Free resource · Cambridge IGCSE Mathematics 0580
IGCSE Mathematics 0580 past paper questions by topic (2022–2025)
Every question from the 56 Extended papers of 2022–2025 — Paper 2 (Non-calculator), Paper 4 (Calculator) — sorted into the 26 chapters of our Mathematics notes: 1,237 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.
This page lists question references only. Download the question papers and mark schemes from the Cambridge International website or your school. Notes Bazar is independent and not endorsed by or affiliated with Cambridge University Press & Assessment. Topic labels are our own.
- Number: Types, Sets and Fractions (112)
- Indices, Standard Form and Surds (60)
- Accuracy, Calculators, Time and Money (71)
- Ratio, Proportion and Rates (36)
- Percentages, Growth and Decay (52)
- Algebraic Manipulation (84)
- Equations and Formulas (93)
- Inequalities (20)
- Sequences (33)
- Direct and Inverse Proportion (21)
- Graphs in Practical Situations (15)
- Graphs of Functions and Sketching Curves (30)
- Differentiation (32)
- Functions (31)
- Coordinate Geometry (29)
- Geometrical Terms, Constructions and Symmetry (31)
- Angles and Similarity (67)
- Circle Theorems (33)
- Mensuration (82)
- Pythagoras and Trigonometry (43)
- Sine Rule, Cosine Rule and 3D Trigonometry (61)
- Transformations (27)
- Vectors (38)
- Probability (55)
- Statistics: Averages, Charts and Scatter Diagrams (54)
- Cumulative Frequency and Histograms (27)
Chapter 1: Number: Types, Sets and Fractions
112 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 98 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q10 | 2 | Set notation and listing elements |
| Oct/Nov 2025 · Paper 21 | Q11 | 2 | Recurring decimal to a fraction |
| Oct/Nov 2025 · Paper 22 | Q1 | 1 | Temperature change with negative numbers |
| Oct/Nov 2025 · Paper 22 | Q2 | 1 | Common factors of two numbers |
| Oct/Nov 2025 · Paper 22 | Q9 | 3 | Fraction of a quantity remaining |
| Oct/Nov 2025 · Paper 22 | Q13 | 4 | Prime factors in index form; cube numbers |
| Oct/Nov 2025 · Paper 23 | Q2 | 1 | Common factors of two numbers |
| Oct/Nov 2025 · Paper 23 | Q7 | 3 | Sums of prime numbers |
| Oct/Nov 2025 · Paper 23 | Q18 | 2 | Shading Venn diagram regions |
| Oct/Nov 2025 · Paper 23 | Q20 | 3 | Adding recurring decimals as a fraction |
| May/June 2025 · Paper 21 | Q4 | 3 | Fraction calculation without a calculator |
| May/June 2025 · Paper 21 | Q7 | 3 | Recurring decimal to fraction |
| May/June 2025 · Paper 22 | Q8 | 2 | Highest common factor |
| May/June 2025 · Paper 22 | Q14 | 2 | Recurring decimal to fraction |
| May/June 2025 · Paper 23 | Q7 | 5 | Fraction calculations without a calculator |
| May/June 2025 · Paper 23 | Q8 | 4 | Prime factors and highest common factor |
| May/June 2025 · Paper 23 | Q14 | 2 | Lowest common multiple of algebraic terms |
| May/June 2025 · Paper 23 | Q16 | 3 | Recurring decimal to fraction |
| Feb/March 2025 · Paper 22 | Q17 | 4 | Adding recurring decimals as a fraction |
| Feb/March 2025 · Paper 22 | Q19 | 1 | Shading a three-set Venn region |
| Oct/Nov 2024 · Paper 21 | Q2 | 1 | Reciprocal of a mixed number |
| Oct/Nov 2024 · Paper 21 | Q3 | 2 | Comparing fractions, decimals and percentages |
| Oct/Nov 2024 · Paper 21 | Q11 | 3 | Subtracting mixed numbers without a calculator |
| Oct/Nov 2024 · Paper 21 | Q19 | 3 | Set notation with three sets |
| Oct/Nov 2024 · Paper 22 | Q3 | 3 | Natural, irrational numbers and reciprocals |
| Oct/Nov 2024 · Paper 22 | Q7 | 2 | Dividing fractions without a calculator |
| Oct/Nov 2024 · Paper 22 | Q18 | 4 | Venn diagram of number types; shading regions |
| Oct/Nov 2024 · Paper 23 | Q1 | 2 | Cube and prime numbers from a list |
| Oct/Nov 2024 · Paper 23 | Q10 | 3 | Subtracting mixed numbers without a calculator |
| Oct/Nov 2024 · Paper 23 | Q21 | 2 | Three-set Venn diagram: notation and counting |
| May/June 2024 · Paper 21 | Q4 | 2 | Common odd factor of two numbers |
| May/June 2024 · Paper 21 | Q15 | 3 | Recurring decimal to fraction |
| May/June 2024 · Paper 21 | Q16 | 2 | Venn diagrams: shading and three-set count |
| May/June 2024 · Paper 22 | Q1 | 1 | Difference between temperatures |
| May/June 2024 · Paper 22 | Q4 | 3 | Fractions of an amount |
| May/June 2024 · Paper 22 | Q7 | 1 | Shading a union on a Venn diagram |
| May/June 2024 · Paper 22 | Q13 | 3 | Dividing mixed numbers without a calculator |
| May/June 2024 · Paper 22 | Q17 | 2 | Completing a two-set Venn diagram |
| May/June 2024 · Paper 22 | Q23 (a) | 1 | Three-set Venn diagram notation count |
| May/June 2024 · Paper 23 | Q1 | 1 | Writing a number from words in figures |
| May/June 2024 · Paper 23 | Q2 | 1 | Inserting brackets in a calculation |
| May/June 2024 · Paper 23 | Q8 | 2 | Subtracting fractions without a calculator |
| May/June 2024 · Paper 23 | Q13 | 2 | Venn diagrams: shading and set notation |
| May/June 2024 · Paper 23 | Q21 | 2 | Recurring decimal to fraction |
| Feb/March 2024 · Paper 22 | Q11 | 3 | Subtracting mixed numbers without a calculator |
| Feb/March 2024 · Paper 22 | Q16 | 2 | Completing a Venn diagram from set definitions |
| Feb/March 2024 · Paper 22 | Q18 | 2 | Highest common factor of algebraic terms |
| Oct/Nov 2023 · Paper 21 | Q9 | 2 | Highest common factor |
| Oct/Nov 2023 · Paper 21 | Q12 | 3 | Recurring decimal to a fraction |
| Oct/Nov 2023 · Paper 21 | Q14 | 4 | Venn diagram: counting and shading three sets |
| Oct/Nov 2023 · Paper 22 | Q2 | 1 | Adding to a negative number |
| Oct/Nov 2023 · Paper 22 | Q6 | 2 | Prime numbers |
| Oct/Nov 2023 · Paper 22 | Q8 | 3 | Subtracting mixed numbers without a calculator |
| Oct/Nov 2023 · Paper 22 | Q9 | 2 | Product of prime factors |
| Oct/Nov 2023 · Paper 22 | Q15 | 3 | Venn diagram: shading and completing counts |
| Oct/Nov 2023 · Paper 22 | Q16 | 2 | LCM of algebraic terms |
| Oct/Nov 2023 · Paper 23 | Q2 | 2 | Identifying cube and prime numbers |
| Oct/Nov 2023 · Paper 23 | Q7 | 3 | Dividing mixed numbers without a calculator |
| Oct/Nov 2023 · Paper 23 | Q8 | 2 | Highest common factor |
| May/June 2023 · Paper 21 | Q10 | 3 | Dividing mixed numbers without a calculator |
| May/June 2023 · Paper 22 | Q1 | 1 | Negative numbers: temperature change |
| May/June 2023 · Paper 22 | Q2 | 2 | Identifying prime numbers in a list |
| May/June 2023 · Paper 22 | Q6 | 3 | Set notation: elements, intersection, membership |
| May/June 2023 · Paper 22 | Q7 | 3 | Dividing fractions without a calculator |
| May/June 2023 · Paper 22 | Q16 | 3 | Recurring decimal to fraction |
| May/June 2023 · Paper 22 | Q20 | 1 | Shading a region in a three-set Venn diagram |
| May/June 2023 · Paper 23 | Q6 | 2 | Finding the whole from a fraction |
| May/June 2023 · Paper 23 | Q10 | 3 | Adding mixed numbers without a calculator |
| May/June 2023 · Paper 23 | Q11 | 3 | Venn diagram: completing and shading sets |
| May/June 2023 · Paper 23 | Q14 | 3 | Recurring decimal to fraction |
| Feb/March 2023 · Paper 22 | Q1 | 2 | Cube numbers and primes from a list |
| Feb/March 2023 · Paper 22 | Q3 | 1 | Shading a region on a Venn diagram |
| Feb/March 2023 · Paper 22 | Q6 | 2 | Dividing fractions without a calculator |
| Feb/March 2023 · Paper 22 | Q11 | 2 | Highest common factor of algebraic terms |
| Oct/Nov 2022 · Paper 21 | Q1 | 1 | Common multiple of two numbers |
| Oct/Nov 2022 · Paper 21 | Q3 | 2 | One quantity as a fraction of another |
| Oct/Nov 2022 · Paper 21 | Q7 | 2 | Set notation from a Venn diagram |
| Oct/Nov 2022 · Paper 21 | Q9 | 2 | Adding mixed numbers without a calculator |
| Oct/Nov 2022 · Paper 22 | Q3 | 1 | Squares of positive and negative numbers |
| Oct/Nov 2022 · Paper 22 | Q7 | 2 | Subtracting fractions without a calculator |
| Oct/Nov 2022 · Paper 22 | Q12 | 2 | Products of prime factors |
| Oct/Nov 2022 · Paper 22 | Q16 | 4 | Venn diagrams: shading regions and completing counts |
| Oct/Nov 2022 · Paper 22 | Q18 | 3 | Recurring decimal to a fraction |
| Oct/Nov 2022 · Paper 23 | Q2 | 2 | Identifying square and cube numbers |
| Oct/Nov 2022 · Paper 23 | Q5 | 2 | Subtracting fractions without a calculator |
| Oct/Nov 2022 · Paper 23 | Q7 | 2 | Lowest common multiple |
| Oct/Nov 2022 · Paper 23 | Q13 | 2 | Recurring decimal to a fraction |
| May/June 2022 · Paper 21 | Q1 | 1 | Prime number in a range |
| May/June 2022 · Paper 21 | Q6 | 2 | Product of prime factors |
| May/June 2022 · Paper 21 | Q7 | 2 | Subtracting fractions without a calculator |
| May/June 2022 · Paper 22 | Q1 | 1 | Difference between negative temperatures |
| May/June 2022 · Paper 22 | Q13 | 3 | Subtracting mixed numbers without a calculator |
| May/June 2022 · Paper 22 | Q15 | 2 | Highest common factor of algebraic terms |
| May/June 2022 · Paper 22 | Q16 (a)–(b) | 2 | Three-set Venn diagram: notation and counts |
| May/June 2022 · Paper 23 | Q8 | 2 | Dividing fractions without a calculator |
| May/June 2022 · Paper 23 | Q10 | 1 | Venn diagram: number in a complement region |
| May/June 2022 · Paper 23 | Q12 | 4 | Factors, multiples and primes |
| Feb/March 2022 · Paper 22 | Q15 | 3 | Multiplying mixed numbers without a calculator |
Paper 4 (Calculator): 14 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q12 | 2 | Venn diagram counts and set notation |
| Oct/Nov 2025 · Paper 43 | Q8 | 2 | Ordering fractions and percentages of a quantity |
| Oct/Nov 2025 · Paper 43 | Q9 | 1 | Equivalent calculation for dividing by a fraction |
| May/June 2025 · Paper 41 | Q10 (a) | 2 | Listing factors of a number |
| May/June 2025 · Paper 43 | Q3 | 2 | Identifying natural and irrational numbers |
| May/June 2025 · Paper 43 | Q7 | 3 | Set notation: counting, intersection and union |
| May/June 2025 · Paper 43 | Q17 | 1 | Shading a three-set Venn diagram region |
| Feb/March 2025 · Paper 42 | Q1 | 1 | Prime factor of a number |
| Oct/Nov 2024 · Paper 41 | Q1 (a) | 6 | Prime factors, HCF and LCM |
| May/June 2023 · Paper 41 | Q9 | 8 | Venn diagrams: elements, shading, three sets |
| Feb/March 2023 · Paper 42 | Q7 (a)–(b) | 4 | Two-set Venn diagram and set notation |
| Oct/Nov 2022 · Paper 41 | Q2 (b), (f) | 3 | Prime numbers; recurring decimal to a fraction |
| May/June 2022 · Paper 41 | Q8 (a) | 3 | Set notation and shading Venn regions |
| May/June 2022 · Paper 42 | Q1 (a), (d) | 3 | LCM; recurring decimal as a fraction |
Chapter 2: Indices, Standard Form and Surds
60 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 41 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q6 | 3 | Index laws and fractional indices |
| Oct/Nov 2025 · Paper 21 | Q15 | 3 | Standard form calculations |
| Oct/Nov 2025 · Paper 21 | Q19 | 3 | Exponential equation using index laws |
| Oct/Nov 2025 · Paper 21 | Q21 | 4 | Surds: expanding and rationalising |
| Oct/Nov 2025 · Paper 22 | Q14 | 4 | Negative and fractional indices |
| Oct/Nov 2025 · Paper 22 | Q18 | 3 | Rationalising a surd denominator |
| Oct/Nov 2025 · Paper 22 | Q24 | 2 | Solving with index laws |
| Oct/Nov 2025 · Paper 23 | Q9 | 1 | Index laws: finding a power |
| Oct/Nov 2025 · Paper 23 | Q12 | 5 | Zero and negative indices; powers of three |
| Oct/Nov 2025 · Paper 23 | Q24 | 6 | Surds: simplifying, area and rationalising |
| May/June 2025 · Paper 21 | Q15 | 4 | Expanding surds; rationalising the denominator |
| May/June 2025 · Paper 21 | Q19 | 2 | Evaluating negative fractional indices |
| May/June 2025 · Paper 22 | Q11 | 3 | Standard form: writing and adding |
| May/June 2025 · Paper 22 | Q17 | 4 | Fractional and negative indices |
| May/June 2025 · Paper 22 | Q18 | 4 | Surds: rationalising and expanding |
| May/June 2025 · Paper 23 | Q15 | 6 | Surds: simplifying and rationalising |
| Feb/March 2025 · Paper 22 | Q20 | 5 | Simplifying surds; rationalising the denominator |
| Feb/March 2025 · Paper 22 | Q23 | 6 | Fractional indices; solving an index equation |
| Oct/Nov 2024 · Paper 23 | Q17 | 4 | Simplifying algebraic indices |
| May/June 2024 · Paper 22 | Q10 | 1 | Writing a number in standard form |
| May/June 2024 · Paper 23 | Q12 | 4 | Simplifying algebraic indices and roots |
| May/June 2024 · Paper 23 | Q17 | 4 | Standard form multiplication and addition |
| Feb/March 2024 · Paper 22 | Q21 | 3 | Indices: finding a power; simplifying |
| Oct/Nov 2023 · Paper 21 | Q10 | 5 | Simplifying with laws of indices |
| Oct/Nov 2023 · Paper 22 | Q13 | 4 | Index equation and fractional powers |
| Oct/Nov 2023 · Paper 23 | Q17 (a) | 2 | Simplifying fractional powers |
| May/June 2023 · Paper 21 | Q17 | 2 | Simplifying fractional indices |
| May/June 2023 · Paper 23 | Q5 | 1 | Dividing powers of the same base |
| Feb/March 2023 · Paper 22 | Q8 | 2 | Calculating with standard form answer |
| Feb/March 2023 · Paper 22 | Q15 | 2 | Simplifying fractional indices |
| Oct/Nov 2022 · Paper 21 | Q10 | 2 | Dividing algebraic terms with indices |
| Oct/Nov 2022 · Paper 21 | Q17 | 2 | Simplifying fractional powers and roots |
| Oct/Nov 2022 · Paper 22 | Q20 | 3 | Simplifying with fractional and negative indices |
| May/June 2022 · Paper 21 | Q2 | 1 | Evaluating powers |
| May/June 2022 · Paper 21 | Q13 | 2 | Subtracting numbers in standard form |
| May/June 2022 · Paper 21 | Q15 | 1 | Solving an index equation |
| May/June 2022 · Paper 21 | Q22 | 2 | Simplifying fractional indices |
