The Most-Tested Topics in A-Level Further Mathematics (9231)
A topic-by-topic breakdown of every 9231 past paper, 2018–2024.
1,104questions analysed
144past papers
2018–2024years covered
4papers (P1–S2)
Further Pure Mathematics 1 (Paper 1)
42 papers analysed · top 15 of 24 topics
| # | Topic | Appears in | Questions | Avg marks |
|---|---|---|---|---|
| 1 | Asymptotes of rational functions | 100% | 47 | 11.8 |
| 2 | Area in polar coordinates | 100% | 44 | 12.6 |
| 3 | Sketching rational function graphs | 100% | 46 | 11.9 |
| 4 | Sum and product of roots (cubic and quartic) | 100% | 42 | 8.3 |
| 5 | Polar curve sketching (r = f(θ)) | 98% | 41 | 12.6 |
| 6 | Method of differences | 93% | 39 | 8.2 |
| 7 | Vector and Cartesian equations of planes | 86% | 36 | 12.1 |
| 8 | Matrices as linear transformations | 79% | 33 | 11.7 |
| 9 | Symmetric functions of roots (sum of squares, etc.) | 79% | 33 | 8.4 |
| 10 | Distance from point to line/plane | 71% | 30 | 11.8 |
| 11 | Determinants of 2x2 and 3x3 matrices | 67% | 29 | 11.1 |
| 12 | Induction on sums and series | 62% | 27 | 7.4 |
| 13 | Substitution method for related roots | 60% | 25 | 8.7 |
| 14 | Conversion between polar and Cartesian | 50% | 21 | 12.4 |
| 15 | Angle between lines and planes | 48% | 20 | 12.5 |
Further Pure Mathematics 2 (Paper 2)
42 papers analysed · top 15 of 22 topics
| # | Topic | Appears in | Questions | Avg marks |
|---|---|---|---|---|
| 1 | Characteristic equation and eigenvalues | 71% | 30 | 11.3 |
| 2 | Second-order non-homogeneous ODEs (particular integral) | 71% | 32 | 9.8 |
| 3 | First-order linear ODEs (integrating factor) | 69% | 29 | 10.1 |
| 4 | De Moivre's theorem | 62% | 26 | 10.3 |
| 5 | Diagonalization of matrices | 55% | 23 | 12.2 |
| 6 | Hyperbolic identities | 50% | 22 | 11.5 |
| 7 | Advanced implicit differentiation | 45% | 20 | 8.2 |
| 8 | Differentiation of hyperbolic functions | 38% | 17 | 9.8 |
| 9 | Arc length of a curve | 38% | 16 | 9.3 |
| 10 | Hyperbolic functions sinh, cosh, tanh | 36% | 17 | 9 |
| 11 | nth roots of complex numbers | 36% | 15 | 7.3 |
| 12 | Reduction formulae | 31% | 13 | 10.7 |
| 13 | Second-order homogeneous ODEs | 31% | 14 | 8.9 |
| 14 | Inverse hyperbolic functions and log forms | 26% | 11 | 10.2 |
| 15 | Surface area of revolution | 21% | 10 | 10.1 |
Further Mechanics (Paper 3)
30 papers analysed · top 15 of 17 topics
| # | Topic | Appears in | Questions | Avg marks |
|---|---|---|---|---|
| 1 | Oblique (2D) collisions | 100% | 31 | 8 |
| 2 | Vertical circular motion | 100% | 30 | 7.2 |
| 3 | Energy problems with elastic strings | 90% | 28 | 6.3 |
| 4 | Centre of mass of composite/compound bodies | 83% | 25 | 7 |
| 5 | Hooke's law for strings and springs | 80% | 26 | 6.1 |
| 6 | Horizontal circular motion | 80% | 24 | 5.7 |
| 7 | Motion with force dependent on velocity F(v) | 70% | 22 | 7.8 |
| 8 | Sliding vs toppling of rigid body | 70% | 21 | 7.4 |
| 9 | Motion of a projectile: components, range, greatest height | 57% | 17 | 8.2 |
| 10 | Elastic potential energy | 37% | 11 | 6.3 |
| 11 | Conical pendulum | 33% | 10 | 6.5 |
| 12 | Motion with force dependent on time F(t) | 30% | 12 | 7.2 |
| 13 | Centre of mass of uniform bodies (lamina, solid) | 20% | 6 | 6.3 |
| 14 | Motion with force dependent on position F(x) | 17% | 5 | 8.6 |
| 15 | Direct (1D) collisions with restitution | 17% | 5 | 8.4 |
Further Probability & Statistics (Paper 4)
30 papers analysed · top 15 topics
| # | Topic | Appears in | Questions | Avg marks |
|---|---|---|---|---|
| 1 | Continuous random variables: PDF and CDF | 100% | 30 | 9.4 |
| 2 | t-test for population mean | 83% | 32 | 8.4 |
| 3 | Expectation and variance of continuous RV | 80% | 34 | 9.1 |
| 4 | Wilcoxon signed rank test | 77% | 24 | 8.4 |
| 5 | Median, mode, percentiles of continuous RV | 73% | 23 | 9.8 |
| 6 | Probability generating functions (formulation, mean and variance) | 70% | 21 | 9.2 |
| 7 | Chi-squared goodness of fit test | 57% | 17 | 8.2 |
| 8 | CI for population mean (unknown variance, t-distribution) | 57% | 17 | 6.7 |
| 9 | Distribution of sample mean (central limit theorem) | 47% | 14 | 7.7 |
| 10 | Chi-squared contingency table test | 43% | 13 | 7.2 |
| 11 | CI for population mean (known variance) | 33% | 10 | 6.8 |
| 12 | Z-test for population mean | 27% | 8 | 9 |
| 13 | Wilcoxon rank sum test (Mann-Whitney) | 23% | 7 | 10 |
| 14 | Sign test | 10% | 3 | 6.3 |
| 15 | Linear combinations of normal random variables | 7% | 2 | 7 |
How this was measured
Based on OwlsPrep's database of official CIE 9231 past papers (2018–2024), every question tagged to its syllabus topic and marks. “Appears in X% of papers” = the share of that paper's variants containing at least one question on the topic. Figures are aggregate statistics from question metadata — no exam questions or mark schemes are reproduced.
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