What to study for the maths paper

Where the 70 questions come from

The paper follows the syllabus units almost exactly. No unit can be skipped: each one is worth about 14 of the 200 marks.

A 12-week plan

Every unit is worth about 14 marks, so the plan starts with the most marks per hour, not the hardest units. Short on time? Keep the order and shorten each phase.

1. Weeks 1–2: repeats and the short units

   Work through the 21 ideas asked in both papers until you can do each with new numbers. Then number theory and the methods unit: both are short, formula-driven and grew in 2026. See the repeats

2. Weeks 3–6: the big calculation units

   Linear algebra (up to 10 questions), complex analysis, ODE and PDE, and OR and numerical. Practise two-step problems, most of all in linear algebra.

3. Weeks 7–10: the theory units

   Algebra, analysis, topology and geometry, and mechanics. Learn the standard examples and counterexamples: most of these questions ask which statement must hold.

4. Weeks 11–12: gaps and timed papers

   One pass over the topics not asked yet, listed on each unit page. Then sit the 2025 and 2026 papers under exam timing and mark them with the solved keys.

Units by priority

Growing units first, then analysis, which swung from 9 questions to 3, then the steady ones. Tap a unit for its likely questions and past answers.

• 2Linear algebra8–10expectedRising

  The biggest unit. It grew to 10 questions in 2026, with Jordan forms and quadratic forms.

• 7Calculus of variations, integral equations, transforms5–8expectedRising

  Grew from 5 to 8. Integral equations alone went from 2 questions to 6.

• 10Number theory, Vedic maths and history6–7expectedRising

  Number theory itself went from 3 questions to 7, three of them on Legendre symbols.

• 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.

• 5Topology and differential geometry7–8expectedSteady

  About half topology, half curves and surfaces. Manifolds are new in the syllabus and appeared in 2026.

• 9Operations research and numerical analysis7–8expectedSteady

  Seven or eight questions, roughly half linear programming and half numerical methods.

• 1Abstract algebra6–7expectedSteady

  Six or seven questions every time, mostly short calculations on groups and fields.

• 4Complex analysis6–7expectedSteady

  Six or seven questions, mostly residues, contour integrals and Möbius maps.

• 6Ordinary and partial differential equations7expectedSteady

  Exactly 7 in both papers. The same ideas repeat: singular solutions and PDE types.

• 8Mechanics and fluid dynamics7expectedSteady

  Exactly 7 in both papers. Mostly Lagrangian and Hamiltonian ideas, with two or three fluid questions.

How the paper is changing