Deep Dive: Modelling Assumptions and Show That Discipline

Provenance (2026-09-29): read research/veridian/WME01-verified-facts.md in full — §1 (spec text), §4 topic 1 (modelling assumptions), §4 topic 6's rod cross-reference, §7 ("topics genuinely thin"), and both dated audit entries in §9 for modelling-assumptions-and-show-that-discipline.ts and momentum-impulse-sign-convention.ts (2026-09-12); read content/veridian/curriculum/wme01/modelling-assumptions-and-show-that-discipline.ts (649 lines) in full; read content/veridian/technique-hub/wme01/forge-exam-technique-guide.md, codex-formula-and-method-bank.md and signal-frequency-and-boundaries.md for existing coverage; grepped content/veridian/question-bank/wme01.ts and confirmed it has no spec-1.1-tagged item. No new primary-source PDF was independently fetched for this document — every citation below traces to the facts bank or the three technique-hub documents just named, each already checked against the primary Pearson PDFs per their own headers. Not affiliated with or endorsed by Pearson Edexcel.

#CODEX Deep-Dive: Modelling Assumptions And Show That Discipline (WME01 · Mechanics 1)

#1. Scope, and what this adds

Spec item 1.1 ("mathematical models in mechanics") is the thinnest topic in this unit's archive: across the 17 series this course's research has reviewed in some depth, it never anchors a full question on its own — it only ever rides as a late sub-part on a kinematics or dynamics question that has already been solved (facts bank §4 topic 1, §7). In the two series mapped question-by- question in full (Jan 2025, Jun 2025), modelling scored 0 of 2 as a standalone topic — every other spec sub-topic scored 2 of 2 (signal-frequency-and-boundaries.md §1). "Hence show that" discipline is the second strand this course bundles into the same lesson, and it is genuinely unit-wide rather than topic-specific.

content/veridian/curriculum/wme01/modelling-assumptions-and-show-that-discipline.ts already teaches both strands in full — vocabulary-as-consequence prose, a 10-mark incline-and-pulley marked solution threading a modelling critique through a show-that derivation, three MCQs, a four-item trap taxonomy — and codex-formula-and-method-bank.md §1.2 already has the 12-term vocabulary table. Neither is reproduced here. This document's job is the piece neither one does:

1. A coverage map of the 12 named vocabulary terms against real exam anchors — which one has actually been the subject of a term-specific critique question, and which are definitional only.
2. A taxonomy of "show that" target types, pulling together real per-question anchors that sit scattered across four different spec sub-topics and three different course documents — the lesson itself only names its own Oct 2019 anchor plus a five-series hedge; it does not cross-reference the further real anchors that a sibling lesson's audit trail and the FORGE guide's own mark tables independently confirm.
3. An honest account of what the archive does not support, so nothing here reads as more evidenced than it is.

#2. The real theory, briefly

Spec 1.1's own guidance names a list of terms and states, in substance, that a candidate should know not just the word but the assumption it licenses. That single idea — a modelling term is a stated trade-off, not a label — is the whole of the theory here; the lesson file's teach block already spells out each term's specific consequence (particle removes rotation from consideration; inextensible string forces equal accelerations; light smooth pulley forces equal tension; and so on) and is not repeated below. The second half of this topic, "hence show that," rests on one distinction: an ordinary "find" part marks the destination, a "show that" (ag, "answer given") part marks the argument — because the destination is already printed on the page, reaching it proves nothing by itself.

#3. Vocabulary-term coverage map

Of the 12 terms spec 1.1 names, the archive reviewed for this course supports exactly one term-specific critique anchor:

This is an honest gap, not a claim that Pearson has never tested the other 11 terms directly — 6–7 of the 17 series in the facts bank's own archive were keyword-searched rather than read start- to-finish (facts bank sourcing note, §5/§8), so a term-specific anchor for e.g. bead-on-a-wire could exist in an unread series. It is not claimed here because it has not been found here.

