Battle Card

Provenance: compiled 2026-09-29. Primary source is research/veridian/WMA11-verified-facts.md (read in full before this document was started), cross-checked against codex-formula-and-method-bank.md, forge-exam-technique-guide.md and signal-frequency-and-boundaries.md in this same folder — all three read first, specifically so this card does not restate what they already cover. This is the fourth and shortest WMA11 technique-hub document: a single condensed last-look sheet, not a fifth re-teach. No new primary-source extraction was done for this pass; every formula, mark-scheme rule and trap below is a direct, deliberately-compressed pull from those four sources, each individually provenance-checked in the verified-facts bank. Not affiliated with or endorsed by Pearson Edexcel.

#WMA11 — Battle Card

#Pearson Edexcel IAL Mathematics, Unit 1: Pure Mathematics P1 — last-look reference

Use this in the last 10 minutes, not the last 10 hours. Everything here is stated, not explained — for the reasoning, the worked methods, or the full trap write-ups, go to codex-formula-and-method-bank.md, forge-exam-technique-guide.md and signal-frequency-and-boundaries.md, which this card exists to summarise, never to duplicate.

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#1. Memorise — the exam booklet does NOT give you these

Per the spec's own list (P1.2): these are "expected to know... will not appear in the booklet."

• Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a
• Sine rule: a/sin A = b/sin B = c/sin C
• Area of a triangle: ½ab sin C
• Arc length: s = rθ (θ in radians)
• Sector area: A = ½r²θ (θ in radians)
• Differentiation: xⁿ → nxⁿ⁻¹
• Integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c, n ≠ −1

#2. What IS in the booklet — the whole P1 section, verbatim two entries

Don't waste memory here — it's given:

• Cosine rule: a² = b² + c² − 2bc cos A
• Sphere surface area 4πr²; cone curved surface = πr × slant height

That's the entire P1 section (formula booklet, Issue 2, Jan 2021). Nothing else on this paper is provided.

#3. Definition-cues, cold recall

• Discriminant Δ = b² − 4ac. Δ>0 two distinct roots · Δ=0 repeated root · Δ<0 no real roots. Parameter alert: if the leading coefficient is the parameter, exclude it = 0 separately (that case isn't quadratic at all) — the discriminant range alone won't catch it.
• Parallel m₁ = m₂. Perpendicular m₁ × m₂ = −1. A "prove perpendicular" answer needs a closing sentence naming the right angle — the arithmetic alone is not the proof.
• Periods: sin x and cos x → 2π. tan x → π. The period is a length, never an interval — don't answer with a domain like −π/2 < x < π/2.
• Transformations of y = f(x): af(x) = vertical ×a · f(x)+a = vertical shift (0,a) · f(x+a) = horizontal shift (−a,0) · f(ax) = horizontal ×(1/a). The required word is "translation" — "shift"/"move" do not earn the mark, even when the maths is right.
• Ambiguous case (sine rule): sin θ = sin(180°−θ) → two candidate angles, both to be checked (angle sum, side-length consistency) — don't report only the calculator's default acute value.
• Reciprocal inequality a/x < b → multiply by x² (never negative, never flips the inequality, and hands you the x=0 boundary for free): ax < bx². State x ≠ 0.
• Zero-gradient tangent: f′(a) = 0 still gives a real tangent — the horizontal line y = f(a). The normal's −1/f′(a) formula is undefined there; treat it as its own case, don't stall.

