Paper Comparison
December 2025 against December 2024
What one sitting asked that the other did not — as a share of each paper, because December 2025 carries 98 subject questions and December 2024 carries 200. Comparing raw counts across papers of different sizes invents a trend in every row.
December 2025 vs June 2025December 2025 vs December 2024December 2025 vs June 2024December 2025 vs December 2023June 2025 vs December 2025June 2025 vs December 2024June 2025 vs June 2024June 2025 vs December 2023December 2024 vs December 2025December 2024 vs June 2025December 2024 vs June 2024December 2024 vs December 2023June 2024 vs December 2025June 2024 vs June 2025June 2024 vs December 2024June 2024 vs December 2023December 2023 vs December 2025December 2023 vs June 2025December 2023 vs December 2024December 2023 vs June 2024
Asked more in December 2025
- Probability+2.1 pp
7.1% (7) in December 2025 · 5.0% (10) in December 2024
- Singularities and Residues+2.1 pp
4.1% (4) in December 2025 · 2.0% (4) in December 2024
- The Real Line+1.6 pp
7.1% (7) in December 2025 · 5.5% (11) in December 2024
Asked more in December 2024
- Limit Theorems and Markov Chains-2.4 pp
4.1% (4) in December 2025 · 6.5% (13) in December 2024
- Ordinary Differential Equations-1.9 pp
4.1% (4) in December 2025 · 6.0% (12) in December 2024
- Determinants and Matrix Tricks-1.5 pp
0.0% (0) in December 2025 · 1.5% (3) in December 2024
Present on one paper and absent from the other
Absent from one sitting is not absent from the syllabus. A topic carrying two questions one session and none the next has told you almost nothing.
Only in December 2025
- — none
Only in December 2024
- Determinants and Matrix Tricks · 3
Every topic, both papers
| Topic | December 2025 | December 2024 | Change |
|---|---|---|---|
| Eigenvalues and Canonical FormsAnalysis & Linear Algebra | 7.1% (7) | 6.0% (12) | +1.1 pp |
| The Real LineAnalysis & Linear Algebra | 7.1% (7) | 5.5% (11) | +1.6 pp |
| ProbabilityProbability, Statistics & Linear Programming | 7.1% (7) | 5.0% (10) | +2.1 pp |
| EstimationProbability, Statistics & Linear Programming | 5.1% (5) | 6.0% (12) | -0.9 pp |
| Limit Theorems and Markov ChainsProbability, Statistics & Linear Programming | 4.1% (4) | 6.5% (13) | -2.4 pp |
| Linear Models and MultivariateProbability, Statistics & Linear Programming | 5.1% (5) | 5.0% (10) | +0.1 pp |
| Ordinary Differential EquationsODE, PDE & Applied Mathematics | 4.1% (4) | 6.0% (12) | -1.9 pp |
| GroupsComplex Analysis, Algebra & Topology | 5.1% (5) | 4.5% (9) | +0.6 pp |
| Partial Differential EquationsODE, PDE & Applied Mathematics | 5.1% (5) | 4.0% (8) | +1.1 pp |
| Rings and FieldsComplex Analysis, Algebra & Topology | 3.1% (3) | 4.5% (9) | -1.4 pp |
| Hypothesis TestingProbability, Statistics & Linear Programming | 3.1% (3) | 4.5% (9) | -1.4 pp |
| Inner Product Spaces and FormsAnalysis & Linear Algebra | 3.1% (3) | 3.5% (7) | -0.4 pp |
| Singularities and ResiduesComplex Analysis, Algebra & Topology | 4.1% (4) | 2.0% (4) | +2.1 pp |
| Calculus of VariationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (6) | +0.1 pp |
| Numerical AnalysisODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (6) | +0.1 pp |
| Vector Spaces and Linear MapsAnalysis & Linear Algebra | 3.1% (3) | 3.0% (6) | +0.1 pp |
| Sampling and Design of ExperimentsProbability, Statistics & Linear Programming | 3.1% (3) | 2.0% (4) | +1.1 pp |
| Linear Integral EquationsODE, PDE & Applied Mathematics | 3.1% (3) | 2.0% (4) | +1.1 pp |
| IntegrationAnalysis & Linear Algebra | 3.1% (3) | 2.0% (4) | +1.1 pp |
| TopologyComplex Analysis, Algebra & Topology | 3.1% (3) | 2.0% (4) | +1.1 pp |
| Sequences and Series of FunctionsAnalysis & Linear Algebra | 2.0% (2) | 3.0% (6) | -1.0 pp |
| Continuity and DifferentiationAnalysis & Linear Algebra | 2.0% (2) | 2.5% (5) | -0.5 pp |
| Analytic FunctionsComplex Analysis, Algebra & Topology | 2.0% (2) | 2.5% (5) | -0.5 pp |
| Cauchy TheoryComplex Analysis, Algebra & Topology | 2.0% (2) | 2.0% (4) | +0.0 pp |
| Functions of Several VariablesAnalysis & Linear Algebra | 2.0% (2) | 2.0% (4) | +0.0 pp |
| Classical MechanicsODE, PDE & Applied Mathematics | 1.0% (1) | 2.0% (4) | -1.0 pp |
| Zeros and MappingsComplex Analysis, Algebra & Topology | 1.0% (1) | 1.5% (3) | -0.5 pp |
| Linear ProgrammingProbability, Statistics & Linear Programming | 1.0% (1) | 1.0% (2) | +0.0 pp |
| Metric SpacesAnalysis & Linear Algebra | 1.0% (1) | 1.0% (2) | +0.0 pp |
| Lebesgue Measure and IntegrationAnalysis & Linear Algebra | 1.0% (1) | 1.0% (2) | +0.0 pp |
| Determinants and Matrix TricksAnalysis & Linear Algebra | 0.0% (0) | 1.5% (3) | -1.5 pp |
25 of 31 topics moved by less than 1.5 percentage points and are greyed out — at four to thirteen questions a topic, a swing of one or two questions is noise, not a signal.
Two sittings are two sittings. Everything above describes what these two papers contained. None of it predicts the next one, and a topic that fell here is not a topic to drop — the examiners are not running a trend. The aggregate across every complete paper is the more reliable number, and it is still only four papers.