition |
| Oct/Nov 2025 · Paper 12 | Q2 | 3 | Term independent of x in binomial expansion |
| Oct/Nov 2025 · Paper 12 | Q8 | 11 | Geometric and arithmetic progressions with relationship |
| Oct/Nov 2025 · Paper 13 | Q1 | 5 | Binomial expansion and coefficient of product |
| Oct/Nov 2025 · Paper 13 | Q4 | 6 | Arithmetic and geometric progression comparison |
| May/June 2025 · Paper 11 | Q3 | 7 | Geometric progression terms and sum to infinity |
| May/June 2025 · Paper 11 | Q5 | 7 | Binomial expansion terms and coefficient condition |
| May/June 2025 · Paper 12 | Q3 | 4 | Binomial coefficient with unknown constant |
| May/June 2025 · Paper 12 | Q10 | 10 | Arithmetic and geometric progression sums |
| May/June 2025 · Paper 13 | Q2 | 4 | Geometric progression with trig terms |
| May/June 2025 · Paper 13 | Q4 | 6 | Binomial expansion used for approximation |
| May/June 2025 · Paper 13 | Q6 | 6 | Arithmetic progression with unknown term and sum |
| Feb/March 2025 · Paper 12 | Q3 | 6 | Binomial expansion and coefficient of a product |
| Feb/March 2025 · Paper 12 | Q5 | 6 | Sum of arithmetic terms in a range |
| Feb/March 2025 · Paper 12 | Q8 | 7 | Geometric progression ratio and tail sum |
| Oct/Nov 2024 · Paper 11 | Q1 | 4 | Term independent of x and coefficient in binomial |
| Oct/Nov 2024 · Paper 11 | Q10 | 8 | Arithmetic and geometric progression linked terms |
| Oct/Nov 2024 · Paper 12 | Q2 | 5 | Arithmetic progression sums with doubling condition |
| Oct/Nov 2024 · Paper 12 | Q4 | 6 | Term independent of x in expansions |
| Oct/Nov 2024 · Paper 13 | Q1 | 3 | Arithmetic progression terms from two conditions |
| Oct/Nov 2024 · Paper 13 | Q3 | 6 | Binomial coefficients and product coefficient |
| Oct/Nov 2024 · Paper 13 | Q6 | 5 | Geometric progression sums with ratio condition |
| May/June 2024 · Paper 11 | Q3 | 5 | Binomial coefficient and product expansion |
| May/June 2024 · Paper 11 | Q8 | 8 | Arithmetic term and geometric sum to infinity |
| May/June 2024 · Paper 12 | Q1 | 3 | Comparing binomial coefficients to find constant |
| May/June 2024 · Paper 12 | Q5 | 9 | Arithmetic and geometric sums with trig terms |
| May/June 2024 · Paper 13 | Q1 | 4 | Coefficient in product with binomial expansion |
| May/June 2024 · Paper 13 | Q7 | 7 | Arithmetic progression terms within a range |
| May/June 2024 · Paper 13 | Q10 | 8 | Geometric progression ratio, sum and sum to infinity |
| Feb/March 2024 · Paper 12 | Q6 | 5 | Binomial coefficient with unknown constant |
| Feb/March 2024 · Paper 12 | Q8 | 8 | Arithmetic sum and geometric sum to infinity |
| Oct/Nov 2023 · Paper 11 | Q1 | 4 | Binomial expansion and coefficient of a product |
| Oct/Nov 2023 · Paper 11 | Q7 | 7 | Geometric progression with conditions on sums |
| Oct/Nov 2023 · Paper 12 | Q1 | 4 | Binomial coefficient relation for a constant |
| Oct/Nov 2023 · Paper 12 | Q5 | 6 | Geometric progression with trig terms |
| Oct/Nov 2023 · Paper 13 | Q4 | 7 | Binomial product coefficient with unknown constant |
| Oct/Nov 2023 · Paper 13 | Q5 | 7 | Geometric progression with unknown constant and sum |
| May/June 2023 · Paper 11 | Q2 | 6 | Binomial expansions and coefficient of product |
| May/June 2023 · Paper 11 | Q6 | 5 | Arithmetic progression then geometric sum to infinity |
| May/June 2023 · Paper 12 | Q2 | 4 | Binomial coefficients with unknown constant |
| May/June 2023 · Paper 12 | Q9 | 8 | Geometric progression terms and ratio comparison |
| May/June 2023 · Paper 13 | Q3 | 6 | Binomial expansion with coefficient conditions |
| May/June 2023 · Paper 13 | Q8 | 10 | Geometric and arithmetic progression conditions |
| Feb/March 2023 · Paper 12 | Q4 | 5 | Arithmetic and geometric progression comparison |
| Feb/March 2023 · Paper 12 | Q6 | 6 | Binomial coefficient condition for unknown constant |
| Oct/Nov 2022 · Paper 11 | Q4 | 6 | Binomial coefficient condition for constants |
| Oct/Nov 2022 · Paper 11 | Q7 | 7 | Geometric progression in a practical setting |
| Oct/Nov 2022 · Paper 12 | Q2 | 5 | Arithmetic progression defined by unknown constant |
| Oct/Nov 2022 · Paper 12 | Q4 | 4 | Geometric progression terms from two conditions |
| Oct/Nov 2022 · Paper 13 | Q3 | 6 | Binomial expansion and coefficient of product |
| Oct/Nov 2022 · Paper 13 | Q9 | 9 | Geometric progression sum and matched arithmetic terms |
| May/June 2022 · Paper 11 | Q2 | 5 | Arithmetic progression terms and sums |
| May/June 2022 · Paper 11 | Q3 | 6 | Binomial coefficients with unknown constant |
| May/June 2022 · Paper 12 | Q1 | 4 | Equating binomial coefficients to find a constant |
| May/June 2022 · Paper 12 | Q2 | 4 | Sum to infinity of geometric progression |
| May/June 2022 · Paper 12 | Q4 | 5 | Arithmetic progression with unknown parameter |
| May/June 2022 · Paper 13 | Q1 | 4 | Binomial coefficient equation for a constant |
| May/June 2022 · Paper 13 | Q3 | 5 | Arithmetic progression sum and nth term |
| Feb/March 2022 · Paper 12 | Q3 | 6 | Term independent of x in binomial expansions |
| Feb/March 2022 · Paper 12 | Q4 | 6 | Linking geometric and arithmetic progression terms |
Chapter 7: P1 Differentiation
61 past-paper questions
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Paper 1 (Pure Mathematics 1): 61 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q7 (b) | 6 | Related rates for area and arc length |
| Oct/Nov 2025 · Paper 11 | Q11 (a)–(b) | 6 | Normal and rate of change of gradient |
| Oct/Nov 2025 · Paper 12 | Q5 (a) | 3 | Maximum point of a curve |
| Oct/Nov 2025 · Paper 12 | Q9 (a) | 4 | Derivative and increasing test |
| Oct/Nov 2025 · Paper 13 | Q3 | 3 | Gradients of chords approaching derivative |
| Oct/Nov 2025 · Paper 13 | Q11 | 13 | Tangent intersection and stationary point analysis |
| May/June 2025 · Paper 11 | Q2 (a) | 2 | Gradient of the normal to a curve |
| May/June 2025 · Paper 11 | Q7 | 9 | Rate of change, stationary points and nature |
| May/June 2025 · Paper 12 | Q4 | 5 | Rate of change of one coordinate with another |
| May/June 2025 · Paper 12 | Q9 | 12 | Stationary points, curve equation, normal |
| May/June 2025 · Paper 13 | Q1 | 4 | Tangent to a curve at a point |
| May/June 2025 · Paper 13 | Q7 (a) | 3 | Set where a curve is decreasing |
| May/June 2025 · Paper 13 | Q10 (a)–(b) | 7 | Stationary points and second derivative test |
| Feb/March 2025 · Paper 12 | Q2 | 5 | Gradient and minimum point of a curve |
| Feb/March 2025 · Paper 12 | Q9 (a) | 2 | Second derivative test for nature |
| Oct/Nov 2024 · Paper 11 | Q2 | 4 | Stationary point with unknown constants |
| Oct/Nov 2024 · Paper 11 | Q5 (a) | 3 | Point on curve with given gradient |
| Oct/Nov 2024 · Paper 11 | Q7 (a) | 4 | Tangent to a curve at a point |
| Oct/Nov 2024 · Paper 11 | Q9 | 8 | Decreasing interval and tangent condition |
| Oct/Nov 2024 · Paper 12 | Q3 | 5 | Gradient of chord and derivative from limit |
| Oct/Nov 2024 · Paper 13 | Q11 | 12 | Derivatives, stationary point and tangent intersection |
| May/June 2024 · Paper 11 | Q4 | 3 | Gradient from chords as derivative limit |
| May/June 2024 · Paper 11 | Q11 | 13 | Decreasing intervals and triangle from tangent and normal |
| May/June 2024 · Paper 12 | Q9 (a) | 4 | Set where a function is decreasing |
| May/June 2024 · Paper 12 | Q10 (a) | 4 | Rates of change along a curve |
| May/June 2024 · Paper 13 | Q5 | 7 | Stationary point, nature and increasing test |
| May/June 2024 · Paper 13 | Q9 (a) | 5 | Tangent to a curve |
| Feb/March 2024 · Paper 12 | Q5 | 6 | Normal to a curve at a point |
| Feb/March 2024 · Paper 12 | Q11 (a) | 4 | Minimum point of a curve with fractional powers |
| Oct/Nov 2023 · Paper 11 | Q3 | 3 | Rate of change of volume with edge length |
| Oct/Nov 2023 · Paper 11 | Q10 (a) | 3 | Gradient function from second derivative |
| Oct/Nov 2023 · Paper 11 | Q10 (c)–(d) | 5 | Other stationary point and tangent at intercept |
| Oct/Nov 2023 · Paper 12 | Q3 (a) | 2 | Normal to a curve at a point |
| Oct/Nov 2023 · Paper 12 | Q10 | 7 | Stationary points, nature, increasing interval |
| Oct/Nov 2023 · Paper 13 | Q9 | 8 | Normal, rates of change along a curve |
| Oct/Nov 2023 · Paper 13 | Q11 (a) | 4 | Stationary point verification |
| May/June 2023 · Paper 11 | Q9 | 6 | Rate of change of depth from volume |
| May/June 2023 · Paper 11 | Q10 (b) | 6 | Tangent and normal at a point, triangle area |
| May/June 2023 · Paper 11 | Q11 (a)–(b) | 4 | Stationary point and its nature |
| May/June 2023 · Paper 11 | Q11 (d) | 2 | Other stationary points |
| May/June 2023 · Paper 12 | Q11 | 8 | Stationary point and normal with given gradient |
| May/June 2023 · Paper 13 | Q9 (b)–(c) | 6 | Tangent meeting curve again |
| May/June 2023 · Paper 13 | Q10 (a) | 4 | Maximum point of a curve |
| Feb/March 2023 · Paper 12 | Q3 | 4 | Rates of change along a curve |
| Feb/March 2023 · Paper 12 | Q10 (a) | 1 | Using gradient to find a constant |
| Feb/March 2023 · Paper 12 | Q10 (c)–(d) | 5 | Stationary point and its nature |
| Oct/Nov 2022 · Paper 11 | Q2 (a) | 2 | Tangent to a curve at a point |
| Oct/Nov 2022 · Paper 11 | Q3 | 5 | Stationary point with unknown constant |
| Oct/Nov 2022 · Paper 11 | Q10 (b) | 5 | Angle between tangents using gradients |
| Oct/Nov 2022 · Paper 12 | Q8 (b)–(c) | 3 | Stationary point and increasing interval |
| Oct/Nov 2022 · Paper 12 | Q11 (a) | 3 | Minimum point of a quadratic curve |
| Oct/Nov 2022 · Paper 12 | Q11 (c) | 3 | Rate of change along a curve |
| Oct/Nov 2022 · Paper 13 | Q4 | 5 | Rate of change of volume with depth |
| Oct/Nov 2022 · Paper 13 | Q7 (a) | 4 | Points on a curve with given gradient |
| May/June 2022 · Paper 11 | Q10 (a) | 1 | Nature of stationary point from second derivative |
| May/June 2022 · Paper 11 | Q10 (c)–(d) | 6 | Uniqueness of stationary point and related rates |
| May/June 2022 · Paper 12 | Q9 | 7 | Derivatives and stationary point nature |
| May/June 2022 · Paper 12 | Q10 (e) | 6 | Tangent to a curve and triangle area |
| May/June 2022 · Paper 13 | Q8 (a) | 4 | Tangent to a curve at a point |
| May/June 2022 · Paper 13 | Q10 (b) | 6 | Related rates along a curve |
| Feb/March 2022 · Paper 12 | Q11 | 9 | Stationary points, nature and increasing function test |
Chapter 8: P1 Integration
53 past-paper questions
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Paper 1 (Pure Mathematics 1): 53 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 11 | Q8 | 7 | Area and volume of revolution about y-axis |
| Oct/Nov 2025 · Paper 11 | Q11 (c) | 5 | Curve equation by integration |
| Oct/Nov 2025 · Paper 12 | Q4 | 6 | Constant from gradient and curve through points |
| Oct/Nov 2025 · Paper 12 | Q5 (b) | 5 | Exact area under curve |
| Oct/Nov 2025 · Paper 13 | Q9 | 8 | Exact volume of revolution about the x-axis |
| May/June 2025 · Paper 11 | Q2 (b) | 4 | Curve equation from gradient function |
| May/June 2025 · Paper 11 | Q4 | 5 | Area between curve and line |
| May/June 2025 · Paper 12 | Q6 | 6 | Area of region under curve and line |
| May/June 2025 · Paper 13 | Q3 | 4 | Definite integral with unknown constant |
| May/June 2025 · Paper 13 | Q7 (b) | 4 | Curve equation from derivative and maximum |
| Feb/March 2025 · Paper 12 | Q9 (b) | 7 | Finding a curve from second derivative |
| Feb/March 2025 · Paper 12 | Q10 | 9 | Area under a curve and region beside tangent |
| Oct/Nov 2024 · Paper 11 | Q5 (b) | 4 | Curve equation from gradient |
| Oct/Nov 2024 · Paper 11 | Q7 (b) | 4 | Area under curve between lines |
| Oct/Nov 2024 · Paper 12 | Q7 | 8 | Quadratic vertex and area under chord |
| Oct/Nov 2024 · Paper 12 | Q10 | 10 | Normal, function from derivative, increasing test |
| Oct/Nov 2024 · Paper 13 | Q9 (b) | 4 | Area between two curves |
| May/June 2024 · Paper 11 | Q9 | 6 | Volume of revolution about the x-axis |
| May/June 2024 · Paper 12 | Q6 | 9 | Minimum point and area between curve and line |
| May/June 2024 · Paper 12 | Q9 (b) | 4 | Finding function from derivative |
| May/June 2024 · Paper 13 | Q6 (a) | 4 | Finding curve from gradient and point |
| May/June 2024 · Paper 13 | Q9 (b) | 3 | Volume of revolution about the x-axis |
| Feb/March 2024 · Paper 12 | Q1 | 3 | Exact value of a definite integral |
