Units at a glance
How each syllabus unit moved between the 2025 and 2026 papers, and how often each topic came up.
What changed from 2025 to 2026
Most units held steady. Analysis fell sharply, while linear algebra, methods and number theory grew.
- 2025
- 2026
Unit
Show the data
| Unit | 2025 | 2026 |
|---|---|---|
| Algebra | 7 | 6 |
| Linear algebra | 8 | 10 |
| Analysis | 9 | 3 |
| Complex | 6 | 7 |
| Topology and DG | 7 | 8 |
| ODE and PDE | 7 | 7 |
| Methods | 5 | 8 |
| Mechanics | 7 | 7 |
| OR and numerical | 8 | 7 |
| Number theory | 6 | 7 |
Every topic, every paper
Darker means more questions. Sorted by the total across 2025 and 2026, out of 140. The 2019 column covers the 35 questions that survive, so it is shown apart.
| Topic | 2019 | 2025 | 2026 | Both |
|---|---|---|---|---|
| Linear algebra | 7 | 8 | 10 | 18 |
| Complex analysis | 9 | 6 | 7 | 13 |
| Abstract algebra | 3 | 7 | 6 | 13 |
| Number theory | · | 3 | 7 | 10 |
| Mechanics | · | 4 | 6 | 10 |
| Real analysis | 1 | 7 | 3 | 10 |
| Differential geometry | · | 4 | 5 | 9 |
| Integral equations | · | 2 | 6 | 8 |
| ODE | · | 4 | 4 | 8 |
| Operations research | 1 | 4 | 4 | 8 |
| Numerical analysis | · | 4 | 3 | 7 |
| Topology | 3 | 3 | 3 | 6 |
| PDE | · | 3 | 3 | 6 |
| Fluid dynamics | · | 3 | 1 | 4 |
| Calculus of variations | 1 | 2 | 1 | 3 |
| History of maths | · | 3 | · | 3 |
| Transforms | · | 1 | 1 | 2 |
| Functional analysis | 5 | 2 | · | 2 |
| Coordinate geometry | 2 | · | · | 0 |
| Measure theory | 3 | · | · | 0 |
All 10 units
- 1Abstract algebra6–7expectedSteady
Six or seven questions every time, mostly short calculations on groups and fields.
- 2Linear algebra8–10expectedRising
The biggest unit. It grew to 10 questions in 2026, with Jordan forms and quadratic forms.
- 3Real and functional analysis3–9expectedFell in 2026
Fell from 9 questions to 3 in 2026. With only two full papers that is a range, not a trend: plan for anything from 3 to 9.
- 4Complex analysis6–7expectedSteady
Six or seven questions, mostly residues, contour integrals and Möbius maps.
- 5Topology and differential geometry7–8expectedSteady
About half topology, half curves and surfaces. Manifolds are new in the syllabus and appeared in 2026.
- 6Ordinary and partial differential equations7expectedSteady
Exactly 7 in both papers. The same ideas repeat: singular solutions and PDE types.
- 7Calculus of variations, integral equations, transforms5–8expectedRising
Grew from 5 to 8. Integral equations alone went from 2 questions to 6.
- 8Mechanics and fluid dynamics7expectedSteady
Exactly 7 in both papers. Mostly Lagrangian and Hamiltonian ideas, with two or three fluid questions.
- 9Operations research and numerical analysis7–8expectedSteady
Seven or eight questions, roughly half linear programming and half numerical methods.
- 10Number theory, Vedic maths and history6–7expectedRising
Number theory itself went from 3 questions to 7, three of them on Legendre symbols.