Deep Dive: Show That Answer Discipline

#CODEX Deep-Dive — "Show That" Answer Discipline (WST01, cross-cutting; anchor spec 6.1)

Provenance (2026-09-29): Read/checked for this document — research/veridian/WST01-verified-facts.md in full, grepped specifically for "show that", "showing your working", "ans only", "cso", and "isw" (§1 spec/mark-code definitions, §4 mark-scheme conventions, §5 Section 2/3/4/5/6 trap catalogue, §6 the cross-cutting synthesis paragraph, §8 flagged gaps, and the per-lesson audit-log entries for show-that-answer-discipline.ts and normal-distribution-standardisation-and-conditional-probability.ts); the live lesson file content/veridian/curriculum/wst01/show-that-answer-discipline.ts in full; the sibling lesson content/veridian/curriculum/wst01/normal-distribution-standardisation-and-conditional-probability.ts (grepped for its own "ans only"/precision caveat); the three existing technique-hub documents in this folder (codex-formula-and-method-bank.md, forge-exam-technique-guide.md, signal-frequency-and-boundaries.md); and content/veridian/question-bank/wst01.ts (grepped for "show that" — no matching item found there). For cross-qualification corroboration only, not as WST01 evidence: research/veridian/WMA12-verified-facts.md (its Jan 2021 Q9(b)(i) mark-scheme audit) and research/veridian/WME01-verified-facts.md (its standing "hence show that" rubric note). No new PDF fetches were made. All arithmetic in the fresh micro-examples below was independently checked before being written in.

#Scope — what this adds, and what it deliberately does not repeat

The live lesson already derives the M/A dependency mechanism in full, drills two complete worked exemplars end to end (a Normal-distribution probability and a grouped-frequency IQR), carries four named trap-taxonomy items, four MCQs, a reference card, and the isw/misread conventions. None of that is reproduced here. This document does three things the lesson's own pedagogical shape has no room for:

1. Lays out the complete real sub-case structure of "show that" instructions across the whole paper — not just the two topics the lesson's worked exemplars happen to cover — with a short, fresh micro-example for each sub-case the lesson does not already illustrate.
2. States the necessary converse: the real, verified boundary case where a bare final answer does score full marks, and exactly how precision-conditional that allowance is — content that lives in a sibling lesson file, not in the show-that lesson itself, and is genuinely additive here.
3. Checks the discipline against two other Pearson IAL papers (Mechanics, Pure Mathematics) to see whether "show that" marking is a WST01 quirk or a qualification-wide convention with paper-specific notation — clearly flagged as corroboration, not WST01 evidence.

#1. The mechanism, restated once, precisely

The lesson's own mechanism block already derives this from the mark schemes' general marking instructions; it is restated here in one paragraph only because every sub-case below depends on it. An M mark requires a method to be visible on the page to be awarded at all. An A mark is dependent — it "can only be awarded if the previous M mark has been earned" (verified, §4 of the facts bank). On an ordinary question a correct final value is itself indirect evidence a correct method was used, so the dependency rarely bites. A "show that" question destroys that evidence on purpose, by printing the target in the stem — so a correct final line is consistent with genuine working and with copying the given value, and the mark scheme's only defence is to refuse the accuracy mark unless the method is independently visible. Two mark-code conventions exist specifically to encode this: cso ("correct solution only... there must be no errors in this part of the question to obtain this mark," per the facts bank's abbreviations list) and a dedicated printed-answer symbol for "the answer is printed on the paper" — both real enough to have their own line in every one of the 14 mark schemes reviewed, not editorial description.

#2. The real sub-case structure, with a fresh micro-example for each

#2.1 Sub-case A — a "show that" that resolves via a numeric or algebraic chain

The richest sub-case, and the one the lesson's own two exemplars (Normal-distribution probability; grouped-frequency IQR) already own in full, alongside the regression-coefficient precision example (Jun 2024 Q4(c)) and the PMCC precision example (also Jun 2024 Q4(c), cross-cited in the facts bank's §5 Section 4) that the lesson's "two more places" teach block already covers. Rather than re-deriving either, here is a fresh instance of the same sub-case from a different spec section the lesson does not draw its exemplars from: solving for an unknown probability via the sum-to-one self-check. Pearson's own examiner commentary on a real probability-function question records candidates missing a domain value and adds that checking whether probabilities summed to 1 would have caught it (paraphrased; Oct 2021 Q4(d)). Framed as a "show that" chain: a discrete random variable $X$ takes values 1, 2, 3 with $P(X{=}1)=0.2$, $P(X{=}2)=p$, $P(X{=}3)=0.3$; show that $p=0.5$. Method: write $\sum P(X{=}x)=1$ as its own line — $0.2+p+0.3=1$ — then solve: $p=0.5$. The mark scheme's structure would attach a method mark to writing the summation equation and an accuracy mark to solving it correctly, exactly the M-then-A shape §1 describes; a script that wrote only "$p=0.5$" with no summation line shown would face the identical objection Oct 2021's Q6(a) candidates faced on the Normal-distribution case.