| Feb/March 2024 · Paper 12 | Q3 | 5 | Finding a point on a curve by integration |
| Feb/March 2024 · Paper 12 | Q11 (b) | 7 | Area between curve and chord |
| Oct/Nov 2023 · Paper 11 | Q8 (b) | 5 | Exact area between two curves |
| Oct/Nov 2023 · Paper 11 | Q10 (b) | 3 | Curve equation from derivative |
| Oct/Nov 2023 · Paper 12 | Q3 (b) | 4 | Curve equation from gradient function |
| Oct/Nov 2023 · Paper 12 | Q9 (b) | 5 | Area between two curves |
| Oct/Nov 2023 · Paper 13 | Q1 | 4 | Curve equation from gradient and point |
| Oct/Nov 2023 · Paper 13 | Q11 (b) | 6 | Exact area of region under curve |
| May/June 2023 · Paper 11 | Q10 (a) | 5 | Volume of revolution about the x-axis |
| May/June 2023 · Paper 11 | Q11 (c) | 3 | Curve equation from derivative |
| May/June 2023 · Paper 12 | Q1 | 3 | Curve equation by integrating gradient |
| May/June 2023 · Paper 12 | Q5 | 4 | Area between curve and x-axis |
| May/June 2023 · Paper 13 | Q9 (a) | 4 | Curve equation from gradient function |
| May/June 2023 · Paper 13 | Q10 (c) | 5 | Area of region between curve and line |
| Feb/March 2023 · Paper 12 | Q10 (b) | 4 | Finding a curve by integration |
| Feb/March 2023 · Paper 12 | Q11 (b) | 9 | Volume of revolution about the y-axis |
| Oct/Nov 2022 · Paper 11 | Q2 (b) | 4 | Curve equation from gradient function |
| Oct/Nov 2022 · Paper 11 | Q10 (a) | 5 | Area between two curves |
| Oct/Nov 2022 · Paper 12 | Q8 (a) | 4 | Curve equation from gradient function |
| Oct/Nov 2022 · Paper 12 | Q11 (b) | 5 | Area between two curves |
| Oct/Nov 2022 · Paper 13 | Q7 (b) | 3 | Function from derivative and point |
| Oct/Nov 2022 · Paper 13 | Q10 (b) | 4 | Volume of revolution of region |
| May/June 2022 · Paper 11 | Q7 (b) | 5 | Area between curve and line |
| May/June 2022 · Paper 11 | Q10 (b) | 5 | Finding curve from second derivative |
| May/June 2022 · Paper 12 | Q3 | 4 | Finding a curve through a point by integration |
| May/June 2022 · Paper 12 | Q6 | 5 | Exact area between line and curve |
| May/June 2022 · Paper 13 | Q8 (b) | 4 | Area of region bounded by curve and line |
| May/June 2022 · Paper 13 | Q10 (a) | 4 | Integral to infinity of a power function |
| Feb/March 2022 · Paper 12 | Q1 | 4 | Finding a curve by integrating its gradient |
| Feb/March 2022 · Paper 12 | Q8 (b) | 5 | Volume of revolution of a segment |
Chapter 9: P3 Algebra
58 past-paper questions
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Paper 3 (Pure Mathematics 3): 58 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q10 | 11 | Partial fractions and series expansion |
| Oct/Nov 2025 · Paper 32 | Q1 | 3 | Modulus graph and inequality |
| Oct/Nov 2025 · Paper 32 | Q5 | 7 | Repeated factor and polynomial coefficients |
| Oct/Nov 2025 · Paper 32 | Q9 (a) | 5 | Partial fractions with parameter |
| Oct/Nov 2025 · Paper 33 | Q1 | 4 | Modulus inequality |
| Oct/Nov 2025 · Paper 33 | Q2 | 3 | Polynomial division quotient and remainder |
| Oct/Nov 2025 · Paper 33 | Q10 (a) | 2 | Partial fractions of simple rational function |
| May/June 2025 · Paper 31 | Q1 | 3 | Modulus graph and inequality |
| May/June 2025 · Paper 31 | Q5 | 5 | Remainder theorem with parameters |
| May/June 2025 · Paper 31 | Q10 (a) | 3 | Division of polynomials |
| May/June 2025 · Paper 32 | Q2 | 5 | Binomial expansion negative power and validity |
| May/June 2025 · Paper 32 | Q10 (a) | 2 | Algebraic division with quotient and remainder |
| May/June 2025 · Paper 33 | Q1 | 4 | Modulus graph and inequality |
| May/June 2025 · Paper 33 | Q7 | 8 | Partial fractions, expansion and validity |
| Feb/March 2025 · Paper 32 | Q9 | 10 | Factor theorem, factorising and solving inequality |
| Feb/March 2025 · Paper 32 | Q10 (a) | 5 | Partial fractions with quadratic factor |
| Oct/Nov 2024 · Paper 31 | Q1 | 5 | Factor and remainder theorem relation |
| Oct/Nov 2024 · Paper 31 | Q7 | 9 | Partial fractions and series coefficient |
| Oct/Nov 2024 · Paper 32 | Q1 | 4 | Binomial expansion with fractional power |
| Oct/Nov 2024 · Paper 33 | Q8 | 8 | Partial fractions, expansion and validity |
| Oct/Nov 2024 · Paper 33 | Q9 (a) | 3 | Polynomial division with quotient and remainder |
| May/June 2024 · Paper 31 | Q1 | 4 | Expanding a product with binomial power |
| May/June 2024 · Paper 32 | Q1 | 3 | Modulus graph sketch and inequality |
| May/June 2024 · Paper 32 | Q2 | 5 | Partial fractions of improper fraction |
| May/June 2024 · Paper 33 | Q5 | 5 | Partial fractions of rational function |
| May/June 2024 · Paper 33 | Q7 (a)–(b) | 3 | Factor theorem and polynomial division |
| Feb/March 2024 · Paper 32 | Q1 | 3 | Polynomial division with quotient and remainder |
| Feb/March 2024 · Paper 32 | Q2 | 5 | Binomial expansion with validity range |
| Feb/March 2024 · Paper 32 | Q10 (a) | 5 | Partial fractions with repeated linear factors |
| Oct/Nov 2023 · Paper 31 | Q10 | 11 | Partial fractions, expansion and validity |
| Oct/Nov 2023 · Paper 32 | Q1 | 5 | Modulus graph and inequality |
| Oct/Nov 2023 · Paper 32 | Q3 | 5 | Factor and remainder theorem |
| Oct/Nov 2023 · Paper 33 | Q3 | 5 | Remainder theorems with two conditions |
| Oct/Nov 2023 · Paper 33 | Q9 | 11 | Partial fractions, expansion and validity |
| May/June 2023 · Paper 31 | Q2 | 4 | Sketch modulus graph and solve inequality |
| May/June 2023 · Paper 31 | Q3 | 4 | Coefficient in binomial expansion with product |
| May/June 2023 · Paper 31 | Q8 (a) | 5 | Partial fractions with repeated factor |
| May/June 2023 · Paper 32 | Q1 | 4 | Solving a modulus inequality |
| May/June 2023 · Paper 32 | Q9 (a) | 5 | Partial fractions with quadratic factor |
| May/June 2023 · Paper 33 | Q2 | 3 | Polynomial division quotient and remainder |
| May/June 2023 · Paper 33 | Q10 | 10 | Partial fractions and series expansion |
| Feb/March 2023 · Paper 32 | Q3 | 5 | Polynomial remainder with a quadratic divisor |
| Feb/March 2023 · Paper 32 | Q11 (a) | 5 | Partial fractions with quadratic factor |
| Oct/Nov 2022 · Paper 31 | Q1 | 4 | Modulus graph and inequality |
| Oct/Nov 2022 · Paper 31 | Q10 | 10 | Partial fractions and series expansion |
| Oct/Nov 2022 · Paper 32 | Q2 (a) | 2 | Factor theorem for unknown constant |
| Oct/Nov 2022 · Paper 32 | Q2 (b) | 4 | Factorising cubic and solving inequality |
| Oct/Nov 2022 · Paper 32 | Q10 (a) | 5 | Partial fractions with repeated factor |
| Oct/Nov 2022 · Paper 33 | Q2 | 5 | Binomial expansion of a quotient |
| Oct/Nov 2022 · Paper 33 | Q11 (a) | 5 | Partial fractions with quadratic factor |
| May/June 2022 · Paper 31 | Q2 | 5 | Binomial expansion negative power and validity |
| May/June 2022 · Paper 31 | Q5 | 8 | Factor theorem with derivative and factorising |
| May/June 2022 · Paper 32 | Q3 | 5 | Factor and remainder theorem |
| May/June 2022 · Paper 32 | Q8 (a) | 5 | Partial fractions with quadratic factor |
| May/June 2022 · Paper 33 | Q1 | 4 | Modulus inequality with parameter |
| May/June 2022 · Paper 33 | Q7 | 10 | Partial fractions and series expansion |
| Feb/March 2022 · Paper 32 | Q1 | 4 | Solving a modulus inequality |
| Feb/March 2022 · Paper 32 | Q8 (a) | 3 | Algebraic division with quotient and remainder |
Chapter 10: P3 Logarithmic and Exponential Functions
29 past-paper questions
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Paper 3 (Pure Mathematics 3): 29 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q2 | 5 | Logarithm equation reduced to quadratic |
| Oct/Nov 2025 · Paper 32 | Q2 | 4 | Solving exponential equation with logarithms |
| Oct/Nov 2025 · Paper 33 | Q3 | 4 | Solving exponential equation with logarithms |
| May/June 2025 · Paper 31 | Q2 | 3 | Combining logarithms to make a variable subject |
| May/June 2025 · Paper 32 | Q1 | 5 | Solving exponential equation numerically |
| May/June 2025 · Paper 33 | Q2 | 4 | Combining logarithms and solving |
| Feb/March 2025 · Paper 32 | Q1 | 3 | Solving a logarithmic and exponential equation |
| Oct/Nov 2024 · Paper 32 | Q4 | 3 | Solving exponential equation with logarithms |
| Oct/Nov 2024 · Paper 32 | Q6 | 4 | Linearising an exponential relation |
| Oct/Nov 2024 · Paper 33 | Q3 | 5 | Exponential model from log graph |
| May/June 2024 · Paper 31 | Q2 | 4 | Solving equation with natural logarithms |
| May/June 2024 · Paper 31 | Q3 | 4 | Reducing exponential relation to straight line graph |
| May/June 2024 · Paper 32 | Q3 | 5 | Linearising an exponential relation |
| May/June 2024 · Paper 33 | Q1 | 4 | Solving exponential equation using logarithms |
| May/June 2024 · Paper 33 | Q4 | 4 | Linearising exponential model from graph |
| Feb/March 2024 · Paper 32 | Q4 | 4 | Manipulating logarithm expressions |
| Oct/Nov 2023 · Paper 31 | Q3 | 4 | Linearising an exponential relation from graph |
| Oct/Nov 2023 · Paper 33 | Q1 | 4 | Exponential inequality solved numerically |
| May/June 2023 · Paper 31 | Q1 | 3 | Solving exponential equation with logarithms |
| May/June 2023 · Paper 32 | Q2 | 3 | Combining logarithms into exact equation |
| May/June 2023 · Paper 33 | Q1 | 4 | Logarithm equation solved numerically |
| Feb/March 2023 · Paper 32 | Q1 | 3 | Rearranging a logarithmic equation |
| Oct/Nov 2022 · Paper 31 | Q3 | 4 | Solving exponential equation with logarithms |
| Oct/Nov 2022 · Paper 32 | Q1 | 4 | Solving exponential equation with logarithms |
| Oct/Nov 2022 · Paper 33 | Q1 | 4 | Solving logarithmic equation numerically |
| May/June 2022 · Paper 31 | Q1 | 4 | Solving exponential equation with logarithms |
| May/June 2022 · Paper 32 | Q1 | 4 | Logarithm equation solved numerically |
| May/June 2022 · Paper 33 | Q3 | 5 | Logarithm equation reduced to quadratic |
| Feb/March 2022 · Paper 32 | Q3 | 5 | Reducing a power equation to a linear graph |
Chapter 11: P3 Trigonometry
30 past-paper questions
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Paper 3 (Pure Mathematics 3): 30 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q3 | 8 | Harmonic form and solving equation |
| Oct/Nov 2025 · Paper 32 | Q8 (a) | 3 | Proving multiple-angle identity |
| Oct/Nov 2025 · Paper 33 | Q5 | 8 | Proving identity and solving trig equation |
| May/June 2025 · Paper 31 | Q7 | 8 | Harmonic form and solving equation |
| May/June 2025 · Paper 32 | Q4 | 6 | Cotangent equation with double angle |
| May/June 2025 · Paper 32 | Q7 | 7 | Harmonic form and solving equation |
| May/June 2025 · Paper 33 | Q8 | 8 | Proving identity and solving trig equation |
| Feb/March 2025 · Paper 32 | Q4 | 6 | Reducing trig equation to a quadratic in tan |
| Oct/Nov 2024 · Paper 31 | Q4 | 8 | Proving identity and solving trig equation |
| Oct/Nov 2024 · Paper 32 | Q7 | 6 | Tangent identity and solving |
| Oct/Nov 2024 · Paper 33 | Q5 | 6 | Proving trig identity and solving |
| May/June 2024 · Paper 32 | Q7 (a) | 3 | Proving a trig identity |
| May/June 2024 · Paper 33 | Q7 (c) | 3 | Solving cubic in cosine |
| May/June 2024 · Paper 33 | Q8 (a) | 3 | Harmonic form of trig expression |
| Feb/March 2024 · Paper 32 | Q8 | 9 | Harmonic form and solving |
| Oct/Nov 2023 · Paper 31 | Q5 | 6 | Compound angle equation to find tangent |
| Oct/Nov 2023 · Paper 32 | Q7 | 8 | Triple angle identity and solving |
| Oct/Nov 2023 · Paper 33 | Q6 | 6 | Double angle equation in cotangent |
| May/June 2023 · Paper 31 | Q4 | 6 | Double angle equation reduced to homogeneous form |
| May/June 2023 · Paper 32 | Q4 | 5 | Double angle equation in cosine |
| May/June 2023 · Paper 33 | Q6 | 8 | Harmonic form and solving equation |
| Feb/March 2023 · Paper 32 | Q6 | 7 | Harmonic form and solving equation |
| Oct/Nov 2022 · Paper 31 | Q4 | 5 | Tangent and cotangent equation |
| Oct/Nov 2022 · Paper 31 | Q6 | 7 | Proving multiple-angle identity and solving |
| Oct/Nov 2022 · Paper 32 | Q4 | 8 | Harmonic form and solving equation |
| Oct/Nov 2022 · Paper 33 | Q7 | 8 | Harmonic form and solving equation |
| May/June 2022 · Paper 31 | Q3 | 6 | Double angle cotangent equation |
| May/June 2022 · Paper 32 | Q2 | 5 | Double angle equation in cosine |
| May/June 2022 · Paper 33 | Q2 | 5 | Compound angle equation |
| Feb/March 2022 · Paper 32 | Q5 | 6 | Compound angle formula with tangents |
Chapter 12: P3 Differentiation
53 past-paper questions
