Mathematics Written: The Dependent Part C
In a four-hour mathematics written paper, 20 minutes remain. A candidate has finished all questions except two. The probability question has parts (a)–(c). Part (b) asked for P(B) and the candidate wrote 0.52. Part (c) says 'Hence find P(A|B)' and is worth 3 marks; using 0.52 gives 0.26. A quick recheck of part (a) suggests P(B) should be 0.35, which would give 0.14. A six-mark geometry proof is untouched; the candidate can see the first two steps but not the finish. The paper's instructions say to show all working. The candidate has a habit of losing method marks by crossing out correct early work. Ten minutes would be enough to redo part (b) carefully; the geometry proof would take at least 12 minutes to attempt fully.
1. Rank the three actions (redo (b), do (c), attempt geometry) and justify using mark value and dependency.
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Rank geometry first by mark value, but secure part (c) method marks before repairing part (b). The geometry proof is worth 6 marks, more than any single probability part, so it must be attempted. Part (c) is worth 3 marks and depends on part (b), but examiners often award method marks for a correct conditional-probability formula even with a wrong substituted value. Part (b) itself may be worth 2 or 3 marks, and the arithmetic recheck suggests 0.35 is correct. The efficient order is: write part (c) immediately using the current value so the formula and substitution are visible; then redo part (b) carefully; then update part (c); then attempt geometry. This avoids leaving part (c) blank and protects method marks if the redo fails. Do not cross out the original part (b) until the replacement is complete and clearly labelled.
2. Give a minute-by-minute plan for the last 20 minutes.
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0–2 minutes: write part (c) with the formula P(A|B) = P(A ∩ B)/P(B), substitute the current values, and state 0.26. 2–6 minutes: redo part (b) carefully from the given information and the part (a) check; if it gives 0.35, write the corrected calculation clearly. 6–8 minutes: update part (c) to 0.14, showing the substitution again. 8–18 minutes: attempt the geometry proof-write the given information, the construction, the first two congruence or similarity steps, and state what remains to be shown. 18–20 minutes: check that every answer is boxed or clearly stated and that no corrected value contradicts an earlier line. This plan accepts that the geometry proof may be incomplete but ensures it earns several method marks, while the probability question is left in a coherent state.
3. If she runs out of time, how should she present partial work in part (c) and the geometry proof to maximise credit?
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For part (c), leave a clean formula line, the substitution, and a boxed value, even if the value is based on an uncorrected part (b). Add a brief note only if it clarifies: 'using P(B) from part (b)'. Do not cross out the formula. For the geometry proof, write the 'Given' and 'To prove' lines, the construction or auxiliary line, and the first two logical steps with reasons. Then state the remaining goal in one sentence, for example: 'It remains to show that triangle X is congruent to triangle Y, which would give the required angle equality.' This converts an unfinished proof into visible method. Avoid starting a new approach in the final minute; incomplete but connected reasoning scores better than a fresh, unsupported claim.