| May/June 2022 · Paper 22 | Q11 | 1 | Finding a power using index laws |
| May/June 2022 · Paper 23 | Q6 | 2 | Index laws: division and zero index |
| May/June 2022 · Paper 23 | Q25 | 3 | Solving an index equation |
| Feb/March 2022 · Paper 22 | Q13 | 3 | Laws of indices: simplifying and finding a power |
Paper 4 (Calculator): 19 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 43 | Q6 | 3 | Simplifying algebraic indices |
| Oct/Nov 2025 · Paper 43 | Q11 | 2 | Standard form: recognising and ordering |
| May/June 2025 · Paper 41 | Q21 | 3 | Equating powers: one index in terms of another |
| May/June 2025 · Paper 42 | Q21 | 4 | Simplifying products and roots with indices |
| May/June 2025 · Paper 43 | Q6 | 2 | Calculating with standard form |
| May/June 2025 · Paper 43 | Q9 | 3 | Laws of indices: simplifying and solving |
| May/June 2025 · Paper 43 | Q12 | 3 | Indices with powers of ten |
| Feb/March 2025 · Paper 42 | Q9 | 3 | Standard form: writing and calculating |
| Oct/Nov 2024 · Paper 41 | Q1 (b), (d) | 6 | Index laws and an exponential equation |
| May/June 2024 · Paper 41 | Q3 (d) | 3 | Simplifying negative fractional indices |
| May/June 2024 · Paper 42 | Q5 (a) | 2 | Simplifying fractional algebraic indices |
| Oct/Nov 2023 · Paper 41 | Q3 | 14 | Standard form with astronomical data |
| Oct/Nov 2023 · Paper 43 | Q2 (d) | 3 | Standard form and population density |
| May/June 2023 · Paper 42 | Q9 (a) | 5 | Simplifying algebraic indices |
| Oct/Nov 2022 · Paper 41 | Q2 (c)–(e) | 4 | Negative indices and standard form |
| Oct/Nov 2022 · Paper 42 | Q6 (d) | 2 | Indices: sum of equal powers |
| Oct/Nov 2022 · Paper 43 | Q2 (a) | 6 | Simplifying with indices |
| May/June 2022 · Paper 42 | Q1 (c) | 2 | Dividing numbers in standard form |
| Feb/March 2022 · Paper 42 | Q1 (c) | 2 | Number in words and standard form |
Chapter 3: Accuracy, Calculators, Time and Money
71 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 40 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q9 | 2 | Lower bound of a distance |
| Oct/Nov 2025 · Paper 22 | Q10 (a) | 3 | Estimating by rounding to one significant figure |
| Feb/March 2025 · Paper 22 | Q2 | 1 | Journey time in hours and minutes |
| Feb/March 2025 · Paper 22 | Q9 | 3 | Estimating using one significant figure |
| Oct/Nov 2024 · Paper 21 | Q1 | 1 | Finishing time using the 24-hour clock |
| Oct/Nov 2024 · Paper 22 | Q10 | 1 | Using a calculator with powers and roots |
| Oct/Nov 2024 · Paper 23 | Q2 | 1 | Journey time across midnight |
| Oct/Nov 2024 · Paper 23 | Q24 | 3 | Upper bound of a rectangle width |
| May/June 2024 · Paper 21 | Q5 | 2 | Calculator work with roots and powers |
| May/June 2024 · Paper 22 | Q2 | 2 | Money: hourly charge plus fixed fee |
| May/June 2024 · Paper 22 | Q5 | 2 | Completing a timetable |
| May/June 2024 · Paper 22 | Q6 | 1 | Rounding to significant figures |
| Feb/March 2024 · Paper 22 | Q1 | 1 | Time across midnight |
| Feb/March 2024 · Paper 22 | Q2 | 1 | Calculator work with powers |
| Oct/Nov 2023 · Paper 21 | Q4 | 3 | Shopping costs: completing a table |
| Oct/Nov 2023 · Paper 21 | Q7 | 1 | Currency conversion |
| Oct/Nov 2023 · Paper 21 | Q8 | 1 | Calculating with mixed numbers on a calculator |
| Oct/Nov 2023 · Paper 21 | Q16 | 3 | Bounds of a perimeter formula |
| Oct/Nov 2023 · Paper 22 | Q1 | 2 | Rounding to decimal places and nearest ten |
| Oct/Nov 2023 · Paper 22 | Q20 | 3 | Upper bound of a width |
| Oct/Nov 2023 · Paper 23 | Q1 | 1 | Arrival time from journey length |
| May/June 2023 · Paper 21 | Q2 | 1 | Finishing time of a journey |
| May/June 2023 · Paper 21 | Q4 | 2 | Estimating using one significant figure |
| May/June 2023 · Paper 23 | Q2 | 1 | Start time from duration and end time |
| May/June 2023 · Paper 23 | Q13 | 1 | Using a calculator with powers and roots |
| May/June 2023 · Paper 23 | Q23 | 4 | Upper bound of a journey time |
| Feb/March 2023 · Paper 22 | Q21 | 3 | Lower bound of a speed |
| Oct/Nov 2022 · Paper 21 | Q2 | 1 | Elapsed time across midnight |
| Oct/Nov 2022 · Paper 21 | Q24 | 2 | Upper bound of a difference |
| Oct/Nov 2022 · Paper 22 | Q10 | 3 | Using a calculator efficiently |
| Oct/Nov 2022 · Paper 23 | Q1 | 1 | Elapsed time across midnight |
| Oct/Nov 2022 · Paper 23 | Q3 | 1 | Evaluating an expression with a calculator |
| May/June 2022 · Paper 21 | Q3 | 1 | Time taken using 12-hour clock |
| May/June 2022 · Paper 21 | Q4 | 2 | Calculator work: significant figures |
| May/June 2022 · Paper 21 | Q5 | 2 | Currency conversion |
| May/June 2022 · Paper 22 | Q3 | 3 | Money: number bought and change |
| May/June 2022 · Paper 22 | Q4 | 1 | Calculator work with roots and powers |
| May/June 2022 · Paper 23 | Q21 | 3 | Bounds of a remaining length |
| Feb/March 2022 · Paper 22 | Q2 | 2 | Calculator work: rounding to decimal places |
| Feb/March 2022 · Paper 22 | Q3 | 1 | Time taken across midnight |
Paper 4 (Calculator): 31 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q4 | 1 | Finishing time using the 24-hour clock |
| Oct/Nov 2025 · Paper 41 | Q8 | 1 | Calculator work with powers |
| Oct/Nov 2025 · Paper 42 | Q5 | 2 | Comparing prices using an exchange rate |
| Oct/Nov 2025 · Paper 42 | Q20 | 3 | Lower bound of a volume from density |
| Oct/Nov 2025 · Paper 43 | Q25 | 3 | Bounds of a remaining length |
| May/June 2025 · Paper 41 | Q2 | 2 | Calculator work rounded to significant figures |
| May/June 2025 · Paper 41 | Q3 | 3 | Comparing prices with currency and unit conversion |
| May/June 2025 · Paper 41 | Q22 | 3 | Upper bound of a calculated quantity |
| May/June 2025 · Paper 42 | Q5 | 1 | Currency conversion |
| May/June 2025 · Paper 42 | Q8 | 1 | Evaluating an expression with a calculator |
| May/June 2025 · Paper 42 | Q12 | 2 | Lower bound of a perimeter |
| May/June 2025 · Paper 43 | Q22 | 4 | Bounds of mass and density |
| Feb/March 2025 · Paper 42 | Q4 | 2 | Calculator work: rounding to decimal places |
| Feb/March 2025 · Paper 42 | Q20 | 3 | Lower bound of a density |
| Oct/Nov 2024 · Paper 41 | Q4 (b) | 3 | Lower and upper bounds of a distance |
| Oct/Nov 2024 · Paper 42 | Q7 (b) | 3 | Upper bound of a rectangle width |
| May/June 2024 · Paper 41 | Q1 (b) | 3 | Upper bound of a difference |
| May/June 2024 · Paper 42 | Q1 (e) | 3 | Bounds: fitting objects between shelves |
| May/June 2024 · Paper 43 | Q7 (a) | 5 | Time from speed; bounds of a speed |
| Feb/March 2024 · Paper 42 | Q1 (c) | 3 | Upper bound of a number of bags |
| Oct/Nov 2023 · Paper 43 | Q1 (a)–(b) | 4 | Currency conversion using exchange rates |
| May/June 2023 · Paper 41 | Q1 (b) | 5 | Money: change and currency conversion |
| May/June 2023 · Paper 41 | Q3 (b)–(c) | 7 | Significant figures, standard form and bounds |
| May/June 2023 · Paper 42 | Q2 (a) | 3 | Currency exchange there and back |
| May/June 2023 · Paper 42 | Q10 (b) | 4 | Bounds in a cuboid calculation |
| Oct/Nov 2022 · Paper 41 | Q2 (a) | 3 | Rounding to decimal places and significant figures |
| Oct/Nov 2022 · Paper 42 | Q10 (a) | 2 | Upper bound of a perimeter |
| Oct/Nov 2022 · Paper 43 | Q1 (c) | 3 | Bounds of lengths on a shelf |
| May/June 2022 · Paper 42 | Q6 (d) | 5 | Bounds of a time and a rate |
| May/June 2022 · Paper 43 | Q1 (a)–(b) | 3 | Reading a bus timetable |
| Feb/March 2022 · Paper 42 | Q7 (b), (d) | 5 | Upper bound of an area; currency comparison |
Chapter 4: Ratio, Proportion and Rates
36 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 10 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q1 | 2 | Sharing an amount in a ratio |
| Feb/March 2025 · Paper 22 | Q1 | 1 | Cost from a price per kilogram |
| Oct/Nov 2024 · Paper 21 | Q4 | 2 | Dividing a length in a given ratio |
| Feb/March 2024 · Paper 22 | Q14 | 3 | Time for a train to cross a bridge |
| Oct/Nov 2023 · Paper 23 | Q11 | 4 | Mass of a sphere from density |
| May/June 2023 · Paper 21 | Q7 | 2 | Map scale: actual length |
| Oct/Nov 2022 · Paper 21 | Q4 | 2 | Dividing an amount in a ratio |
| Oct/Nov 2022 · Paper 22 | Q5 | 3 | Finding a unit cost from a total |
| May/June 2022 · Paper 21 | Q14 | 3 | Train passing through a station: speed |
| May/June 2022 · Paper 23 | Q9 | 2 | Converting units of speed |
Paper 4 (Calculator): 26 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q9 | 2 | Converting a speed between units |
| Oct/Nov 2025 · Paper 42 | Q1 | 2 | Ratio in the form one to n with units |
| Oct/Nov 2025 · Paper 42 | Q4 (a) | 2 | Working at a constant rate |
| Oct/Nov 2025 · Paper 43 | Q21 | 4 | Work rates: percentage increase in rate |
| May/June 2025 · Paper 42 | Q3 | 3 | Ratio problem with a known difference |
| May/June 2025 · Paper 42 | Q6 | 3 | Mass of a cone from volume and density |
| Oct/Nov 2024 · Paper 41 | Q4 (a) | 14 | Swimming: percentage, ratio, speed and time |
| Oct/Nov 2024 · Paper 42 | Q1 (c) | 2 | Rate of fuel consumption |
| Oct/Nov 2024 · Paper 42 | Q5 (b) | 3 | Average speed around a track |
| Oct/Nov 2024 · Paper 43 | Q1 (a)–(b) | 5 | Ratio problems including algebraic ratio |
| Oct/Nov 2024 · Paper 43 | Q5 | 8 | Average speed and time expressions |
| May/June 2024 · Paper 42 | Q1 (a)–(b) | 5 | Simplifying a ratio; sharing in a ratio |
| Feb/March 2024 · Paper 42 | Q1 (a)–(b) | 9 | Costs, ratio of masses, profit and price change |
| Oct/Nov 2023 · Paper 43 | Q1 (c) | 8 | Sharing in a ratio with currency conversion |
| May/June 2023 · Paper 41 | Q1 (a) | 8 | Ratio sharing, means and fractions of a total |
| May/June 2023 · Paper 41 | Q2 (e) | 3 | Mass of a prism from density |
| May/June 2023 · Paper 43 | Q1 (a) | 7 | Sharing an amount in a ratio |
| Feb/March 2023 · Paper 42 | Q1 (b) | 2 | Sharing in a ratio |
| Oct/Nov 2022 · Paper 42 | Q1 (b) | 7 | Ratio with algebraic expressions and an equation |
| Oct/Nov 2022 · Paper 42 | Q5 (b) | 3 | Average speed with unit conversion |
| Oct/Nov 2022 · Paper 43 | Q1 (a) | 6 | Scaling a recipe in proportion |
| Oct/Nov 2022 · Paper 43 | Q5 (b) | 3 | Rate of flow: time to empty |
| May/June 2022 · Paper 41 | Q2 (a) | 2 | Sharing in a ratio |
| May/June 2022 · Paper 42 | Q1 (b), (e) | 5 | Sharing in a ratio; density |
| May/June 2022 · Paper 43 | Q1 (c)–(d) | 6 | Average speed; ratio and ticket costs |
| Feb/March 2022 · Paper 42 | Q1 (b) | 2 | Dividing a quantity in a ratio |
Chapter 5: Percentages, Growth and Decay
52 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 18 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 22 | Q4 | 2 | Percentage decrease in a sale |
| May/June 2025 · Paper 21 | Q3 | 3 | Simple interest: total value |
| Feb/March 2025 · Paper 22 | Q11 (c)–(d) | 5 | Percentage increase and reverse percentage |
| Oct/Nov 2024 · Paper 21 | Q8 | 2 | Simple interest earned |
| Oct/Nov 2024 · Paper 22 | Q15 | 2 | Exponential growth over several periods |
| May/June 2024 · Paper 21 | Q9 | 2 | Exponential depreciation |
| May/June 2024 · Paper 21 | Q10 | 3 | Compound interest: finding the rate |
| May/June 2024 · Paper 22 | Q8 | 3 | Simple interest: finding the rate |
| Oct/Nov 2023 · Paper 21 | Q13 | 3 | Exponential decay of a population |
| Oct/Nov 2023 · Paper 23 | Q4 | 2 | Simple interest earned |
| Oct/Nov 2023 · Paper 23 | Q12 | 3 | Reverse percentage increase |
| May/June 2023 · Paper 21 | Q13 | 3 | Compound interest: finding the rate |
| May/June 2023 · Paper 23 | Q15 | 2 | Exponential decay over several years |
| Oct/Nov 2022 · Paper 21 | Q6 | 2 | Percentage decrease in a sale |
| Oct/Nov 2022 · Paper 23 | Q12 | 3 | Compound interest earned |
| May/June 2022 · Paper 22 | Q7 | 2 | Percentage decrease: sale price |
| May/June 2022 · Paper 22 | Q14 | 3 | Compound interest: finding the rate |
| Feb/March 2022 · Paper 22 | Q12 | 6 | Simple interest; compound interest rate |
Paper 4 (Calculator): 34 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q11 | 4 | Percentage decrease and reverse percentage |
| Oct/Nov 2025 · Paper 41 | Q19 | 3 | Exponential decay: whole periods to a threshold |
| Oct/Nov 2025 · Paper 41 | Q22 | 3 | Compound interest: finding the rate |
| Oct/Nov 2025 · Paper 42 | Q4 (b) | 2 | Percentage profit |
| Oct/Nov 2025 · Paper 42 | Q14 | 8 | Compound interest, percentage profit, depreciation formula |
| Oct/Nov 2025 · Paper 43 | Q15 | 5 | Exponential decay: decrease and years to threshold |
| May/June 2025 · Paper 41 | Q8 | 4 | Payment plan: total cost and percentage increase |
| May/June 2025 · Paper 41 | Q9 | 2 | Reverse percentage: finding the original price |
| May/June 2025 · Paper 41 | Q16 | 3 | Compound interest: finding the rate |
| May/June 2025 · Paper 42 | Q11 | 2 | Reverse percentage: original price before discount |
| May/June 2025 · Paper 42 | Q17 | 10 | Simple and compound interest; successive percentage increases |
| May/June 2025 · Paper 43 | Q14 | 3 | Compound interest: finding the rate |
| Feb/March 2025 · Paper 42 | Q6 | 3 | Pay including an overtime percentage increase |
| Feb/March 2025 · Paper 42 | Q11 | 5 | Compound interest: value and rate for doubling |
| Oct/Nov 2024 · Paper 42 | Q1 (a), (b), (d) | 10 | Discount, finance plan percentage and depreciation |
| Oct/Nov 2024 · Paper 43 | Q1 (c)–(d) | 4 | Percentage profit and reverse percentage |
| Oct/Nov 2024 · Paper 43 | Q3 | 9 | Simple and compound interest: rates and interest |
