Topic Brief: Separable Differential Equations

Provenance: compiled 2026-09-29. Sources checked directly for this document: research/veridian/WMA14-verified-facts.md §5.5 (the Jan 2024 Q4 rates-of-change citation and the spec 5.1/5.2 boundary it sits on), §5.6 (this topic's own five citations under spec 6.4, including the Jan 2026 Q3 addition and its independent re-verification note), §6 (series/document-count methodology), §7 (standalone-lesson evidence bar), §8 (flagged evidence-strength gaps); the full header of content/veridian/curriculum/wma14/separable-differential-equations.ts (its own scope note — "exactly THREE series... FOUR questions" for the trap-taxonomy, plus the Jan 2026 addition on top); content/veridian/technique-hub/wma14/codex-deep-dive-separable-differential-equations.md in full (its §2 antiderivative-family taxonomy, §3 setup-stage failures and §5 synthesis table, cross-checked to avoid restating them); signal-frequency-and-boundaries.md §1's existing row for this topic ("4 of 7") and §3's flagged gaps; forge-exam-technique-guide.md §1's real per-question mark/timing table. content/veridian/question-bank/wma14.ts was checked directly and contains no entry for this topic. No fresh PDF extraction was performed — every fact below reuses citations already verified elsewhere in this facts bank; this document's contribution is holding the "which series, what pattern, what to expect" question in one narrow place rather than requiring it be reassembled from the four documents above. Not affiliated with or endorsed by Pearson Edexcel.

#SIGNAL Topic Master Brief — Separable Differential Equations, and Forming Them from Rates of Change (spec 5.2, 6.4)

#Frequency: seen in 4 of 7 series checked

Of the 11 WMA14 series with at least one primary document in this facts bank, only 7 received real, question-by-question mining rather than a boilerplate-only check: January 2021, October 2021, June 2022, October 2022, January 2024, October 2024, January 2026 (signal-frequency-and-boundaries.md §1). Four of those seven carry a verified citation for this topic: January 2021 (Q10), October 2021 (Q2 and Q9 — two separate questions in the same series), January 2024 (Q4), and January 2026 (Q3). June 2022, October 2022 and October 2024 — all three mined question-by-question — show no citation for this topic in either an examiner's report or a mark scheme. That is read as absence-from-this-course's-review, not confirmed absence from those papers (WMA14-verified-facts.md §8's own caution applies here as everywhere else in this facts bank).

One of the four is a boundary case, stated as such rather than folded in silently: January 2024 Q4 forms a rates-of-change equation from a cone's geometry (spec 5.1/5.2) but is a differentiation-only question — it is never carried through to a separable equation and solved. It is counted here because the lesson file itself bundles 5.2 and 6.4 under one title, on the grounds that a rates-of-change context is genuinely how this equation usually reaches the page (codex-deep-dive...md §"Scope"); a stricter count of spec 6.4 alone — separating, integrating and solving — would be 3 of 7 (Jan 2021, Oct 2021, Jan 2026), not 4.

#Mark-tariff pattern: one full real question sized, three data points on structure only

Only one of the four citations has a captured total: January 2026 Q3, 8 marks, split 6 (solve the equation) + 2 (hence find a limiting value) — roughly 10 exam minutes at this paper's own 1.2-min/mark reading (forge-exam-technique-guide.md §1). Jan 2021 Q10, Oct 2021 Q2 and Oct 2021 Q9 have no total mark figure captured in either source document reviewed for this brief — what is confirmed for each is structure, not size: every one of the four real questions runs across at least two stages (form or state the equation → separate → integrate → apply a boundary condition), several with a further closing part on top (a limiting value in Jan 2026; a units-sensitive numerical answer in Oct 2021 Q9). The one sized example is consistent with this being a mid-tariff, multi-part item on this paper rather than a short single-mark-scheme-line question, but three of the four citations cannot confirm or contradict that at the level of a specific number.

#Recurring context and angle

Every full separable-equation citation in this facts bank is a modelling context, never a bare "solve this equation" prompt with no story attached: a water-tank inflow/outflow problem (Oct 2021 Q9), a cone or similar geometric rates-of-change setup (Jan 2024 Q4), and a shrub-height growth model (Jan 2026 Q3) all dress the equation in a real-world scenario that has to be translated into calculus before separation can even start. Jan 2021 Q10 is the one exception with no scenario named in the citation available to this brief — the facts bank records only the logarithm-handling difficulty, not the question's own framing. Two structurally distinct antiderivative families recur across the citations that do have a recoverable equation: pure reverse-power-rule on both sides (Jan 2026 Q3), and a mix involving at least one logarithm-producing side (Jan 2021 Q10, and the constant-integrated-as-a-log trap in Oct 2021 Q9) — both are real, neither is more common than the other on this small a count (codex-deep-dive...md §2 develops this split in full; it is cited, not repeated here).

The one genuinely new element on record, confirmed on exactly one question, is a closing "hence" part that asks for a long-run limiting value from the solved closed form (Jan 2026 Q3(b)) — every separable-DE citation before that series stops at a particular solution from a boundary condition. Whether this extension recurs is not knowable from this facts bank; it is stated as a single confirmed instance, not a pattern.

#If this topic appears: what to expect

Expect a context-driven setup, not an equation handed over ready to separate — reading the scenario correctly (the right geometric formula, a two-term rate kept as two terms, a quantity that varies substituted in rather than treated as fixed) is independently documented as its own failure point, separate from and prior to the calculus (codex-deep-dive...md §3). Once separated, check which antiderivative family each side actually belongs to before integrating — a plain constant integrates to a linear term, not a logarithm, and a power of a linear expression needs the $\tfrac1a$ scaling factor, not just the power rule. If the question prints a "show that" target, treat any mismatch as a real error to trace back, not a cue to adjust a line to fit the given form — this is independently confirmed as something examiners are trained to catch on this exact topic (Jan 2021 Q10). If a closing part follows the "hence" solution, do not assume it asks for another boundary-condition substitution; on the one real instance available, the intended route was reading a limiting value directly off the closed rational form, with the calculus-flavoured "differentiate and set to zero" instinct confirmed as a dead end for that specific equation. No grade-boundary figure exists anywhere in this course's WMA14 source review for any topic, this one included, and none is implied here.

#Sources used

research/veridian/WMA14-verified-facts.md §5.5 (Jan 2024 Q4), §5.6 (the topic's five direct citations), §6, §7, §8; content/veridian/curriculum/wma14/separable-differential-equations.ts header; content/veridian/technique-hub/wma14/codex-deep-dive-separable-differential-equations.md §2–§5; signal-frequency-and-boundaries.md §1, §3; forge-exam-technique-guide.md §1. No new primary Pearson document was fetched for this brief.