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Paper 3 (Pure Mathematics 3): 53 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q4 | 5 | Maximum point of exponential trig function |
| Oct/Nov 2025 · Paper 31 | Q7 | 5 | Parametric differentiation |
| Oct/Nov 2025 · Paper 32 | Q7 | 8 | Implicit differentiation and vertical normals |
| Oct/Nov 2025 · Paper 33 | Q8 (a) | 3 | Stationary point condition for exponential log product |
| Oct/Nov 2025 · Paper 33 | Q11 (a) | 6 | Minimum point of secant-type function |
| May/June 2025 · Paper 31 | Q4 | 6 | Tangent to a parametric curve |
| May/June 2025 · Paper 31 | Q11 (a) | 6 | Maximum point of trig product |
| May/June 2025 · Paper 32 | Q11 (a) | 6 | Maximum point of a trig product |
| May/June 2025 · Paper 33 | Q5 | 6 | Implicit differentiation and tangent gradients |
| May/June 2025 · Paper 33 | Q11 (a) | 4 | Maximum point condition for product with trig |
| Feb/March 2025 · Paper 32 | Q2 | 5 | Implicit differentiation gradient at a point |
| Feb/March 2025 · Paper 32 | Q7 (a) | 3 | Maximum point condition from product derivative |
| Oct/Nov 2024 · Paper 31 | Q3 | 4 | Implicit differentiation at a point |
| Oct/Nov 2024 · Paper 31 | Q6 (a) | 4 | Minimum point of trig product |
| Oct/Nov 2024 · Paper 32 | Q8 | 8 | Parametric derivative and normal |
| Oct/Nov 2024 · Paper 32 | Q11 (a) | 5 | Stationary point of exponential rational function |
| Oct/Nov 2024 · Paper 33 | Q7 | 8 | Parametric derivative and normal |
| Oct/Nov 2024 · Paper 33 | Q11 (a) | 5 | Minimum point of trig quotient |
| May/June 2024 · Paper 31 | Q5 | 7 | Derivative of exponential over trig, stationary points |
| May/June 2024 · Paper 31 | Q10 (a) | 3 | Derivative of inverse tangent relation |
| May/June 2024 · Paper 32 | Q4 | 6 | Implicit differentiation at a point |
| May/June 2024 · Paper 32 | Q6 (a) | 4 | Maximum point of exponential product |
| May/June 2024 · Paper 32 | Q10 (a) | 2 | Derivative of secant via quotient |
| May/June 2024 · Paper 33 | Q2 | 5 | Stationary point of exponential trig product |
| Feb/March 2024 · Paper 32 | Q6 | 7 | Implicit differentiation and tangent condition |
| Oct/Nov 2023 · Paper 31 | Q1 | 5 | Points on a curve with given gradient |
| Oct/Nov 2023 · Paper 31 | Q6 | 6 | Parametric derivative and normal gradient |
| Oct/Nov 2023 · Paper 31 | Q9 (a) | 4 | Maximum point of exponential product |
| Oct/Nov 2023 · Paper 32 | Q2 | 4 | Parametric curve gradient at a point |
| Oct/Nov 2023 · Paper 32 | Q9 (a) | 5 | Maximum point of trig product |
| Oct/Nov 2023 · Paper 33 | Q5 | 6 | Stationary points of exponential quotient |
| Oct/Nov 2023 · Paper 33 | Q7 | 8 | Implicit differentiation and horizontal tangents |
| Oct/Nov 2023 · Paper 33 | Q10 (a) | 4 | Tangent to curve of product with trig |
| May/June 2023 · Paper 31 | Q5 | 8 | Implicit differentiation and vertical tangents |
| May/June 2023 · Paper 32 | Q7 | 9 | Implicit differentiation and parallel tangents |
| May/June 2023 · Paper 32 | Q10 (a) | 5 | Maximum point of a product function |
| May/June 2023 · Paper 33 | Q4 | 5 | Parametric differentiation with trig |
| May/June 2023 · Paper 33 | Q5 (a) | 3 | Maximum point condition of product |
| Feb/March 2023 · Paper 32 | Q5 | 6 | Parametric derivative and normal |
| Feb/March 2023 · Paper 32 | Q8 (a) | 4 | Minimum point of a product with logarithm |
| Oct/Nov 2022 · Paper 31 | Q7 (a) | 3 | Gradient condition for quotient curve |
| Oct/Nov 2022 · Paper 31 | Q9 (a) | 5 | Minimum point of exponential product |
| Oct/Nov 2022 · Paper 32 | Q3 | 6 | Stationary point of trig product |
| Oct/Nov 2022 · Paper 33 | Q4 | 5 | Parametric differentiation with trig |
| Oct/Nov 2022 · Paper 33 | Q8 (a) | 3 | Stationary point condition for exponential quotient |
| May/June 2022 · Paper 31 | Q8 | 9 | Implicit differentiation and tangents |
| May/June 2022 · Paper 31 | Q10 (a) | 4 | Stationary point condition of a product |
| May/June 2022 · Paper 32 | Q4 | 6 | Stationary point of trig product |
| May/June 2022 · Paper 32 | Q7 | 9 | Implicit differentiation and horizontal tangents |
| May/June 2022 · Paper 33 | Q4 | 7 | Derivative of exponential times trig, stationary points |
| May/June 2022 · Paper 33 | Q6 | 8 | Parametric differentiation and tangent |
| Feb/March 2022 · Paper 32 | Q4 | 5 | Parametric differentiation with trig identity |
| Feb/March 2022 · Paper 32 | Q11 (a) | 6 | Finding a stationary point of a trig product |
Chapter 13: P3 Integration
46 past-paper questions
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Paper 3 (Pure Mathematics 3): 46 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q1 | 4 | Exact definite integral with logarithm |
| Oct/Nov 2025 · Paper 32 | Q4 | 6 | Exact integral by parts |
| Oct/Nov 2025 · Paper 32 | Q8 (b) | 5 | Exact integral using identity |
| Oct/Nov 2025 · Paper 32 | Q9 (b) | 4 | Exact definite integral of partial fractions |
| Oct/Nov 2025 · Paper 33 | Q6 | 6 | Exact integral by parts |
| Oct/Nov 2025 · Paper 33 | Q11 (b) | 6 | Exact area using substitution |
| May/June 2025 · Paper 31 | Q9 (a) | 5 | Integration by parts to form an equation |
| May/June 2025 · Paper 31 | Q11 (b) | 5 | Volume of revolution of trig curve |
| May/June 2025 · Paper 32 | Q10 (b) | 6 | Integration by parts with inverse tangent |
| May/June 2025 · Paper 32 | Q11 (b) | 5 | Area using substitution |
| May/June 2025 · Paper 33 | Q3 | 4 | Exact definite integral of squared trig |
| Feb/March 2025 · Paper 32 | Q10 (b) | 6 | Exact integral of partial fractions |
| Feb/March 2025 · Paper 32 | Q11 | 6 | Definite integral by parts |
| Oct/Nov 2024 · Paper 31 | Q2 | 5 | Exact integral by parts with logarithm |
| Oct/Nov 2024 · Paper 31 | Q6 (b) | 4 | Exact area of region under trig curve |
| Oct/Nov 2024 · Paper 32 | Q11 (b) | 9 | Integration using substitution and partial fractions |
| Oct/Nov 2024 · Paper 33 | Q9 (b) | 5 | Definite integral using division |
| Oct/Nov 2024 · Paper 33 | Q11 (b) | 6 | Exact area using substitution |
| May/June 2024 · Paper 31 | Q8 | 7 | Definite integral using substitution |
| May/June 2024 · Paper 31 | Q10 (b) | 7 | Integration by parts with arctangent |
| May/June 2024 · Paper 32 | Q6 (b) | 5 | Exact integral by parts |
| May/June 2024 · Paper 32 | Q7 (b) | 6 | Exact definite integral using identity |
| May/June 2024 · Paper 33 | Q8 (b) | 5 | Exact integral using harmonic form |
| May/June 2024 · Paper 33 | Q11 | 9 | Exact integral by trig substitution |
| Feb/March 2024 · Paper 32 | Q10 (b) | 5 | Definite integral of partial fractions |
| Oct/Nov 2023 · Paper 31 | Q9 (b) | 5 | Exact area using substitution |
| Oct/Nov 2023 · Paper 32 | Q5 | 6 | Exact integral of rational function |
| Oct/Nov 2023 · Paper 32 | Q9 (b) | 4 | Exact area under trig curve |
| Oct/Nov 2023 · Paper 33 | Q10 (b) | 5 | Exact area by parts |
| May/June 2023 · Paper 31 | Q8 (b) | 5 | Exact definite integral of partial fractions |
| May/June 2023 · Paper 31 | Q9 (a) | 5 | Integration by parts to form an equation |
| May/June 2023 · Paper 32 | Q9 (b) | 5 | Exact definite integral of rational function |
| May/June 2023 · Paper 32 | Q10 (b) | 5 | Area using substitution |
| May/June 2023 · Paper 33 | Q7 | 8 | Definite integral using substitution |
| Feb/March 2023 · Paper 32 | Q8 (b) | 5 | Area using integration by parts |
| Feb/March 2023 · Paper 32 | Q11 (b) | 5 | Integrating partial fractions exactly |
| Oct/Nov 2022 · Paper 31 | Q9 (b) | 5 | Area under curve with exponential |
| Oct/Nov 2022 · Paper 32 | Q8 | 8 | Exact area using substitution |
| Oct/Nov 2022 · Paper 32 | Q10 (b) | 5 | Exact integral of partial fractions |
| Oct/Nov 2022 · Paper 33 | Q3 | 5 | Definite integral by parts |
| Oct/Nov 2022 · Paper 33 | Q11 (b) | 5 | Exact integral of partial fractions |
| May/June 2022 · Paper 31 | Q6 | 8 | Trig substitution for definite integral |
| May/June 2022 · Paper 32 | Q8 (b) | 5 | Integrating partial fractions |
| May/June 2022 · Paper 33 | Q10 (a) | 5 | Definite integral by parts |
| Feb/March 2022 · Paper 32 | Q8 (b) | 5 | Integrating a quotient after division |
| Feb/March 2022 · Paper 32 | Q11 (b) | 5 | Area by substitution |
Chapter 14: P3 Numerical Solution of Equations
26 past-paper questions
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Paper 3 (Pure Mathematics 3): 26 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q9 | 8 | Graph sketch, bracketing, iteration |
| Oct/Nov 2025 · Paper 32 | Q6 | 7 | Graph sketch, bracketing, iteration |
| Oct/Nov 2025 · Paper 33 | Q8 (b)–(d) | 7 | Sketch, bracketing and iteration |
| May/June 2025 · Paper 31 | Q9 (b)–(c) | 5 | Root location and iteration |
| May/June 2025 · Paper 32 | Q6 | 7 | Graph sketch, bracketing, iteration |
| May/June 2025 · Paper 33 | Q11 (b)–(d) | 7 | Root location and iteration |
| Feb/March 2025 · Paper 32 | Q7 (b)–(c) | 5 | Locating a root and iterating |
| Oct/Nov 2024 · Paper 31 | Q5 | 7 | Graph sketch, bracketing, iteration |
| Oct/Nov 2024 · Paper 32 | Q2 | 3 | Graph sketch and iteration convergence |
| Oct/Nov 2024 · Paper 33 | Q2 | 5 | Iterative formula and convergence |
| May/June 2024 · Paper 31 | Q6 | 9 | Graph sketch, bracketing, iteration convergence |
| May/June 2024 · Paper 32 | Q5 | 6 | Root bracketing and iteration convergence |
| Feb/March 2024 · Paper 32 | Q7 | 8 | Minimum point equation, root location, iteration |
| Oct/Nov 2023 · Paper 31 | Q8 | 8 | Graph sketch, bracketing, iteration convergence |
| Oct/Nov 2023 · Paper 32 | Q6 | 7 | Graph sketch, bracketing, iteration |
| May/June 2023 · Paper 31 | Q9 (b)–(c) | 5 | Root location and iteration |
| May/June 2023 · Paper 32 | Q6 | 7 | Root bracketing and iteration |
| May/June 2023 · Paper 33 | Q5 (b) | 3 | Iterative formula for a root |
| Feb/March 2023 · Paper 32 | Q7 (b)–(c) | 5 | Locating a root and iterating |
| Oct/Nov 2022 · Paper 31 | Q7 (b)–(c) | 5 | Root location and iteration |
| Oct/Nov 2022 · Paper 32 | Q9 (b)–(c) | 5 | Root location and iteration |
| Oct/Nov 2022 · Paper 33 | Q8 (b)–(c) | 5 | Root location and iteration |
| May/June 2022 · Paper 31 | Q10 (b)–(d) | 7 | Root location and iteration |
| May/June 2022 · Paper 32 | Q5 | 7 | Graph sketch, root bracketing, iteration |
| May/June 2022 · Paper 33 | Q10 (b)–(c) | 5 | Root location and iteration |
| Feb/March 2022 · Paper 32 | Q7 | 7 | Graph sketch, sign change and iteration |
Chapter 15: P3 Vectors
28 past-paper questions
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Paper 3 (Pure Mathematics 3): 28 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q11 | 10 | Line equations, intersection and foot of perpendicular |
| Oct/Nov 2025 · Paper 32 | Q11 | 9 | Vectors, angle between vectors and triangle area |
| Oct/Nov 2025 · Paper 33 | Q9 | 9 | Intersecting lines, angle and intersection point |
| May/June 2025 · Paper 31 | Q8 | 9 | Line equation, skew lines and angle |
| May/June 2025 · Paper 32 | Q9 | 9 | Line equation, scalar product, triangle area |
| May/June 2025 · Paper 33 | Q9 | 8 | Line, foot of perpendicular and reflection |
| Feb/March 2025 · Paper 32 | Q8 | 8 | Skew lines and angle between lines |
| Oct/Nov 2024 · Paper 31 | Q9 | 10 | Line equation, point on line, angle between lines |
| Oct/Nov 2024 · Paper 32 | Q9 | 11 | Trapezium with vectors, diagonals, angle |
| Oct/Nov 2024 · Paper 33 | Q6 | 7 | Intersecting lines, angle and triangle area |
| May/June 2024 · Paper 31 | Q9 | 9 | Perpendicular and intersecting lines, reflection |
| May/June 2024 · Paper 32 | Q8 | 12 | Line equation, intersection and distance condition |
| May/June 2024 · Paper 33 | Q10 | 11 | Angle between lines and intersection of lines |
| Feb/March 2024 · Paper 32 | Q9 | 8 | Showing a rectangle with vectors, diagonal angle |
| Oct/Nov 2023 · Paper 31 | Q11 | 10 | Cuboid vectors, angle and perpendicular length |
| Oct/Nov 2023 · Paper 32 | Q10 | 9 | Angle between lines and perpendicular distance |
| Oct/Nov 2023 · Paper 33 | Q11 | 9 | Unit vector, line equation and line relationship |
| May/June 2023 · Paper 31 | Q6 | 10 | Parallelogram with vectors, angle and area |
| May/June 2023 · Paper 32 | Q11 | 9 | Skew lines and foot of perpendicular |