| May/June 2024 · Paper 41 | Q1 (a) | 12 | Areas: percentages, ratio, fractions and standard form |
| May/June 2024 · Paper 42 | Q1 (c)–(d) | 4 | Percentage profit; exponential growth |
| May/June 2024 · Paper 43 | Q1 | 13 | Membership: totals, percentages, ratio, exponential decay |
| Feb/March 2024 · Paper 42 | Q9 | 9 | Simple and compound interest rates; exponential growth |
| Oct/Nov 2023 · Paper 42 | Q3 | 15 | Depreciation, simple and compound interest, decay |
| Oct/Nov 2023 · Paper 43 | Q2 (a), (c) | 4 | Percentage of a total; percentage increase |
| May/June 2023 · Paper 42 | Q2 (b)–(c) | 10 | Percentages and compound interest |
| May/June 2023 · Paper 43 | Q1 (b)–(c) | 4 | Simple interest; reverse percentage |
| Feb/March 2023 · Paper 42 | Q1 (a), (c), (d) | 14 | Percentages, simple and compound interest, rate |
| Oct/Nov 2022 · Paper 41 | Q4 | 14 | Simple and compound interest; exponential growth and decay |
| Oct/Nov 2022 · Paper 42 | Q1 (a) | 9 | Ratio, percentage decrease and reverse percentage |
| Oct/Nov 2022 · Paper 43 | Q1 (b) | 5 | Reverse percentage and percentage change in cost |
| May/June 2022 · Paper 41 | Q2 (b)–(d) | 11 | Percentage reductions, interest and exponential decay |
| May/June 2022 · Paper 42 | Q6 (c) | 2 | Reverse percentage: full price |
| May/June 2022 · Paper 43 | Q3 | 13 | Percentages, ratio and population growth |
| Feb/March 2022 · Paper 42 | Q1 (a), (d), (e) | 8 | Percentage increase, fractions of totals, successive increases |
| Feb/March 2022 · Paper 42 | Q7 (c) | 2 | Reverse percentage: original price |
Chapter 6: Algebraic Manipulation
84 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 55 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q7 | 4 | Simplifying algebraic fractions |
| Oct/Nov 2025 · Paper 21 | Q17 (a) | 2 | Substituting into a formula |
| Oct/Nov 2025 · Paper 21 | Q25 | 4 | Simplifying algebraic fraction by factorising |
| Oct/Nov 2025 · Paper 22 | Q8 | 2 | Writing an expression for change |
| Oct/Nov 2025 · Paper 22 | Q15 | 3 | Factorising: difference of squares, common bracket |
| Oct/Nov 2025 · Paper 23 | Q15 | 4 | Factorising a quadratic and by grouping |
| Oct/Nov 2025 · Paper 23 | Q26 | 5 | Adding and subtracting algebraic fractions |
| Oct/Nov 2025 · Paper 23 | Q28 | 4 | Simplifying algebraic fraction by factorising |
| May/June 2025 · Paper 21 | Q1 | 2 | Collecting like terms |
| May/June 2025 · Paper 21 | Q16 | 3 | Expanding a product of three brackets |
| May/June 2025 · Paper 21 | Q23 | 3 | Simplifying an algebraic fraction by factorising |
| May/June 2025 · Paper 22 | Q19 | 7 | Multiplying and adding algebraic fractions |
| May/June 2025 · Paper 23 | Q19 | 3 | Simplifying an algebraic fraction by factorising |
| Feb/March 2025 · Paper 22 | Q4 (a) | 2 | Substituting into a formula |
| Feb/March 2025 · Paper 22 | Q12 | 4 | Adding algebraic fractions; factorising by grouping |
| Oct/Nov 2024 · Paper 21 | Q7 | 1 | Factorising a linear expression |
| Oct/Nov 2024 · Paper 21 | Q22 (a) | 2 | Expanding a product to show a cubic |
| Oct/Nov 2024 · Paper 21 | Q23 | 2 | Identity: comparing coefficients after expanding |
| Oct/Nov 2024 · Paper 22 | Q11 | 5 | Factorising fully, including difference of two squares |
| Oct/Nov 2024 · Paper 22 | Q21 | 3 | Expanding a product of three brackets |
| Oct/Nov 2024 · Paper 23 | Q3 | 2 | Simplifying by collecting like terms |
| Oct/Nov 2024 · Paper 23 | Q8 | 2 | Writing an expression for a total cost |
| Oct/Nov 2024 · Paper 23 | Q25 | 4 | Simplifying an algebraic fraction by factorising |
| May/June 2024 · Paper 21 | Q19 | 5 | Factorising: difference of squares and grouping |
| May/June 2024 · Paper 23 | Q3 | 2 | Collecting like terms |
| May/June 2024 · Paper 23 | Q6 | 2 | Factorising completely |
| May/June 2024 · Paper 23 | Q23 | 3 | Adding algebraic fractions |
| May/June 2024 · Paper 23 | Q25 | 4 | Simplifying an algebraic fraction by factorising |
| Feb/March 2024 · Paper 22 | Q3 | 2 | Collecting like terms |
| Oct/Nov 2023 · Paper 21 | Q5 | 3 | Factorising: common factor and difference of squares |
| Oct/Nov 2023 · Paper 21 | Q20 | 6 | Simplifying and combining algebraic fractions |
| Oct/Nov 2023 · Paper 22 | Q3 | 2 | Substituting into a formula |
| Oct/Nov 2023 · Paper 22 | Q10 | 2 | Expanding and simplifying brackets |
| Oct/Nov 2023 · Paper 22 | Q24 | 4 | Simplifying an algebraic fraction by factorising |
| Oct/Nov 2023 · Paper 23 | Q9 | 3 | Substituting into a formula to find a value |
| Oct/Nov 2023 · Paper 23 | Q17 (b) | 2 | Simplifying an algebraic fraction |
| Oct/Nov 2023 · Paper 23 | Q20 | 3 | Expanding a triple product to match coefficients |
| May/June 2023 · Paper 22 | Q22 | 3 | Adding algebraic fractions |
| May/June 2023 · Paper 23 | Q4 | 2 | Substitution into a formula with negatives |
| May/June 2023 · Paper 23 | Q21 | 4 | Simplifying an algebraic fraction by factorising |
| Feb/March 2023 · Paper 22 | Q5 | 2 | Factorising completely: common factor |
| Feb/March 2023 · Paper 22 | Q23 | 4 | Simplifying an algebraic fraction by factorising |
| Oct/Nov 2022 · Paper 21 | Q19 | 3 | Expanding a triple product |
| Oct/Nov 2022 · Paper 21 | Q20 | 5 | Factorising completely: grouping and difference of squares |
| Oct/Nov 2022 · Paper 22 | Q2 | 1 | Simplifying by collecting like terms |
| Oct/Nov 2022 · Paper 22 | Q4 | 2 | Expanding a single bracket |
| Oct/Nov 2022 · Paper 23 | Q22 | 7 | Expanding a triple product; dividing algebraic fractions |
| May/June 2022 · Paper 21 | Q8 (a) | 1 | Substituting into a formula |
| May/June 2022 · Paper 21 | Q9 | 2 | Factorising completely: common factor |
| May/June 2022 · Paper 21 | Q21 | 2 | Factorising by grouping |
| May/June 2022 · Paper 22 | Q20 | 5 | Factorising by grouping; difference of squares |
| May/June 2022 · Paper 23 | Q2 | 2 | Substituting into an expression |
| May/June 2022 · Paper 23 | Q13 | 4 | Factorising: common factor and grouping |
| May/June 2022 · Paper 23 | Q22 | 3 | Simplifying an algebraic fraction |
| Feb/March 2022 · Paper 22 | Q9 | 2 | Factorising completely: common factor |
Paper 4 (Calculator): 29 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q6 | 1 | Expanding a single bracket |
| Oct/Nov 2025 · Paper 42 | Q13 | 2 | Adding algebraic fractions |
| Oct/Nov 2025 · Paper 42 | Q17 | 3 | Expanding a product of three brackets |
| Oct/Nov 2025 · Paper 43 | Q3 | 1 | Substituting into a formula |
| Oct/Nov 2025 · Paper 43 | Q16 | 4 | Expanding and simplifying brackets |
| May/June 2025 · Paper 41 | Q6 | 2 | Expanding a single bracket |
| May/June 2025 · Paper 41 | Q10 (b)–(c) | 4 | Factorising by grouping; integer solutions |
| May/June 2025 · Paper 42 | Q14 | 2 | Factorising by grouping |
| May/June 2025 · Paper 42 | Q23 | 3 | Simplifying an algebraic fraction |
| May/June 2025 · Paper 43 | Q8 | 4 | Factorising: common factor and grouping |
| May/June 2025 · Paper 43 | Q10 | 5 | Expanding single, double and triple brackets |
| Feb/March 2025 · Paper 42 | Q2 | 2 | Collecting like terms |
| Feb/March 2025 · Paper 42 | Q18 | 5 | Factorising difference of squares; expanding three brackets |
| Oct/Nov 2024 · Paper 42 | Q3 (a) | 6 | Simplifying expressions and algebraic fractions |
| Oct/Nov 2024 · Paper 43 | Q6 (a)–(b) | 5 | Algebraic fraction multiplication; expanding three brackets |
| May/June 2024 · Paper 41 | Q3 (a)–(c) | 10 | Substitution, algebraic fractions and expanding |
| May/June 2024 · Paper 42 | Q5 (c) | 3 | Expanding a product of three brackets |
| May/June 2024 · Paper 42 | Q7 (b)–(c) | 4 | Factorising: common factor, difference of squares |
| Feb/March 2024 · Paper 42 | Q5 (a)–(d) | 14 | Factorising, algebraic fractions, expanding |
| Oct/Nov 2023 · Paper 41 | Q2 (a), (c), (e) | 6 | Substitution, expanding and factorising by grouping |
| Oct/Nov 2023 · Paper 41 | Q9 (e) | 3 | Expanding a product of three brackets |
| Oct/Nov 2023 · Paper 43 | Q10 (a)–(b) | 7 | Expanding and factorising expressions |
| May/June 2023 · Paper 41 | Q7 (a) | 5 | Factorising: difference of squares, grouping |
| May/June 2023 · Paper 42 | Q9 (b) | 4 | Factorising and simplifying algebraic fractions |
| Feb/March 2023 · Paper 42 | Q5 (a), (c) | 7 | Expanding brackets and factorising completely |
| Oct/Nov 2022 · Paper 42 | Q6 (b), (c), (g) | 7 | Factorising, algebraic fractions and expanding |
| May/June 2022 · Paper 42 | Q8 (e) | 3 | Expanding three brackets |
| May/June 2022 · Paper 43 | Q6 (a)–(c) | 7 | Simplifying, expanding, algebraic fractions |
| Feb/March 2022 · Paper 42 | Q10 (a), (c) | 6 | Expanding triple brackets; simplifying algebraic fraction |
Chapter 7: Equations and Formulas
93 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 45 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q8 | 5 | Forming and solving simultaneous equations |
| Oct/Nov 2025 · Paper 21 | Q17 (b) | 3 | Rearranging a formula with a square |
| Oct/Nov 2025 · Paper 21 | Q22 | 5 | Equation with algebraic fractions |
| Oct/Nov 2025 · Paper 22 | Q10 (b) | 2 | Rearranging a formula with a common factor |
| Oct/Nov 2025 · Paper 22 | Q22 | 3 | Quadratic from its minimum point |
| Oct/Nov 2025 · Paper 23 | Q27 | 6 | Simultaneous equations: one linear, one quadratic |
| May/June 2025 · Paper 21 | Q18 | 10 | Forming and solving a quadratic from journey times |
| May/June 2025 · Paper 22 | Q6 | 5 | Solving linear equations |
| May/June 2025 · Paper 22 | Q24 | 5 | Intersection of a line and a quadratic curve |
| May/June 2025 · Paper 23 | Q9 | 5 | Solving quadratic equations |
| May/June 2025 · Paper 23 | Q10 | 4 | Linear simultaneous equations |
| May/June 2025 · Paper 23 | Q18 | 4 | Rearranging a formula: subject appears twice |
| Feb/March 2025 · Paper 22 | Q4 (b) | 2 | Solving for a squared variable |
| Oct/Nov 2024 · Paper 21 | Q12 | 3 | Simultaneous linear equations |
| Oct/Nov 2024 · Paper 21 | Q17 | 4 | Quadratic formula to two decimal places |
| Oct/Nov 2024 · Paper 23 | Q7 | 2 | Solving a linear equation |
| Oct/Nov 2024 · Paper 23 | Q11 | 2 | Simultaneous linear equations |
| Oct/Nov 2024 · Paper 23 | Q12 | 2 | Rearranging a formula with a square |
| Oct/Nov 2024 · Paper 23 | Q23 | 2 | Completing the square |
| May/June 2024 · Paper 21 | Q12 | 4 | Linear simultaneous equations |
| May/June 2024 · Paper 22 | Q21 | 5 | Simultaneous equations: one linear, one quadratic |
| May/June 2024 · Paper 23 | Q11 | 2 | Linear simultaneous equations |
| May/June 2024 · Paper 23 | Q16 | 2 | Rearranging a formula |
| Feb/March 2024 · Paper 22 | Q24 | 2 | Completing the square: perfect square |
| Oct/Nov 2023 · Paper 21 | Q3 | 2 | Completing simple equation statements |
| Oct/Nov 2023 · Paper 22 | Q14 | 3 | Rearranging a formula with a square |
| Oct/Nov 2023 · Paper 22 | Q21 | 4 | Intersection of a line and a curve |
| Oct/Nov 2023 · Paper 23 | Q15 | 3 | Rearranging a linear formula |
| Oct/Nov 2023 · Paper 23 | Q22 | 5 | Intersection of a line and a curve |
| May/June 2023 · Paper 22 | Q8 (a) | 1 | Solving a simple fractional equation |
| May/June 2023 · Paper 22 | Q12 | 3 | Quadratic equation with unknown coefficients |
| May/June 2023 · Paper 22 | Q18 | 4 | Rearranging a formula: subject appears twice |
| May/June 2023 · Paper 23 | Q17 | 4 | Rearranging a formula: subject appears twice |
| May/June 2023 · Paper 23 | Q19 | 4 | Quadratic formula to two decimal places |
| Feb/March 2023 · Paper 22 | Q7 | 4 | Solving linear equations |
| Feb/March 2023 · Paper 22 | Q9 | 3 | Linear simultaneous equations |
| Feb/March 2023 · Paper 22 | Q19 | 3 | Solving a linear–quadratic pair |
| Oct/Nov 2022 · Paper 21 | Q11 | 2 | Simultaneous linear equations |
| Oct/Nov 2022 · Paper 22 | Q23 | 7 | Equation with algebraic fractions leading to a quadratic |
| Oct/Nov 2022 · Paper 23 | Q9 | 2 | Simultaneous linear equations |
| May/June 2022 · Paper 21 | Q8 (b) | 2 | Rearranging a formula with a square |
| May/June 2022 · Paper 21 | Q23 | 4 | Completing the square and solving |
| May/June 2022 · Paper 21 | Q27 | 4 | Line and curve intersection points |
| Feb/March 2022 · Paper 22 | Q18 | 3 | Forming and solving a linear equation |
| Feb/March 2022 · Paper 22 | Q20 | 5 | Simultaneous equations: one linear, one quadratic |
Paper 4 (Calculator): 48 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q2 | 2 | Solving a linear equation |
| Oct/Nov 2025 · Paper 41 | Q24 | 11 | Forming and solving a quadratic from journey times |
| Oct/Nov 2025 · Paper 41 | Q26 | 4 | Simultaneous equations: one linear, one quadratic |
| Oct/Nov 2025 · Paper 42 | Q2 | 2 | Solving a linear equation |
| Oct/Nov 2025 · Paper 42 | Q19 | 6 | Simultaneous equations: one linear, one quadratic |
| Oct/Nov 2025 · Paper 43 | Q10 | 2 | Simultaneous linear equations |
| Oct/Nov 2025 · Paper 43 | Q14 | 5 | Forming and solving equations from equal expressions |
| Oct/Nov 2025 · Paper 43 | Q17 | 3 | Changing the subject of a formula |
| May/June 2025 · Paper 41 | Q1 | 2 | Solving a linear equation |
| May/June 2025 · Paper 41 | Q13 | 3 | Rearranging a formula with a squared term |
| May/June 2025 · Paper 41 | Q18 | 3 | Completing the square with a leading coefficient |
| May/June 2025 · Paper 42 | Q7 | 2 | Rearranging a linear formula |
| May/June 2025 · Paper 42 | Q9 | 3 | Simultaneous linear equations |
| May/June 2025 · Paper 42 | Q10 | 3 | Forming and solving a linear equation for cost |
