Worked Exemplars

Watch the same question solved two ways — the careless path and the precise path — and the gap between 1300 and 1600 becomes a set of visible, copyable moves. These exemplars stitch the FORGE methods together on complete questions. Every item is MERIDIAN-original (not a real test question); each shows the wrong-reasoning path, the right path, and the exact move that separates them.

Annotation key: ✗ = trap reasoning · ✓ = correct move · ▶ = the decisive step.

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#R&W

#EX-1 · Boundaries (grammar)

Stem: "The startup scaled rapidly ___ within two years it employed three hundred people." (A) , (B) ; (C) : (D) , and that

• ✗ ~700: picks (A) — "a pause fits." → comma splice (IC + IC). [T: bare comma between sentences]
• ▶ Boundary test: "The startup scaled rapidly" = IC; "within two years it employed three hundred people" = IC. IC + IC needs a full stop.
• ✓ (B) semicolon. (C) colon would need the second part to explain/list — it's a separate fact, so semicolon is cleaner; (A) splice; (D) ungrammatical. Move: labelled both sides IC → full stop. [1 R&W question; Module-1 ceiling risk]

#EX-2 · Inference

Passage: "The survey found that employees who used the new tool reported higher satisfaction. However, only employees who volunteered to trial the tool were surveyed. Therefore ___" (A) the tool causes higher satisfaction. (B) all employees would prefer the tool. (C) the reported satisfaction may reflect who chose to participate rather than the tool itself. (D) the tool should be adopted company-wide.

• ✗ ~700: (A) — "higher satisfaction → tool works." [T3 correlation→causation; T2 one-step-too-far — ignores the self-selection flagged in sentence 2]
• ▶ What MUST be true given only this? The sample self-selected (volunteers), so the result can't isolate the tool's effect.
• ✓ (C) — the cautious, fully-supported conclusion. (A) causal overreach; (B) too-extreme/outside; (D) a recommendation, not an entailment. Move: chose the modest claim and used the "volunteered" detail. [the signature inference move]

#EX-3 · Command of Evidence (textual)

Claim: "The researcher argues the city's air improved because of the new transit line, not the factory closure." Which finding best supports this? (A) Air quality improved the year the transit line opened. (B) Air quality improved most in districts far from the closed factory but near the new line. (C) The factory had been a major polluter. (D) Public transit use rose after the line opened.

• ✗ ~700: (A) — "improvement + transit line, same year." [T5 on-topic, wrong claim — timing alone doesn't separate transit from closure]
• ▶ The claim must distinguish transit from factory closure. Evidence that isolates the line = improvement where the line reaches but the factory's effect wouldn't.
• ✓ (B) — geographically separates the two causes. (A) doesn't isolate; (C) supports the rival explanation; (D) shows usage, not air effect. Move: pinned the specific claim (transit, not closure) and tested each option against it.

#EX-4 · Rhetorical Synthesis

Goal: "emphasize a contrast between the two methods." Notes: Method X is cheap but slow; Method Y is fast but expensive. (A) "Method X is cheap, and Method Y is fast." (B) "Although Method X is inexpensive, it is far slower than the costlier Method Y." (C) "Both methods have trade-offs." (D) "Method X and Method Y are widely used."

• ✗ ~700: (C) — "trade-offs sounds balanced." [T9 right-info-wrong-purpose — states that there are trade-offs, doesn't contrast them]
• ▶ Goal = contrast. The choice must set X against Y on shared dimensions.
• ✓ (B) — "Although… far slower than…" directly contrasts cost vs speed. (A) lists, no contrast; (C) names trade-offs without drawing one; (D) off-goal. Move: judged each choice against the literal goal "contrast."

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#MATH

#EX-5 · Advanced Math (Desmos, quadratic)

Problem: "The function f(x) = x² − 8x + 12. What is the minimum value of f?"

• ✗ ~700: computes f(0)=12, answers 12. [misread — f(0) is not the minimum]
• ▶ Minimum of an upward parabola = the vertex y-value. Vertex x = −b/2a = 8/2 = 4; f(4) = 16 − 32 + 12 = −4. Desmos: graph f; click the vertex dot → (4, −4).
• ✓ −4. Move: knew "minimum = vertex," used x=−b/2a (or the Desmos dot), answered the value (y), not f(0). [a dropped-concept trap; Module-1 ceiling risk]

#EX-6 · Problem-Solving & Data (conditional probability)

Two-way table: 50 students. Took Spanish: 30 (passed 24, failed 6). Took French: 20 (passed 12, failed 8). "Given a student passed, what is the probability they took French?"

• ✗ ~700: 12/20 = 0.6. [T: wrong denominator — that's "given French, P(pass)", the reverse]
• ▶ "Given passed" → denominator = all who passed = 24 + 12 = 36. French-and-passed = 12.
• ✓ 12/36 = 1/3. Move: conditioned on the right group (passers), not French. (Annotate "given passed" → denominator = passers.)

#EX-7 · Grid-in format

Result obtained: x = 9/2.

• ✗ ~700: types "4 1/2". [mixed number → engine reads 41/2 → wrong; full question lost]
• ✓ types 9/2 (or 4.5). Move: mixed numbers rejected → exact fraction (no rounding risk) → confirmed the ask. [format slip = −1 with no warning]

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#HOW TO USE THESE

1. Cover the ✓ lines; attempt each cold. 2. Compare your reasoning to the ✗/▶/✓ path. 3. If your path matched the ✗, log the trap number (Reading Trap Taxonomy) or the careless signature (Careless-Error Elimination). 4. Re-attempt in two days (spaced).

#REFERENCE CARD — EXEMPLARS

Pattern in every item: the ✗ path picks the plausible/obvious answer; the ▶ step reframes
(boundary test · must-be-true · pin-the-claim · obey-the-goal · vertex=min · right denominator · grid format);
the ✓ answer is the proven/precise one. Copy the ▶ moves; they are the 1300→1600 gap.

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MERIDIAN · CODEX · WORKED EXEMPLARS | v1.0