Pure Mathematics 3

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

  • Functions — composition, inverse, domain/range

    1.2

    Anchored a multi-part opener in 9 of the 13 series checked for this course's own research. The function being inverted is more often a linear-over-linear ("Möbius") fraction than the taught lesson's own quadratic examples — 5 of those 9 anchors invert one.

  • Numerical methods (sign-change + iteration)

    6.1–6.2

    Anchored a sign-change-then-iteration question in at least 9 of the 13 series checked, tied with functions as the most consistently evidenced topic in the archive. Every fully-detailed anchor pairs a transcendental term (log, eˣ, sec x, or xe²ˣ) with a polynomial one — never a bare polynomial.

Also very heavily tested

  • Exponential/log real-world modelling

    3.1–3.2

    Anchored a named real-world growth-or-decay story — mining, tree biology, medicine, pond ecology, temperature, finance, household waste — in 8 of the 13 series checked, and is described in the source research as often the paper's single largest question, 9–12 marks.

  • Product / quotient / chain rule

    4.2

    Anchored a "show that f′(x) = …" step, usually 4 marks (M1 A1 dM1 A1), in 7 of the 13 series checked. "Quote the rule before substituting" is the single most consistently repeated piece of exam advice in the whole archive for this topic, verified verbatim across five series.

  • Exponential growth and decay (differentiation)

    4.4

    Anchored a differentiation-or-reasoning step inside a real-world model in 6 of the 13 series checked — and in one series (Oct 2024) surfaced twice in the same paper as two separately-marked events. Never found as a bare "find dN/dt" prompt with no story attached.

Solidly, repeatedly tested

  • The modulus function

    1.3

    Anchored a "|linear| = / > linear" equation or inequality, worth around 4 marks, in 5 of the 13 series checked — the more frequently-anchored half of the modulus-and-transformations lesson by a clear margin over combined transformations.

  • Double angle, compound angle and harmonic form

    2.3

    Anchored a full question — never fewer than 4 marks when it appears — in 5 of the 13 series checked. Only two of those five (Oct 2020, Jan 2022) have their question text independently transcribed; the harmonic-form construction specifically was confirmed head-on in exactly 1 of the 13, so treat that narrower construction as thinner than this row's count suggests.

  • Algebraic division / rational expressions

    1.1

    Anchored a "show [constant] = …" division step in 4 of the 13 series checked, one real worked case each of the three sub-cases the spec's own denominator rule allows: a factorisable quadratic, an irreducible quadratic, and a linear divisor.

  • dy/dx = 1/(dx/dy)

    4.3

    Anchored a turning-point-of-x=f(y) or vertical-tangent step in 4 of the 13 series checked, always as part of a larger differentiation question rather than standing alone.

  • Integration (standard + by recognition)

    5.1–5.2

    Anchored a recognition-integral step — power-form or log-form — in 4 of the 13 series checked, worth 2 marks indefinite or 4 marks definite where the tariff is confirmed. Never located as the entirety of a question, always a sub-part.

Thinner, but examinable

  • Combined transformations

    1.4

    Anchored only 2 of the 13 series checked (Jan 2024, Jun 2026), each as a small 2–3 mark tail part bolted onto a longer question built on different content — not yet seen as its own multi-part question in this archive.

  • Log-linear graph parameter estimation

    3.3

    Anchored a standalone log-linear-graph question in 2 of the 13 series checked (Jun 2023, Jun 2026), worth 5–6 marks. Too thin a base for more than: expect gradient/intercept reading, and an interpret-in-words part worth its own mark.

  • Reciprocal and inverse trigonometric functions

    2.1–2.2

    The thinnest data in this set: a dedicated graded mark for this content was found in exactly 1 of the 13 series checked (worth 1 of that question's 5 marks), though the underlying facts are used as a silent precondition inside 4 of the 13. Too thin to tier as its own exam target — treat it as background knowledge other questions assume rather than a topic examined in its own right.