| May/June 2025 · Paper 42 | Q24 | 8 | Forming and solving a quadratic from journey times |
| Feb/March 2025 · Paper 42 | Q22 | 6 | Line and curve intersection: quadratic formula |
| Oct/Nov 2024 · Paper 41 | Q1 (c), (e) | 7 | Solving equations; substitution and changing subject |
| Oct/Nov 2024 · Paper 41 | Q10 (a) | 6 | Forming and solving a quadratic from an area |
| Oct/Nov 2024 · Paper 42 | Q3 (b)–(d) | 11 | Linear, quadratic formula and simultaneous equations |
| Oct/Nov 2024 · Paper 43 | Q6 (c) | 4 | Quadratic formula to two decimal places |
| May/June 2024 · Paper 41 | Q8 (c) | 6 | Intersection of a line and a curve |
| May/June 2024 · Paper 42 | Q5 (d) | 7 | Forming and solving a quadratic from fractions |
| May/June 2024 · Paper 42 | Q5 (e) | 4 | Equal surface areas: deriving a formula |
| May/June 2024 · Paper 42 | Q7 (a) | 2 | Solving a linear equation |
| May/June 2024 · Paper 43 | Q4 | 9 | Forming and solving a quadratic from areas |
| May/June 2024 · Paper 43 | Q7 (b) | 6 | Forming and solving an equation from journey times |
| Feb/March 2024 · Paper 42 | Q5 (e) | 6 | Simultaneous equations: one linear, one quadratic |
| Oct/Nov 2023 · Paper 41 | Q2 (b), (d) | 6 | Linear equation; rearranging a formula |
| Oct/Nov 2023 · Paper 42 | Q5 | 9 | Forming linear and quadratic equations from costs |
| Oct/Nov 2023 · Paper 43 | Q10 (c) | 7 | Forming and solving an equation from journey times |
| May/June 2023 · Paper 41 | Q7 (b)–(d) | 13 | Fractional equation, quadratic formula, rearranging |
| May/June 2023 · Paper 42 | Q3 (a) | 9 | Forming and solving a quadratic from area |
| May/June 2023 · Paper 42 | Q9 (c) | 6 | Simultaneous equations: one linear, one quadratic |
| May/June 2023 · Paper 43 | Q8 (a)–(b) | 8 | Forming a linear equation; simultaneous with quadratic |
| Feb/March 2023 · Paper 42 | Q5 (b) | 5 | Substituting and rearranging a formula |
| Feb/March 2023 · Paper 42 | Q8 (b) | 6 | Forming and solving a quadratic from area |
| Oct/Nov 2022 · Paper 41 | Q3 (c) | 7 | Solving equations with fractions |
| Oct/Nov 2022 · Paper 41 | Q9 | 14 | Forming and solving quadratics from areas |
| Oct/Nov 2022 · Paper 42 | Q6 (a), (e) | 5 | Solving linear and quadratic equations |
| Oct/Nov 2022 · Paper 43 | Q2 (d)–(e) | 7 | Linear equation; quadratic formula |
| Oct/Nov 2022 · Paper 43 | Q6 (a) | 5 | Substituting and rearranging a formula |
| May/June 2022 · Paper 41 | Q3 | 16 | Forming and solving equations; index and trig simultaneous |
| May/June 2022 · Paper 41 | Q9 | 14 | Forming and solving quadratics from areas and volumes |
| May/June 2022 · Paper 42 | Q8 (a)–(d) | 15 | Linear, fractional and simultaneous equations; subject |
| May/June 2022 · Paper 43 | Q6 (d)–(e) | 7 | Solving an equation; changing the subject |
| May/June 2022 · Paper 43 | Q8 (b) | 6 | Line and curve intersection points |
| Feb/March 2022 · Paper 42 | Q8 | 13 | Forming and solving a quadratic from times |
| Feb/March 2022 · Paper 42 | Q10 (b) | 4 | Changing the subject: variable appears twice |
Chapter 8: Inequalities
20 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 11 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q16 | 4 | Inequalities defining a region |
| Oct/Nov 2025 · Paper 22 | Q7 | 2 | Inequality on a number line |
| Feb/March 2025 · Paper 22 | Q7 | 2 | Inequality shown on a number line |
| Oct/Nov 2024 · Paper 22 | Q13 | 4 | Region defined by inequalities on a grid |
| May/June 2024 · Paper 21 | Q11 | 4 | Inequalities defining a region |
| Oct/Nov 2023 · Paper 21 | Q11 | 3 | Solving a linear inequality |
| Oct/Nov 2023 · Paper 21 | Q15 | 5 | Region defined by inequalities |
| Oct/Nov 2023 · Paper 23 | Q13 | 4 | Region defined by inequalities |
| May/June 2023 · Paper 22 | Q8 (b) | 3 | Solving a linear inequality |
| May/June 2022 · Paper 23 | Q15 | 2 | Solving a linear inequality |
| Feb/March 2022 · Paper 22 | Q7 | 1 | Inequality shown on a number line |
Paper 4 (Calculator): 9 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q7 | 4 | Number line inequality; integer solutions |
| May/June 2025 · Paper 41 | Q7 | 2 | Inequality shown on a number line |
| May/June 2025 · Paper 43 | Q16 | 5 | Region defined by three inequalities |
| Oct/Nov 2024 · Paper 41 | Q7 (a)–(c) | 10 | Forming inequalities and shading a region |
| May/June 2024 · Paper 42 | Q8 (a)–(b) | 9 | Forming and graphing inequalities in two variables |
| May/June 2023 · Paper 41 | Q8 (a)–(c) | 10 | Forming and graphing inequalities in two variables |
| Oct/Nov 2022 · Paper 41 | Q3 (a)–(b) | 6 | Solving inequalities and listing integers |
| Oct/Nov 2022 · Paper 43 | Q6 (b), (c)(i) | 9 | Linear inequality and region on a graph |
| May/June 2022 · Paper 42 | Q10 (a), (b)(i) | 5 | Integer solutions; region defined by inequalities |
Chapter 9: Sequences
33 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 22 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 23 | Q16 | 5 | nth terms of linear, quadratic and geometric sequences |
| May/June 2025 · Paper 22 | Q7 | 3 | Linear sequence: next term and nth term |
| Oct/Nov 2024 · Paper 21 | Q13 | 5 | Quadratic and cubic sequences: terms and nth term |
| Oct/Nov 2024 · Paper 22 | Q1 | 2 | Missing terms of a linear sequence |
| Oct/Nov 2024 · Paper 22 | Q20 | 2 | nth term of a geometric sequence |
| Oct/Nov 2024 · Paper 23 | Q13 | 4 | nth term: linear and geometric sequences |
| May/June 2024 · Paper 21 | Q3 | 4 | Linear and quadratic sequence terms |
| May/June 2024 · Paper 21 | Q8 | 2 | nth term of a linear sequence |
| Feb/March 2024 · Paper 22 | Q8 | 4 | Terms from nth term; geometric nth term |
| Oct/Nov 2023 · Paper 22 | Q19 | 4 | nth term: linear and geometric sequences |
| May/June 2023 · Paper 21 | Q8 | 4 | Terms from nth term; nth term of linear sequence |
| May/June 2023 · Paper 23 | Q22 | 5 | Quadratic-plus-cubic sequence: finding coefficients |
| Feb/March 2023 · Paper 22 | Q4 | 3 | Next term and nth term of linear sequence |
| Feb/March 2023 · Paper 22 | Q20 | 4 | nth term: cubic and geometric sequences |
| Oct/Nov 2022 · Paper 21 | Q8 | 3 | Next term and nth term of sequences |
| Oct/Nov 2022 · Paper 22 | Q6 | 6 | Continuing sequences and finding nth terms |
| May/June 2022 · Paper 21 | Q10 | 3 | Next term and nth term of linear sequence |
| May/June 2022 · Paper 22 | Q8 | 2 | Terms from a quadratic nth term |
| May/June 2022 · Paper 22 | Q21 | 5 | Quadratic sequence: finding coefficients |
| May/June 2022 · Paper 23 | Q5 | 2 | Terms from a quadratic nth term |
| May/June 2022 · Paper 23 | Q14 | 2 | nth term of a quadratic sequence |
| Feb/March 2022 · Paper 22 | Q10 | 4 | Terms from nth term; nth term of linear sequence |
Paper 4 (Calculator): 11 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q20 | 3 | Geometric sequence: next term and nth term |
| Oct/Nov 2025 · Paper 42 | Q10 | 4 | nth term: linear and quadratic sequences |
| Oct/Nov 2025 · Paper 43 | Q1 | 2 | Sequence from an nth term: term and maximum |
| May/June 2025 · Paper 41 | Q5 | 6 | Sequences: cubes, quadratic nth term, sum of terms |
| May/June 2025 · Paper 43 | Q11 | 8 | Completing terms and nth terms of sequences |
| Feb/March 2025 · Paper 42 | Q13 | 6 | nth terms of cubic, linear and geometric sequences |
| May/June 2024 · Paper 42 | Q5 (b) | 2 | nth term of a geometric sequence |
| May/June 2024 · Paper 43 | Q2 | 12 | Sequences: cubic, geometric and quadratic nth terms |
| Oct/Nov 2023 · Paper 41 | Q6 | 11 | Completing linear, quadratic and geometric sequences |
| May/June 2023 · Paper 42 | Q6 | 8 | Sequences: fractional, cubic and geometric nth terms |
| Oct/Nov 2022 · Paper 43 | Q2 (b)–(c) | 6 | Terms and nth terms of sequences |
Chapter 10: Direct and Inverse Proportion
21 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 17 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| May/June 2025 · Paper 22 | Q20 | 4 | Inverse proportion to the square root |
| Oct/Nov 2024 · Paper 22 | Q12 | 3 | Direct proportion to a square root |
| Oct/Nov 2024 · Paper 23 | Q19 | 2 | Inverse proportion: finding the formula |
| May/June 2024 · Paper 22 | Q19 | 4 | Direct and inverse proportion |
| Feb/March 2024 · Paper 22 | Q22 | 2 | Inverse proportion to a square: formula |
| Oct/Nov 2023 · Paper 22 | Q22 | 2 | Inverse proportion to a square root |
| Oct/Nov 2023 · Paper 23 | Q18 | 3 | Proportion: percentage change in a product |
| May/June 2023 · Paper 21 | Q14 | 3 | Direct proportion to a square |
| May/June 2023 · Paper 22 | Q19 | 3 | Inverse proportion to a square |
| May/June 2023 · Paper 23 | Q18 | 3 | Inverse proportion to a cube root |
| Feb/March 2023 · Paper 22 | Q16 | 3 | Inverse proportion to a square |
| Oct/Nov 2022 · Paper 21 | Q23 | 3 | Combined direct and inverse proportion |
| Oct/Nov 2022 · Paper 23 | Q17 | 3 | Direct proportion to a square |
| May/June 2022 · Paper 21 | Q25 | 3 | Combined direct and inverse proportion |
| May/June 2022 · Paper 22 | Q18 | 4 | Direct proportion to a cube root; inverse square |
| May/June 2022 · Paper 23 | Q24 | 3 | Inverse proportion to a cube |
| Feb/March 2022 · Paper 22 | Q19 | 3 | Inverse proportion to a square root |
Paper 4 (Calculator): 4 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q23 | 2 | Inverse proportion: finding the formula |
| Oct/Nov 2025 · Paper 42 | Q21 | 4 | Combined inverse and direct proportion |
| May/June 2025 · Paper 43 | Q15 | 3 | Inverse proportion to a square root |
| Oct/Nov 2022 · Paper 42 | Q6 (f) | 5 | Direct and inverse proportion |
Chapter 11: Graphs in Practical Situations
15 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 11 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2024 · Paper 22 | Q14 | 4 | Speed-time graph: acceleration and distance |
| May/June 2024 · Paper 22 | Q16 | 4 | Speed-time graph: deceleration and distance |
| Feb/March 2024 · Paper 22 | Q19 | 3 | Distance from a speed–time graph |
| Oct/Nov 2023 · Paper 22 | Q12 | 3 | Speed–time graph: deceleration and distance |
| May/June 2023 · Paper 23 | Q9 | 3 | Distance-time graph: speed and return journey |
| Feb/March 2023 · Paper 22 | Q13 | 2 | Distance from a speed–time graph |
| Oct/Nov 2022 · Paper 21 | Q13 | 3 | Speed–time graph: acceleration and distance |
| Oct/Nov 2022 · Paper 23 | Q15 | 5 | Speed–time graph: acceleration and journey time |
| May/June 2022 · Paper 21 | Q20 | 3 | Speed–time graph: deceleration and distance |
| May/June 2022 · Paper 22 | Q12 | 6 | Drawing a distance–time graph; average speed |
| May/June 2022 · Paper 23 | Q16 | 4 | Interpreting sections of a speed–time graph |
Paper 4 (Calculator): 4 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q18 | 4 | Speed-time graph: distance and total time |
| Oct/Nov 2025 · Paper 42 | Q9 | 3 | Distance from a speed-time graph |
| Feb/March 2025 · Paper 42 | Q16 (a), (c) | 4 | Speed–time graph: acceleration and average speed |
| Oct/Nov 2022 · Paper 42 | Q5 (a) | 5 | Speed–time graph for two vehicles |
Chapter 12: Graphs of Functions and Sketching Curves
30 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 10 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 23 | Q14 | 2 | Quadratic curve: symmetry line and completed square |
| May/June 2025 · Paper 21 | Q6 | 3 | Solving simultaneous equations graphically |
| May/June 2025 · Paper 22 | Q15 | 6 | Reciprocal graph: intercept, asymptotes, solving |
| May/June 2025 · Paper 22 | Q21 (a) | 3 | Roots of a cubic graph as exact values |
| Oct/Nov 2024 · Paper 21 | Q22 (b) | 4 | Solving a cubic using a drawn line |
| May/June 2024 · Paper 21 | Q18 | 3 | Solving a cubic equation using a drawn line |
| May/June 2024 · Paper 22 | Q22 (a) | 2 | Recognising types of graph |
| May/June 2023 · Paper 21 | Q20 | 7 | Quadratic graph: table, drawing, solving with a line |
| Oct/Nov 2022 · Paper 21 | Q21 | 2 | Sketching a cubic from gradient information |
| Oct/Nov 2022 · Paper 22 | Q11 | 3 | Cubic graph in factorised form: intercepts |
Paper 4 (Calculator): 20 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 42 | Q11 | 10 | Cubic graph: table, drawing and solving |
| Oct/Nov 2025 · Paper 43 | Q13 | 3 | Exponential curve: finding base and a value |
| May/June 2025 · Paper 41 | Q14 | 11 | Cubic graph: table, drawing, solving with a line |
| Oct/Nov 2024 · Paper 41 | Q8 (b) | 3 | Sketching an exponential graph and asymptote |
| Oct/Nov 2024 · Paper 42 | Q2 (a), (b), (d) | 10 | Cubic graph: table, drawing and solving |
| May/June 2024 · Paper 41 | Q8 (a) | 4 | Sketching a quadratic with intercepts |
| May/June 2024 · Paper 43 | Q5 | 13 | Using a curve: solving equations and lines |
| Feb/March 2024 · Paper 42 | Q8 (a)–(b) | 4 | Sketching linear and quadratic graphs |
| Feb/March 2024 · Paper 42 | Q10 | 12 | Cubic graph: table, drawing, solving with lines |
| Oct/Nov 2023 · Paper 43 | Q11 (a) | 4 | Sketch of a quadratic: intercepts and roots |
| May/June 2023 · Paper 42 | Q8 (a) | 6 | Expanding and sketching a cubic graph |
| May/June 2023 · Paper 43 | Q7 (a)–(b) | 5 | Recognising and sketching graphs; reciprocal equation |
| May/June 2023 · Paper 43 | Q10 | 12 | Exponential graph: table, drawing and solving |
| Oct/Nov 2022 · Paper 41 | Q10 (a) | 3 | Number of solutions from a sketched curve |
