Pure Mathematics 2

Battle Card

Provenance: written 2026-09-29, against research/veridian/WMA12-verified-facts.md (read in full, §1–§9 — the primary provenance-checked source for every spec/booklet/mark-scheme fact below) and the three existing technique-hub documents for this paper, forge-exam-technique-guide.md, codex-formula-and-method-bank.md and signal-frequency-and-boundaries.md (each read in full). Those three already carry the exam-craft, formula/method and frequency/boundary material in depth — this document adds nothing new to any of them; it re-packages their already-cited findings into a single dense page for last-look use, and every line below traces back to a citation that already exists in one of those four documents. content/veridian/curriculum/wma12/paper-anatomy.ts was also re-read to cross-check the paper-vitals numbers for consistency.

#WMA12 — Battle Card

#Pure Mathematics 2 (Pearson Edexcel IAL) — last-look reference, not a lesson

What this is. The one page to scan in the last ten minutes before the exam, or between questions if you freeze. It is deliberately not a re-teach — no derivations, no worked examples, nothing you haven't already met in the 11 curriculum lessons or the technique-hub documents above. If a claim below needs its full citation, it's already sourced in full in one of those.

#Paper vitals

90 minutes, 75 marks, 9–11 questions — question count is not fixed, so budget off the number printed next to the question, not memory of a practice paper.
Calculator allowed on the entire paper (no non-calculator section exists) — but specific questions carry a bold "show all stages of your working" instruction, and calculator-only working with no method shown is not credited.
Yellow booklet = Mathematical Formulae and Statistical Tables, Issue 2 (Jan 2021).
Average pace 72 sec/mark, but real per-question spread is 3–14 marks — the paper is not evenly weighted question to question.
"Students must answer all questions" — no choice, no sections.

#Formula & definition-cue masterlist

GIVEN = printed in the yellow booklet for P2. MEMORIZE = not printed anywhere on the P2 page (or, for two topics, the P1 page you're still on the hook for).

Proof (1.1–1.3) — no formula at all. MEMORIZE the three techniques: exhaustion (list every case in a finite domain); counter-example (one failing case is enough, with its reason stated); general algebraic proof / proof by contradiction (rearrange to compare-with-zero, then factorise or complete the square).

Algebra (2.1) MEMORIZE — remainder theorem: dividing f(x) by (ax−b) leaves remainder f(b/a). Factor theorem: (ax−b) is a factor ⟺ f(b/a)=0. Divisor restricted to (ax+b)/(ax−b) only.

Circle (3.1) MEMORIZE — (x−a)²+(y−b)²=r², centre (a,b), radius r. General form x²+y²+2gx+2fy+c=0 → centre (−g,−f), r=√(g²+f²−c). Plus three named properties: angle in a semicircle is 90°; the perpendicular from the centre bisects a chord; radius ⊥ tangent.

Sequences & series (4.1–4.5)

GIVEN: uₙ=a+(n−1)d; Sₙ=½n(a+l)=½n[2a+(n−1)d]; uₙ=ar^(n−1); Sₙ=a(1−rⁿ)/(1−r); S∞=a/(1−r) for |r|<1; combinatorial (a+b)ⁿ with ⁿCᵣ=n!/(r!(n−r)!) — positive-integer n only at P2.
MEMORIZE: both sum-formula proofs — the spec names this explicitly, not just the formulae. Arithmetic: write Sₙ, write it reversed, add pairwise. Geometric: write Sₙ, form rSₙ, subtract, factor.
Booklet trap: the general series (1+x)ⁿ, n∈ℝ, sits on the same page as (a+b)ⁿ. P2 never needs it — use (a+b)ⁿ.

Exponentials & logs (5.1–5.3)

GIVEN: change of base only — logₐx = log_b x / log_b a.
MEMORIZE: addition, subtraction and power laws; logₐ(1/x)=−logₐx; logₐa=1. Graph of y=aˣ: through (0,1), always positive, asymptotic to y=0.

