ChatGPT’s student revision guide: a topic heatmap for both papers together, then Paper 1 and Paper 2 separately, then the recurring question families for each paper with past-year questions to practise.
Ten years of papers, distilled into revision priorities. The gold divider marks the current syllabus years.
Same topic order on all three heatmaps. The gold divider marks the 4052 syllabus years (2023 onwards); 4048 before.
| Topic | 4048 syllabus | 4052 syllabus | 2023–25 avg marks | Years seen 2016–25 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2016 | 2017 | 2018 | 2019 | 2020* | 2021* | 2022 | 2023 | 2024 | 2025 | |||
| Algebra & formulae | 19 | 14 | 13 | 11 | 14 | 16 | 16 | 19 | 22 | 14 | 18.3 | 10/10 |
| Equations & inequalities | 13 | 18 | 18 | 9 | 11 | 12 | 17 | 13 | 19 | 21 | 17.7 | 10/10 |
| Pythagoras, trig & bearings | 11 | 15 | 24 | 15 | 10 | 6 | 12 | 13 | 22 | 14 | 16.3 | 10/10 |
| Mensuration | 18 | 14 | 10 | 12 | 17 | 14 | 14 | 17 | 16 | 11 | 14.7 | 10/10 |
| Functions & graphs | 16 | 17 | 6 | 15 | 14 | 12 | 11 | 14 | 11 | 17 | 14.0 | 10/10 |
| Statistics | 9 | 15 | 16 | 14 | 13 | 15 | 13 | 11 | 16 | 13 | 13.3 | 10/10 |
| Integrated real-world problem | 10 | 10 | 11 | 10 | 10 | 11 | 11 | 10 | 11 | 9 | 10.0 | 10/10 |
| Numbers & indices | 4 | 8 | 9 | 7 | 11 | 10 | 8 | 7 | 9 | 10 | 8.7 | 10/10 |
| Ratio, proportion & scales | 6 | 2 | 3 | 9 | 8 | 3 | 3 | 8 | 6 | 10 | 8.0 | 10/10 |
| Coordinate geometry | 4 | 9 | 0 | 4 | 6 | 11 | 6 | 9 | 9 | 6 | 8.0 | 9/10 |
| Probability | 8 | 5 | 5 | 7 | 13 | 6 | 10 | 7 | 4 | 10 | 7.0 | 10/10 |
| Vectors | 10 | 4 | 8 | 12 | 10 | 12 | 5 | 9 | 6 | 3 | 6.0 | 10/10 |
| Percentages | 5 | 9 | 2 | 6 | 6 | 8 | 2 | 9 | 2 | 6 | 5.7 | 10/10 |
| Sequences & patterns | 9 | 5 | 11 | 15 | 3 | 8 | 4 | 13 | 2 | 0 | 5.0 | 9/10 |
| Financial arithmetic | 5 | 3 | 15 | 5 | 3 | 5 | 11 | 5 | 7 | 2 | 4.7 | 10/10 |
| Matrices | 4 | 5 | 5 | 4 | 6 | 7 | 6 | 5 | 5 | 3 | 4.3 | 10/10 |
| Angles & polygons | 9 | 3 | 4 | 0 | 6 | 2 | 5 | 0 | 3 | 9 | 4.0 | 8/10 |
| Circle properties | 4 | 8 | 5 | 6 | 4 | 6 | 6 | 6 | 3 | 3 | 4.0 | 10/10 |
| Congruence & similarity | 8 | 8 | 8 | 8 | 9 | 6 | 14 | 1 | 3 | 8 | 4.0 | 10/10 |
| Rates, speed & travel graphs | 5 | 2 | 5 | 4 | 3 | 7 | 0 | 2 | 2 | 4 | 2.7 | 9/10 |
| Sets | 2 | 3 | 2 | 4 | 3 | 3 | 2 | 2 | 2 | 4 | 2.7 | 10/10 |
| Construction | 1 | 3 | 0 | 3 | 0 | 0 | 4 | 0 | 0 | 3 | 1.0 | 5/10 |
| Total printed marks | 180 marks each year (all ten years) | 180.0 | ||||||||||
0 = no marks assigned to this primary topic. Avg = 2023–25 mean; it is not a forecast.