| May/June 2023 · Paper 33 | Q9 | 10 | Perpendicular lines and point on extended perpendicular |
| Feb/March 2023 · Paper 32 | Q10 | 9 | Angle between vectors and line intersection |
| Oct/Nov 2022 · Paper 31 | Q11 | 11 | Vectors in a solid figure, angle, perpendicular distance |
| Oct/Nov 2022 · Paper 32 | Q6 | 8 | Scalar product, angle and triangle area |
| Oct/Nov 2022 · Paper 33 | Q9 | 9 | Midpoints, line equation and line intersection |
| May/June 2022 · Paper 31 | Q9 | 9 | Vectors in a cuboid and perpendicular distance |
| May/June 2022 · Paper 32 | Q9 | 10 | Intersecting and perpendicular lines in 3D |
| May/June 2022 · Paper 33 | Q9 | 9 | Angle, foot of perpendicular and reflection |
| Feb/March 2022 · Paper 32 | Q10 | 10 | Lines in 3D: equation, angle, non-intersection |
Chapter 16: P3 Differential Equations
28 past-paper questions
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Paper 3 (Pure Mathematics 3): 28 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q8 | 8 | Separable differential equation with exponentials |
| Oct/Nov 2025 · Paper 32 | Q10 | 9 | Tank filling differential equation |
| Oct/Nov 2025 · Paper 33 | Q10 (b) | 6 | Separable differential equation after partial fractions |
| May/June 2025 · Paper 31 | Q10 (b) | 5 | Separable differential equation with rational function |
| May/June 2025 · Paper 32 | Q8 | 7 | Separable differential equation with trig |
| May/June 2025 · Paper 33 | Q10 | 10 | Separable differential equation with trig |
| Feb/March 2025 · Paper 32 | Q6 | 7 | Separable differential equation with trig |
| Oct/Nov 2024 · Paper 31 | Q10 | 10 | Tank draining differential equation |
| Oct/Nov 2024 · Paper 32 | Q10 | 13 | Balloon volume rate as differential equation |
| Oct/Nov 2024 · Paper 33 | Q10 | 8 | Tank filling and leaking differential equation |
| May/June 2024 · Paper 31 | Q11 | 11 | Modelling disease spread by differential equation |
| May/June 2024 · Paper 32 | Q10 (b) | 8 | Separable differential equation with trig |
| May/June 2024 · Paper 33 | Q9 | 11 | Forming and solving differential equation for volume |
| Feb/March 2024 · Paper 32 | Q11 | 9 | Separable differential equation with trig |
| Oct/Nov 2023 · Paper 31 | Q7 | 7 | Separable differential equation with trig |
| Oct/Nov 2023 · Paper 32 | Q11 | 9 | Separable differential equation with limiting behaviour |
| Oct/Nov 2023 · Paper 33 | Q8 | 7 | Separable differential equation with trig |
| May/June 2023 · Paper 31 | Q7 | 8 | Separable differential equation with trig |
| May/June 2023 · Paper 32 | Q8 | 8 | Separable differential equation with limit behaviour |
| May/June 2023 · Paper 33 | Q8 | 8 | Separable differential equation with initial condition |
| Feb/March 2023 · Paper 32 | Q9 | 7 | Separable differential equation with trig |
| Oct/Nov 2022 · Paper 31 | Q8 | 8 | Separable differential equation with exponential decay |
| Oct/Nov 2022 · Paper 32 | Q7 | 8 | Separable differential equation with trig |
| Oct/Nov 2022 · Paper 33 | Q10 | 9 | Modelling tank filling with differential equation |
| May/June 2022 · Paper 31 | Q4 | 7 | Separable differential equation |
| May/June 2022 · Paper 32 | Q6 | 8 | Separable differential equation with exponentials |
| May/June 2022 · Paper 33 | Q8 | 9 | Differential equation model with trig rate |
| Feb/March 2022 · Paper 32 | Q9 | 9 | Separating variables in a differential equation |
Chapter 17: P3 Complex Numbers
48 past-paper questions
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Paper 3 (Pure Mathematics 3): 48 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 31 | Q5 | 6 | Argand region inequalities and least argument |
| Oct/Nov 2025 · Paper 31 | Q6 | 5 | Complex quadratic with complex coefficients |
| Oct/Nov 2025 · Paper 32 | Q3 | 5 | Argand region, special point and greatest argument |
| Oct/Nov 2025 · Paper 33 | Q4 | 5 | Argand region from modulus inequalities |
| Oct/Nov 2025 · Paper 33 | Q7 | 6 | Complex equation with conjugate |
| May/June 2025 · Paper 31 | Q3 | 6 | Complex numbers with real quotient and modulus |
| May/June 2025 · Paper 31 | Q6 | 6 | Complex numbers in exponential form and geometry |
| May/June 2025 · Paper 32 | Q3 | 5 | Argand region with modulus and argument inequalities |
| May/June 2025 · Paper 32 | Q5 | 5 | Square roots of a complex number |
| May/June 2025 · Paper 33 | Q4 | 6 | Conjugate of product and complex roots |
| May/June 2025 · Paper 33 | Q6 | 6 | Complex numbers with real quotient and modulus |
| Feb/March 2025 · Paper 32 | Q3 | 6 | Argand region inequalities and greatest modulus |
| Feb/March 2025 · Paper 32 | Q5 | 5 | Square roots of a complex number |
| Oct/Nov 2024 · Paper 31 | Q8 | 9 | Complex reciprocal, loci and geometric description |
| Oct/Nov 2024 · Paper 32 | Q3 | 5 | Square roots of a complex number |
| Oct/Nov 2024 · Paper 32 | Q5 | 4 | Argument of complex quotient and conjugate geometry |
| Oct/Nov 2024 · Paper 33 | Q1 | 4 | Argand loci and transformed locus |
| Oct/Nov 2024 · Paper 33 | Q4 | 5 | Complex equation solved for a number |
| May/June 2024 · Paper 31 | Q4 | 4 | Polar and exponential forms of complex numbers |
| May/June 2024 · Paper 31 | Q7 | 6 | Loci on Argand diagram and least distance |
| May/June 2024 · Paper 32 | Q9 | 10 | Complex numbers: forms, geometry and exact trig value |
| May/June 2024 · Paper 33 | Q3 | 5 | Square roots of a complex number |
| May/June 2024 · Paper 33 | Q6 | 7 | Argand region and greatest argument |
| Feb/March 2024 · Paper 32 | Q3 | 6 | Polar form and modulus-argument of complex numbers |
| Feb/March 2024 · Paper 32 | Q5 | 6 | Argand region and greatest argument |
| Oct/Nov 2023 · Paper 31 | Q2 | 4 | Argand region from modulus and argument inequalities |
| Oct/Nov 2023 · Paper 31 | Q4 | 5 | Cartesian form of complex quotient and argument |
| Oct/Nov 2023 · Paper 32 | Q4 | 6 | Argand region and greatest argument |
| Oct/Nov 2023 · Paper 32 | Q8 | 7 | Equal complex expressions and unknown constants |
| Oct/Nov 2023 · Paper 33 | Q2 | 5 | Argand region from modulus inequalities |
| Oct/Nov 2023 · Paper 33 | Q4 | 5 | Complex quadratic with complex coefficients |
| May/June 2023 · Paper 31 | Q10 | 12 | Factor theorem and complex roots of polynomial |
| May/June 2023 · Paper 32 | Q3 | 4 | Circle locus and least modulus |
| May/June 2023 · Paper 32 | Q5 | 6 | Complex polynomial values, modulus and argument |
| May/June 2023 · Paper 33 | Q3 | 4 | Shading Argand region from two inequalities |
| May/June 2023 · Paper 33 | Q11 | 9 | Complex quotient argument and polar form of power |
| Feb/March 2023 · Paper 32 | Q2 | 5 | Argand region and least argument |
| Feb/March 2023 · Paper 32 | Q4 | 5 | Solving a complex equation with conjugate |
| Oct/Nov 2022 · Paper 31 | Q2 | 4 | Shading region on Argand diagram |
| Oct/Nov 2022 · Paper 31 | Q5 | 4 | Quotient of complex numbers in exponential form |
| Oct/Nov 2022 · Paper 32 | Q5 | 8 | Complex quadratic roots and geometric properties |
| Oct/Nov 2022 · Paper 33 | Q5 | 6 | Argand region and greatest argument |
| Oct/Nov 2022 · Paper 33 | Q6 | 6 | Solving complex quadratic with complex coefficients |
| May/June 2022 · Paper 31 | Q7 | 8 | Complex number in Cartesian and polar form |
| May/June 2022 · Paper 32 | Q10 | 11 | Complex roots, locus and greatest argument |
| May/June 2022 · Paper 33 | Q5 | 8 | Argand diagram points and argument identity |
| Feb/March 2022 · Paper 32 | Q2 | 4 | Shading an Argand diagram locus region |
| Feb/March 2022 · Paper 32 | Q6 | 6 | Solving an equation with complex conjugate |
Chapter 18: M1 Forces and Equilibrium
33 past-paper questions
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Paper 4 (Mechanics): 33 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q3 | 6 | Resultant of four coplanar forces |
| Oct/Nov 2025 · Paper 41 | Q5 | 6 | Limiting equilibrium on rough inclined plane |
| Oct/Nov 2025 · Paper 42 | Q7 | 11 | Forces on a ring in equilibrium, friction |
| Oct/Nov 2025 · Paper 43 | Q7 | 7 | Equilibrium on rough plane with horizontal force |
| May/June 2025 · Paper 41 | Q2 | 4 | Resultant of three forces |
| May/June 2025 · Paper 42 | Q3 | 4 | Particle held by string and force |
| May/June 2025 · Paper 43 | Q4 | 6 | Equilibrium of three blocks on strings |
| Feb/March 2025 · Paper 42 | Q1 | 4 | Equilibrium of three forces, angle and magnitude |
| Oct/Nov 2024 · Paper 41 | Q3 | 4 | Equilibrium of three forces |
| Oct/Nov 2024 · Paper 41 | Q6 | 6 | Particle on rough plane held by horizontal force |
| Oct/Nov 2024 · Paper 42 | Q4 | 6 | Equilibrium of particles on strings |
| Oct/Nov 2024 · Paper 43 | Q2 | 6 | Missing force for equilibrium of coplanar forces |
| May/June 2024 · Paper 41 | Q2 | 7 | Resultant of two forces and component condition |
| May/June 2024 · Paper 42 | Q3 | 6 | Equilibrium of four forces |
| May/June 2024 · Paper 42 | Q5 | 8 | Particle on rough plane in equilibrium |
| May/June 2024 · Paper 43 | Q2 | 3 | Particle in equilibrium with string and force |
| Feb/March 2024 · Paper 42 | Q4 | 6 | Equilibrium of four forces with angle |
| Oct/Nov 2023 · Paper 41 | Q2 | 5 | Particle held by two strings |
| Oct/Nov 2023 · Paper 42 | Q2 | 5 | Smooth ring on string in equilibrium |
| Oct/Nov 2023 · Paper 42 | Q3 | 5 | Block on rough plane with angled force |
| Oct/Nov 2023 · Paper 43 | Q5 | 8 | Particle on string under horizontal force |
| May/June 2023 · Paper 41 | Q5 | 9 | Equilibrium of four forces and resultant |
| May/June 2023 · Paper 42 | Q3 | 6 | Equilibrium of forces with trig condition |
| May/June 2023 · Paper 42 | Q5 | 6 | Particle on rough plane with horizontal force |
| May/June 2023 · Paper 43 | Q3 | 5 | Smooth ring on string in equilibrium |
| Feb/March 2023 · Paper 42 | Q5 | 6 | Equilibrium of a block on struts |
| Oct/Nov 2022 · Paper 41 | Q1 | 5 | Equilibrium of four forces |
| Oct/Nov 2022 · Paper 42 | Q3 | 6 | Particle held by two strings |
| Oct/Nov 2022 · Paper 43 | Q3 | 6 | Ring on smooth wire held by string |
| May/June 2022 · Paper 41 | Q4 | 6 | Three forces in equilibrium |
| May/June 2022 · Paper 42 | Q2 | 6 | Resultant of coplanar forces |
| May/June 2022 · Paper 43 | Q4 | 8 | Equilibrium with strings and horizontal force |
| Feb/March 2022 · Paper 42 | Q5 | 7 | Equilibrium of coplanar forces and resultant |
Chapter 19: M1 Kinematics of Motion in a Straight Line
56 past-paper questions
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Paper 4 (Mechanics): 56 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q7 | 9 | Velocity as function of time: distance travelled |
| Oct/Nov 2025 · Paper 42 | Q1 | 3 | Displacement-time graph with constant acceleration |
| Oct/Nov 2025 · Paper 42 | Q4 | 9 | Two projected particles colliding and coalescing |
| Oct/Nov 2025 · Paper 42 | Q6 | 8 | Acceleration function and distance until rest |
| Oct/Nov 2025 · Paper 43 | Q1 | 3 | Velocity-time graph deceleration and distance |
| Oct/Nov 2025 · Paper 43 | Q4 | 10 | Displacement function, minimum velocity, acceleration |
| May/June 2025 · Paper 41 | Q3 | 7 | Velocity-time graph and displacement-time graph |
| May/June 2025 · Paper 41 | Q7 | 13 | Displacement function, rest and distance |
| May/June 2025 · Paper 42 | Q4 | 11 | Velocity-time graph with unknown time |
| May/June 2025 · Paper 42 | Q6 | 9 | Velocity function and maximum velocity |
| May/June 2025 · Paper 43 | Q3 | 7 | Velocity-time graph unknown time and acceleration |
| May/June 2025 · Paper 43 | Q7 | 10 | Displacement and acceleration functions, distance |
| Feb/March 2025 · Paper 42 | Q2 | 5 | Constant acceleration then constant speed motion |
| Feb/March 2025 · Paper 42 | Q7 | 11 | Velocity function with unknown constants and distance |
| Oct/Nov 2024 · Paper 41 | Q4 | 6 | Velocity-time graph for bus journey |
| Oct/Nov 2024 · Paper 41 | Q5 | 10 | Two projected particles colliding and coalescing |
| Oct/Nov 2024 · Paper 41 | Q8 | 7 | Acceleration function, rest times and distance |
| Oct/Nov 2024 · Paper 42 | Q1 | 5 | Velocity-time graph with unknown time |
| Oct/Nov 2024 · Paper 42 | Q6 | 10 | Piecewise acceleration, velocity and distance |
| Oct/Nov 2024 · Paper 43 | Q6 | 10 | Acceleration, velocity graph and total distance |