#4. Tariff & mark-scheme reminders

• 75 marks, 90 minutes, all questions compulsory, typically 10–11 questions. Budget = marks × 72 seconds — Pearson's own printed rule, not a course estimate.
• Quote the formula before you substitute. If the substituted working then slips, the method mark can survive on the quoted formula alone.
• A 3-term quadratic earns its method mark via exactly one of three named routes: factorisation, the formula (values substituted), or completing the square in (x±b/2)²±q±c=0. A bare correct root pair with none of these shown is scored as an answer, not a method.
• Diff/int method marks are per TERM: any single xⁿ→xⁿ⁻¹ (or →xⁿ⁺¹) shift earns it, even if the rest of the expression is still wrong.
• "ft" only ever tags A or B marks — never M. A method mark is earned on its own working or not at all.
• Watch for "solutions relying on calculator technology are not acceptable" on individual sub-parts (confirmed on scattered questions across every series checked) — it's a cue to write full algebraic lines from the first step, not generic boilerplate.
• Exact-value or surd-explicit questions lose marks to a decimal answer, even a correct-looking one.
• Inexact numeric answers: 3 significant figures, unless the question states otherwise.
• Never state a region "in terms of R." Mark schemes score this M0 — a lost method mark, not just a lost accuracy mark.
• isw protects work written after a correct final answer; it does not restore a correct answer you've since crossed out and replaced with a worse one.

#5. Top 5 danger warnings, ranked by real damage seen

1. Stops halfway — solves the intermediate value, never finishes the actual question. The single most repeated failure shape in this paper's history, seen across four unrelated topics: hidden-quadratic substitution (solves for p = 3ˣ, never solves back for x — Jan 2023 Q5, Jan 2025 Q4(b), two independent series, identical trap); simultaneous equations (finds x, forgets y — Jan 2023 Q7(d)); two-stage integration (defers both constants to the very end instead of fixing each right after its own integration — Jan 2023 Q11(b)); zero-gradient tangent (computes f(⅓)=0 and stops, never writes the tangent line — Oct 2021 Q6(c)). Rule of thumb: after every substitution, ask "is this what the question actually asked for?"
2. Constant of integration, omitted. The single most-repeated "silly" mark loss in the whole corpus — confirmed independently in four series (Jan 2023 Q3, Oct 2021 Q1, Oct 2020 Q9, Jan 2025 Q6(b)). Every indefinite integration gets its own +c, every time.
3. Sector/arc: dropped ½, or the wrong angle. The single most consistently recurring question type across the whole bank (3 of 7 series read in full). Jan 2023 Q6: "the most common error was to omit the ½ in the area formula." Oct 2021 Q7: the common mistake used the minor angle where the major (reflex) angle was needed — always check which angle the formula actually wants before substituting.
4. Discriminant-with-parameter: the a≠0 (or k≠0) exclusion, and the strict boundary. Jan 2023 Q4: "many candidates ignored the solution, k = 0" — losing the lower bound entirely; a real minority went on to submit 0 ≤ k ≤ 5/9 instead of the strict 0 < k. Jan 2019 Q9: candidates fail to even form the quadratic in x before reaching for the discriminant at all.
5. Period of tan x, answered as an interval. The single worst-scoring item found anywhere in this pass: "more than half of all candidates scored no marks" on this exact question (Jan 2023 Q9(a)) — the common wrong answer was a domain like −π/2 < x < π/2, not a number. Period ≠ domain. The answer is π.

#6. Not on this paper — don't burn revision time here

Confirmed excluded from P1 by the spec's own unit-content sections: proof (exhaustion/counterexample), the factor and remainder theorems, circle geometry, sequences and series, exponentials and logarithms, the chain rule (explicitly excluded, spec 4.1), and n = −1 in integration (needs ln|x|, which is P2 content). All of that is P2/P3 — real content, just not this paper's.

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Honest gap, stated rather than hidden: this card inherits the underlying facts bank's own coverage limits — nine series touched, five with a fully-read examiner report (Jan 2019, Oct 2020, Oct 2021, Jan 2023, Jan 2025), the rest partial or single-question. "Top 5" above means top 5 of what this pass has verified, not a claim that nothing else on the paper is dangerous. No grade boundary appears anywhere in this course's WMA11 materials, for the reason given in signal-frequency-and-boundaries.md §2 — none is stated here either.