#2.2 Sub-case B — a "show that" that resolves via a count, not a value

Confirmed directly (paraphrased; Oct 2021 Q3(c)): candidates who found the correct outlier fences did not go on to name the outliers that fall outside them, when the question specifically asked to "show that there are 3 outliers." The trap-taxonomy item already existing in the lesson (shown-result-not-fully-stated) names this, but with no accompanying worked numbers — the fences alone were never reconstructed there. Fresh micro-example, isolating the counting step from the interpolation step the lesson's own IQR chain already owns: ordered data 12, 15, 18, 19, 21, 22, 24, 25, 45, with $Q_1=15$ and $Q_3=24$ given (so no interpolation is being tested here). $IQR=9$; fences $15-1.5(9)=1.5$ and $24+1.5(9)=37.5$. Show that there is exactly 1 outlier: every value from 12 to 25 lies inside $[1.5,\,37.5]$; only 45 lies above 37.5. The boundaries alone show where an outlier would sit; naming 45 specifically is the separate, required step Oct 2021's candidates are recorded skipping.

#2.3 Sub-case C — the same discipline under different wording: "showing your working" with no printed target to reverse-engineer

A distinct real instance, confirmed directly from a mark scheme rather than an examiner-report quote: a real discrete-random-variable question instructs a candidate to find $\text{Var}(B)$ "showing your working" (verified verbatim mark-scheme wording, Jan 2025 Q1(d)) — with no numeric target printed in the stem to check the answer against. This is mechanically different from sub-cases A and B, where a printed answer is what makes bare working risky: here nothing is printed, so a wrong final number is simply wrong, yet the instruction still requires every intermediate step to be visible, not only the final value. Fresh micro-example: a random variable $X$ takes value $0$ with probability $0.6$ and $1$ with probability $0.4$. Find $\text{Var}(X)$, showing your working. Method: $E(X)=0(0.6)+1(0.4)=0.4$; $E(X^2)=0^2(0.6)+1^2(0.4)=0.4$; $\text{Var}(X)=E(X^2)-[E(X)]^2=0.4-0.16=0.24$. A script that wrote only "$\text{Var}(X)=0.24$" would satisfy an ordinary find question's minimum requirement (§2.4 below) but not this specific instruction, which names "showing your working" as its own explicit demand independent of whether the final answer is right.

#2.4 Sub-case D — the necessary converse: when a bare answer does score full marks, and exactly how conditional that is

This is the boundary case that defines where the rest of this taxonomy applies, and it does not live in the show-that lesson at all — it was added, during that lesson's own coverage audit, to the sibling Normal-distribution lesson's trap-taxonomy instead (per the facts bank's per-lesson audit log, 2026-09-12 entry for wst01-normal-distribution-standardisation-and-conditional-probability), so it is genuinely new material for a document about this exact topic. On an ordinary find/calculate part (not phrased as "show that"), the real Jan 2021 WST01 Q3(a) mark scheme awards full marks for a bare correct answer with no working at all — "Ans only 3/3," verified verbatim, for an answer in the range 0.0692 to 0.0694. But the same paper's Q3(b) shows this allowance is precision-conditional, not unconditional: a bare "23.6" earns only M1B0A1 (2 of 3 marks), while a bare "awrt 23.60" earns the full 3/3 — the extra trailing zero, proving four-decimal-place accuracy rather than three-significant-figure rounding, is what the mark scheme is actually checking for when no working is shown. The teaching point this adds to the lesson's own discipline: skipping working is genuinely safe only when the final figure is both exactly correct and carries enough precision to prove itself without help — a bar that a "show that" question's printed target can never clear, since the printed target's precision was fixed by the question, not produced by the candidate.