Algebra, equations, trig, mensuration, graphs, statistics and the real-world problem form the top seven. Practise these deeply, then cover the remaining topics.
Equations: 13, 19, 21 marks in 2023-25. Sequences: 13, 2, 0. A recent absence does not make a topic 'due'. Keep revising every topic.
P1 rewards fluency across short, mixed questions. P2 asks you to sustain a method through linked parts. Use the separate heatmaps to plan both kinds of practice.
Source: the audited past-paper collection, main series only. Each mark is counted once; the final integrated problem is kept whole, including its supporting skills. *2020-21 use full printed papers, which may differ from adjusted exams. Historical frequency does not give a 2026 probability.
Short, varied questions. Prioritise algebra, then keep number, geometry and data skills ready to use.
Same topic order on all three heatmaps. The gold divider marks the 4052 syllabus years (2023 onwards); 4048 before.
| Topic | 4048 syllabus | 4052 syllabus | 2023–25 avg marks | Years seen 2016–25 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2016 | 2017 | 2018 | 2019 | 2020* | 2021* | 2022 | 2023 | 2024 | 2025 | |||
| Algebra & formulae | 13 | 10 | 8 | 5 | 9 | 9 | 13 | 15 | 18 | 9 | 14.0 | 10/10 |
| Equations & inequalities | 0 | 4 | 6 | 5 | 3 | 5 | 11 | 5 | 7 | 11 | 7.7 | 9/10 |
| Pythagoras, trig & bearings | 2 | 3 | 9 | 3 | 4 | 6 | 5 | 13 | 13 | 3 | 9.7 | 10/10 |
| Mensuration | 11 | 3 | 4 | 0 | 4 | 2 | 3 | 4 | 9 | 5 | 6.0 | 9/10 |
| Functions & graphs | 3 | 8 | 6 | 3 | 1 | 6 | 1 | 3 | 0 | 10 | 4.3 | 9/10 |
| Statistics | 4 | 6 | 10 | 6 | 7 | 9 | 5 | 7 | 11 | 8 | 8.7 | 10/10 |
| Integrated real-world problem | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.0 | 0/10 |
| Numbers & indices | 4 | 6 | 9 | 6 | 9 | 9 | 7 | 6 | 5 | 7 | 6.0 | 10/10 |
| Ratio, proportion & scales | 4 | 2 | 3 | 9 | 8 | 3 | 3 | 5 | 4 | 4 | 4.3 | 10/10 |
| Coordinate geometry | 4 | 0 | 0 | 4 | 0 | 0 | 0 | 2 | 0 | 0 | 0.7 | 3/10 |
| Probability | 2 | 0 | 0 | 2 | 5 | 2 | 3 | 2 | 0 | 4 | 2.0 | 7/10 |
| Vectors | 10 | 0 | 5 | 3 | 7 | 0 | 0 | 5 | 6 | 3 | 4.7 | 7/10 |
| Percentages | 2 | 3 | 0 | 2 | 3 | 2 | 2 | 5 | 0 | 5 | 3.3 | 8/10 |
| Sequences & patterns | 0 | 5 | 0 | 6 | 3 | 0 | 4 | 3 | 2 | 0 | 1.7 | 6/10 |
| Financial arithmetic | 5 | 3 | 3 | 3 | 3 | 2 | 0 | 5 | 7 | 2 | 4.7 | 9/10 |
| Matrices | 0 | 5 | 0 | 4 | 0 | 7 | 6 | 5 | 0 | 0 | 1.7 | 5/10 |
| Angles & polygons | 4 | 3 | 4 | 0 | 6 | 2 | 5 | 0 | 3 | 3 | 2.0 | 8/10 |
| Circle properties | 4 | 8 | 5 | 0 | 2 | 0 | 4 | 2 | 3 | 3 | 2.7 | 8/10 |
| Congruence & similarity | 2 | 3 | 3 | 8 | 3 | 6 | 4 | 1 | 0 | 6 | 2.3 | 9/10 |
| Rates, speed & travel graphs | 3 | 2 | 3 | 4 | 0 | 7 | 0 | 0 | 0 | 4 | 1.3 | 6/10 |
| Sets | 2 | 3 | 2 | 4 | 3 | 3 | 0 | 2 | 2 | 0 | 1.3 | 8/10 |
| Construction | 1 | 3 | 0 | 3 | 0 | 0 | 4 | 0 | 0 | 3 | 1.0 | 5/10 |
| Total printed marks | 90 marks each year (all ten years) | 90.0 | ||||||||||
0 = no marks assigned to this primary topic. Avg = 2023–25 mean; it is not a forecast.