| Oct/Nov 2022 · Paper 42 | Q2 (a) | 7 | Drawing and using a cubic volume graph |
| Oct/Nov 2022 · Paper 43 | Q9 (a) | 8 | Sketching straight-line, quadratic and reciprocal graphs |
| May/June 2022 · Paper 41 | Q6 (a) | 7 | Using a given graph to solve equations |
| May/June 2022 · Paper 43 | Q9 (a) | 4 | Sketching a cubic with intercepts |
| Feb/March 2022 · Paper 42 | Q2 | 8 | Reciprocal-type curve: table, graph, solving |
| Feb/March 2022 · Paper 42 | Q12 (b) | 3 | Sketching a cubic curve |
Chapter 13: Differentiation
32 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 9 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q23 | 4 | Turning point of a quadratic curve |
| May/June 2025 · Paper 21 | Q11 | 5 | Tangent from an external point to a curve |
| May/June 2025 · Paper 21 | Q22 | 6 | Derivative coefficients and turning points |
| May/June 2025 · Paper 22 | Q21 (b) | 6 | Differentiating a cubic; turning points |
| May/June 2025 · Paper 23 | Q21 | 6 | Differentiating a cubic; turning points |
| Feb/March 2025 · Paper 22 | Q22 | 9 | Stationary points of a cubic; nature and roots |
| May/June 2024 · Paper 22 | Q18 | 3 | Estimating a gradient by drawing a tangent |
| Oct/Nov 2023 · Paper 22 | Q25 | 2 | Differentiation: finding unknown constants |
| May/June 2023 · Paper 21 | Q21 | 6 | Gradient at a point and turning points |
Paper 4 (Calculator): 23 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 43 | Q20 | 4 | Differentiation: gradient of a cubic at a point |
| May/June 2025 · Paper 42 | Q26 | 2 | Differentiation: finding unknown coefficients and powers |
| Feb/March 2025 · Paper 42 | Q16 (b) | 2 | Tangent to a curve to estimate acceleration |
| Oct/Nov 2024 · Paper 42 | Q2 (c) | 3 | Tangent to a curve to estimate gradient |
| Oct/Nov 2024 · Paper 42 | Q10 | 9 | Differentiation: turning points and their nature |
| Oct/Nov 2024 · Paper 43 | Q10 | 11 | Differentiation: tangent, perpendicular line, maximum |
| May/June 2024 · Paper 41 | Q8 (b) | 5 | Derivative and turning point of a quadratic |
| May/June 2024 · Paper 42 | Q11 | 7 | Stationary points and tangent gradient |
| May/June 2024 · Paper 43 | Q10 | 11 | Derivative, tangent equation and turning points |
| Feb/March 2024 · Paper 42 | Q8 (c) | 8 | Turning points of a cubic and their nature |
| Oct/Nov 2023 · Paper 41 | Q11 | 10 | Stationary points and their nature |
| Oct/Nov 2023 · Paper 42 | Q9 | 8 | Differentiation: maximum point and gradient |
| Oct/Nov 2023 · Paper 43 | Q11 (b)–(c) | 5 | Differentiating a quadratic; point with given gradient |
| May/June 2023 · Paper 42 | Q8 (b) | 7 | Tangents of given gradient using differentiation |
| May/June 2023 · Paper 43 | Q12 | 8 | Differentiation: three turning points and nature |
| Feb/March 2023 · Paper 42 | Q9 | 9 | Gradient, turning points and sketch of cubic |
| Oct/Nov 2022 · Paper 41 | Q10 (b) | 5 | Stationary points by differentiation |
| Oct/Nov 2022 · Paper 42 | Q6 (h) | 2 | Differentiating a quadratic |
| Oct/Nov 2022 · Paper 43 | Q9 (b) | 9 | Derivative, gradient and tangent of a cubic |
| May/June 2022 · Paper 41 | Q6 (b)–(c) | 7 | Differentiation: gradient and stationary point |
| May/June 2022 · Paper 42 | Q12 | 11 | Gradient to find coefficient; stationary points; sketch |
| May/June 2022 · Paper 43 | Q9 (b) | 12 | Turning points of a cubic; number of roots |
| Feb/March 2022 · Paper 42 | Q12 (c) | 6 | Stationary points to find unknown coefficients |
Chapter 14: Functions
31 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 13 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q18 | 4 | Composite function identity: finding coefficients |
| Oct/Nov 2025 · Paper 22 | Q20 | 11 | Functions: composite, inverse and solving |
| May/June 2025 · Paper 21 | Q14 | 8 | Functions: evaluate, inverse, composite |
| May/June 2025 · Paper 23 | Q22 | 8 | Functions: evaluate, inverse, composite equation |
| Oct/Nov 2024 · Paper 21 | Q18 | 3 | Solving with a function; inverse function value |
| May/June 2024 · Paper 23 | Q20 | 4 | Exponential function and its inverse |
| May/June 2023 · Paper 22 | Q14 | 2 | Inverse of a linear function |
| May/June 2023 · Paper 23 | Q20 | 6 | Function substitution, inverse and composite value |
| Feb/March 2023 · Paper 22 | Q25 | 2 | Inverse of a cubic function |
| Oct/Nov 2022 · Paper 22 | Q17 | 6 | Functions: evaluating, inverse and composite |
| Oct/Nov 2022 · Paper 23 | Q19 | 6 | Functions: composite and inverse |
| May/June 2022 · Paper 22 | Q19 | 4 | Inverse function; solving with composite |
| May/June 2022 · Paper 23 | Q19 | 7 | Functions: evaluating, composite and inverse |
Paper 4 (Calculator): 18 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q28 | 3 | Function and inverse function values |
| Oct/Nov 2025 · Paper 43 | Q19 | 8 | Function values, inverse and composite equation |
| May/June 2025 · Paper 42 | Q19 | 6 | Functions: domain, range and inverse |
| Feb/March 2025 · Paper 42 | Q14 | 5 | Function evaluation and inverse function |
| Oct/Nov 2024 · Paper 41 | Q8 (a) | 16 | Functions: inverse, composite, sketch and tangent |
| Oct/Nov 2024 · Paper 42 | Q9 | 8 | Function values, inverse and composite expression |
| Oct/Nov 2024 · Paper 43 | Q11 | 14 | Functions: composite, inverse and algebraic fractions |
| May/June 2024 · Paper 41 | Q9 | 12 | Functions: composite, inverse, solving |
| May/June 2024 · Paper 42 | Q7 (d) | 5 | Functions: evaluate, composite, solve |
| Feb/March 2024 · Paper 42 | Q11 | 10 | Composite and inverse functions; solving |
| Oct/Nov 2023 · Paper 41 | Q9 (a)–(d) | 12 | Functions: evaluation, inverse and composite |
| Oct/Nov 2023 · Paper 42 | Q11 | 14 | Functions: inverse, composite and algebra |
| Oct/Nov 2023 · Paper 43 | Q6 | 12 | Function values, inverse, composite and algebraic fractions |
| May/June 2023 · Paper 41 | Q10 | 9 | Functions: evaluate, inverse, composite |
| Feb/March 2023 · Paper 42 | Q11 | 10 | Function evaluation, composites and self-inverse |
| Oct/Nov 2022 · Paper 41 | Q7 | 16 | Functions: composite, inverse and algebra |
| May/June 2022 · Paper 41 | Q4 | 11 | Functions: composite, inverse, algebraic fraction |
| Feb/March 2022 · Paper 42 | Q3 | 6 | Composite and inverse functions |
Chapter 15: Coordinate Geometry
29 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 15 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 22 | Q17 | 11 | Kite: length as surd, midpoint, line equation |
| Oct/Nov 2025 · Paper 23 | Q22 | 3 | Equation of a perpendicular line |
| May/June 2025 · Paper 23 | Q24 | 7 | Midpoint, gradient and dividing a line in a ratio |
| Feb/March 2025 · Paper 22 | Q21 | 6 | Intercept; equation of perpendicular bisector |
| Oct/Nov 2024 · Paper 22 | Q22 | 5 | Equation of a perpendicular bisector |
| May/June 2024 · Paper 21 | Q1 | 2 | Coordinates of a parallelogram vertex |
| May/June 2024 · Paper 22 | Q14 | 2 | Equation of a line through two points |
| May/June 2024 · Paper 23 | Q10 | 2 | Gradient between two points |
| Feb/March 2024 · Paper 22 | Q9 | 2 | Intersection of two straight lines |
| Feb/March 2024 · Paper 22 | Q26 | 5 | Equation of a perpendicular bisector |
| May/June 2023 · Paper 22 | Q15 | 7 | Midpoint, gradient and perpendicular bisector |
| Oct/Nov 2022 · Paper 23 | Q8 | 2 | Midpoint of a line segment |
| Oct/Nov 2022 · Paper 23 | Q16 | 3 | Perpendicular line equation for a kite diagonal |
| Feb/March 2022 · Paper 22 | Q5 | 2 | Gradient and y-intercept of a straight line |
| Feb/March 2022 · Paper 22 | Q16 | 4 | Line through two points; perpendicular line |
Paper 4 (Calculator): 14 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q17 | 3 | Equation of a line through two points |
| May/June 2025 · Paper 42 | Q25 | 5 | Equation of a perpendicular bisector |
| May/June 2025 · Paper 43 | Q13 | 6 | Line equations: intercepts and perpendicular line |
| Feb/March 2025 · Paper 42 | Q5 | 3 | Coordinates of vertices in a rotated pattern |
| May/June 2024 · Paper 41 | Q5 (a) | 13 | Chord: vector, length, midpoint, perpendicular bisector |
| May/June 2024 · Paper 42 | Q10 | 12 | Midpoint, length, gradient and perpendicular line |
| Oct/Nov 2023 · Paper 42 | Q12 (b)–(d) | 9 | Line equation, perpendicular bisector and length |
| Oct/Nov 2023 · Paper 43 | Q9 | 14 | Triangle from coordinates: lengths, line, perpendicular bisector |
| May/June 2023 · Paper 41 | Q6 | 14 | Square vertices; midpoint, length, parallel line |
| May/June 2023 · Paper 43 | Q11 | 9 | Length, gradient and perpendicular bisector |
| Feb/March 2023 · Paper 42 | Q6 | 11 | Line equations; perpendicular line and intersections |
| Oct/Nov 2022 · Paper 42 | Q8 | 9 | Midpoint, perpendicular bisector and triangle area |
| May/June 2022 · Paper 42 | Q3 | 12 | Length, perpendicular bisector, points at a distance |
| May/June 2022 · Paper 43 | Q8 (a) | 12 | Midpoint, length, line equations, perpendicular line |
Chapter 16: Geometrical Terms, Constructions and Symmetry
31 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 18 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 23 | Q3 | 1 | Completing the net of a dice |
| May/June 2025 · Paper 22 | Q1 | 2 | Completing a diagram for given symmetry |
| May/June 2025 · Paper 22 | Q2 | 3 | Scale drawing: distance and bearing |
| May/June 2025 · Paper 23 | Q3 | 2 | Symmetry of a square-based pyramid |
| Feb/March 2025 · Paper 22 | Q3 | 1 | Naming a quadrilateral from its properties |
| Oct/Nov 2024 · Paper 23 | Q4 | 3 | Scale drawing: distance and measured bearing |
| May/June 2024 · Paper 22 | Q15 | 3 | Bearings with an equilateral triangle |
| May/June 2024 · Paper 23 | Q7 | 2 | Map scale: actual distance |
| Feb/March 2024 · Paper 22 | Q4 | 4 | Net of a cuboid: missing lengths |
| Feb/March 2024 · Paper 22 | Q13 | 2 | Back bearing |
| Oct/Nov 2023 · Paper 22 | Q7 | 2 | Finding a bearing |
| May/June 2023 · Paper 22 | Q4 | 2 | Map scale: actual distance |
| May/June 2023 · Paper 23 | Q1 | 3 | Line and rotational symmetry of a diagram |
| Oct/Nov 2022 · Paper 23 | Q14 | 2 | Map scale: converting an area |
| May/June 2022 · Paper 22 | Q9 | 2 | Back bearing |
| May/June 2022 · Paper 23 | Q18 | 3 | Bearings in a given ratio |
| Feb/March 2022 · Paper 22 | Q1 | 1 | Measuring an angle with a protractor |
| Feb/March 2022 · Paper 22 | Q6 | 2 | Constructing a triangle from three sides |
Paper 4 (Calculator): 13 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q1 | 1 | Naming a quadrilateral from its symmetry |
| Oct/Nov 2025 · Paper 41 | Q5 | 5 | Constructing a triangle; scale and bearing |
| Oct/Nov 2025 · Paper 42 | Q3 | 1 | Rotational symmetry of a regular polygon |
| Oct/Nov 2025 · Paper 43 | Q4 | 4 | Scale drawing with bearings; back bearing |
| May/June 2025 · Paper 41 | Q11 | 3 | Area on a scale plan with unit conversion |
| May/June 2025 · Paper 42 | Q1 | 1 | Naming a quadrilateral from its symmetry |
| May/June 2025 · Paper 42 | Q2 | 1 | Identifying a solid from its net |
| May/June 2025 · Paper 43 | Q2 | 3 | Scale drawing: constructing a triangle |
| Feb/March 2025 · Paper 42 | Q3 | 1 | Completing a pattern with lines of symmetry |
| Feb/March 2025 · Paper 42 | Q8 | 5 | Scale drawing: distance and construction |
| May/June 2023 · Paper 43 | Q3 (a) | 5 | Scale drawing: measuring angles and lengths |
| May/June 2023 · Paper 43 | Q4 (a) | 3 | Bearings with an isosceles triangle |
| May/June 2022 · Paper 42 | Q5 (a) | 2 | Lines of symmetry of a rectangle |
Chapter 17: Angles and Similarity
67 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 46 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q2 | 3 | Angles with an isosceles triangle |
| Oct/Nov 2025 · Paper 21 | Q3 | 2 | Interior angle of a regular polygon |
| Oct/Nov 2025 · Paper 21 | Q14 (b) | 3 | Similar triangles in a circle: length and area |
| Oct/Nov 2025 · Paper 22 | Q6 | 4 | Angles with parallel lines in a quadrilateral |
| Oct/Nov 2025 · Paper 22 | Q11 | 7 | Similar triangles: proof, length and area |
| Oct/Nov 2025 · Paper 22 | Q16 | 4 | Angles of two regular polygons |
| Oct/Nov 2025 · Paper 23 | Q1 | 2 | Angles in an isosceles triangle |
| Oct/Nov 2025 · Paper 23 | Q5 | 2 | Angles with an equilateral triangle in a rectangle |
| May/June 2025 · Paper 21 | Q2 | 4 | Angles with parallel lines |
| May/June 2025 · Paper 21 | Q5 | 2 | Regular polygon sides from interior angle |
| May/June 2025 · Paper 22 | Q3 | 3 | Angles with parallel lines |
| May/June 2025 · Paper 23 | Q2 | 4 | Angles in a quadrilateral and isosceles triangle |
| May/June 2025 · Paper 23 | Q17 | 3 | Similar solids: height from surface areas |
| Feb/March 2025 · Paper 22 | Q10 | 5 | Regular polygons meeting at a point |
| Oct/Nov 2024 · Paper 21 | Q6 | 3 | Angles in a triangle and quadrilateral |
| Oct/Nov 2024 · Paper 21 | Q9 | 3 | Regular polygon from interior and exterior angles |
| Oct/Nov 2024 · Paper 21 | Q14 | 4 | Similar solids with mass and density |
| Oct/Nov 2024 · Paper 22 | Q2 | 2 | Angles in an isosceles triangle |
| Oct/Nov 2024 · Paper 22 | Q8 | 4 | Parallelogram angles from algebraic expressions |
| Oct/Nov 2024 · Paper 22 | Q23 | 3 | Similar solids: volume percentage to length |
| Oct/Nov 2024 · Paper 23 | Q6 | 1 | Angles at a point |
| Oct/Nov 2024 · Paper 23 | Q9 | 2 | Interior angle of a regular polygon |
| Oct/Nov 2024 · Paper 23 | Q18 | 3 | Similar solids: height from volumes |