| May/June 2024 · Paper 41 | Q1 | 4 | Velocity-time graph and distance |
| May/June 2024 · Paper 41 | Q6 | 11 | Velocity function, maximum and distance travelled |
| May/June 2024 · Paper 42 | Q2 | 5 | Velocity function, acceleration sign, return to origin |
| May/June 2024 · Paper 43 | Q3 | 6 | Constant acceleration over successive intervals |
| May/June 2024 · Paper 43 | Q4 | 7 | Velocity function, distance condition, minimum velocity |
| Feb/March 2024 · Paper 42 | Q1 | 5 | Displacement-time graph to velocity-time graph |
| Feb/March 2024 · Paper 42 | Q2 | 4 | Vertical projection, speeds and distance |
| Feb/March 2024 · Paper 42 | Q5 | 8 | Velocity function, distance and zero acceleration |
| Oct/Nov 2023 · Paper 41 | Q3 | 8 | Velocity-time graph with unknown deceleration |
| Oct/Nov 2023 · Paper 41 | Q7 | 9 | Piecewise velocity, rest point and distance |
| Oct/Nov 2023 · Paper 42 | Q5 | 8 | Vertical projection and collision with falling particle |
| Oct/Nov 2023 · Paper 42 | Q7 | 12 | Cubic velocity function, rest times and distance |
| Oct/Nov 2023 · Paper 43 | Q1 | 3 | Vertical projection from heights at given times |
| Oct/Nov 2023 · Paper 43 | Q6 | 8 | Acceleration function, rest and total distance |
| May/June 2023 · Paper 41 | Q2 | 6 | Vertical projection and bounce with energy loss |
| May/June 2023 · Paper 41 | Q3 | 4 | Calculus kinematics from displacement function |
| May/June 2023 · Paper 41 | Q4 | 8 | Velocity-time graph distances and speeds |
| May/June 2023 · Paper 42 | Q6 | 11 | Velocity function, rest and return to origin |
| May/June 2023 · Paper 43 | Q5 | 10 | Acceleration function, velocity and distance |
| May/June 2023 · Paper 43 | Q6 (a)–(b) | 5 | Velocity-time graph and distance of elevator |
| Feb/March 2023 · Paper 42 | Q2 | 5 | Vertical motion of two particles meeting |
| Feb/March 2023 · Paper 42 | Q3 | 5 | Calculus kinematics with equal speed and distance |
| Oct/Nov 2022 · Paper 41 | Q5 | 10 | Acceleration function, velocity graph and distance |
| Oct/Nov 2022 · Paper 42 | Q7 | 12 | Piecewise acceleration, velocity and distance |
| Oct/Nov 2022 · Paper 43 | Q1 | 3 | Vertical projection and greatest height |
| Oct/Nov 2022 · Paper 43 | Q4 | 7 | Constant acceleration from distances in given seconds |
| Oct/Nov 2022 · Paper 43 | Q5 | 8 | Two particles meeting with velocity functions |
| May/June 2022 · Paper 41 | Q1 | 6 | Constant acceleration, velocity-time graph, average speed |
| May/June 2022 · Paper 41 | Q6 | 10 | Velocity function and return to start |
| May/June 2022 · Paper 42 | Q4 | 9 | Displacement comparison of two particles |
| May/June 2022 · Paper 42 | Q7 | 9 | Piecewise velocity, acceleration change and distance |
| May/June 2022 · Paper 43 | Q2 | 5 | Vertical projection and time above speed |
| May/June 2022 · Paper 43 | Q3 | 5 | Displacement-time graph speed and acceleration |
| May/June 2022 · Paper 43 | Q7 | 10 | Velocity function with unknown constants and distance |
| Feb/March 2022 · Paper 42 | Q2 | 5 | Vertical motion under gravity |
| Feb/March 2022 · Paper 42 | Q6 | 11 | Calculus kinematics with acceleration function |
Chapter 20: M1 Momentum
23 past-paper questions
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Paper 4 (Mechanics): 23 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q2 | 5 | Collision with two possible outcomes, energy loss |
| Oct/Nov 2025 · Paper 41 | Q6 | 6 | Collision on smooth incline, then distance moved |
| Oct/Nov 2025 · Paper 43 | Q6 | 7 | Collision conditions and bounds on mass |
| May/June 2025 · Paper 41 | Q5 | 7 | Momentum and energy of colliding particles |
| May/June 2025 · Paper 42 | Q2 | 4 | Collision of particles moving apart |
| May/June 2025 · Paper 43 | Q1 | 5 | Collision conditions and kinetic energy loss |
| Feb/March 2025 · Paper 42 | Q5 | 7 | Collisions along a line then meeting time |
| Oct/Nov 2024 · Paper 42 | Q5 | 9 | Projectile and collision then fall to ground |
| Oct/Nov 2024 · Paper 43 | Q4 | 6 | Collision of two particles |
| May/June 2024 · Paper 41 | Q7 | 10 | Vertical projection, collision and rebound |
| May/June 2024 · Paper 42 | Q6 | 11 | Two successive collisions on smooth track |
| May/June 2024 · Paper 43 | Q1 | 3 | Collision of two particles |
| Oct/Nov 2023 · Paper 41 | Q4 | 9 | Friction, collision energy loss and sliding distance |
| Oct/Nov 2023 · Paper 43 | Q2 | 5 | Hammer and nail impact, resistance force |
| May/June 2023 · Paper 41 | Q1 | 4 | Collision and coalescence with unknown mass |
| May/June 2023 · Paper 42 | Q2 | 4 | Collision of opposing particles and energy loss |
| May/June 2023 · Paper 43 | Q1 | 3 | Collision with speeds given |
| Oct/Nov 2022 · Paper 41 | Q2 | 5 | Collision of spheres with opposing velocities |
| Oct/Nov 2022 · Paper 42 | Q6 | 9 | Successive collisions and coalescence |
| May/June 2022 · Paper 41 | Q7 | 9 | Collision on smooth incline then rebound |
| May/June 2022 · Paper 42 | Q1 | 5 | Collision of spheres and energy loss |
| May/June 2022 · Paper 43 | Q1 | 4 | Collision then coalescence |
| Feb/March 2022 · Paper 42 | Q7 (b) | 6 | Collision on a wire then second meeting time |
Chapter 21: M1 Newton's Laws of Motion
42 past-paper questions
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Paper 4 (Mechanics): 42 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q8 | 8 | Connected bodies under an angled pulling force |
| Oct/Nov 2025 · Paper 42 | Q2 | 5 | Locomotive and coach down a hill |
| Oct/Nov 2025 · Paper 42 | Q5 | 6 | Block pulled down rough plane |
| Oct/Nov 2025 · Paper 43 | Q5 | 10 | Pulley with hanging particles, motion after release |
| May/June 2025 · Paper 41 | Q1 | 4 | Block pulled up rough plane |
| May/June 2025 · Paper 41 | Q6 (a) | 5 | Connected particles on smooth plane |
| May/June 2025 · Paper 42 | Q5 | 12 | Connected particles on rough slope and tensions |
| May/June 2025 · Paper 42 | Q7 | 6 | Particle projected up rough slope |
| May/June 2025 · Paper 43 | Q2 | 4 | Van and trailer with resistances |
| Feb/March 2025 · Paper 42 | Q4 | 7 | Connected particles over a pulley, then rise |
| Feb/March 2025 · Paper 42 | Q6 | 10 | Block on rough incline with applied force |
| Oct/Nov 2024 · Paper 41 | Q1 | 4 | Connected particles hanging over pulley |
| Oct/Nov 2024 · Paper 42 | Q7 | 11 | Pulley and incline motion, then energy and distance |
| Oct/Nov 2024 · Paper 43 | Q5 | 8 | Particle pulled with string across rough plane |
| Oct/Nov 2024 · Paper 43 | Q7 | 10 | Pulley system on plane and time above height |
| May/June 2024 · Paper 41 | Q4 | 6 | Car and trailer with resistances |
| May/June 2024 · Paper 41 | Q5 | 8 | Sliding down slope with and without friction |
| May/June 2024 · Paper 42 | Q7 (a) | 5 | Acceleration of particles on pulley and incline |
| May/June 2024 · Paper 43 | Q5 | 11 | Van and trailer on hill with tow-bar |
| Feb/March 2024 · Paper 42 | Q6 (a) | 5 | Car and trailer on slope, acceleration and tension |
| Feb/March 2024 · Paper 42 | Q7 | 12 | Particles on incline, collision, friction |
| Oct/Nov 2023 · Paper 41 | Q5 | 7 | Connected particles on two inclined planes |
| Oct/Nov 2023 · Paper 42 | Q4 | 7 | Limiting friction then motion on horizontal plane |
| Oct/Nov 2023 · Paper 42 | Q6 | 9 | Engine and coupling on slope, change of incline |
| Oct/Nov 2023 · Paper 43 | Q3 | 6 | Block sliding down rough plane |
| Oct/Nov 2023 · Paper 43 | Q7 | 13 | Pulley system on rough plane, equilibrium and motion |
| May/June 2023 · Paper 41 | Q6 | 8 | Connected particles with friction on plane |
| May/June 2023 · Paper 42 | Q7 | 13 | Pulley system on incline and time taken |
| May/June 2023 · Paper 43 | Q2 | 4 | Car and trailer with resistance |
| May/June 2023 · Paper 43 | Q6 (c)–(d) | 6 | Cable tension and force on crate |
| Feb/March 2023 · Paper 42 | Q6 | 9 | Block on rough incline with angled rope |
| Oct/Nov 2022 · Paper 41 | Q4 | 9 | Block pulled up rough plane by angled string |
| Oct/Nov 2022 · Paper 41 | Q6 | 12 | Pulley with particles, limiting friction and motion |
| Oct/Nov 2022 · Paper 42 | Q2 | 7 | Limiting friction then motion under extra force |
| Oct/Nov 2022 · Paper 42 | Q5 | 7 | Connected blocks on a slope |
| Oct/Nov 2022 · Paper 43 | Q7 | 12 | Friction on slope, collision and energy loss |
| May/June 2022 · Paper 41 | Q2 | 5 | Two particles connected by string with applied force |
| May/June 2022 · Paper 41 | Q3 | 5 | Friction on a crate pulled at an angle |
| May/June 2022 · Paper 42 | Q3 | 7 | Pulley system and subsequent motion |
| May/June 2022 · Paper 42 | Q5 | 6 | Block on incline with angled string |
| May/June 2022 · Paper 43 | Q6 | 15 | Connected particles on plane and energy method |
| Feb/March 2022 · Paper 42 | Q7 (a) | 6 | Friction on a bead on an incline |
Chapter 22: M1 Energy, Work and Power
48 past-paper questions
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Paper 4 (Mechanics): 48 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q1 | 4 | Driving force and power at an instant |
| Oct/Nov 2025 · Paper 41 | Q4 | 6 | Energy method for connected particles on plane |
| Oct/Nov 2025 · Paper 42 | Q3 | 8 | Uniform acceleration, average power, steady speed |
| Oct/Nov 2025 · Paper 43 | Q2 | 6 | Maximum power and resistance proportional to speed |
| Oct/Nov 2025 · Paper 43 | Q3 | 7 | Work against friction and energy method |
| May/June 2025 · Paper 41 | Q4 | 6 | Power of lorry on level and uphill road |
| May/June 2025 · Paper 41 | Q6 (b) | 4 | Energy method with friction |
| May/June 2025 · Paper 42 | Q1 | 4 | Work and power at constant speed |
| May/June 2025 · Paper 43 | Q5 | 9 | Power with speed-squared resistance on slope |
| May/June 2025 · Paper 43 | Q6 | 9 | Work against resistance on waterslide |
| Feb/March 2025 · Paper 42 | Q3 | 6 | Aircraft power, resistance and work on ascent |
| Oct/Nov 2024 · Paper 41 | Q2 | 5 | Energy method for sliding on slope |
| Oct/Nov 2024 · Paper 41 | Q7 | 8 | Maximum power and resistance proportional to speed |
| Oct/Nov 2024 · Paper 42 | Q2 | 4 | Block sliding with resistance on slope |
| Oct/Nov 2024 · Paper 42 | Q3 | 5 | Cyclist power, resistance and hill speed |
| Oct/Nov 2024 · Paper 43 | Q1 | 4 | Work done by athlete against resistance |
| Oct/Nov 2024 · Paper 43 | Q3 | 6 | Power and acceleration of car on slope |
| May/June 2024 · Paper 41 | Q3 | 4 | Work, resistance and power of ascending train |
| May/June 2024 · Paper 42 | Q1 | 3 | Work done to change speed against resistance |
| May/June 2024 · Paper 42 | Q4 | 7 | Power with speed-dependent resistance |
| May/June 2024 · Paper 42 | Q7 (b) | 5 | Energy method for connected particles |
| May/June 2024 · Paper 43 | Q6 | 11 | Cyclist power, steady speed and energy downhill |
| May/June 2024 · Paper 43 | Q7 | 9 | Track with friction and energy |
| Feb/March 2024 · Paper 42 | Q3 | 5 | Power of a winch on a rough slope |
| Feb/March 2024 · Paper 42 | Q6 (b) | 5 | Energy method for final speed |
| Oct/Nov 2023 · Paper 41 | Q1 | 3 | Energy method for projectile up smooth slope |
| Oct/Nov 2023 · Paper 41 | Q6 | 9 | Power and resistance depending on speed down slope |
| Oct/Nov 2023 · Paper 42 | Q1 | 4 | Energy method for block sliding down plane |
| Oct/Nov 2023 · Paper 43 | Q4 | 7 | Car power and work against variable resistance |
| May/June 2023 · Paper 41 | Q7 | 11 | Power, resistance and energy up a hill |
| May/June 2023 · Paper 42 | Q1 | 3 | Work against air resistance using energy |
| May/June 2023 · Paper 42 | Q4 | 7 | Power and driving force on a slope |
| May/June 2023 · Paper 43 | Q4 | 7 | Constant power and resistance of a lorry |
| May/June 2023 · Paper 43 | Q7 | 10 | Energy method with friction on slide |
| Feb/March 2023 · Paper 42 | Q1 | 5 | Power, resistance and time under constant rate |
| Feb/March 2023 · Paper 42 | Q4 | 7 | Towing with power and tension in coupling |
| Feb/March 2023 · Paper 42 | Q7 | 13 | Smooth track, collision and projectile motion |
| Oct/Nov 2022 · Paper 41 | Q3 | 9 | Power, steady speed and towing uphill |
| Oct/Nov 2022 · Paper 42 | Q1 | 3 | Work-energy for cyclist with constant driving force |
| Oct/Nov 2022 · Paper 42 | Q4 | 6 | Constant power and distance via energy |
