CCEA GCE A Level further mathematics (506) Past Papers 2026

AS Unit 1: Pure Mathematics

Duration: 1h 30m

AS Unit 2: Applied Mathematics (choice of two from Mechanics 1, Mechanics 2, Statistics, Discrete & Decision)

Duration: 1h 30m

A2 Unit 1: Pure Mathematics

Duration: 2h 15m

A2 Unit 2: Applied Mathematics (choice of two sections)

Duration: 2h 15m

Proof by induction — base case, step rigour, and closing statement

Every A2 1 Pure report (2023–2025) flags incomplete or vague induction proofs. The base case is sometimes proved for n = 2 instead of n = 1. The closing statement omits reference to the Principle of Mathematical Induction or is phrased so vaguely it earns no mark. The algebraic manipulation in the inductive step often contains unexplained jumps or careless errors in the matrix context (bottom-left element of Aᵏ⁺¹).

A2 1 Pure

Presentation and rigour in 'show that' / 'prove' questions

Examiners across all three years describe 'dubious working', 'bluffed final lines', answers that 'miraculously appear from incorrect working', and evidence of candidates manipulating incorrect working to produce the printed result. This appears in both pure units and Applied sections requiring derivations.

AS 1 Pure, A2 1 Pure, AS 2 Applied, A2 2 Applied

Invariant lines vs lines of invariant points (matrix transformations)

In 2023 AS 1 many candidates set up the equation for lines of invariant points (Tr = r) instead of invariant lines (Tr = kr), losing all subsequent marks. In 2025 AS 1 the same confusion was noted with approximately half the candidature gaining full marks. The distinction between k = 1 (invariant points) and general k (invariant lines) is a persistent gap.

AS 1 Pure

Sampling distribution variance and choice of z vs t in hypothesis tests

Using σ² instead of σ²/n for the sampling distribution variance appears in all three years of Statistics reports. Choosing the z-distribution when the population variance is unknown (requiring t) cost marks in the 2025 A2 2 report specifically. Confusing paired and two-sample t-tests also appeared in 2025.

AS 2 Applied — Statistics, A2 2 Applied — Statistics

Reduction formulae and integration — finding I₀, splitting integrands correctly

In 2023 A2 1, candidates who tried to find I₆ directly without first setting up the reduction integral, and those unable to find I₀, lost most of the marks. Splitting the integrand as tan x × tanⁿ⁻¹ x instead of sec² x × tanⁿ⁻² x was the most common structural error. The 2025 report noted errors in finding I₀ and general numerical accuracy in exponential substitutions.

A2 1 Pure

Hyperbolic function proofs — not referencing sinh, cosh, and exponential forms explicitly

In the 2024 A2 1 report, candidates who did not explicitly reference tanh x in terms of sinh x and cosh x were not awarded full marks even when their algebra was correct. Candidates were also penalised for working simultaneously from both sides of a hyperbolic identity.

A2 1 Pure

Poisson and geometric distributions — assumptions, inequality direction, and combining classes in χ²

In 2023 AS 2, roughly half the candidates were unable to use the Poisson cumulative table correctly; the discrete nature of the distribution caused confusion with P(Y > 12) vs P(Y ≥ 12). In 2024, Poisson assumptions were poorly stated (restating given information instead of stating independence/randomness). In 2025 χ² goodness-of-fit tests, the final two classes were not combined despite expected frequencies below 5.

AS 2 Applied — Statistics, A2 2 Applied — Statistics

Centre of mass problems — missing removed components and incorrect sub-division of the body

Across all three A2 2 Applied reports, candidates failed to subtract the moments and masses of removed triangles, circles, or cones. In 2024 and 2025, some candidates omitted the removed plastic hemisphere or the light rods, and others split composite bodies into non-standard sub-shapes that created additional algebraic complexity and opportunities for error.

A2 2 Applied — Mechanics 1, A2 2 Applied — Mechanics 2