Factorise, simplify algebraic fractions and change the subject. Solve equations and inequalities. Then mix in indices, scale factors and proportion.
Statistics appeared in 10/10 P1s. Revise graphs, averages and spread; explain misleading displays and sampling. Show geometric reasons clearly.
P1 graphs varied 3, 0, 10 marks in 2023-25. Trig varied 13, 13, 3. Practise mixed timed sets. P1 rose from 80 to 90 marks in 2023.
Source: the audited past-paper collection, main series only. Each mark is counted once; the final integrated problem is kept whole, including its supporting skills. *2020-21 use full printed papers, which may differ from adjusted exams. Historical frequency does not give a 2026 probability.
Longer, linked questions. Build models, interpret results and keep your working easy to follow.
Same topic order on all three heatmaps. The gold divider marks the 4052 syllabus years (2023 onwards); 4048 before.
| Topic | 4048 syllabus | 4052 syllabus | 2023–25 avg marks | Years seen 2016–25 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2016 | 2017 | 2018 | 2019 | 2020* | 2021* | 2022 | 2023 | 2024 | 2025 | |||
| Algebra & formulae | 6 | 4 | 5 | 6 | 5 | 7 | 3 | 4 | 4 | 5 | 4.3 | 10/10 |
| Equations & inequalities | 13 | 14 | 12 | 4 | 8 | 7 | 6 | 8 | 12 | 10 | 10.0 | 10/10 |
| Pythagoras, trig & bearings | 9 | 12 | 15 | 12 | 6 | 0 | 7 | 0 | 9 | 11 | 6.7 | 8/10 |
| Mensuration | 7 | 11 | 6 | 12 | 13 | 12 | 11 | 13 | 7 | 6 | 8.7 | 10/10 |
| Functions & graphs | 13 | 9 | 0 | 12 | 13 | 6 | 10 | 11 | 11 | 7 | 9.7 | 9/10 |
| Statistics | 5 | 9 | 6 | 8 | 6 | 6 | 8 | 4 | 5 | 5 | 4.7 | 10/10 |
| Integrated real-world problem | 10 | 10 | 11 | 10 | 10 | 11 | 11 | 10 | 11 | 9 | 10.0 | 10/10 |
| Numbers & indices | 0 | 2 | 0 | 1 | 2 | 1 | 1 | 1 | 4 | 3 | 2.7 | 8/10 |
| Ratio, proportion & scales | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 6 | 3.7 | 4/10 |
| Coordinate geometry | 0 | 9 | 0 | 0 | 6 | 11 | 6 | 7 | 9 | 6 | 7.3 | 7/10 |
| Probability | 6 | 5 | 5 | 5 | 8 | 4 | 7 | 5 | 4 | 6 | 5.0 | 10/10 |
| Vectors | 0 | 4 | 3 | 9 | 3 | 12 | 5 | 4 | 0 | 0 | 1.3 | 7/10 |
| Percentages | 3 | 6 | 2 | 4 | 3 | 6 | 0 | 4 | 2 | 1 | 2.3 | 9/10 |
| Sequences & patterns | 9 | 0 | 11 | 9 | 0 | 8 | 0 | 10 | 0 | 0 | 3.3 | 5/10 |
| Financial arithmetic | 0 | 0 | 12 | 2 | 0 | 3 | 11 | 0 | 0 | 0 | 0.0 | 4/10 |
| Matrices | 4 | 0 | 5 | 0 | 6 | 0 | 0 | 0 | 5 | 3 | 2.7 | 5/10 |
| Angles & polygons | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 2.0 | 2/10 |
| Circle properties | 0 | 0 | 0 | 6 | 2 | 6 | 2 | 4 | 0 | 0 | 1.3 | 5/10 |
| Congruence & similarity | 6 | 5 | 5 | 0 | 6 | 0 | 10 | 0 | 3 | 2 | 1.7 | 7/10 |
| Rates, speed & travel graphs | 2 | 0 | 2 | 0 | 3 | 0 | 0 | 2 | 2 | 0 | 1.3 | 5/10 |
| Sets | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 4 | 1.3 | 2/10 |
| Construction | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.0 | 0/10 |