#4. "Hence show that" — a taxonomy of real target types

The lesson's own framing cites one verified single-series anchor (Oct 2019 Q6) plus a hedge — examiner reports across five series (Jan 2020, Jan 2023, Oct 2022, Jun 2024, Oct 2023) each repeat "some form of" the same standing instruction, not five identical verbatim sentences. Sitting outside that lesson's own citations, three further real, named, per-question anchors for this same command word exist elsewhere in this course's research — in a sibling lesson's audit trail and in the FORGE guide's mark-by-mark tables — and collecting all of them together shows "show that" targets fall into four genuinely distinct shapes, not one:

#4.1 Plain numeric target, reached by cross-part substitution

Anchor: Oct 2019 Q6(c) — a value found in an earlier part is substituted into a further equation to reach the part's own printed numeric target; coded a plain M1 (a fresh substitution), not a dependent DM1 (which requires two things set up within the same part). Already fully illustrated with a worked, mark-coded example in the lesson's own part (c) (finding $T$ by substituting the acceleration found in part (b)) — not re-illustrated here.

#4.2 Special/boundary-value target

Anchor: Oct 2022 Q3(a) — "show that $F=0$," i.e. showing an applied force exactly balances a weight component so that no friction is needed, immediately followed by a part (b) where friction is at its limiting value on the same setup. This is a genuinely different target shape from 4.1: a degenerate value (zero) rather than a generic number, used specifically to test whether a candidate can tell equilibrium-without-friction apart from limiting friction. Already fully covered, with its own worked example (a balancing parallel force reducing $F$ to zero), in friction-equilibrium-and-motion-on-a-rough-plane.ts — not re-illustrated here.

#4.3 Inequality / relational target on an unknown parameter

Anchor: Jan 2020 Q1(c), spec 4.3 (momentum/impulse) — "hence show that $m_2 > \tfrac34 m_1$," M1 for the correct sign-inequality on a found velocity, A1* for the given-answer algebra. This anchor sits in momentum-impulse-sign-convention.ts's own audit trail (facts bank §9), not in the modelling lesson, and neither lesson cross-references it as an instance of the same command word. That sibling lesson's own trap-taxonomy item does apply the mechanism to its own scenario — isolating a velocity from conservation of momentum and requiring a stated sign on it — but stops there, without carrying the algebra through to a concluded numeric bound on the mass ratio. The micro-example below completes that missing last step: VERIDIAN-original throughout, and using a different mass ratio and collision setup from the real $\tfrac34$ figure:

Particles A (mass $m$) and B (mass $km$, $k>0$) move toward each other in a straight line, A at $6$ m s⁻¹ and B at $2$ m s⁻¹, and collide, coalescing into one particle. By conservation of momentum, $6m - 2km = (m+km)v$, so $v = \dfrac{6-2k}{1+k}$. Given that the combined particle continues moving in A's original direction, hence show that $k < 3$.

Since $k>0$, the denominator $1+k$ is positive, so $v>0$ requires $6-2k>0$, i.e. $k<3$ — a bound on the unknown mass ratio, not a number, reached by turning a physical requirement (direction of travel) into a sign condition on the algebra already set up for an earlier part.

#4.4 Exact-fraction-precision target

Anchor: Jun 2025 Q6, spec 4.4/5.2/5.3 (friction on an incline) — the mark scheme states the final given-answer mark can only be earned from working carried through in the exact fractional form of $\sin\alpha$/$\cos\alpha$ (e.g. $\tfrac35$, $\tfrac45$); a decimal substitution anywhere in the chain breaks the mark even if it happens to round to the right-looking answer (forge-exam-technique-guide.md's rounding-convention section). Jan 2025 Q6 is a second, independent "show that a limiting-angle result" question in the same sub-topic (forge-exam-technique-guide.md §1), though the exact-fraction requirement is confirmed in the sources read for this document only for Jun 2025. This is a precision discipline, distinct from all three shapes above — the target form itself, not just the destination, is part of what's being marked. No worked example of this specific fraction-exactness discipline exists elsewhere in this course's WME01 material; a short, VERIDIAN-original illustration:

A block rests in limiting equilibrium on a rough plane inclined at $\alpha$, where $\sin\alpha=\tfrac35$, $\cos\alpha=\tfrac45$. Hence show that $\mu=\tfrac34$.