#3. Cross-qualification corroboration: the same discipline, different mark-code notation

Two other Pearson IAL papers' own verified-facts files (read for this document as corroboration only, not as WST01 evidence, per this course's established convention from the mathematical-modelling deep-dive) show the identical discipline enforced under a different mark-code label:

• Mechanics (WME01) carries a standing rubric, repeated in near-identical form across five separate series' examiner reports: a "hence show that" instruction requires a full explanation using the earlier parts of the question, not merely reaching the printed target (paraphrased; the facts bank's own citation spans Jan 2020 through Jun 2024). This is the same "answer alone proves nothing" logic §1 states, applied to Mechanics rather than Statistics.
• Pure Mathematics (WMA12) encodes exactly the same idea with a different mark-code symbol: a real WMA12 mark scheme (Jan 2021 Q9(b)(i)) awards an M1 for substituting a given point into an equation and attempting to expand it, then an A1* — not cso — for reaching the printed target "with no errors." A1* (answer-given, "ag") is the Pure/Mechanics-side notation for exactly the mark WST01 calls cso; both encode the identical rule (§1) with a different symbol, confirming this is a shared Pearson marking convention applied qualification-wide, not a WST01-specific invention, and that the notation — not the logic — is what varies by paper.
• The same WMA12 audit independently confirms sub-case A's reverse-engineering failure (§2.2 of this document's WST01 evidence, sub-case B's sibling) generalises across papers: its own lesson coverage gap noted that jumping straight to a printed algebraic target without showing the expansion step is exactly what a fudged, reverse-fit answer would look like — the identical shape as WST01's own reverse-engineered-ages trap (Oct 2021 Q3(b)), on a completely different topic and paper.

#4. Synthesis — every real angle this exact topic has actually been tested from in WST01

Following this course's own stated frequency convention (signal-frequency-and-boundaries.md): "N of 6" means confirmed by a specific citation in N of the 6 WST01 series with a fully-read examiner report (Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024).

Honest frequency statement. Some instance of this discipline — a specific worked question, a general comment, or the converse boundary case — is confirmed in 4 of the 6 fully-read examiner-report series (Jan 2021, Oct 2021, Jan 2023, Jun 2024); no citation was found for Jun 2019 or Jun 2022 in the facts bank as it stands. This is a lower bound on a partially-read archive (8 of 14 series have no located examiner report, per the facts bank's own §3/§8), not a claim the discipline was absent from either uncited series.

#5. Honest boundaries — where the real evidence currently runs out

• Jan 2023 Q3(a)/Q4(i)(a) is cited once, by series and question number, in the facts bank's own §6 cross-cutting synthesis paragraph as an "algebra" instance of this discipline — but no verbatim examiner-report or mark-scheme quote for that specific instance survives anywhere else in the document. It is recorded here as a real, named citation, not built into a worked micro-example, because doing so would require inventing detail the source does not supply.
• Jun 2024 Q3(c) ("coding," per the same §6 sentence) has the identical problem: named once, no supporting quote located elsewhere in the facts bank. Flagged rather than filled in.
• No likelihood percentages or grade boundaries are stated anywhere above. Frequency claims use only "confirmed in N of 6 series checked" language, per this course's own standing convention; signal-frequency-and-boundaries.md §2 already records that no real WST01 grade-boundary data exists in the source material at all.
• The WMA12/WME01 material in §3 is cross-paper corroboration, not WST01 evidence — flagged explicitly there and again here so neither is mistaken for a WST01 citation on a future re-read of this document.
• 8 of the 14 WST01 mark-scheme series have no independently-verified examiner report read yet (per the facts bank's own §3/§8); the "4 of 6" figure in §4 is a lower bound on a partially-searched archive.

#Sources

• research/veridian/WST01-verified-facts.md — §1 (mark-code abbreviations), §4 (mark-scheme conventions, cso/M/A definitions), §5 Section 2 (Oct 2021 Q3(b)/(c)), Section 4 (Jun 2024 Q4(c)), Section 5 (Oct 2021 Q4(d), Jan 2025 Q1(d)), Section 6 (Oct 2021 Q6(a)), §6 (the cross-cutting synthesis paragraph and its Jan 2023/Jun 2024 citations), §8 (flagged gaps), and the 2026-09-12 audit-log entries for show-that-answer-discipline.ts and wst01-normal-distribution-standardisation-and-conditional-probability (source of the Jan 2021 Q3(a)/(b) "Ans only 3/3" / precision-conditional finding).
• content/veridian/curriculum/wst01/show-that-answer-discipline.ts — read in full to confirm what the taught lesson already covers.
• content/veridian/curriculum/wst01/normal-distribution-standardisation-and-conditional-probability.ts — grepped and read for its own show-that-standardisation-not-shown trap-taxonomy item, source of §2.4's converse case.
• content/veridian/technique-hub/wst01/codex-formula-and-method-bank.md, forge-exam-technique-guide.md, signal-frequency-and-boundaries.md — read/grepped for existing show-that coverage and this course's frequency-reporting convention, reused in §4 above.
• content/veridian/question-bank/wst01.ts — grepped; no "show that" item found there.
• Cross-paper corroboration only, not WST01 evidence: research/veridian/WMA12-verified-facts.md (Jan 2021 WMA12/01 Q9(b)(i) mark-scheme audit); research/veridian/WME01-verified-facts.md ("hence show that" standing rubric note, §4 item 1).