| Total printed marks | 90 marks each year (all ten years) | 90.0 | ||||||||||
0 = no marks assigned to this primary topic. Avg = 2023–25 mean; it is not a forecast.
Build equations from a situation; use quadratic and fractional equations. Practise graph plotting, tangents and straight-line intersections. Coordinate geometry: 6-9 marks in 2023-25.
For mensuration, draw and label the solids. For probability, show complete cases and changing totals without replacement. Explain what a statistical comparison means.
Practise unit conversions, costs, time and a justified decision. State assumptions and limitations. Finance can sit inside this question. P2 fell from 100 to 90 marks in 2023.
Source: the audited past-paper collection, main series only. Each mark is counted once; the final integrated problem is kept whole, including its supporting skills. *2020-21 use full printed papers, which may differ from adjusted exams. Historical frequency does not give a 2026 probability.
without notes.
Family seen in 3/3 P1s (2023-25)
Factorise by grouping, expand brackets, simplify algebraic fractions and change the subject. The mix of skills changes each year.
Check: Cancel common factors, not terms. Keep brackets when substituting.
Family seen in 3/3 P1s (2023-25)
Translate area or perimeter conditions into equations. Solve quadratics by the required method, including equations with algebraic fractions.
Check: Clear denominators carefully. Check roots in the original equation.
Family seen in 3/3 P1s (2023-25)
Use prime-power form for HCF, LCM, squares and cubes. Simplify expressions with fractional or negative indices.
Check: Prime exponents: even for a square; multiples of 3 for a cube.
Family seen in 3/3 P1s (2023-25)
Set up direct or inverse proportion, convert map units, square an area scale and find the limiting ingredient in a recipe.
Check: Match units before scaling. Check whether the scale is linear or area.
Family seen in 3/3 P1s (2023-25)
Work backwards through a percentage of a remainder. Distinguish simple interest, compound amount and interest earned.
Check: Use the correct original amount as the percentage base.
Sources: the 2023, 2024 and 2025 O Math 4052 P1 & P2 (With Worked Solutions) files. [ ] gives marks for the cited parts only. Family counts apply to the named paper; individual skills vary and cross-paper extras are excluded. These are revision priorities, not 2026 guarantees.
without notes.
Family seen in 3/3 P1s (2023-25)
Read median and IQR from cumulative frequency. Use grouped means and standard deviation. Explain weaknesses in sampling and displays.
Check: Compare both average and spread, in context. Avoid unsupported claims.
Family seen in 3/3 P1s (2023-25)
Choose Pythagoras, right-angle trig, the sine rule or cosine rule. Build the triangle first and relate its angles to north.
Check: Use full working for bearings; do not round intermediate lengths.