| May/June 2024 · Paper 21 | Q6 | 3 | Angles in congruent kites around a point |
| May/June 2024 · Paper 22 | Q20 | 3 | Similar solids: height from volumes |
| May/June 2024 · Paper 23 | Q18 | 3 | Exterior angle of a regular polygon |
| Oct/Nov 2023 · Paper 21 | Q1 | 2 | Angles in an isosceles triangle |
| Oct/Nov 2023 · Paper 22 | Q5 | 2 | Angles with parallel lines |
| Oct/Nov 2023 · Paper 22 | Q11 | 4 | Similar shapes: length and area |
| Oct/Nov 2023 · Paper 23 | Q5 | 3 | Quadrilateral from a rotation: name and angle |
| May/June 2023 · Paper 21 | Q1 | 2 | Angles in a triangle on a straight line |
| May/June 2023 · Paper 21 | Q3 | 4 | Angles with parallel lines and reasons |
| May/June 2023 · Paper 21 | Q9 | 2 | Similar triangles: missing length |
| Feb/March 2023 · Paper 22 | Q10 | 3 | Similar triangles between parallel lines |
| Feb/March 2023 · Paper 22 | Q12 | 3 | Regular polygon from angle ratio |
| Feb/March 2023 · Paper 22 | Q18 | 3 | Similar solids: surface area from volumes |
| Oct/Nov 2022 · Paper 21 | Q5 | 2 | Angles with parallel lines |
| Oct/Nov 2022 · Paper 21 | Q12 | 3 | Similar triangles: length and area |
| Oct/Nov 2022 · Paper 22 | Q1 | 2 | Angles in an isosceles triangle |
| Oct/Nov 2022 · Paper 22 | Q9 (a) | 1 | Identifying congruent triangles |
| Oct/Nov 2022 · Paper 22 | Q22 | 3 | Similar solids: height from volumes |
| Oct/Nov 2022 · Paper 23 | Q11 | 4 | Regular polygon angles with algebra |
| Oct/Nov 2022 · Paper 23 | Q18 | 3 | Similar solids: height from capacities |
| May/June 2022 · Paper 21 | Q11 | 4 | Similar triangles and similar prisms |
| May/June 2022 · Paper 21 | Q12 | 3 | Pentagon angles in a given ratio |
| May/June 2022 · Paper 23 | Q3 | 2 | Angles in a quadrilateral and on a line |
Paper 4 (Calculator): 21 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q3 | 2 | Angles with parallel lines |
| Oct/Nov 2025 · Paper 43 | Q5 | 4 | Regular polygon angles and symmetry |
| Oct/Nov 2025 · Paper 43 | Q22 | 5 | Similar triangles; similar containers capacity |
| May/June 2025 · Paper 42 | Q13 | 4 | Similar triangles and volumes of similar prisms |
| May/June 2025 · Paper 42 | Q15 | 2 | Number of sides from an interior angle |
| Oct/Nov 2024 · Paper 42 | Q4 (a) | 2 | Quadrilateral angle sum with a ratio |
| May/June 2024 · Paper 41 | Q2 (b) | 3 | Area after successive enlargements |
| May/June 2024 · Paper 42 | Q2 (a)–(b) | 4 | Parallel line angles; interior angle of polygon |
| May/June 2024 · Paper 43 | Q8 (b) | 3 | Similar solids: surface area and volume |
| Feb/March 2024 · Paper 42 | Q2 (b)–(c) | 6 | Similar triangles: proof, lengths and area ratio |
| Oct/Nov 2023 · Paper 42 | Q10 (a) | 2 | Identifying congruent triangles in a hexagon |
| Oct/Nov 2023 · Paper 43 | Q4 (a) | 2 | Interior angle of a regular polygon |
| Oct/Nov 2023 · Paper 43 | Q8 (b) | 3 | Areas of similar sectors |
| May/June 2023 · Paper 42 | Q1 (a)–(c) | 10 | Angles in triangles, at a point, polygons |
| May/June 2023 · Paper 42 | Q3 (b) | 4 | Similar triangles: angle and length from area |
| May/June 2023 · Paper 43 | Q3 (b) | 5 | Density and similar solids |
| May/June 2022 · Paper 42 | Q9 | 7 | Similar triangles: reasons, lengths and area |
| May/June 2022 · Paper 43 | Q2 (b) | 2 | Area of an enlarged shape |
| May/June 2022 · Paper 43 | Q4 (a) | 1 | Interior angle of a regular polygon |
| Feb/March 2022 · Paper 42 | Q6 (a) | 2 | Sides of a regular polygon from interior angle |
| Feb/March 2022 · Paper 42 | Q7 (a) | 3 | Similar shapes: lengths from areas |
Chapter 18: Circle Theorems
33 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 20 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q14 (a) | 6 | Circle theorems with geometrical reasons |
| Oct/Nov 2025 · Paper 23 | Q13 | 4 | Circle theorems with tangents and parallel lines |
| Oct/Nov 2025 · Paper 23 | Q21 | 4 | Cyclic quadrilateral angles with a ratio |
| May/June 2025 · Paper 21 | Q10 | 4 | Circle theorems with a tangent |
| May/June 2025 · Paper 22 | Q12 | 2 | Angle in a semicircle with reasons |
| May/June 2025 · Paper 23 | Q13 | 4 | Circle theorems: tangent and parallel chords |
| Feb/March 2025 · Paper 22 | Q14 | 5 | Circle theorems with a tangent |
| Oct/Nov 2024 · Paper 22 | Q17 | 2 | Tangents from an external point and angles |
| Oct/Nov 2024 · Paper 23 | Q14 | 4 | Circle theorems: tangent, cyclic and centre angles |
| May/June 2024 · Paper 21 | Q13 | 3 | Cyclic quadrilateral angles |
| May/June 2024 · Paper 23 | Q14 | 3 | Alternate segment and isosceles triangle angles |
| Oct/Nov 2023 · Paper 21 | Q17 | 3 | Alternate segment theorem and isosceles triangle |
| Oct/Nov 2023 · Paper 22 | Q17 | 4 | Circle theorems: centre and alternate segment |
| May/June 2023 · Paper 21 | Q12 (b) | 3 | Circle theorems with tangent and parallel lines |
| May/June 2023 · Paper 22 | Q13 | 2 | Circle theorems with parallel chords |
| Feb/March 2023 · Paper 22 | Q17 | 6 | Cyclic quadrilateral and tangent angles |
| Oct/Nov 2022 · Paper 21 | Q16 | 4 | Angles in a circle formed by chords |
| Oct/Nov 2022 · Paper 22 | Q15 | 1 | Reason for a cyclic quadrilateral |
| May/June 2022 · Paper 21 | Q18 | 3 | Circle theorems with tangent and parallel lines |
| May/June 2022 · Paper 23 | Q11 | 1 | Identifying a diameter from angles |
Paper 4 (Calculator): 13 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q15 | 3 | Tangents from an external point |
| Oct/Nov 2025 · Paper 42 | Q12 | 4 | Circle theorems with a tangent and reasons |
| May/June 2025 · Paper 42 | Q18 | 4 | Circle theorems: angles in a cyclic figure |
| Oct/Nov 2024 · Paper 42 | Q4 (b) | 5 | Circle theorems with a tangent |
| May/June 2024 · Paper 42 | Q2 (c)–(d) | 5 | Circle theorems: tangent and cyclic quadrilateral |
| Feb/March 2024 · Paper 42 | Q2 (a) | 2 | Cyclic quadrilateral exterior angle reason |
| Oct/Nov 2023 · Paper 41 | Q5 (b) | 2 | Centre of a circle through a right-angled triangle |
| Oct/Nov 2023 · Paper 43 | Q4 (b) | 5 | Circle theorems with a tangent and parallel chords |
| May/June 2023 · Paper 42 | Q1 (d) | 5 | Proving a quadrilateral is cyclic |
| May/June 2023 · Paper 43 | Q4 (b)–(c) | 10 | Circle theorems with tangents |
| Oct/Nov 2022 · Paper 43 | Q8 (b) | 3 | Circle theorems: centre and tangent angles |
| May/June 2022 · Paper 42 | Q2 | 7 | Circle theorems with reasons and tangent |
| Feb/March 2022 · Paper 42 | Q6 (b)–(d) | 8 | Circle theorems: angles and similarity proof |
Chapter 19: Mensuration
82 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 41 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q4 | 2 | Height of a triangle from its area |
| Oct/Nov 2025 · Paper 21 | Q12 | 4 | Sector perimeter and area in terms of pi |
| Oct/Nov 2025 · Paper 22 | Q3 | 2 | Volume of a cuboid |
| Oct/Nov 2025 · Paper 22 | Q23 | 7 | Sector folded into a cone: arc and volume |
| Oct/Nov 2025 · Paper 23 | Q4 | 2 | Perimeter of a compound shape |
| Oct/Nov 2025 · Paper 23 | Q19 | 5 | Sector area and major arc in terms of pi |
| Oct/Nov 2025 · Paper 23 | Q29 | 5 | Composite solid and cone volumes in algebra |
| May/June 2025 · Paper 21 | Q13 | 8 | Hemisphere, cone and cylinder volumes |
| May/June 2025 · Paper 22 | Q10 | 2 | Arc length of a sector in terms of pi |
| May/June 2025 · Paper 22 | Q16 | 4 | Surface area of a hemisphere and cylinder |
| May/June 2025 · Paper 23 | Q20 | 3 | Major arc length in terms of pi |
| Feb/March 2025 · Paper 22 | Q5 | 2 | Ordering lengths in different units |
| Feb/March 2025 · Paper 22 | Q6 | 2 | Area of a trapezium |
| Feb/March 2025 · Paper 22 | Q13 | 4 | Cylinder and sphere of equal volume |
| Oct/Nov 2024 · Paper 21 | Q16 | 4 | Sphere and cylinder of equal volume: curved surface |
| Oct/Nov 2024 · Paper 22 | Q5 | 1 | Converting square metres to square centimetres |
| Oct/Nov 2024 · Paper 22 | Q6 | 2 | Trapezium area: finding a missing side |
| Oct/Nov 2024 · Paper 22 | Q9 | 3 | Circle around a square: exact area |
| Oct/Nov 2024 · Paper 22 | Q19 | 7 | Volume and surface area: cylinder with hemisphere |
| May/June 2024 · Paper 21 | Q7 | 7 | Triangle and semicircle: area and perimeter |
| May/June 2024 · Paper 21 | Q14 | 3 | Area of a major sector |
| May/June 2024 · Paper 23 | Q4 | 2 | Height of a cuboid from volume |
| Feb/March 2024 · Paper 22 | Q10 | 2 | Area of a trapezium |
| Oct/Nov 2023 · Paper 21 | Q22 | 4 | Shaded area from sectors in a rhombus |
| Oct/Nov 2023 · Paper 22 | Q4 | 1 | Converting length units |
| Oct/Nov 2023 · Paper 22 | Q18 | 4 | Total surface area of a cylinder |
| Oct/Nov 2023 · Paper 23 | Q16 | 4 | Cylinder volume from curved surface area |
| May/June 2023 · Paper 21 | Q6 | 2 | Volume of a sphere |
| May/June 2023 · Paper 22 | Q11 | 3 | Area of a shape made from sectors |
| May/June 2023 · Paper 23 | Q3 | 3 | Surface area of a cuboid |
| May/June 2023 · Paper 23 | Q16 | 3 | Radius of a cylinder from its volume |
| Feb/March 2023 · Paper 22 | Q14 | 3 | Arc length from radius and chord |
| Oct/Nov 2022 · Paper 21 | Q15 | 3 | Sector angle from its perimeter |
| Oct/Nov 2022 · Paper 22 | Q21 | 4 | Volume of a cone frustum |
| May/June 2022 · Paper 21 | Q17 | 3 | Radius of a hemisphere from volume |
| May/June 2022 · Paper 22 | Q5 | 3 | Total surface area of a cuboid |
| May/June 2022 · Paper 22 | Q23 | 4 | Cone and hemisphere: slant height from surface area |
| May/June 2022 · Paper 23 | Q20 | 4 | Percentage of a square covered by a sector |
| Feb/March 2022 · Paper 22 | Q4 | 3 | Total surface area of a cuboid |
| Feb/March 2022 · Paper 22 | Q14 | 2 | Circumference of a circle |
| Feb/March 2022 · Paper 22 | Q17 | 5 | Percentage of a rectangle shaded by a sector |
Paper 4 (Calculator): 41 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q14 | 10 | Sphere in a cube: volume, mass, recast cylinder |
| Oct/Nov 2025 · Paper 42 | Q7 (a) | 4 | Parallelogram perimeter equal to a circumference |
| May/June 2025 · Paper 41 | Q19 | 4 | Perimeter of a major sector |
| May/June 2025 · Paper 41 | Q20 (b) | 5 | Volume of a pyramid frustum |
| May/June 2025 · Paper 42 | Q4 | 2 | Area of a trapezium |
| May/June 2025 · Paper 43 | Q4 | 3 | Area of a compound shape: finding a length |
| May/June 2025 · Paper 43 | Q5 | 2 | Converting area and volume units |
| May/June 2025 · Paper 43 | Q18 (a)–(b) | 4 | Volume and surface area of a cuboid |
| May/June 2025 · Paper 43 | Q21 | 4 | Sector area within an equilateral triangle |
| May/June 2025 · Paper 43 | Q23 | 4 | Volume of a cone frustum |
| Feb/March 2025 · Paper 42 | Q12 | 2 | Total surface area of a cone |
| Feb/March 2025 · Paper 42 | Q23 | 7 | Tunnel cross-section: major segment volume |
| Oct/Nov 2024 · Paper 41 | Q9 (a)–(b) | 4 | Volume and surface area of a cuboid |
| Oct/Nov 2024 · Paper 41 | Q10 (b) | 8 | Segment area and perimeter of a sector |
| Oct/Nov 2024 · Paper 42 | Q4 (c) | 8 | Tangents to a circle: arc length and sector |
| Oct/Nov 2024 · Paper 43 | Q4 | 15 | Mass, volume and surface area of solids |
| Oct/Nov 2024 · Paper 43 | Q7 | 15 | Trapezium area equation, sector and arc shape |
| May/June 2024 · Paper 41 | Q7 | 15 | Open box surface area; cone volume from density |
| May/June 2024 · Paper 42 | Q4 (a)–(b) | 11 | Half-cylinder tank; displaced water volume |
| May/June 2024 · Paper 42 | Q9 (a) | 3 | Area between two sectors |
| May/June 2024 · Paper 43 | Q8 (a) | 11 | Cylinder and cone: volume and surface area |
| May/June 2024 · Paper 43 | Q11 (a) | 3 | Arc lengths: finding a sector angle |
| Feb/March 2024 · Paper 42 | Q4 | 11 | Pyramid volume and surface area; cone and hemisphere toy |
| Feb/March 2024 · Paper 42 | Q12 | 7 | Circle with sector removed: perimeter; cake volume |
| Oct/Nov 2023 · Paper 41 | Q8 | 14 | Composite solid; arc length and sector |
| Oct/Nov 2023 · Paper 42 | Q4 | 12 | Cone from a sector; solids inside solids |
| May/June 2023 · Paper 41 | Q4 (b)–(c) | 10 | Half-cylinder volume; shaded area with circle |
| May/June 2023 · Paper 42 | Q1 (e) | 3 | Perimeter of a circle with a sector removed |
| May/June 2023 · Paper 42 | Q5 | 13 | Cone volume; filling a cylinder at a rate |
| May/June 2023 · Paper 43 | Q8 (c) | 4 | Equal surface areas of cylinder and sphere |
| May/June 2023 · Paper 43 | Q9 (a) | 6 | Square and sectors: area and perimeter |
| Feb/March 2023 · Paper 42 | Q3 | 9 | Cylinder and sphere: water level and volumes |
| Feb/March 2023 · Paper 42 | Q8 (a) | 2 | Area of a triangle |
| Oct/Nov 2022 · Paper 41 | Q1 | 15 | Volume, mass and surface area of solids |
| Oct/Nov 2022 · Paper 42 | Q2 (b) | 5 | Surface area of a cuboid at maximum volume |
| Oct/Nov 2022 · Paper 42 | Q10 (b)–(c) | 6 | Sector area and sector perimeters |
| Oct/Nov 2022 · Paper 43 | Q5 (a), (c) | 8 | Prism and cylinder volume and capacity |
| May/June 2022 · Paper 41 | Q5 (b) | 8 | Volume and capacity of a container |
| May/June 2022 · Paper 42 | Q11 | 12 | Cylinder from a sheet; cone slant height from volume |
| May/June 2022 · Paper 43 | Q4 (c) | 3 | Volume of a prism |
| Feb/March 2022 · Paper 42 | Q9 | 10 | Cone opened into sector; flow through a pipe |
Chapter 20: Pythagoras and Trigonometry
43 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 26 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q26 | 3 | Tangent equation using exact values |
