Written Exam Clash: Economics and History on Consecutive Days
Tomás is an s7 student with two written exams on consecutive days: Economics on Day 1 morning and History on Day 2 morning. His school weights the final mark as 40% preliminary mark and 60% written exam. His preliminary marks are Economics 82/100 and History 65/100. He wants a final grade of at least 85 in Economics (required for his university Economics programme) and at least 70 in History. His practice exam scores are Economics 80/100 and History 72/100. He has two days of revision time left and must decide how to allocate his study hours between the two subjects. He estimates that each hour of focused revision adds roughly 1 point to his written exam score in either subject, up to a maximum of 90. He has 10 hours available. He also needs sleep and rest. He is confident in History content but finds Economics data-response questions challenging. He needs to decide how many hours to allocate to each subject to maximize his chances of meeting both targets.
1. Calculate the written exam score Tomás needs in each subject to reach his final grade targets. Then, using his practice scores and the 1-point-per-hour estimate, determine how many hours he should allocate to each subject to meet both targets. Assume he can allocate a minimum of 0 hours and a maximum of 10 hours.
Read the worked answer
Required written scores:
- Economics: 0.4 × 82 + 0.6 × W_e = 85 → 32.8 + 0.6W_e = 85 → 0.6W_e = 52.2 → W_e = 87.
- History: 0.4 × 65 + 0.6 × W_h = 70 → 26 + 0.6W_h = 70 → 0.6W_h = 44 → W_h = 73.33.
Gaps from practice scores:
- Economics: 87 − 80 = 7 points → needs 7 hours.
- History: 73.33 − 72 = 1.33 points → needs about 1.33 hours, round up to 2 hours.
Total hours needed = 7 + 2 = 9 hours, within his 10-hour budget. He should allocate 7 hours to Economics and 2 hours to History, leaving 1 hour for rest or a final review. This allocation meets both targets if his 1-point-per-hour estimate holds. He should monitor his progress and adjust if Economics practice scores improve faster than expected.
2. Suppose Tomás only needs a final grade of 80 in Economics (not 85). How would the allocation change? Explain the trade-off.
Read the worked answer
If the Economics target is 80: 0.4 × 82 + 0.6 × W_e = 80 → 32.8 + 0.6W_e = 80 → 0.6W_e = 47.2 → W_e = 78.67. His practice score of 80 already exceeds this, so he needs 0 additional hours to reach 80. He could then reallocate time to History to exceed 70, or use the time for rest. The trade-off: with a lower Economics target, the marginal benefit of revising Economics falls sharply. He might still revise Economics briefly to build a buffer (e.g., 1–2 hours) against exam-day nerves, but the bulk of his time should shift to History or other subjects. The allocation could become 0–2 hours Economics, up to 8 hours History, and the rest for rest. This reduces the risk of burnout and acknowledges diminishing returns. However, he should not completely ignore Economics, because a very low written score could still pull his final grade below 80 if his practice score overestimates his exam performance.