Two Aggregate Formulas, One Re-sit: The Bonus That Cannot Break a Subject Floor
A candidate has one sitting of marks, each out of 100: Mathematics 82, Physics 68, Chemistry 74, English 55. Two programmes publish different aggregate formulas.
Electrical Engineering: Mathematics 40%, Physics 30%, Chemistry 20%, English 10%; qualifying aggregate 70; no subject floor.
Computer Science: Mathematics 30%, Physics 25%, Chemistry 15%, English 30%; qualifying aggregate 70; plus English at least 60.
A sports bonus of 2 aggregate points is added when the raw aggregate is at least 68; it can never lift a candidate past a subject floor. A re-sit mark replaces the original mark completely, and every calculation uses unrounded marks, with the final aggregate rounded to one decimal place.
Her teacher says: 'Re-sit Mathematics. Two more marks there and Computer Science is yours.' She has time for exactly one re-sit and wants the least risky route to a place.
1. Compute both aggregates from the current marks and decide which programme, if either, she currently qualifies for.
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Electrical Engineering: 0.40(82) + 0.30(68) + 0.20(74) + 0.10(55) = 32.8 + 20.4 + 14.8 + 5.5 = 73.5 73.5 ≥ 70 and there is no subject floor, so she qualifies for Electrical Engineering now.
Computer Science: 0.30(82) + 0.25(68) + 0.15(74) + 0.30(55) = 24.6 + 17.0 + 11.1 + 16.5 = 69.2
Raw 69.2 is below 70, but it is at least 68, so the sports bonus applies: 69.2 + 2 = 71.2, which clears 70. That is the trap: the aggregate now looks fine, yet the second condition - English at least 60 - is failed, and the rules state the bonus cannot lift a candidate past a subject floor. English is 55.
Conclusion: she qualifies for Electrical Engineering only; Computer Science is blocked by the English floor, not by the aggregate.
2. Test the teacher's claim that two extra Mathematics marks secure Computer Science. Quantify everything.
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Mathematics 82 + 2 = 84.
New Computer Science aggregate: 0.30(84) = 25.2; 25.2 + 17.0 + 11.1 + 16.5 = 69.8 raw. With the bonus: 69.8 + 2 = 71.8, which passes 70.
So on the aggregate the teacher is right - but only because the bonus is doing the work. Two problems:
- The English floor is untouched. A Mathematics re-sit cannot change English 55 into 60, and the rules explicitly say the bonus cannot carry a candidate past a subject floor. She would still be rejected.
- The teacher's arithmetic is looser than it sounds. Without the bonus, the raw aggregate needed is 70, i.e. 0.30m + 44.6 = 70, so m = 84.67, meaning 85 in Mathematics, not 84. Two marks give 69.8, which fails on raw aggregate alone.
So the claim fails twice over: it understates the Mathematics requirement and it ignores the condition that actually blocks her. A re-sit is a scarce resource, and this plan spends it on the constraint that is not binding.
3. Recommend the single re-sit that gives the least risky route to Computer Science, and prove that it does not endanger her Electrical Engineering place.
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Recommendation: re-sit English and target 60.
Why it is sufficient. English 60 clears the subject floor exactly. Recompute Computer Science: 0.30(82) = 24.6; 0.25(68) = 17.0; 0.15(74) = 11.1; 0.30(60) = 18.0. Total = 24.6 + 17.0 + 11.1 + 18.0 = 70.7, which clears 70 without needing the bonus at all. The floor is satisfied at the same time, so both conditions fail together and both are repaired together.
Why the alternatives lose. A Mathematics re-sit needs 85 to reach 70 raw (a 3-mark gain) and still leaves English at 55, so it cannot succeed at any Mathematics mark. Crashing the Mathematics paper upward would only change the margin, not the eligibility: with English below 60, no aggregate value matters.
Check the downside. English 60 under the Electrical formula: 32.8 + 20.4 + 14.8 + 0.30(60) = 32.8 + 20.4 + 14.8 + 6.0 = 74.0, still well above 70, so the place she already holds is not put at risk.
The least risky route is therefore the one that moves the binding constraint - the 55 in English - and overshoots it by zero, not the one that adds points to a subject that is already the strongest on the sheet.