| Oct/Nov 2025 · Paper 22 | Q21 | 5 | Cosine graph sketch and trigonometric equation |
| Oct/Nov 2025 · Paper 23 | Q10 | 4 | Exact Pythagoras and cosine ratio |
| Oct/Nov 2025 · Paper 23 | Q17 | 4 | Cosine graph sketch; reflex angle solution |
| May/June 2025 · Paper 21 | Q20 | 4 | Exact trigonometric values in a triangle |
| May/June 2025 · Paper 22 | Q22 | 4 | Exact value; solving a sine equation |
| May/June 2025 · Paper 23 | Q23 | 6 | Exact trigonometric values in joined triangles |
| Feb/March 2025 · Paper 22 | Q18 | 9 | Exact trig values and surd perimeter |
| Oct/Nov 2024 · Paper 21 | Q20 | 5 | Right-angled trigonometry in two triangles |
| Oct/Nov 2024 · Paper 21 | Q21 | 3 | Solving a tangent equation over a full turn |
| Oct/Nov 2024 · Paper 23 | Q16 | 3 | Shortest distance using right-angled trigonometry |
| Oct/Nov 2024 · Paper 23 | Q20 | 3 | Solving a tangent equation over a full turn |
| May/June 2024 · Paper 21 | Q20 | 3 | Solving a sine equation in a range |
| May/June 2024 · Paper 22 | Q12 | 2 | Pythagoras in a right-angled triangle |
| May/June 2024 · Paper 22 | Q22 (b) | 5 | Sketching sine graph; solving a sine equation |
| May/June 2024 · Paper 23 | Q9 | 2 | Side of a right-angled triangle using trigonometry |
| May/June 2024 · Paper 23 | Q22 | 3 | Solving a tangent equation in a range |
| Feb/March 2024 · Paper 22 | Q23 | 4 | Cosine graph and solving cos equation |
| Oct/Nov 2023 · Paper 21 | Q19 | 4 | Cosine graph and reflex angle solution |
| May/June 2023 · Paper 21 | Q19 | 5 | Cosine graph and solving cos equation |
| May/June 2023 · Paper 22 | Q21 | 3 | Solving a sine equation in a range |
| Oct/Nov 2022 · Paper 21 | Q22 | 4 | Sketching cosine graph; solving a trig equation |
| Oct/Nov 2022 · Paper 23 | Q10 | 4 | Pythagoras: side and perimeter of a triangle |
| Oct/Nov 2022 · Paper 23 | Q20 | 5 | Sketching sine graph; solving a trig equation |
| May/June 2022 · Paper 22 | Q17 | 5 | Sine graph and solving sin equation |
| May/June 2022 · Paper 23 | Q23 | 3 | Solving a sine equation |
Paper 4 (Calculator): 17 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q13 | 3 | Angle of elevation between two poles |
| May/June 2025 · Paper 42 | Q20 (a), (d) | 5 | Right-angled trigonometry in a quadrilateral |
| May/June 2025 · Paper 43 | Q25 | 5 | Sketching sine graph; solving a trig equation |
| Feb/March 2025 · Paper 42 | Q19 | 3 | Solving a cosine equation |
| May/June 2024 · Paper 43 | Q6 (a)–(b) | 5 | Pythagoras and bearing from right triangles |
| Oct/Nov 2023 · Paper 41 | Q5 (a) | 5 | Right-angled trigonometry in a triangle |
| Oct/Nov 2023 · Paper 42 | Q6 | 7 | Pythagoras with algebraic sides, then an angle |
| Oct/Nov 2023 · Paper 43 | Q7 | 11 | Graph of a cosine function: drawing and solving |
| May/June 2023 · Paper 41 | Q2 (c) | 3 | Shortest distance using right-angled trigonometry |
| May/June 2023 · Paper 41 | Q4 (a) | 4 | Right-angled triangle: area and angle |
| May/June 2023 · Paper 43 | Q7 (c) | 5 | Sketching sine graph; solving a sine equation |
| Feb/March 2023 · Paper 42 | Q10 (a)–(b) | 4 | Right-angled trigonometry in a quadrilateral |
| Feb/March 2023 · Paper 42 | Q12 | 4 | Tangent graph and solving tan equation |
| Oct/Nov 2022 · Paper 42 | Q9 | 5 | Sketching sine graph; solving a trig equation |
| May/June 2022 · Paper 41 | Q5 (a) | 9 | Regular octagon: angles, area and circumcircle |
| May/June 2022 · Paper 43 | Q4 (b) | 7 | Polygon in a circle: radius and segment perimeter |
| Feb/March 2022 · Paper 42 | Q12 (a) | 2 | Solving a tangent equation in a range |
Chapter 21: Sine Rule, Cosine Rule and 3D Trigonometry
61 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 18 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 22 | Q19 | 3 | Longest rod in a cuboid |
| Oct/Nov 2025 · Paper 23 | Q23 | 3 | Triangle area using half ab sin C |
| Oct/Nov 2024 · Paper 23 | Q22 | 4 | Angle between a cuboid diagonal and base |
| May/June 2024 · Paper 21 | Q17 | 2 | Area of a triangle using sine |
| May/June 2024 · Paper 21 | Q21 | 4 | Angle between a diagonal and a base |
| May/June 2024 · Paper 23 | Q24 | 4 | Angle between a line and a base in a prism |
| Feb/March 2024 · Paper 22 | Q20 | 2 | Area of a triangle using sine |
| Oct/Nov 2023 · Paper 21 | Q18 | 3 | Sine rule with an obtuse angle |
| Oct/Nov 2023 · Paper 21 | Q21 | 4 | Angle between a diagonal and a face of a cuboid |
| Oct/Nov 2023 · Paper 23 | Q19 | 4 | Sine rule: finding an obtuse angle |
| Oct/Nov 2023 · Paper 23 | Q21 | 6 | Length and angle in a cuboid |
| May/June 2023 · Paper 21 | Q18 | 4 | Bearing using sine and cosine rule |
| May/June 2023 · Paper 22 | Q17 | 2 | Angle from area of a triangle |
| Feb/March 2023 · Paper 22 | Q22 | 4 | Prism: angle between line and plane |
| Oct/Nov 2022 · Paper 21 | Q18 | 4 | Sine rule to find a side |
| Oct/Nov 2022 · Paper 23 | Q21 | 5 | Sine rule with bearings |
| May/June 2022 · Paper 21 | Q24 | 3 | Diagonal of a cuboid |
| Feb/March 2022 · Paper 22 | Q21 | 7 | Open box: angle between line and plane |
Paper 4 (Calculator): 43 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q21 | 2 | Triangle area using half ab sin C |
| Oct/Nov 2025 · Paper 41 | Q27 | 4 | Angle between a diagonal and a face of a prism |
| Oct/Nov 2025 · Paper 41 | Q29 | 8 | Sine and cosine rules in two triangles |
| Oct/Nov 2025 · Paper 42 | Q7 (b) | 4 | Parallelogram area using sine; tiling cost |
| Oct/Nov 2025 · Paper 42 | Q15 | 10 | Field: cosine rule, sine rule and area |
| Oct/Nov 2025 · Paper 43 | Q18 | 6 | Cosine rule and sine rule in a quadrilateral |
| Oct/Nov 2025 · Paper 43 | Q24 | 6 | Cuboid: Pythagoras and angle with base |
| May/June 2025 · Paper 41 | Q12 | 3 | Shortest distance in a non-right-angled triangle |
| May/June 2025 · Paper 41 | Q17 | 10 | Sine and cosine rules and area in a quadrilateral |
| May/June 2025 · Paper 41 | Q20 (a) | 4 | Angle between pyramid edge and base |
| May/June 2025 · Paper 42 | Q20 (b)–(c) | 8 | Area and perimeter using sine and cosine rules |
| May/June 2025 · Paper 42 | Q27 | 4 | Angle between a cube diagonal and the base |
| May/June 2025 · Paper 43 | Q18 (c) | 4 | Angle between a line and a plane in a cuboid |
| Feb/March 2025 · Paper 42 | Q17 | 9 | Bearings with sine and cosine rule |
| Oct/Nov 2024 · Paper 41 | Q6 | 11 | Field: cosine rule, sine rule and area cost |
| Oct/Nov 2024 · Paper 41 | Q9 (c)–(d) | 8 | 3D trigonometry inside a cuboid |
| Oct/Nov 2024 · Paper 42 | Q7 (a) | 17 | Field: sine and cosine rules and bearings |
| Oct/Nov 2024 · Paper 43 | Q12 | 10 | Quadrilateral: cosine rule, sine rule, perimeter |
| May/June 2024 · Paper 41 | Q6 | 17 | Bearings and distances using sine and cosine rules |
| May/June 2024 · Paper 42 | Q4 (c) | 4 | Angle between a diagonal and the base |
| May/June 2024 · Paper 42 | Q6 | 10 | Quadrilateral: cosine rule, sine rule, shortest distance |
| May/June 2024 · Paper 42 | Q9 (b) | 7 | Regular hexagon: side from area using sine |
| May/June 2024 · Paper 43 | Q6 (c)–(d) | 10 | Sine and cosine rules in quadrilaterals |
| May/June 2024 · Paper 43 | Q11 (b) | 6 | Sector and triangle area using sine |
| Feb/March 2024 · Paper 42 | Q6 | 9 | Sine and cosine rule; shortest distance |
| Oct/Nov 2023 · Paper 41 | Q5 (c) | 7 | Cosine rule; angles in a given ratio |
| Oct/Nov 2023 · Paper 42 | Q7 | 16 | 3D elevation, sine rule and triangle area |
| Oct/Nov 2023 · Paper 43 | Q8 (a) | 14 | Compound shape: sector, right triangle, cosine rule, area |
| May/June 2023 · Paper 41 | Q2 (a), (b), (d) | 10 | Triangular prism: area, cosine rule, 3D angle |
| May/June 2023 · Paper 42 | Q7 | 11 | Bearings with sine and cosine rules; speed |
| May/June 2023 · Paper 42 | Q10 (a) | 4 | Cuboid space diagonal |
| May/June 2023 · Paper 43 | Q5 | 12 | Trigonometry in 3D and non-right triangles |
| May/June 2023 · Paper 43 | Q9 (b) | 4 | Angle between a diagonal and a plane |
| Feb/March 2023 · Paper 42 | Q10 (c)–(e) | 11 | Cosine and sine rule; shortest distance |
| Oct/Nov 2022 · Paper 41 | Q8 | 16 | Cosine rule, area and 3D angles |
| Oct/Nov 2022 · Paper 42 | Q7 | 18 | Cosine rule, 3D cuboid and bearings |
| Oct/Nov 2022 · Paper 43 | Q5 (d) | 4 | Length of a diagonal rod in a prism |
| Oct/Nov 2022 · Paper 43 | Q8 (a), (c), (d) | 11 | Cosine and sine rules; triangle area in a circle |
| May/June 2022 · Paper 41 | Q7 | 16 | Sine and cosine rule; distance and bearing |
| May/June 2022 · Paper 42 | Q4 | 10 | Sine and cosine rule in a trapezium; area |
| May/June 2022 · Paper 43 | Q7 | 14 | Cosine and sine rule in a field; area |
| May/June 2022 · Paper 43 | Q10 | 7 | Cuboid: lengths and angle with base |
| Feb/March 2022 · Paper 42 | Q4 | 12 | Sine and cosine rule in triangles and quadrilateral |
Chapter 22: Transformations
27 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 12 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q5 | 4 | Describing a transformation; enlargement |
| May/June 2025 · Paper 22 | Q5 | 4 | Translation and describing a transformation |
| May/June 2025 · Paper 23 | Q5 | 7 | Describing a transformation; reflection and rotation |
| May/June 2024 · Paper 22 | Q9 | 5 | Describing a transformation; translation by vector |
| May/June 2024 · Paper 23 | Q19 | 5 | Describing a transformation; negative enlargement |
| Feb/March 2024 · Paper 22 | Q15 | 7 | Describing transformations; rotation |
| May/June 2023 · Paper 21 | Q11 | 6 | Describing transformations |
| May/June 2023 · Paper 22 | Q10 | 6 | Describing a transformation; rotation; negative enlargement |
| May/June 2023 · Paper 23 | Q8 | 3 | Describing a single transformation |
| Oct/Nov 2022 · Paper 21 | Q14 | 3 | Describing a single transformation |
| May/June 2022 · Paper 21 | Q16 | 3 | Describing a single transformation |
| Feb/March 2022 · Paper 22 | Q8 | 6 | Reflection, translation and describing a transformation |
Paper 4 (Calculator): 15 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 42 | Q8 | 8 | Translation, reflection and describing a transformation |
| Oct/Nov 2025 · Paper 43 | Q7 | 5 | Describing transformations on a grid |
| May/June 2025 · Paper 41 | Q4 | 7 | Describing and drawing transformations |
| Feb/March 2025 · Paper 42 | Q10 | 7 | Reflection, translation and describing a transformation |
| Oct/Nov 2024 · Paper 41 | Q2 | 9 | Reflection, enlargement and describing a transformation |
| Oct/Nov 2024 · Paper 43 | Q2 (b) | 7 | Rotation, reflection and describing a transformation |
| May/June 2024 · Paper 41 | Q2 (a) | 5 | Reflection, translation and enlargement on a grid |
| Oct/Nov 2023 · Paper 41 | Q1 | 9 | Describing transformations; reflection and negative enlargement |
| Oct/Nov 2023 · Paper 42 | Q1 | 11 | Translation, reflection, rotation and negative enlargement |
| Oct/Nov 2023 · Paper 43 | Q3 | 9 | Reflection, translation and enlargement on a grid |
| Feb/March 2023 · Paper 42 | Q4 (a) | 9 | Enlargement, rotation, reflection and describing |
| Oct/Nov 2022 · Paper 42 | Q4 | 10 | Describing and drawing transformations |
| Oct/Nov 2022 · Paper 43 | Q4 | 7 | Reflection, enlargement and describing a transformation |
| May/June 2022 · Paper 42 | Q5 (b) | 9 | Describing and drawing transformations |
| May/June 2022 · Paper 43 | Q2 (a) | 7 | Reflection, translation and describing a transformation |
Chapter 23: Vectors
38 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 23 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q24 | 4 | Position vector of a midpoint |
| Oct/Nov 2025 · Paper 23 | Q8 | 5 | Column vector: multiple, magnitude and end point |
| May/June 2025 · Paper 21 | Q8 | 4 | Column vectors: combination and magnitude |
| May/June 2025 · Paper 21 | Q21 | 5 | Vectors in a rhombus; proving a trapezium |
| May/June 2025 · Paper 22 | Q9 | 6 | Vectors: coordinates, magnitude, dividing a line |
| May/June 2025 · Paper 22 | Q23 | 3 | Position vector of a midpoint |
| May/June 2025 · Paper 23 | Q12 | 5 | Column vectors: scalar multiple and journeys |
| Feb/March 2025 · Paper 22 | Q15 | 7 | Column vectors: coordinates and scalar multiples |
| Oct/Nov 2024 · Paper 21 | Q5 | 2 | Column vectors: scalar multiple and addition |
| Oct/Nov 2024 · Paper 23 | Q26 | 4 | Vector path using ratio and midpoint |
| May/June 2024 · Paper 22 | Q24 | 5 | Vectors in a parallelogram; position vector |
| May/June 2024 · Paper 23 | Q26 | 4 | Position vector with ratios on intersecting lines |
| Feb/March 2024 · Paper 22 | Q6 | 1 | Column vector from a grid |
| Oct/Nov 2023 · Paper 22 | Q26 | 3 | Vector geometry in a parallelogram |
| Oct/Nov 2023 · Paper 23 | Q10 | 3 | Multiplying a vector; magnitude |
| May/June 2023 · Paper 21 | Q16 | 3 | Magnitude of a vector; vectors in a triangle |
| May/June 2023 · Paper 22 | Q9 | 5 | Column vectors: scalar multiple, sum, magnitude |
| May/June 2023 · Paper 23 | Q12 | 3 | Position vector and magnitude |
| Feb/March 2023 · Paper 22 | Q2 | 2 | Column vectors: subtraction and scalar multiple |
| May/June 2022 · Paper 21 | Q26 | 4 | Vectors in a triangle and parallelogram |
| May/June 2022 · Paper 22 | Q10 | 4 | Column vectors and magnitude |
| May/June 2022 · Paper 22 | Q22 | 2 | Vectors: finding a ratio on a line |
| Feb/March 2022 · Paper 22 | Q22 | 4 | Vectors in a trapezium; position vector |
