Pure Mathematics 4

Topic frequency

How often each topic actually gets tested

Not an official Pearson weighting — Pearson doesn’t publish one for this paper. This is what this course’s own research found by reading real mark schemes and examiner reports series by series, counted honestly rather than assumed. Use it to prioritise review time, not to assume a topic near the bottom won’t appear.

Richest by series count

  • Proof by contradiction

    1.1

    Seen in 6 of the 7 series with real, question-by-question mining for this course's WMA14 research (Jan 2021, Oct 2021, Jun 2022, Jan 2024, Oct 2024, Jan 2026) — the highest count of any WMA14 spec point. Only 3 of those 6 sightings carry a confirmed mark total in this course's sources (4–5 marks each); the other three are attested through examiner-report commentary only.

Also very heavily tested

  • Binomial expansion for rational n

    4.1

    Seen in 5 of the 7 series mined (Jan 2021, Oct 2021, Oct 2022, Jan 2024, Oct 2024) — Q1 in both January series checked, Q4 in two of the three October series, shifting to Q1 in the most recent, October 2024. Most often followed by a numerical-approximation step (3 of 5 citations) rather than a range-of-validity step (1 of 5).

  • Implicit & parametric differentiation, tangents and normals

    5.1

    Seen in 4 of the 7 series mined (Jan 2021, Oct 2021, Oct 2022, Jan 2024).

  • Scalar product, angle between lines, and skew/parallel lines

    7.6–7.7

    Seen in 4 of the 7 series mined (Jan 2021, Oct 2022, Jan 2024, Jan 2026) — the joint-most-frequently-evidenced WMA14 topic after proof by contradiction. In 2 of those 4 series it appeared as two separate, unconnected questions on the same paper, not once. Only one sighting (Jan 2026 Q9) carries a confirmed mark total: 11 marks.

  • Separable differential equations, and forming them from rates of change

    5.2 / 6.4

    Seen in 4 of the 7 series mined (Jan 2021, Oct 2021, Jan 2024, Jan 2026); a stricter count of the separating-and-solving step alone, rather than the rates-of-change setup, would be 3 of 7. Only one sighting (Jan 2026 Q3) has a confirmed mark total: 8 marks, split 6+2.

Solidly, repeatedly tested

  • Partial fractions, including integration via partial fractions

    2.1 / 6.3

    Seen in 3 of the 7 series mined (Oct 2021, Oct 2022, Jan 2024), all three sourced from examiner reports only. No single confirmed mark-scheme total exists for it anywhere in this course's evidence base; when tested it tends to split into a decomposition part and a separate part applying the result.

  • Parametric equations: conversion and domain/range

    3.1

    Seen in 3 of the 7 series mined (Jan 2021, Oct 2021, Oct 2022). Only one sighting (Jan 2021 Q4) has a confirmed mark total: 7 marks, split 5+2 between the conversion/domain part and the range part.

  • Volume of revolution

    6.1

    Seen in 3 of the 7 series mined (Jan 2021, Oct 2022, Jan 2024) — a compulsory, explicitly spec-listed skill, so this count is read as this course's sourcing coverage to date, not evidence it's tested only occasionally. Only one sighting (Jan 2021 Q9) has a confirmed mark total: 10 marks, split 7+3.

  • Integration by parts and by substitution

    6.2

    Seen in 3 of the 7 series mined (Oct 2021, Oct 2022, Jan 2024).

Thinner, but examinable

  • Position vectors, distance, and the foot of a perpendicular

    7.4–7.5

    Seen in only 1 of the 7 series mined (Oct 2021, 9 marks split 7+2). This course's own research names this row, alongside area under a parametric curve, as the thinnest-evidenced content in the whole WMA14 facts bank — a sourcing gap, not confirmation the topic is rarely tested; both spec points are compulsory. Don't deprioritise it on this count alone.

  • Area under a parametric curve

    6.5

    Seen in only 1 of the 7 series mined (Jan 2026) — but it's the largest single confirmed real question anywhere in the WMA14 facts bank, 16 marks across four parts. Spec 6.5 is a compulsory, explicitly spec-listed skill that had zero citations anywhere in this course's research until that series was reviewed; treat the low count as an evidence gap, not permission to under-revise the skill.