Resolving perpendicular to the plane: $R = mg\cos\alpha$. At the limiting value, $F=\mu R = mg\sin\alpha$. Dividing, $\mu = \dfrac{\sin\alpha}{\cos\alpha} = \dfrac{3/5}{4/5} = \tfrac34$ — note $m$ and $g$ cancel entirely, so the result depends only on the angle. Carried through as $0.6/0.8$ instead, the division still gives $0.75$ here — but the real Jun 2025 mark scheme's own condition is that the fractional form must be used throughout the chain, not that a decimal substitution always happens to survive; it is the exactness of the method, confirmed for that series, that is being marked, not merely whether this particular quotient rounds cleanly.

Four distinct target shapes, five named series/questions (Oct 2019, Jan 2020, Oct 2022, Jan 2025, Jun 2025) — a broader real base than either lesson currently cross-references on its own, though still five confirmed points inside a 17-series archive, not a majority of it.

#5. "Critique the model" — organising the one real anchor's own answer set

Oct 2019 Q6(e) is the sole real anchor for the modelling-critique question type, and its own credited/rejected answer list is already quoted and taught in the lesson's mechanism block. Sorted into categories, rather than as a flat list, it separates into exactly two credited shapes and three rejected shapes:

Two of the five credited answers do not relax a simplification the stem states in so many words — they relax an assumption baked into treating the model's own boundary/timing data as exact. The mark scheme also caps credit at two named ways and deducts one mark per incorrect extra beyond that count, so a naming-only part rewards precision, not elaboration. Both facts are already in the lesson's mechanism block and its naming-more-modifications-than-the-question-asked-for trap; the table above is a reorganisation of that same material into an explicit two-credited-category / three-rejected-category structure, not new sourcing.

#6. What has not been seen

Stated plainly, since padding this section is exactly what this document must not do:

• No standalone spec-1.1 question exists anywhere in the 17-series archive reviewed for this course, and it scored 0 of 2 in the two series mapped in full. This is the central honest fact about this topic, and the reason this document is short.
• 11 of the 12 named vocabulary terms have no confirmed term-specific critique anchor in that same archive (§3 above) — only the light rod does.
• The "hence show that" five-series citation is a hedge, not five identical quotes — the facts bank itself frames it as each report repeating "some form of" one instruction, and this document repeats that same hedge rather than upgrading it.
• No citation exists, for WME01 specifically, of a candidate fabricating or reverse-fitting a show-that derivation backward from the printed answer — the lesson's own header already flags this gap honestly, and it is repeated here rather than invented around.
• No question-bank entries exist yet for spec 1.1 in content/veridian/question-bank/wme01.ts.
• No per-topic mark-weighting percentage exists for the wider 17-series archive (signal-frequency-and-boundaries.md itself declines to build one, and this document does not manufacture one); the only frequency claim made anywhere above is the "0 of 2" / "5 of 17-series- archive" style count, not an invented likelihood.

#7. Cross-references

• Full worked exemplars, prequestions, MCQs, four-item trap taxonomy: modelling-assumptions-and-show-that-discipline.ts.
• 12-term vocabulary table: codex-formula-and-method-bank.md §1.2.
• Paper-position/frequency ("0 of 2"): signal-frequency-and-boundaries.md §1.
• Sibling "show that" anchor (§4.3 above): momentum-impulse-sign-convention.ts's own sign-as-mass-constraint-not-just-speed-fix trap.
• Sibling "show that F=0" worked example (§4.2 above): friction-equilibrium-and-motion-on-a-rough- plane.ts.

#Sources

research/veridian/WME01-verified-facts.md §1 (spec text), §4 topic 1, §4 topic 6 (rod cross-reference), §7, and the two dated 2026-09-12 audit entries in §9 for modelling-assumptions-and-show-that-discipline.ts and momentum-impulse-sign-convention.ts; content/veridian/technique-hub/wme01/forge-exam-technique-guide.md (Jan 2025/Jun 2025 question-by-question mark tables and the g/rounding-convention section); signal-frequency-and- boundaries.md §1 (the "0 of 2" topic-frequency table); codex-formula-and-method-bank.md §1.2 (vocabulary table, referenced, not reproduced). No new primary-source PDF was fetched for this document.