| Oct/Nov 2022 · Paper 43 | Q2 | 4 | Change in potential energy and work done |
| Oct/Nov 2022 · Paper 43 | Q6 | 10 | Car and caravan power on level and slope |
| May/June 2022 · Paper 41 | Q5 | 9 | Constant driving force, power and steady speed |
| May/June 2022 · Paper 42 | Q6 | 8 | Work against resistance and power with variable resistance |
| May/June 2022 · Paper 43 | Q5 | 3 | Power and freewheeling downhill |
| Feb/March 2022 · Paper 42 | Q1 | 4 | Work done and average power in lifting |
| Feb/March 2022 · Paper 42 | Q3 | 5 | Work against resistance on a downhill tow |
| Feb/March 2022 · Paper 42 | Q4 | 6 | Power, driving force and steady speed uphill |
Chapter 23: S1 Representation of Data
35 past-paper questions
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Paper 5 (Probability & Statistics 1): 35 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 51 | Q3 | 8 | Stem-and-leaf, quartiles, combined mean and sd |
| Oct/Nov 2025 · Paper 52 | Q5 | 7 | Histogram and grouped mean |
| Oct/Nov 2025 · Paper 53 | Q6 | 10 | Stem-and-leaf, quartiles, box plots |
| May/June 2025 · Paper 51 | Q3 | 12 | Stem-and-leaf, quartiles, combined mean and sd |
| May/June 2025 · Paper 52 | Q5 | 10 | Cumulative frequency graph, mean and sd |
| May/June 2025 · Paper 53 | Q1 | 4 | Coded sums for mean and standard deviation |
| May/June 2025 · Paper 53 | Q4 | 5 | Cumulative frequency graph and box plot |
| Feb/March 2025 · Paper 52 | Q3 | 9 | Cumulative frequency graph, estimate and mean |
| Oct/Nov 2024 · Paper 51 | Q3 | 8 | Cumulative frequency graph, quartiles, mean |
| Oct/Nov 2024 · Paper 52 | Q6 | 10 | Back-to-back stem-and-leaf, quartiles, combined mean and sd |
| Oct/Nov 2024 · Paper 53 | Q4 | 11 | Cumulative frequency graph, mean and sd |
| May/June 2024 · Paper 51 | Q1 | 4 | Combined mean and standard deviation from sums |
| May/June 2024 · Paper 51 | Q3 | 6 | Histogram and bound on interquartile range |
| May/June 2024 · Paper 52 | Q4 | 7 | Stem-and-leaf, quartiles, box plots, average choice |
| May/June 2024 · Paper 53 | Q4 | 8 | Back-to-back stem-and-leaf and box plots |
| Feb/March 2024 · Paper 52 | Q3 | 8 | Histogram, grouped mean and quartile class |
| Oct/Nov 2023 · Paper 51 | Q1 | 4 | Cumulative frequency graph, quartiles and percentile |
| Oct/Nov 2023 · Paper 51 | Q4 | 9 | Histogram, mean and standard deviation |
| Oct/Nov 2023 · Paper 52 | Q4 | 8 | Stem-and-leaf, quartiles and spread comparison |
| Oct/Nov 2023 · Paper 53 | Q4 | 10 | Cumulative frequency graph, mean and sd |
| May/June 2023 · Paper 51 | Q1 | 4 | Standard deviation and mean from coded sums |
| May/June 2023 · Paper 51 | Q5 | 7 | Histogram, median class and interquartile range |
| May/June 2023 · Paper 52 | Q3 | 7 | Stem-and-leaf, quartiles, box plots |
| May/June 2023 · Paper 53 | Q4 | 8 | Stem-and-leaf comparisons and mean adjustment |
| Feb/March 2023 · Paper 52 | Q1 | 8 | Cumulative frequency graph, percentile and grouped mean |
| Oct/Nov 2022 · Paper 51 | Q3 | 9 | Stem-and-leaf, quartiles and comparisons |
| Oct/Nov 2022 · Paper 52 | Q4 | 7 | Histogram and standard deviation estimate |
| Oct/Nov 2022 · Paper 53 | Q1 | 3 | Variance from coded summary data |
| Oct/Nov 2022 · Paper 53 | Q3 | 7 | Cumulative frequency graph, percentile, standard deviation |
| May/June 2022 · Paper 51 | Q3 | 9 | Histogram, standard deviation and effect of data correction |
| May/June 2022 · Paper 52 | Q1 | 3 | Using summary values to find sample size |
| May/June 2022 · Paper 52 | Q3 | 7 | Stem-and-leaf, quartiles and box plots |
| May/June 2022 · Paper 53 | Q1 | 3 | Cumulative frequency graph and percentile |
| May/June 2022 · Paper 53 | Q2 | 3 | Mean, median and suitability of average |
| Feb/March 2022 · Paper 52 | Q3 | 6 | Histogram, median class and skewness |
Chapter 24: S1 Permutations and Combinations
34 past-paper questions
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Paper 5 (Probability & Statistics 1): 34 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 51 | Q7 | 10 | Arrangements of letters and selection probability |
| Oct/Nov 2025 · Paper 52 | Q7 | 10 | Letter arrangements and selection probability |
| Oct/Nov 2025 · Paper 53 | Q2 | 4 | Committee selection with categories |
| Oct/Nov 2025 · Paper 53 | Q3 | 6 | Letter arrangements and probability |
| May/June 2025 · Paper 51 | Q2 (a) | 3 | Arrangements of letters with adjacency conditions |
| May/June 2025 · Paper 51 | Q5 | 7 | Selecting musicians with conditions |
| May/June 2025 · Paper 52 | Q6 | 9 | Letter arrangements and selections |
| May/June 2025 · Paper 53 | Q7 | 12 | Arrangements, groupings and probability of grouping |
| Feb/March 2025 · Paper 52 | Q6 | 10 | Colour arrangements and selections with conditions |
| Oct/Nov 2024 · Paper 51 | Q7 | 9 | Letter arrangements and selection percentage |
| Oct/Nov 2024 · Paper 52 | Q2 | 4 | Arrangements of letters with spacing conditions |
| Oct/Nov 2024 · Paper 52 | Q5 | 6 | Group selections with conditions |
| Oct/Nov 2024 · Paper 53 | Q6 | 11 | Letter arrangements and group probability |
| May/June 2024 · Paper 51 | Q7 | 10 | Arrangements of digits and selection probability |
| May/June 2024 · Paper 52 | Q7 | 10 | Letter arrangements and alternating probability |
| May/June 2024 · Paper 53 | Q6 | 8 | Letter arrangements and grouping probability |
| Feb/March 2024 · Paper 52 | Q6 | 10 | Committee choices and photo arrangements |
| Oct/Nov 2023 · Paper 51 | Q6 | 10 | Table groupings, seating and line arrangements |
| Oct/Nov 2023 · Paper 52 | Q7 | 10 | Arrangements of letters and selection probability |
| Oct/Nov 2023 · Paper 53 | Q6 | 10 | Arrangements of couples and group probability |
| May/June 2023 · Paper 51 | Q2 | 5 | Committee selections with restrictions |
| May/June 2023 · Paper 51 | Q3 (a)–(b) | 3 | Arrangements of letters with positional restrictions |
| May/June 2023 · Paper 52 | Q6 | 10 | Team selections and arrangements |
| May/June 2023 · Paper 53 | Q7 | 9 | Letter arrangements and selections |
| Feb/March 2023 · Paper 52 | Q5 | 3 | Arrangements of objects in boxes |
| Feb/March 2023 · Paper 52 | Q7 | 12 | Arrangements with repeated letters and selections |
| Oct/Nov 2022 · Paper 51 | Q6 | 10 | Committee choices, groupings and arrangements |
| Oct/Nov 2022 · Paper 52 | Q7 | 10 | Letter arrangements and selections |
| Oct/Nov 2022 · Paper 53 | Q6 | 10 | Letter arrangements and selections |
| May/June 2022 · Paper 51 | Q1 | 6 | Arrangements of letters with grouping restrictions |
| May/June 2022 · Paper 51 | Q2 | 6 | Committee selections with conditions |
| May/June 2022 · Paper 52 | Q6 | 10 | Arrangements and selections of letters |
| May/June 2022 · Paper 53 | Q7 | 11 | Dividing groups and selecting teams |
| Feb/March 2022 · Paper 52 | Q5 | 10 | Selections and arrangements with restrictions |
Chapter 25: S1 Probability
26 past-paper questions
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Paper 5 (Probability & Statistics 1): 26 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 51 | Q4 | 5 | Tree diagram with transfer between bags |
| Oct/Nov 2025 · Paper 52 | Q4 | 7 | Probability with two packs and unknown size |
| Oct/Nov 2025 · Paper 53 | Q5 | 8 | Tree diagram with conditional probability |
| May/June 2025 · Paper 52 | Q3 | 5 | Selection without replacement and conditional probability |
| May/June 2025 · Paper 53 | Q5 | 8 | Tree diagram and conditional probability |
| Feb/March 2025 · Paper 52 | Q4 | 7 | Probability without replacement, colour combinations |
| Oct/Nov 2024 · Paper 51 | Q4 | 6 | Tree-style probability with coin and bags |
| Oct/Nov 2024 · Paper 52 | Q1 | 6 | Table probability, independence and binomial |
| May/June 2024 · Paper 51 | Q4 | 6 | Turn-based probability with repeated trials |
| May/June 2024 · Paper 52 | Q2 | 5 | Probability with coin and marble selection |
| May/June 2024 · Paper 53 | Q3 | 7 | Tree diagram with transfer between boxes |
| Feb/March 2024 · Paper 52 | Q1 | 4 | Conditional probability with and without replacement |
| Oct/Nov 2023 · Paper 52 | Q6 | 9 | Tree diagram with chosen bags |
| Oct/Nov 2023 · Paper 53 | Q3 | 7 | Probability with dice-chosen bags, conditional |
| May/June 2023 · Paper 51 | Q3 (c) | 3 | Conditional probability of arrangements |
| May/June 2023 · Paper 52 | Q2 | 6 | Dependent daily weather probabilities |
| May/June 2023 · Paper 53 | Q5 | 7 | Independence of events with dice |
| Feb/March 2023 · Paper 52 | Q4 | 3 | Probability with tree diagram and unknown |
| Oct/Nov 2022 · Paper 51 | Q5 | 10 | Tree diagram, independence and conditional probability |
| Oct/Nov 2022 · Paper 52 | Q1 | 5 | Tree diagram with unknown and conditional probability |
| Oct/Nov 2022 · Paper 52 | Q5 | 7 | Conditional probability and distribution table |
| Oct/Nov 2022 · Paper 53 | Q7 | 8 | Sequential selection without replacement |
| May/June 2022 · Paper 51 | Q6 | 8 | Tree-style probability and conditional probability |
| May/June 2022 · Paper 52 | Q7 | 9 | Probability for selection without replacement |
| May/June 2022 · Paper 53 | Q6 | 10 | Tree diagram and conditional probability |
| Feb/March 2022 · Paper 52 | Q6 (c)–(e) | 9 | Conditional probability without replacement |
Chapter 26: S1 Discrete Random Variables
61 past-paper questions
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Paper 5 (Probability & Statistics 1): 61 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 51 | Q1 | 6 | Distribution table, expectation, conditional probability |
| Oct/Nov 2025 · Paper 51 | Q2 | 4 | Geometric distribution of throws |
| Oct/Nov 2025 · Paper 51 | Q5 | 8 | Binomial probability and normal approximation |
| Oct/Nov 2025 · Paper 52 | Q1 | 3 | Geometric distribution of first success |
| Oct/Nov 2025 · Paper 52 | Q2 | 7 | Distribution table for selection until success |
| Oct/Nov 2025 · Paper 52 | Q6 | 9 | Binomial probabilities and normal approximation |
| Oct/Nov 2025 · Paper 53 | Q1 | 4 | Binomial probabilities from categorical choices |
| Oct/Nov 2025 · Paper 53 | Q4 | 8 | Distribution table, variance and geometric probability |
| May/June 2025 · Paper 51 | Q2 (b)–(c) | 4 | Geometric distribution of dice rolls |
| May/June 2025 · Paper 51 | Q6 | 9 | Distribution of blue marbles and conditional probability |
| May/June 2025 · Paper 52 | Q1 | 3 | Distribution table from three coins |
| May/June 2025 · Paper 52 | Q4 | 6 | Geometric probabilities and combined directions |
| May/June 2025 · Paper 53 | Q2 | 5 | Binomial probabilities of student choices |
| May/June 2025 · Paper 53 | Q3 | 6 | Geometric distribution probabilities |
| Feb/March 2025 · Paper 52 | Q1 | 6 | Distribution table for coin outcomes |
| Feb/March 2025 · Paper 52 | Q2 | 9 | Binomial probabilities and normal approximation |
| Feb/March 2025 · Paper 52 | Q5 (c)–(d) | 3 | Geometric distribution over days |
| Oct/Nov 2024 · Paper 51 | Q1 | 4 | Geometric distribution of first and second six |
| Oct/Nov 2024 · Paper 51 | Q2 | 6 | Probability distribution with function of x |
| Oct/Nov 2024 · Paper 52 | Q3 | 6 | Distribution table and variance from coin and dice |
| Oct/Nov 2024 · Paper 52 | Q7 | 11 | Binomial, geometric and normal approximation for goals |
| Oct/Nov 2024 · Paper 53 | Q1 | 7 | Binomial probability and normal approximation |
| Oct/Nov 2024 · Paper 53 | Q2 | 4 | Distribution table for dice product |
| Oct/Nov 2024 · Paper 53 | Q5 | 10 | Binomial, geometric and conditional probability |
| May/June 2024 · Paper 51 | Q5 (a)–(b) | 5 | Binomial probabilities over days and weeks |
| May/June 2024 · Paper 51 | Q6 | 7 | Distribution table and equation for unknown probability |
| May/June 2024 · Paper 52 | Q1 | 5 | Geometric distribution of first and second success |
| May/June 2024 · Paper 52 | Q5 | 7 | Distribution table for coin values drawn |
| May/June 2024 · Paper 52 | Q6 | 10 | Binomial, normal approximation and probability of selection |
| May/June 2024 · Paper 53 | Q1 | 8 | Distribution table, variance, conditional probability |
| May/June 2024 · Paper 53 | Q5 | 11 | Geometric, binomial and normal approximation |
| Feb/March 2024 · Paper 52 | Q2 | 8 | Binomial and geometric probabilities for goal attempts |
