CCEA GCSE Further Mathematics (507) Past Papers 2026

Differentiation, integration, trigonometry, matrices, algebra, logarithms, coordinate geometry

Duration: 2h

Vectors, kinematics, forces, Newton's laws, moments, connected particles

Duration: 1h

Spearman's rank correlation, regression lines, probability (including conditional), binomial distribution, normal distribution, standard deviation, Venn diagrams

Duration: 1h

Counting and logic, linear programming, time series analysis, decision algorithms

Duration: 1h

Conditional probability — restricting to the correct sample space

Every report for all three years flags conditional probability as the hardest discriminator in Unit 3, typically answered correctly by fewer than 40% of candidates. In 2023 only 25% answered the conditional probability part correctly. The consistent error is treating the total sample space as the denominator instead of the probability of the given condition.

Unit 3: Statistics

Force diagrams — missing arrows, wrong labels, and spurious extra forces

Named in the Unit 2 overview of all three reports as a recurring fundamental error. In 2025 the examiner stated fewer than 50% of candidates achieved full marks on the force diagram part of one question. Common missing forces include normal reactions, correct weight labels (mg not m), and tension arrow directions.

Unit 2: Mechanics

Integration — omitting constant of integration and confusing with differentiation

Across 2023–2025 the constant of integration was omitted by a significant number of candidates in indefinite integration questions. In 2025 many candidates differentiated when integration was required, triggered by seeing the word 'gradient' in the question.

Unit 1: Pure Mathematics

Vector algebra — equating i and j components and solving simultaneous equations

Flagged in Unit 2 in 2023 and 2025. Only stronger candidates successfully equated coefficients of i and j to form simultaneous equations. Carrying i and j into algebraic equations, sign errors when expanding brackets containing −3, and failing to form simultaneous equations were consistently identified.

Unit 2: Mechanics

Quadratic inequalities — identifying the correct region after finding critical values

Across 2023 and 2025, candidates regularly found the critical values correctly but then chose the wrong region for the inequality (e.g. x > 6 and x < −2 instead of −2 < x < 6). Not sketching the parabola was identified as the main cause. In 2023 candidates also included negative values when context required positive values only.

Unit 1: Pure Mathematics

Standard deviation of combined groups — applying the correct formula

In Unit 3 in 2023 and 2025, questions on standard deviation from combined groups consistently served as strong discriminators, answered fully correctly by approximately half or fewer of candidates. Common errors included squaring Σx instead of computing Σx², using the wrong group size in the denominator, and failing to account for adjustments when data is scaled.

Unit 3: Statistics

Tangent and normal to a curve — applying calculus in coordinate geometry contexts

In 2024 and 2025 only a minority of candidates gained full marks on tangent/normal questions. In 2024 a large number did not differentiate at all, setting the curve equal to the line instead. In 2025 many set dy/dx = 0 out of habit instead of equating it to the given gradient value.

Unit 1: Pure Mathematics

Sketching trigonometric graphs — tan asymptotes and cosine boundary behaviour

In 2023, many candidates drew a straight line at ±180° on the cosine curve instead of showing the turning point. In 2025, candidates confused tan with sine or cosine, omitted vertical asymptotes, or drew curves that touched the asymptotes. Failure to label the x-axis with correct values also cost marks.

Unit 1: Pure Mathematics