Paper 4 (Calculator): 15 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q10 | 2 | Translation of a point by a column vector |
| Oct/Nov 2025 · Paper 42 | Q18 | 4 | Vectors in a trapezium with a midpoint |
| Oct/Nov 2025 · Paper 43 | Q26 | 5 | Vectors in a parallelogram with ratios |
| May/June 2025 · Paper 43 | Q26 | 5 | Vector geometry: finding a ratio |
| Feb/March 2025 · Paper 42 | Q21 | 4 | Position vector using a ratio on a line |
| Oct/Nov 2024 · Paper 42 | Q6 | 13 | Column vectors, magnitude and vector geometry |
| Oct/Nov 2024 · Paper 43 | Q2 (a) | 5 | Midpoint and column vectors from coordinates |
| May/June 2024 · Paper 41 | Q5 (b) | 4 | Position vector of a point dividing a line |
| Feb/March 2024 · Paper 42 | Q7 | 7 | Column vectors, magnitude, vectors in a triangle |
| Oct/Nov 2023 · Paper 41 | Q10 | 13 | Column vectors, magnitude and vector geometry |
| Oct/Nov 2023 · Paper 42 | Q12 (a) | 2 | Writing column vectors |
| Feb/March 2023 · Paper 42 | Q4 (b) | 3 | Vectors in a triangle |
| Oct/Nov 2022 · Paper 41 | Q6 | 10 | Column vectors, magnitude and vector geometry |
| Oct/Nov 2022 · Paper 42 | Q11 | 8 | Vectors: magnitude and position vectors in a parallelogram |
| Oct/Nov 2022 · Paper 43 | Q10 | 11 | Drawing vectors and vector geometry in a trapezium |
Chapter 24: Probability
55 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 33 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q20 | 9 | Tree diagram with two bags |
| Oct/Nov 2025 · Paper 22 | Q12 | 6 | Venn diagram and set probabilities |
| Oct/Nov 2025 · Paper 23 | Q11 | 2 | Probability of two independent events |
| Oct/Nov 2025 · Paper 23 | Q25 | 3 | Sample space diagram; conditional probability |
| May/June 2025 · Paper 21 | Q17 | 7 | Probability with and without replacement; tree diagram |
| May/June 2025 · Paper 22 | Q4 | 2 | Probability and expected frequency |
| May/June 2025 · Paper 23 | Q1 | 1 | Probability of an event not happening |
| May/June 2025 · Paper 23 | Q11 | 4 | Sample space table; conditional probability |
| Feb/March 2025 · Paper 22 | Q8 | 3 | Missing probability; expected frequency |
| Feb/March 2025 · Paper 22 | Q16 (b) | 3 | Two picks without replacement |
| Oct/Nov 2024 · Paper 21 | Q10 | 3 | Probabilities summing to one; expected frequency |
| Oct/Nov 2024 · Paper 22 | Q16 | 1 | Conditional probability from a Venn diagram |
| May/June 2024 · Paper 21 | Q2 | 3 | Probability of not; completing a table |
| May/June 2024 · Paper 21 | Q22 | 4 | Combined probability from two bags |
| May/June 2024 · Paper 22 | Q11 | 2 | Expected frequency from a survey |
| May/June 2024 · Paper 22 | Q23 (b) | 2 | Conditional probability from a Venn diagram |
| May/June 2024 · Paper 23 | Q5 | 1 | Probability of an event not happening |
| Feb/March 2024 · Paper 22 | Q5 (b) | 1 | Probability of an event not happening |
| Feb/March 2024 · Paper 22 | Q12 | 1 | Expected frequency from probability |
| Feb/March 2024 · Paper 22 | Q25 | 4 | Two picks without replacement: different colours |
| Oct/Nov 2023 · Paper 23 | Q6 | 3 | Probability table and expected number |
| May/June 2023 · Paper 21 | Q5 | 2 | Missing probability in a table |
| May/June 2023 · Paper 21 | Q15 | 3 | Two picks without replacement |
| May/June 2023 · Paper 22 | Q5 | 2 | Probabilities summing to one |
| May/June 2023 · Paper 22 | Q23 | 3 | Combined probability from two bags |
| May/June 2023 · Paper 23 | Q7 | 4 | Completing a probability table; either event |
| Feb/March 2023 · Paper 22 | Q24 | 2 | Repeated trials: first success probability |
| Oct/Nov 2022 · Paper 21 | Q25 | 8 | Probability with and without replacement |
| Oct/Nov 2022 · Paper 22 | Q19 | 3 | Conditional probability from two choices |
| Oct/Nov 2022 · Paper 23 | Q6 | 3 | Probability table and expected frequency |
| May/June 2022 · Paper 22 | Q6 | 2 | Completing a probability table |
| May/June 2022 · Paper 22 | Q16 (c) | 2 | Conditional probability from a Venn diagram |
| May/June 2022 · Paper 23 | Q1 | 1 | Probability of an event not happening |
Paper 4 (Calculator): 22 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 42 | Q16 (b) | 3 | Probability of two selections from a histogram |
| Oct/Nov 2025 · Paper 43 | Q12 | 2 | Probabilities of complementary events |
| May/June 2025 · Paper 41 | Q15 (b) | 2 | Probability of choosing two from a group |
| May/June 2025 · Paper 42 | Q16 | 4 | Tree diagram: dependent events |
| May/June 2025 · Paper 42 | Q22 | 5 | Probability from a Venn diagram, two selections |
| May/June 2025 · Paper 43 | Q20 | 5 | Independent events from two bags |
| Oct/Nov 2024 · Paper 41 | Q5 | 9 | Tree diagram; selections with and without replacement |
| Oct/Nov 2024 · Paper 42 | Q8 | 8 | Probability with and without replacement |
| Oct/Nov 2024 · Paper 43 | Q9 | 9 | Probability with and without replacement |
| May/June 2024 · Paper 43 | Q9 | 12 | Probability with letter cards, with and without replacement |
| Oct/Nov 2023 · Paper 41 | Q4 | 11 | Probability with two spinners |
| Oct/Nov 2023 · Paper 42 | Q8 | 9 | Probability with two dice |
| Oct/Nov 2023 · Paper 43 | Q5 (d) | 4 | Probability of three selections without replacement |
| May/June 2023 · Paper 42 | Q4 (b) | 4 | Probability of choosing from a frequency table |
| May/June 2023 · Paper 43 | Q2 (b) | 2 | Probability without replacement |
| Feb/March 2023 · Paper 42 | Q7 (c)–(d) | 5 | Probability of two picks without replacement |
| Oct/Nov 2022 · Paper 42 | Q3 (b)–(c) | 6 | Probability from a frequency table, two selections |
| Oct/Nov 2022 · Paper 43 | Q7 | 10 | Probability of combined card scores |
| May/June 2022 · Paper 41 | Q8 (b)–(c) | 11 | Probability with cards and Venn diagram |
| May/June 2022 · Paper 42 | Q6 (a)–(b) | 6 | Estimating from a sample; two picks without replacement |
| May/June 2022 · Paper 43 | Q5 (b) | 5 | Probability of one and two people chosen |
| Feb/March 2022 · Paper 42 | Q11 | 10 | Tree diagram and three-set Venn probability |
Chapter 25: Statistics: Averages, Charts and Scatter Diagrams
54 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 25 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 21 | Q13 | 4 | Unknowns from a mean; interquartile range |
| Oct/Nov 2025 · Paper 22 | Q5 | 5 | Pie chart: reading and completing |
| Oct/Nov 2025 · Paper 23 | Q6 | 4 | Scatter diagram: outlier, plotting and correlation |
| May/June 2025 · Paper 21 | Q9 | 3 | Unknown frequency from a given mean |
| May/June 2025 · Paper 23 | Q4 | 1 | Type of correlation from a statement |
| May/June 2025 · Paper 23 | Q6 | 3 | Range and averages from given conditions |
| Feb/March 2025 · Paper 22 | Q11 (a)–(b) | 5 | Composite bar chart: drawing and reading |
| Feb/March 2025 · Paper 22 | Q16 (a) | 3 | Interquartile range from stem-and-leaf |
| Oct/Nov 2024 · Paper 21 | Q15 (b) | 2 | Comparing distributions using median and IQR |
| Oct/Nov 2024 · Paper 22 | Q4 | 5 | Scatter diagram: plotting, best-fit line, correlation |
| Oct/Nov 2024 · Paper 23 | Q5 | 4 | Median and mean from a frequency table |
| May/June 2024 · Paper 22 | Q3 | 3 | Stem-and-leaf diagram and median |
| Feb/March 2024 · Paper 22 | Q5 (a) | 2 | Pie chart sector angle |
| Feb/March 2024 · Paper 22 | Q7 | 1 | Type of correlation from a statement |
| Feb/March 2024 · Paper 22 | Q17 | 4 | Estimated mean from grouped data |
| Oct/Nov 2023 · Paper 21 | Q2 | 3 | Mode, range and median from stem-and-leaf |
| Oct/Nov 2023 · Paper 21 | Q6 | 3 | Scatter diagram: reading, plotting and correlation |
| Oct/Nov 2023 · Paper 23 | Q3 | 3 | Median and mean from stem-and-leaf |
| May/June 2023 · Paper 22 | Q3 | 3 | Stem-and-leaf diagram and median |
| Oct/Nov 2022 · Paper 22 | Q8 | 3 | Median and choosing a suitable average |
| Oct/Nov 2022 · Paper 23 | Q4 | 3 | Finding values from mean, mode and range |
| May/June 2022 · Paper 22 | Q2 | 2 | Pie chart sector angle |
| May/June 2022 · Paper 23 | Q4 | 3 | Stem-and-leaf diagram and median |
| May/June 2022 · Paper 23 | Q7 | 4 | Scatter diagram: reading, plotting, best fit |
| Feb/March 2022 · Paper 22 | Q11 | 1 | Type of correlation from a statement |
Paper 4 (Calculator): 29 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q16 | 4 | Estimated mean from grouped data |
| Oct/Nov 2025 · Paper 42 | Q6 | 4 | Stem-and-leaf: missing values from averages |
| Oct/Nov 2025 · Paper 43 | Q2 | 4 | Stem-and-leaf: mode, median and percentage |
| Oct/Nov 2025 · Paper 43 | Q23 (a) | 4 | Estimated mean from grouped data |
| May/June 2025 · Paper 41 | Q15 (a) | 4 | Estimating a mean from grouped data |
| May/June 2025 · Paper 43 | Q1 | 1 | Median of a list |
| Feb/March 2025 · Paper 42 | Q7 | 5 | Scatter diagram, correlation and line of best fit |
| Feb/March 2025 · Paper 42 | Q15 (a) | 4 | Estimated mean from grouped data |
| Oct/Nov 2024 · Paper 41 | Q3 (a) | 4 | Estimated mean from grouped data |
| Oct/Nov 2024 · Paper 43 | Q8 (a)–(b) | 6 | Pie chart angle and estimated mean |
| May/June 2024 · Paper 41 | Q4 (b) | 11 | Grouped data: median class, mean, histogram, probability |
| May/June 2024 · Paper 42 | Q3 (a) | 10 | Grouped data: mean and related calculations |
| May/June 2024 · Paper 43 | Q3 | 11 | Averages from frequency tables; grouped mean |
| Feb/March 2024 · Paper 42 | Q3 (a)–(b) | 9 | Range, mean, median, mode; mean problem |
| Oct/Nov 2023 · Paper 41 | Q7 (a) | 4 | Estimating a mean from grouped data |
| Oct/Nov 2023 · Paper 42 | Q2 | 11 | Averages from a frequency table; stem-and-leaf |
| Oct/Nov 2023 · Paper 43 | Q2 (b) | 4 | Pie chart: sector angles and drawing |
| Oct/Nov 2023 · Paper 43 | Q5 (b)–(c) | 5 | Estimated mean from grouped data; interpreting classes |
| May/June 2023 · Paper 41 | Q3 (a) | 6 | Grouped data mean and probability |
| May/June 2023 · Paper 42 | Q4 (a) | 5 | Grouped data: median interval and mean |
| May/June 2023 · Paper 43 | Q2 (a) | 6 | Stem-and-leaf diagram and averages |
| May/June 2023 · Paper 43 | Q6 (b)(i) | 4 | Estimate of mean from grouped data |
| Feb/March 2023 · Paper 42 | Q2 (a), (c) | 13 | Averages from tables; grouped mean and histogram |
| Oct/Nov 2022 · Paper 42 | Q3 (a) | 9 | Grouped data: estimating and comparing means |
| Oct/Nov 2022 · Paper 43 | Q3 (b) | 4 | Estimating a mean from grouped data |
| May/June 2022 · Paper 41 | Q1 (a), (c) | 12 | Stem-and-leaf, quartile, pie chart; grouped mean |
| May/June 2022 · Paper 42 | Q7 (a) | 4 | Estimated mean from grouped data |
| May/June 2022 · Paper 43 | Q5 (a) | 5 | Median class and estimated mean |
| Feb/March 2022 · Paper 42 | Q5 (a) | 4 | Estimated mean from grouped data |
Chapter 26: Cumulative Frequency and Histograms
27 past-paper questions
Free chapter preview →
Paper 2 (Non-calculator): 5 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| May/June 2025 · Paper 21 | Q12 | 4 | Cumulative frequency: IQR and percentile |
| May/June 2025 · Paper 22 | Q13 | 11 | Grouped mean, histogram and cumulative frequency |
| May/June 2024 · Paper 23 | Q15 | 4 | Cumulative frequency: IQR and counts |
| Oct/Nov 2023 · Paper 22 | Q23 | 2 | Histogram bar heights |
| Oct/Nov 2022 · Paper 22 | Q13 | 4 | Cumulative frequency diagram and percentile |
Paper 4 (Calculator): 22 questions
| Paper | Question | Marks | Topic |
|---|---|---|---|
| Oct/Nov 2025 · Paper 41 | Q25 | 3 | Histogram: reading and completing |
| Oct/Nov 2025 · Paper 42 | Q16 (a), (c) | 5 | Histogram: frequencies and estimated mean |
| Oct/Nov 2025 · Paper 43 | Q23 (b) | 3 | Histogram bar heights from frequency density |
| May/June 2025 · Paper 41 | Q15 (c) | 3 | Completing a histogram with unequal widths |
| May/June 2025 · Paper 43 | Q19 | 4 | Cumulative frequency diagram and percentile |
| May/June 2025 · Paper 43 | Q24 | 4 | Reading frequencies from a histogram |
| Feb/March 2025 · Paper 42 | Q15 (b) | 3 | Drawing a histogram with unequal widths |
| Oct/Nov 2024 · Paper 41 | Q3 (b) | 4 | Reading frequencies from a histogram |
| Oct/Nov 2024 · Paper 42 | Q5 (a) | 5 | Cumulative frequency: median, IQR, probability |
| Oct/Nov 2024 · Paper 42 | Q5 (c) | 7 | Histogram: missing frequency and estimated mean |
| Oct/Nov 2024 · Paper 43 | Q8 (c) | 3 | Completing a histogram |
| Feb/March 2024 · Paper 42 | Q3 (c) | 4 | Drawing a histogram |
| Oct/Nov 2023 · Paper 41 | Q7 (b) | 3 | Completing a histogram |
| Oct/Nov 2023 · Paper 43 | Q5 (a) | 5 | Completing a histogram and frequency table |
| May/June 2023 · Paper 41 | Q5 (a)(i), (a)(ii)(b), (b) | 10 | Cumulative frequency estimates and histogram |
| May/June 2023 · Paper 42 | Q4 (c)–(d) | 9 | Cumulative frequency curve, IQR and percentile |
| May/June 2023 · Paper 43 | Q6 (a), (b)(ii) | 11 | Cumulative frequency diagram; histogram heights |
| Oct/Nov 2022 · Paper 41 | Q5 | 14 | Cumulative frequency, grouped mean and histogram |
| Oct/Nov 2022 · Paper 43 | Q3 (a) | 3 | Completing a histogram |
| May/June 2022 · Paper 42 | Q7 (b)–(c) | 8 | Histogram; cumulative frequency table |
| May/June 2022 · Paper 43 | Q5 (c) | 9 | Cumulative frequency: diagram, percentile, percentage |
| Feb/March 2022 · Paper 42 | Q5 (b)–(e) | 14 | Histogram heights; cumulative frequency, median, quartiles, percentile |
Revise the chapter before you practise. Our IGCSE Mathematics 0580 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 2026-10-28. Spotted a question in the wrong chapter? Tell us on WhatsApp and we will fix it.