Family seen in 3/3 P1s (2023-25)
Recognise equal radii, angles in a semicircle and a tangent perpendicular to a radius. Explain each step of an angle argument.
Check: Name the theorem and identify the relevant angle or radius.
Family seen in 3/3 P1s (2023-25)
Relate radius to height in a cone. Use equal or fractional volumes to find water depth or empty-space depth in a composite container.
Check: For similar solids, take a cube root to get the linear scale factor.
Family seen in 3/3 P1s (2023-25)
Build vectors along a route and divide a segment in a given ratio. Prove collinearity; also practise coordinate translation and magnitude.
Check: For collinearity, show a scalar multiple of vectors from one point.
Sources: the 2023, 2024 and 2025 O Math 4052 P1 & P2 (With Worked Solutions) files. [ ] gives marks for the cited parts only. Family counts apply to the named paper; individual skills vary and cross-paper extras are excluded. These are revision priorities, not 2026 guarantees.
without notes.
Family seen in 3/3 P2s (2023-25)
Clear algebraic fractions, form time equations using distance/speed, and turn a geometric condition into a quadratic.
Check: Show how the equation is formed. Reject a root only for a stated reason.
Family seen in 3/3 P2s (2023-25)
Use a suitable straight line to solve an equation on a given curve. Estimate a tangent gradient with units; find exponential parameters.
Check: Make your new equation match the given graph. Label a large gradient triangle.
Family seen in 3/3 P2s (2023-25)
Combine gradients, point-on-line conditions, distances and division ratios. Form the equation of a line through a specified point.
Check: Use the actual direction vector for a gradient; substitute a known point.
Family seen in 3/3 P2s (2023-25)
Connect surface-area and volume formulae. Handle major arcs and overlapping sectors; conserve volume when a solid is melted.
Check: Count exposed surfaces correctly. Use only whole cubes before the remainder.
Family seen in 2/3 P2s (2023-25)
Link sine/cosine rules, triangle area and bearings or elevation. Work with similar right triangles and angles in radians.
Check: Check degree/radian mode. Carry unrounded lengths into later parts.
Sources: the 2023, 2024 and 2025 O Math 4052 P1 & P2 (With Worked Solutions) files. [ ] gives marks for the cited parts only. Family counts apply to the named paper; individual skills vary and cross-paper extras are excluded. These are revision priorities, not 2026 guarantees.
without notes.
Family seen in 3/3 P2s (2023-25)
Read the correct population from a table or chart. Find probabilities for three selections, including exactly two of one type or all alike.
Check: Change denominators after each draw. Add all relevant, distinct cases.
Family seen in 3/3 P2s (2023-25)
Use box plots and cumulative frequency for quartiles and counts. Estimate grouped mean/SD and explain the limits of grouped data.
Check: Use class midpoints for grouped estimates; support comparisons with values.
Family seen in 3/3 P2s (2023-25)
Extract useful information, convert units, estimate quantities and costs, and justify a decision. Discuss assumptions and model limitations.
Check: Finish with a conclusion answering the claim, supported by your calculations.
Family seen in 2/3 P2s (2023-25)
Build matrices with the right dimensions, multiply in the correct order and explain what the entries mean in the situation.
Check: Label rows/columns. Interpret the result as money, quantity or a weighted score.
Family seen in 3/3 P2s (2023-25)
Convert microscopic or map scales. Square the linear factor for areas. Link two ratios and track a transfer between groups.
Check: Use a common unit and common ratio part before applying changes.
Sources: the 2023, 2024 and 2025 O Math 4052 P1 & P2 (With Worked Solutions) files. [ ] gives marks for the cited parts only. Family counts apply to the named paper; individual skills vary and cross-paper extras are excluded. These are revision priorities, not 2026 guarantees.
Prepared by ChatGPT from the audited past-paper collection (2016–25, main series). Revision priorities, not 2026 guarantees. Rebuilt here as a web page from ChatGPT’s 7-page guide; the numbers and wording are unchanged.