| Feb/March 2024 · Paper 52 | Q5 | 8 | Probability distribution table, expectation, variance |
| Oct/Nov 2023 · Paper 51 | Q2 | 7 | Geometric and binomial probabilities with dice sums |
| Oct/Nov 2023 · Paper 51 | Q5 | 9 | Distribution of spinner scores and conditional probability |
| Oct/Nov 2023 · Paper 52 | Q1 | 5 | Unknown probabilities from expectation, variance |
| Oct/Nov 2023 · Paper 52 | Q2 | 5 | Geometric and binomial probabilities for spinner |
| Oct/Nov 2023 · Paper 53 | Q1 | 6 | Distribution table, expectation and variance |
| Oct/Nov 2023 · Paper 53 | Q5 | 11 | Geometric, binomial and normal approximation |
| May/June 2023 · Paper 51 | Q6 | 11 | Distribution of count, expectation, approximation |
| May/June 2023 · Paper 51 | Q7 | 8 | Geometric and binomial probabilities for collection |
| May/June 2023 · Paper 52 | Q1 | 6 | Probability distribution with function of x |
| May/June 2023 · Paper 52 | Q4 | 9 | Geometric distribution, conditional probability, binomial |
| May/June 2023 · Paper 53 | Q1 | 4 | Geometric distribution with coins |
| May/June 2023 · Paper 53 | Q3 | 7 | Distribution with unknown constants and variance |
| Feb/March 2023 · Paper 52 | Q2 | 7 | Distribution of heads count with biased coin |
| Feb/March 2023 · Paper 52 | Q3 | 6 | Binomial and geometric probabilities for opinions |
| Oct/Nov 2022 · Paper 51 | Q1 | 4 | Unknown probabilities from expected value |
| Oct/Nov 2022 · Paper 51 | Q2 | 8 | Binomial probability and normal approximation |
| Oct/Nov 2022 · Paper 52 | Q3 | 5 | Geometric distribution with dice sums |
| Oct/Nov 2022 · Paper 52 | Q6 | 9 | Binomial probability and normal approximation |
| Oct/Nov 2022 · Paper 53 | Q4 | 8 | Distribution of maximum and geometric probabilities |
| Oct/Nov 2022 · Paper 53 | Q5 | 9 | Binomial and normal probabilities |
| May/June 2022 · Paper 51 | Q4 | 10 | Distribution table, expectation, binomial and geometric |
| May/June 2022 · Paper 52 | Q2 | 6 | Distribution of a sum from a die |
| May/June 2022 · Paper 52 | Q5 | 8 | Binomial probability and normal approximation |
| May/June 2022 · Paper 53 | Q3 | 6 | Distribution table with proportional probabilities |
| May/June 2022 · Paper 53 | Q4 | 7 | Geometric and binomial probabilities with dice |
| Feb/March 2022 · Paper 52 | Q1 | 5 | Constructing a distribution table, finding variance |
| Feb/March 2022 · Paper 52 | Q2 | 6 | Binomial probabilities over repeated periods |
| Feb/March 2022 · Paper 52 | Q6 (a)–(b) | 3 | Geometric distribution probabilities |
Chapter 27: S1 The Normal Distribution
34 past-paper questions
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Paper 5 (Probability & Statistics 1): 34 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 51 | Q6 | 9 | Normal expected count and unknown parameters |
| Oct/Nov 2025 · Paper 52 | Q3 | 7 | Normal expected count and unknown sd |
| Oct/Nov 2025 · Paper 53 | Q7 | 10 | Normal probabilities, percentile and expected days |
| May/June 2025 · Paper 51 | Q1 | 3 | Normal distribution finding unknown mean |
| May/June 2025 · Paper 51 | Q4 | 12 | Normal expectation, binomial and approximation |
| May/June 2025 · Paper 52 | Q2 | 5 | Normal approximation to binomial for residents |
| May/June 2025 · Paper 52 | Q7 | 12 | Normal expectation, finding parameters, binomial |
| May/June 2025 · Paper 53 | Q6 | 10 | Normal probabilities, expected count, unknown parameters |
| Feb/March 2025 · Paper 52 | Q5 (a)–(b) | 6 | Normal probability and unknown standard deviation |
| Oct/Nov 2024 · Paper 51 | Q5 | 9 | Normal probability and approximation to binomial |
| Oct/Nov 2024 · Paper 51 | Q6 | 8 | Normal percentiles for mean and sd, binomial count |
| Oct/Nov 2024 · Paper 52 | Q4 | 7 | Normal expected count and unknown standard deviation |
| Oct/Nov 2024 · Paper 53 | Q3 | 7 | Normal probability and finding a bound |
| May/June 2024 · Paper 51 | Q2 | 7 | Normal probability and unknown standard deviation |
| May/June 2024 · Paper 51 | Q5 (c) | 5 | Normal approximation to binomial |
| May/June 2024 · Paper 52 | Q3 | 6 | Normal distribution percentages and boundaries |
| May/June 2024 · Paper 53 | Q2 | 8 | Normal probability and finding mean and sd |
| Feb/March 2024 · Paper 52 | Q4 | 12 | Normal probability, unknown, approximation to binomial |
| Oct/Nov 2023 · Paper 51 | Q3 | 11 | Normal classification, percentile, normal approximation |
| Oct/Nov 2023 · Paper 52 | Q3 | 5 | Normal approximation to binomial for faulty items |
| Oct/Nov 2023 · Paper 52 | Q5 | 8 | Normal probabilities with relation of parameters |
| Oct/Nov 2023 · Paper 53 | Q2 | 6 | Normal probability and unknown standard deviation |
| May/June 2023 · Paper 51 | Q4 | 9 | Normal probabilities and unknown parameters |
| May/June 2023 · Paper 52 | Q5 | 12 | Normal probability and approximation to binomial |
| May/June 2023 · Paper 53 | Q2 | 5 | Normal approximation to binomial for votes |
| May/June 2023 · Paper 53 | Q6 | 10 | Normal distribution, binomial count, expected days |
| Feb/March 2023 · Paper 52 | Q6 | 11 | Normal probabilities and finding mean and sd |
| Oct/Nov 2022 · Paper 51 | Q4 | 9 | Normal probability, unknown sd, within-range count |
| Oct/Nov 2022 · Paper 52 | Q2 | 7 | Normal probability and expected count |
| Oct/Nov 2022 · Paper 53 | Q2 | 5 | Normal approximation to binomial |
| May/June 2022 · Paper 51 | Q5 | 11 | Normal probability and finding mean, sd |
| May/June 2022 · Paper 52 | Q4 | 7 | Normal probability and unknown standard deviation |
| May/June 2022 · Paper 53 | Q5 | 10 | Normal probability, income estimate, unknown value |
| Feb/March 2022 · Paper 52 | Q4 | 11 | Normal distribution probabilities and unknown parameter |
Chapter 28: S2 The Poisson Distribution
43 past-paper questions
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Paper 6 (Probability & Statistics 2): 43 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 61 | Q1 | 9 | Poisson probabilities and normal approximation for totals |
| Oct/Nov 2025 · Paper 61 | Q3 | 6 | Poisson approximation to binomial and finding proportion |
| Oct/Nov 2025 · Paper 62 | Q1 | 8 | Poisson conditions, probabilities and approximation |
| Oct/Nov 2025 · Paper 63 | Q1 | 9 | Poisson probabilities and normal approximation for totals |
| Oct/Nov 2025 · Paper 63 | Q3 | 6 | Poisson approximation to binomial and finding proportion |
| May/June 2025 · Paper 61 | Q1 | 3 | Poisson approximation to binomial |
| May/June 2025 · Paper 61 | Q5 | 11 | Poisson sums and equation for parameter |
| May/June 2025 · Paper 62 | Q3 | 4 | Poisson probability and equal-probability equation |
| May/June 2025 · Paper 62 | Q6 | 10 | Approximating binomial and Poisson distributions |
| May/June 2025 · Paper 63 | Q1 | 8 | Poisson probabilities and approximation |
| Feb/March 2025 · Paper 62 | Q3 | 10 | Poisson sums and normal approximation |
| Oct/Nov 2024 · Paper 61 | Q6 | 9 | Poisson arrivals over varied time periods |
| Oct/Nov 2024 · Paper 61 | Q7 (d) | 4 | Normal approximation to Poisson total |
| Oct/Nov 2024 · Paper 62 | Q1 | 3 | Poisson approximation to binomial |
| Oct/Nov 2024 · Paper 62 | Q5 | 11 | Poisson sums and approximating distributions |
| Oct/Nov 2024 · Paper 63 | Q6 | 9 | Poisson arrivals over varied time periods |
| Oct/Nov 2024 · Paper 63 | Q7 (d) | 4 | Normal approximation to Poisson total |
| May/June 2024 · Paper 61 | Q1 | 3 | Sum of independent Poisson variables |
| May/June 2024 · Paper 61 | Q5 | 8 | Poisson conditions, probabilities and normal approximation |
| May/June 2024 · Paper 61 | Q7 (c) | 4 | Poisson approximation to binomial for rare event |
| May/June 2024 · Paper 62 | Q1 | 5 | Normal approximation to Poisson and justification |
| May/June 2024 · Paper 62 | Q5 | 9 | Poisson goals, sums and conditional probability |
| May/June 2024 · Paper 63 | Q1 | 4 | Poisson approximation to binomial and justification |
| May/June 2024 · Paper 63 | Q7 (a)–(b) | 7 | Poisson sum probabilities and conditional probability |
| Feb/March 2024 · Paper 62 | Q3 | 4 | Poisson approximation to binomial and justification |
| Feb/March 2024 · Paper 62 | Q5 (a)–(c) | 7 | Poisson sums and comparisons |
| Oct/Nov 2023 · Paper 61 | Q3 | 14 | Poisson probabilities, approximation and model check |
| Oct/Nov 2023 · Paper 62 | Q1 | 6 | Normal and Poisson approximations |
| Oct/Nov 2023 · Paper 62 | Q7 | 9 | Poisson probabilities and most likely value |
| Oct/Nov 2023 · Paper 63 | Q3 | 14 | Poisson probabilities, approximation and model check |
| May/June 2023 · Paper 61 | Q1 | 6 | Poisson approximation to binomial and justification |
| May/June 2023 · Paper 61 | Q7 (e) | 4 | Normal approximation for Poisson total |
| May/June 2023 · Paper 62 | Q2 | 5 | Poisson conditions and approximation to binomial |
| May/June 2023 · Paper 62 | Q4 | 10 | Poisson conditions, sums and normal approximation |
| May/June 2023 · Paper 63 | Q6 | 5 | Poisson approximation to binomial and check |
| Feb/March 2023 · Paper 62 | Q2 | 13 | Poisson model assumptions and probabilities |
| Oct/Nov 2022 · Paper 61 | Q3 | 7 | Poisson probability and normal approximation |
| Oct/Nov 2022 · Paper 62 | Q3 | 6 | Poisson approximation to binomial and justification |
| Oct/Nov 2022 · Paper 63 | Q3 | 7 | Poisson probability and normal approximation |
| May/June 2022 · Paper 61 | Q5 | 10 | Poisson probabilities and normal approximation, sums |
| May/June 2022 · Paper 62 | Q3 | 6 | Poisson approximation to binomial and justification |
| May/June 2022 · Paper 63 | Q5 | 9 | Poisson over varying periods and approximation |
| Feb/March 2022 · Paper 62 | Q7 | 10 | Poisson approximations and unknown-parameter ratio |
Chapter 29: S2 Linear Combinations of Random Variables
28 past-paper questions
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Paper 6 (Probability & Statistics 2): 28 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 61 | Q6 | 10 | Total and comparison of normal masses |
| Oct/Nov 2025 · Paper 62 | Q2 | 6 | Standard deviation of linear combinations |
| Oct/Nov 2025 · Paper 63 | Q6 | 10 | Total and comparison of normal masses |
| May/June 2025 · Paper 61 | Q4 | 6 | Linear transformation of mean and variance |
| May/June 2025 · Paper 62 | Q1 (b) | 5 | Difference of two normal times |
| May/June 2025 · Paper 63 | Q5 | 4 | Sum of normal masses and sample size |
| Feb/March 2025 · Paper 62 | Q1 | 5 | Difference of independent normal variables |
| Oct/Nov 2024 · Paper 61 | Q2 | 5 | Total of normal masses compared to another |
| Oct/Nov 2024 · Paper 63 | Q2 | 5 | Total of normal masses compared to another |
| May/June 2024 · Paper 61 | Q2 | 5 | Comparison of normal variable with multiple |
| May/June 2024 · Paper 62 | Q4 | 6 | Comparing independent normal values |
| May/June 2024 · Paper 63 | Q3 | 5 | Total of normal masses compared to another |
| Feb/March 2024 · Paper 62 | Q4 | 10 | Linear combination of normal variables for cost |
| Oct/Nov 2023 · Paper 61 | Q4 | 8 | Income from normal variables compared |
| Oct/Nov 2023 · Paper 62 | Q6 | 7 | Combined yeast and flour mass probability |
| Oct/Nov 2023 · Paper 63 | Q4 | 8 | Income from normal variables compared |
| May/June 2023 · Paper 61 | Q5 | 7 | Combined normal variables for masses |
| May/June 2023 · Paper 62 | Q5 | 11 | Differences and weighted sums of normals |
| May/June 2023 · Paper 63 | Q4 | 6 | Sum of independent daily normal quantities |
| Feb/March 2023 · Paper 62 | Q5 | 11 | Linear combination of normal variables |
| Oct/Nov 2022 · Paper 61 | Q4 | 8 | Total and profit from combined normal variables |
| Oct/Nov 2022 · Paper 62 | Q6 | 10 | Total mass and comparison of normal bags |
| Oct/Nov 2022 · Paper 63 | Q4 | 8 | Total and profit from combined normal variables |
| May/June 2022 · Paper 61 | Q3 | 5 | Difference of normal variables, probability |
| May/June 2022 · Paper 61 | Q4 | 8 | Mean and sd of combined binomial and Poisson |
| May/June 2022 · Paper 62 | Q6 | 10 | Combinations of normal masses, lift capacity |
| May/June 2022 · Paper 63 | Q4 | 10 | Sum and ratio comparison of normal variables |
| Feb/March 2022 · Paper 62 | Q5 | 9 | Sum and difference of normal variables |
Chapter 30: S2 Continuous Random Variables
29 past-paper questions
