Paper Comparison
December 2025 against June 2025
What one sitting asked that the other did not — as a share of each paper, because December 2025 carries 98 subject questions and June 2025 carries 100. 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
- Singularities and Residues+3.1 pp
4.1% (4) in December 2025 · 1.0% (1) in June 2025
- The Real Line+2.1 pp
7.1% (7) in December 2025 · 5.0% (5) in June 2025
- Estimation+2.1 pp
5.1% (5) in December 2025 · 3.0% (3) in June 2025
- Topology+2.1 pp
3.1% (3) in December 2025 · 1.0% (1) in June 2025
Asked more in June 2025
- Probability-3.9 pp
7.1% (7) in December 2025 · 11.0% (11) in June 2025
- Metric Spaces-2.0 pp
1.0% (1) in December 2025 · 3.0% (3) in June 2025
- Rings and Fields-1.9 pp
3.1% (3) in December 2025 · 5.0% (5) in June 2025
- Vector Spaces and Linear Maps-1.9 pp
3.1% (3) in December 2025 · 5.0% (5) in June 2025
Every topic, both papers
| Topic | December 2025 | June 2025 | Change |
|---|---|---|---|
| ProbabilityProbability, Statistics & Linear Programming | 7.1% (7) | 11.0% (11) | -3.9 pp |
| Eigenvalues and Canonical FormsAnalysis & Linear Algebra | 7.1% (7) | 6.0% (6) | +1.1 pp |
| The Real LineAnalysis & Linear Algebra | 7.1% (7) | 5.0% (5) | +2.1 pp |
| Linear Models and MultivariateProbability, Statistics & Linear Programming | 5.1% (5) | 6.0% (6) | -0.9 pp |
| Partial Differential EquationsODE, PDE & Applied Mathematics | 5.1% (5) | 4.0% (4) | +1.1 pp |
| GroupsComplex Analysis, Algebra & Topology | 5.1% (5) | 4.0% (4) | +1.1 pp |
| Ordinary Differential EquationsODE, PDE & Applied Mathematics | 4.1% (4) | 5.0% (5) | -0.9 pp |
| EstimationProbability, Statistics & Linear Programming | 5.1% (5) | 3.0% (3) | +2.1 pp |
| Limit Theorems and Markov ChainsProbability, Statistics & Linear Programming | 4.1% (4) | 4.0% (4) | +0.1 pp |
| Rings and FieldsComplex Analysis, Algebra & Topology | 3.1% (3) | 5.0% (5) | -1.9 pp |
| Vector Spaces and Linear MapsAnalysis & Linear Algebra | 3.1% (3) | 5.0% (5) | -1.9 pp |
| Inner Product Spaces and FormsAnalysis & Linear Algebra | 3.1% (3) | 4.0% (4) | -0.9 pp |
| Hypothesis TestingProbability, Statistics & Linear Programming | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Linear Integral EquationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Numerical AnalysisODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Calculus of VariationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Singularities and ResiduesComplex Analysis, Algebra & Topology | 4.1% (4) | 1.0% (1) | +3.1 pp |
| IntegrationAnalysis & Linear Algebra | 3.1% (3) | 2.0% (2) | +1.1 pp |
| Sampling and Design of ExperimentsProbability, Statistics & Linear Programming | 3.1% (3) | 2.0% (2) | +1.1 pp |
| Sequences and Series of FunctionsAnalysis & Linear Algebra | 2.0% (2) | 3.0% (3) | -1.0 pp |
| Cauchy TheoryComplex Analysis, Algebra & Topology | 2.0% (2) | 3.0% (3) | -1.0 pp |
| TopologyComplex Analysis, Algebra & Topology | 3.1% (3) | 1.0% (1) | +2.1 pp |
| Analytic FunctionsComplex Analysis, Algebra & Topology | 2.0% (2) | 2.0% (2) | +0.0 pp |
| Continuity and DifferentiationAnalysis & Linear Algebra | 2.0% (2) | 2.0% (2) | +0.0 pp |
| Metric SpacesAnalysis & Linear Algebra | 1.0% (1) | 3.0% (3) | -2.0 pp |
| Functions of Several VariablesAnalysis & Linear Algebra | 2.0% (2) | 1.0% (1) | +1.0 pp |
| Classical MechanicsODE, PDE & Applied Mathematics | 1.0% (1) | 2.0% (2) | -1.0 pp |
| Zeros and MappingsComplex Analysis, Algebra & Topology | 1.0% (1) | 2.0% (2) | -1.0 pp |
| Lebesgue Measure and IntegrationAnalysis & Linear Algebra | 1.0% (1) | 1.0% (1) | +0.0 pp |
| Linear ProgrammingProbability, Statistics & Linear Programming | 1.0% (1) | 1.0% (1) | +0.0 pp |
22 of 30 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.