Three hours, five questions, and a blank final part
A candidate sitting the 3-period Mathematics written paper has 180 minutes. Section A has four compulsory short questions worth 40 marks in total; Section B asks candidates to choose two of three extended problems, each worth 30 marks. In mock conditions the candidate's average performance is: A1 8/10 in 15 min; A2 6/10 in 25 min; A3 9/10 in 20 min; A4 4/10 in 30 min; B1 22/30 in 40 min; B2 18/30 in 45 min; B3 25/30 in 55 min. The candidate tends to spend extra time checking A questions and has twice run out of time before finishing Section B. The marking scheme gives method marks, so a partly completed extended problem can still earn substantial credit. The candidate wants to maximise the expected total and has no extra time. A calculator is allowed. The invigilator warns at 30 minutes remaining.
1. Using the practice data, recommend which two Section B problems to attempt and propose a minute-by-minute time budget for the 180 minutes. Justify the choice with expected marks per minute.
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Marks per minute from the practice data:
- A1: 8/15 ≈ 0.53; A2: 6/25 = 0.24; A3: 9/20 = 0.45; A4: 4/30 ≈ 0.13.
- B1: 22/40 = 0.55; B2: 18/45 = 0.40; B3: 25/55 ≈ 0.45.
Section B combinations: B1 + B3 = 47 marks in 95 min; B1 + B2 = 40 marks in 85 min; B2 + B3 = 43 marks in 100 min. B1 + B3 gives the highest expected total and the best marks per minute, so choose B1 and B3.
The practice times sum to 90 min for Section A and 95 min for the chosen B problems, which is 185 min, so 5 minutes must be cut. A defensible budget is: A1 15, A2 20, A3 20, A4 20 = 75 min; B1 40, B3 55 = 95 min; total 170 min, leaving a 10-minute buffer for checking and for finishing a method line. This protects the high-yield A1 and A3, caps the low-yield A4, and preserves the full time for B3. The expected total is roughly 24–25 from Section A plus 47 from Section B, around 71–72, with the buffer used only if the chosen B problems are secure.
2. The candidate is tempted to spend 10 extra minutes on A4 because it feels unfinished. Evaluate this temptation using the marginal expected marks and the risk of losing Section B marks.
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A4 currently earns 4 marks in 30 minutes, about 0.13 marks per minute. Ten extra minutes might raise it from 4 to 6 marks, a marginal gain of about 2 marks, or 0.2 marks per minute. That is below B1 at 0.55 and B3 at 0.45 marks per minute. If the 10 minutes come from B3, the expected loss is about 10 × 0.45 = 4.5 marks, plus the risk of losing method marks on a partly written solution. The net effect is negative.
The temptation is understandable because A4 feels unfinished, but the marking scheme rewards method marks, so an unfinished A4 is not worth sacrificing a started B3. The candidate should spend the extra time on A4 only if it comes from the 10-minute buffer and both chosen B problems are already secure. Otherwise, the correct judgement is to stop A4 at the planned cap and move to Section B.
3. Propose a checkpoint rule for the 30-minute warning that protects the candidate from the observed failure mode. Explain how the rule would work in practice.
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Checkpoint rule: when the invigilator gives the 30-minute warning, all Section A work stops immediately. The candidate must already have started the second chosen B problem; if not, they start it at that moment, beginning with the parts that carry method marks. If B3 is in progress, they write the next method line rather than rereading the whole question. The final 5 minutes are used to check the chosen B problems, not A.
In practice, the rule works because the observed failure mode is overchecking Section A and running out of time before Section B. A hard stop removes the moment-by-moment temptation. The candidate should rehearse the rule in timed mocks: at 30 minutes remaining, say aloud the next B step and write it. This turns the warning into a switching cue rather than a general reminder. The rule also protects method marks, because even a partly completed B problem can earn substantial credit.