Topic Brief: Splitting Fractions Before Integrating

Provenance: compiled 2026-09-29. Source is research/veridian/WMA11-verified-facts.md — specifically §4.5 (the Jan 2023 Q3 entry and its 2026-09-14 mark-scheme-bullet-coverage-audit update) and §2/§7's series-coverage accounting — cross-checked against content/veridian/curriculum/wma11/splitting-fractions-before-integrating.ts (its own header provenance note and body) and this folder's codex-formula-and-method-bank.md (§2.5.1), forge-exam-technique-guide.md and signal-frequency-and-boundaries.md to confirm this brief adds a genuinely new layer rather than restating theirs. No fresh PDF extraction was done for this document itself. Not affiliated with or endorsed by Pearson Edexcel.

#SIGNAL Topic Master Brief — Splitting an Algebraic Fraction Before Integrating (spec 5.1, 5.2)

#Frequency: seen in 1 of 5 series fully mined

The facts bank has fully mined five WMA11 series question-by-question, each with a complete examiner report: Jan 2019, Oct 2020, Oct 2021, Jan 2023, Jan 2025. The exact skill this topic teaches — a numerator with more than one term sitting over a single monomial denominator, split into separate power-of-x terms before integrating termwise — is confirmed in exactly 1 of those 5: Jan 2023 Q3.

That is the honest number, not a softened one. Four other series were touched by this research pass at lower depth and were not checked for this specific sub-skill: Oct 2022 and Jan 2024 are confirmed-genuine mark schemes that were never mined question-by-question at all; June 2022 and June 2023 were each read for one targeted question only (Q5, and Q1–Q2 respectively), neither of which is this topic. Their silence here is a research gap, not a confirmed absence — this brief does not claim the other eight series lack the skill, only that this pass has not checked them for it.

One further point of context: the wider "Integration" spec strand is itself confirmed in 4 of the same 5 series (signal-frequency-and-boundaries.md §1), but that count is not broken down by sub-skill anywhere else in this course's materials. This brief is the first place that narrower number — 1 of 5, specifically for the split-before-integrating step — is stated.

#The one confirmed appearance

Jan 2023 Q3 (WMA11/01, Question Paper Log Number P72066A; mark scheme Publications Code WMA11_01_MS_2301) — 5 marks, a standalone question (not a sub-part of a larger multi-topic item), positioned early in the paper relative to the topic's own late-paper sibling below. Real question, verbatim: "Find $\int \frac{4x^5+3}{2x^2}\,dx$, giving your answer in simplest form. (5)" No point is given; the answer keeps a symbolic c.

Real mark-scheme structure, verbatim: (4x⁵+3)/(2x²) dx = ∫(2x³+³⁄₂x⁻²) dx → M1 A1, then = ½x⁴−³⁄₂x⁻¹+c → dM1 A1 A1. Two structural facts are specific to this question, not general integration lore: the split earns its own attempt/accuracy pair — M1 for "an attempt to write as a sum of two terms with one processed index correct," and a separate A1 for the fully correct split — rather than one combined mark; and the integration step is coded dM1, explicitly "depends on the first M mark," never an independent method mark of its own.

The mark scheme also names three specific wrong splits that still bank the integration method mark, because that mark rewards correctly integrating whatever split was written, not the split's own correctness: 8x³+6x⁻², 4x⁵+6x⁻², 2x⁵+(3/2)x⁻². The examiner report's own framing of the two failure modes this builds around: "some candidates had no idea how to write the expression as the sum of two terms. A small minority attempted to integrate all 3 terms separately before division which resulted in no marks."

#Mark-tariff pattern

One confirmed data point, stated as one: 5 marks, split as M1 A1 (the split itself) then dM1 A1 A1 (the integration and simplification). That is a flatter, shallower dependency chain than this course's other confirmed integration structure — the two-condition "integrate twice, find two constants" question (Jan 2023 Q11(b), 6 marks, M1 → dM1 → dM1 → dddM1, see this folder's own sibling brief) — and it sits earlier in the same paper (Q3 of 11, versus Q11 of 11). Whether that early-paper placement is a pattern or a coincidence of one series cannot be said from a single confirmed instance; it is reported here as a fact about this one paper, not a rule.

#The recurring angle — and what it is not

With only one confirmed instance, no cross-series "recurring angle" can honestly be claimed, and this brief does not invent one. What can be said, from the one confirmed case plus the spec's own worked examples (codex-formula-and-method-bank.md §2.5.1, verbatim from the spec PDF): the tested shape is consistently a fixed-power monomial denominator (x², √x, etc.) under a multi-term numerator, splittable by dividing each numerator term by the denominator separately — never a shifted denominator like 6/(x−2), which is not a valid additive split at all. That shifted-denominator confusion is real and documented (Jan 2023 Q7(c)–(d): "6/(x – 2) was often given as (6/x) – 3"), but it belongs to a different question, in a different context (a line meeting a curve, spec strand 1–2), not to this integration topic — the two are adjacent traps on the same algebraic move, not the same finding, and should not be merged.

This topic is also distinct from the course's other confirmed integration family — "integrate once or twice, then use a point to find a constant" (Oct 2021 Q10, Jan 2023 Q11(b), Jan 2025 Q6(b)) — none of which involve a fraction to split first. The one confirmed fraction-split question, Jan 2023 Q3, carries no point condition at all.

#If this topic appears: what to expect

Expect a standalone integration question, worth around 5 marks, testing the split and the integration as two separately-marked stages rather than one. Expect partial credit to survive a wrong split provided the subsequent integration is done correctly on whatever (wrong) split was written — the method mark for integrating is real even when the accuracy mark for the split itself is not. Expect the two examiner-confirmed failure modes to be: not recognising the expression as a sum of two terms at all, and attempting to integrate the un-split fraction's pieces before dividing (a different, wrong calculation, not a slower correct one). A shifted denominator such as 6/(x−a) is a different algebra pattern entirely and should not be forced into this same split.