Trigonometry (6.1–6.2) MEMORIZE — tanθ≡sinθ/cosθ; sin²θ+cos²θ≡1. Nothing trig-related is printed in the booklet at all.

Differentiation (7.1) MEMORIZE (P1 carry-forward) — d/dx(xⁿ)=nxⁿ⁻¹. Nature test: d²y/dx²>0 ⇒ min, <0 ⇒ max, =0 ⇒ inconclusive by that test alone (needs a further calculus check, not a y-value comparison, to be credited).

Integration (8.1–8.3)

MEMORIZE (P1 carry-forward): ∫xⁿ dx = xⁿ⁺¹/(n+1)+c, n≠−1. Area = ∫ₐᵇ y dx — the spec's own stated form. Integrating with respect to y is explicitly out of scope, not just rare.
GIVEN: trapezium rule in full, ∫ₐᵇ y dx ≈ ½h{(y₀+yₙ)+2(y₁+…+yₙ₋₁)}, h=(b−a)/n.

P1 carry-forward, in neither booklet page: quadratic formula; sine rule; area=½ab sinC; arc length s=rθ; sector area ½r²θ. (The cosine rule is the one exception — it is printed, on the P1 page.)

#Tariff & mark-code reminders

M = a valid method attempted. A = only scores once its gating M is already scored. B = stands alone, no method mark needed first.
dM1 / ddM1 = only scores if one (or two) specific earlier marks already landed — a correct method applied to a number that's never actually substituted forward scores nothing further.
Quote the formula before plugging in numbers: a correct final value with no method line visible scores zero, confirmed as a literal result on real mark schemes, not a style preference.
Exact-answer questions: a correctly-rounded decimal still loses the accuracy mark. A recurring-decimal notation is the one decimal form still treated as exact.
Misreading a question costs 2 marks off the A/B total for that part — never an M mark.
Multiple attempts: cross out the wrong one. If nothing (or everything) is crossed out, the marker scores your worst surviving attempt, not your best.
Glossary: bod (benefit of doubt) · ft (follow-through) · cao (correct answer only) · cso (no errors anywhere in that part) · isw (ignore subsequent working) · awrt (answer which rounds to) · oe (or equivalent) · ag (answer given, printed on the paper).

#Top-5 danger warnings (whole-paper, ranked by cost)

No working shown, no marks — even when the number is right. A calculator-only sum-to-infinity and a bare correct decimal have each been confirmed as a real, literal zero on separate series (Jan 2024 Q5(i); Jan 2025 Q5(a)).
Exact form demanded, decimal delivered. Costs the final accuracy mark on stationary-point x-values, circle radii (r=√20 written as a decimal), and radian answers left un-simplified to the required kπ form — confirmed across several separate series, not a one-off.
Dividing out a common factor instead of factorising — sinθ, cosθ, tanθ, or an algebraic x — silently deletes an entire solution branch. Confirmed on a real trigonometric equation (Oct 2023 Q3); mechanically the same mistake as dividing a quadratic through by x.
"Hence" or "using your answer to (a)" ignored. Reaching the right final answer by an unrequested method scores zero on that part, confirmed where a candidate calculator-solved a cubic instead of using the given factor (Oct 2023 Q4(c)(ii)); redoing earlier work instead of reusing it costs marks and time in the same move (Jun 2025 Q5(b)).
A correct method never carried into its dependent step. On one fully-verified anchor, roughly half of candidates who found a correct second derivative never substituted their own x-value into it — the dM1 simply never fires (Jan 2021 Q2(b)).

#Sources

research/veridian/WMA12-verified-facts.md, §1–§9 — spec content, booklet contents, mark-scheme conventions, per-topic verified findings.
content/veridian/technique-hub/wma12/forge-exam-technique-guide.md, codex-formula-and-method-bank.md, signal-frequency-and-boundaries.md — read in full; every citation above already exists in one of these three, condensed here into single-page form, nothing new asserted.
content/veridian/curriculum/wma12/paper-anatomy.ts — standing spec/timing reference, cross-checked for consistency on the paper-vitals section.