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Paper 6 (Probability & Statistics 2): 29 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 61 | Q7 | 7 | Density function probabilities and median |
| Oct/Nov 2025 · Paper 62 | Q5 | 9 | Density constant, median and conditional probability |
| Oct/Nov 2025 · Paper 63 | Q7 | 7 | Density function probabilities and median |
| May/June 2025 · Paper 61 | Q7 | 8 | Cosine density, probability and mean |
| May/June 2025 · Paper 62 | Q7 | 9 | Power density function, mean and median |
| May/June 2025 · Paper 63 | Q6 | 9 | Linear density function and mean comparison |
| Feb/March 2025 · Paper 62 | Q4 | 11 | Linear density function, mean and median |
| Oct/Nov 2024 · Paper 61 | Q4 | 6 | Density function constant and expected value |
| Oct/Nov 2024 · Paper 62 | Q6 | 11 | Reciprocal-square density, mean and median |
| Oct/Nov 2024 · Paper 63 | Q4 | 6 | Density function constant and expected value |
| May/June 2024 · Paper 61 | Q6 | 8 | Quarter circle density function and mean |
| May/June 2024 · Paper 62 | Q7 | 10 | Density with cosine, median and mean |
| May/June 2024 · Paper 63 | Q5 | 10 | Density function constant, median and mean |
| Feb/March 2024 · Paper 62 | Q6 | 10 | Symmetric density, constant and variance |
| Oct/Nov 2023 · Paper 61 | Q6 | 8 | Symmetric density and probability relations |
| Oct/Nov 2023 · Paper 62 | Q5 | 9 | Density with reciprocal square, mean and median |
| Oct/Nov 2023 · Paper 63 | Q6 | 8 | Symmetric density and probability relations |
| May/June 2023 · Paper 61 | Q2 | 8 | Checking valid probability density functions |
| May/June 2023 · Paper 62 | Q7 | 8 | Linear density function, mean and median |
| May/June 2023 · Paper 63 | Q1 | 3 | Expected value from density function |
| May/June 2023 · Paper 63 | Q7 | 8 | Semicircle density, area and angle |
| Feb/March 2023 · Paper 62 | Q3 | 8 | Symmetric density function and variance |
| Oct/Nov 2022 · Paper 61 | Q6 | 7 | Quadratic density function and probability condition |
| Oct/Nov 2022 · Paper 62 | Q7 | 8 | Symmetric density and probability from constants |
| Oct/Nov 2022 · Paper 63 | Q6 | 7 | Quadratic density function and probability condition |
| May/June 2022 · Paper 61 | Q6 | 9 | Uniform density, median and variance |
| May/June 2022 · Paper 62 | Q5 | 15 | Mean, variance and median of continuous variable |
| May/June 2022 · Paper 63 | Q7 | 9 | Symmetric density functions, mean and constant |
| Feb/March 2022 · Paper 62 | Q6 | 11 | Probability density function, variance and maximum |
Chapter 31: S2 Sampling and Estimation
55 past-paper questions
Free chapter preview →
Paper 6 (Probability & Statistics 2): 55 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 61 | Q4 | 4 | Confidence level and conditional coverage probability |
| Oct/Nov 2025 · Paper 62 | Q3 | 8 | Confidence interval parameters and coverage probability |
| Oct/Nov 2025 · Paper 63 | Q4 | 4 | Confidence level and conditional coverage probability |
| May/June 2025 · Paper 61 | Q2 | 7 | Distribution of sample mean using CLT |
| May/June 2025 · Paper 61 | Q3 (a) | 3 | Unbiased estimates from sample |
| May/June 2025 · Paper 61 | Q6 (c) | 3 | Confidence interval for proportion |
| May/June 2025 · Paper 62 | Q1 (a) | 1 | Random selection method using a die |
| May/June 2025 · Paper 62 | Q2 | 3 | Sum of squares from unbiased variance estimate |
| May/June 2025 · Paper 62 | Q4 | 4 | Confidence interval width and sample proportion |
| May/June 2025 · Paper 63 | Q3 | 8 | Estimates and confidence interval with sample size |
| May/June 2025 · Paper 63 | Q4 | 4 | Judging whether a selection method is random |
| Feb/March 2025 · Paper 62 | Q2 (a) | 3 | Unbiased estimates from summary data |
| Feb/March 2025 · Paper 62 | Q6 | 8 | Sampling method and proportion confidence interval |
| Oct/Nov 2024 · Paper 61 | Q1 | 4 | Confidence interval and its interpretation |
| Oct/Nov 2024 · Paper 61 | Q3 | 6 | Unbiased estimates and distribution of sample mean |
| Oct/Nov 2024 · Paper 62 | Q2 | 4 | Mean, standard deviation from a confidence interval |
| Oct/Nov 2024 · Paper 62 | Q4 | 6 | Distribution of sample mean from normal population |
| Oct/Nov 2024 · Paper 63 | Q1 | 4 | Confidence interval and its interpretation |
| Oct/Nov 2024 · Paper 63 | Q3 | 6 | Unbiased estimates and distribution of sample mean |
| May/June 2024 · Paper 61 | Q3 | 6 | Confidence interval and its interpretation |
| May/June 2024 · Paper 61 | Q4 (a) | 3 | Unbiased estimates from sample |
| May/June 2024 · Paper 62 | Q2 | 6 | Random sample selection and variance estimate |
| May/June 2024 · Paper 62 | Q3 | 4 | Confidence interval for a proportion |
| May/June 2024 · Paper 63 | Q2 | 4 | Confidence interval to estimate standard deviation |
| May/June 2024 · Paper 63 | Q6 (a) | 3 | Unbiased estimates from frequency table |
| May/June 2024 · Paper 63 | Q7 (c) | 6 | Distribution of a sample mean |
| Feb/March 2024 · Paper 62 | Q1 | 4 | Unbiased estimates and conditions |
| Feb/March 2024 · Paper 62 | Q2 | 4 | Confidence interval and claim check |
| Oct/Nov 2023 · Paper 61 | Q1 | 3 | Distribution of a sample mean |
| Oct/Nov 2023 · Paper 61 | Q2 | Confidence interval and confidence level | |
| Oct/Nov 2023 · Paper 62 | Q2 | 5 | Confidence interval and width for a mean |
| Oct/Nov 2023 · Paper 63 | Q1 | 3 | Distribution of a sample mean |
| Oct/Nov 2023 · Paper 63 | Q2 | Confidence interval and confidence level | |
| May/June 2023 · Paper 61 | Q4 | 6 | Confidence interval width and sampling issues |
| May/June 2023 · Paper 61 | Q6 | 3 | Unbiased variance estimate to find a value |
| May/June 2023 · Paper 62 | Q1 | 3 | Approximate confidence interval for a proportion |
| May/June 2023 · Paper 62 | Q3 (a) | 3 | Unbiased estimates of mean and variance |
| May/June 2023 · Paper 63 | Q2 | 3 | Random sampling with random digits |
| May/June 2023 · Paper 63 | Q3 | 5 | Confidence interval for proportion, finding unknown count |
| May/June 2023 · Paper 63 | Q5 (a) | 3 | Unbiased estimates of mean and variance |
| Feb/March 2023 · Paper 62 | Q1 | 4 | Confidence interval for proportion and width |
| Oct/Nov 2022 · Paper 61 | Q1 | 3 | Unbiased estimates for mean and variance |
| Oct/Nov 2022 · Paper 61 | Q5 | 7 | Confidence interval and confidence level from width |
| Oct/Nov 2022 · Paper 62 | Q1 | 7 | Unbiased estimates and confidence level |
| Oct/Nov 2022 · Paper 62 | Q5 | 6 | Distribution of sample mean for binomial |
| Oct/Nov 2022 · Paper 63 | Q1 | 3 | Unbiased estimates for mean and variance |
| Oct/Nov 2022 · Paper 63 | Q5 | 7 | Confidence interval and confidence level from width |
| May/June 2022 · Paper 61 | Q1 | 7 | Confidence interval for a mean and interpretation |
| May/June 2022 · Paper 62 | Q1 | 4 | Confidence interval and its misuse |
| May/June 2022 · Paper 62 | Q7 | 5 | Distribution of a sample mean from Poisson |
| May/June 2022 · Paper 63 | Q1 | 3 | Probability for a sample mean of normal variable |
| May/June 2022 · Paper 63 | Q3 (c) | 3 | Confidence interval for a mean |
| May/June 2022 · Paper 63 | Q6 | 4 | Unbiased variance estimate to find unknown value |
| Feb/March 2022 · Paper 62 | Q1 | 4 | Unbiased estimates and reliability |
| Feb/March 2022 · Paper 62 | Q3 | 5 | Confidence interval for a proportion |
Chapter 32: S2 Hypothesis Tests
55 past-paper questions
Free chapter preview →
Paper 6 (Probability & Statistics 2): 55 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 61 | Q2 | 8 | Test on mean mass from sample data |
| Oct/Nov 2025 · Paper 61 | Q5 | 6 | Binomial test error probabilities and rejection region |
| Oct/Nov 2025 · Paper 62 | Q4 | 7 | Binomial test and Poisson approximation check |
| Oct/Nov 2025 · Paper 62 | Q6 | 12 | Mean test, Type I and Type II errors |
| Oct/Nov 2025 · Paper 63 | Q2 | 8 | Test on mean mass from sample data |
| Oct/Nov 2025 · Paper 63 | Q5 | 6 | Binomial test error probabilities and rejection region |
| May/June 2025 · Paper 61 | Q3 (b) | 5 | One-tailed test for population mean |
| May/June 2025 · Paper 61 | Q6 (a)–(b) | 4 | Hypotheses and Type II error for proportion |
| May/June 2025 · Paper 62 | Q5 | 4 | Hypothesis test on changed mean |
| May/June 2025 · Paper 62 | Q8 | 10 | Binomial test, Type I and Type II errors |
| May/June 2025 · Paper 63 | Q2 | 7 | Test statistic, standard deviation and test |
| May/June 2025 · Paper 63 | Q7 | 10 | Binomial test critical value and error types |
| Feb/March 2025 · Paper 62 | Q2 (b)–(c) | 6 | Mean test and central limit theorem use |
| Feb/March 2025 · Paper 62 | Q5 | 7 | Binomial test significance level and error types |
| Oct/Nov 2024 · Paper 61 | Q5 | 6 | Choice of tails and test for a mean |
| Oct/Nov 2024 · Paper 61 | Q7 (a)–(c) | 10 | Poisson test, Type I and Type II errors |
| Oct/Nov 2024 · Paper 62 | Q3 | 6 | Binomial hypothesis test and model suitability |
| Oct/Nov 2024 · Paper 62 | Q7 | 9 | Mean test and error type claims |
| Oct/Nov 2024 · Paper 63 | Q5 | 6 | Choice of tails and test for a mean |
| Oct/Nov 2024 · Paper 63 | Q7 (a)–(c) | 10 | Poisson test, Type I and Type II errors |
| May/June 2024 · Paper 61 | Q4 (b) | 6 | One-tailed test for mean |
| May/June 2024 · Paper 61 | Q7 (a)–(b) | 7 | Binomial hypothesis test and Type I error |
| May/June 2024 · Paper 62 | Q6 | 10 | Test for mean and Type II error |
| May/June 2024 · Paper 63 | Q4 | 5 | Exact binomial hypothesis test |
| May/June 2024 · Paper 63 | Q6 (b)–(d) | 6 | Hypothesis test, significance and Type I error |
| Feb/March 2024 · Paper 62 | Q5 (d) | 5 | Hypothesis test for Poisson mean |
| Feb/March 2024 · Paper 62 | Q7 | 6 | Type I and Type II errors in z-test |
| Oct/Nov 2023 · Paper 61 | Q5 | 5 | Hypothesis test for Poisson mean |
| Oct/Nov 2023 · Paper 61 | Q7 | 12 | Mean test and Type II error |
| Oct/Nov 2023 · Paper 62 | Q3 | 9 | Binomial test, significance and Type I error |
| Oct/Nov 2023 · Paper 62 | Q4 | 5 | Test on a mean and one-tailed condition |
| Oct/Nov 2023 · Paper 63 | Q5 | 5 | Hypothesis test for Poisson mean |
| Oct/Nov 2023 · Paper 63 | Q7 | 12 | Mean test and Type II error |
| May/June 2023 · Paper 61 | Q3 | 6 | Hypothesis test for a mean with new method |
| May/June 2023 · Paper 61 | Q7 (a)–(d) | 10 | Poisson hypothesis test and critical region |
| May/June 2023 · Paper 62 | Q3 (b) | 5 | Two-tailed test comparing means |
| May/June 2023 · Paper 62 | Q6 | 5 | Binomial test error probabilities |
| May/June 2023 · Paper 63 | Q5 (b)–(c) | 6 | Two-tailed test for mean and central limit theorem |
| May/June 2023 · Paper 63 | Q8 | 11 | Poisson test, error type and probabilities |
| Feb/March 2023 · Paper 62 | Q4 | 5 | Error probabilities in a Poisson test |
| Feb/March 2023 · Paper 62 | Q6 | 9 | One-tailed test conclusions and significance levels |
| Oct/Nov 2022 · Paper 61 | Q2 | 8 | Binomial hypothesis test and rejection region |
| Oct/Nov 2022 · Paper 61 | Q7 | 10 | Mean test and Type II error |
| Oct/Nov 2022 · Paper 62 | Q2 | 5 | One-tailed test of a mean |
| Oct/Nov 2022 · Paper 62 | Q4 | 8 | Poisson hypothesis test, error types |
| Oct/Nov 2022 · Paper 63 | Q2 | 8 | Binomial hypothesis test and rejection region |
| Oct/Nov 2022 · Paper 63 | Q7 | 10 | Mean test and Type II error |
| May/June 2022 · Paper 61 | Q2 | 5 | Hypothesis test on a claim with a die |
| May/June 2022 · Paper 61 | Q7 | 6 | Hypotheses and Type I error for a mean |
| May/June 2022 · Paper 62 | Q2 | 5 | Z-test for a mean |
| May/June 2022 · Paper 62 | Q4 | 5 | Poisson hypothesis test and critical region |
| May/June 2022 · Paper 63 | Q2 | 6 | Error types in a proportion test |
| May/June 2022 · Paper 63 | Q3 (a)–(b) | 6 | Test of mean with sample reason |
| Feb/March 2022 · Paper 62 | Q2 | 5 | Hypothesis test for a binomial proportion |
| Feb/March 2022 · Paper 62 | Q4 | 6 | One-tailed z-test for mean and Type I error |
Revise the chapter before you practise. Our AS & A Level Mathematics 9709 notes cover every syllabus statement with worked examples, common mistakes from examiner reports, 20 MCQs per chapter and original exam-style questions with full mark schemes.
Index updated 2026-11-02. Spotted a question in the wrong chapter? Tell us on WhatsApp and we will fix it.