Higher November 2024 Paper 2 Q13
13. Enrico and Hugo are both boxers.
At the start of a six-week training block:
- Enrico weighs exactly 170 pounds.
- Hugo weighs exactly 175 pounds.
After the six-week training block:
- Enrico has lost 9 pounds, correct to the nearest pound.
- Hugo has lost 12 pounds, correct to the nearest two pounds.
What is the greatest possible difference between Enrico’s percentage weight loss and Hugo’s percentage weight loss? [4]
| Scheme | Marks | Comments |
|---|---|---|
| Use of 8.5 AND 13 | B1 | |
| \(\dfrac{13}{175}(\times 100) - \dfrac{8.5}{170}(\times 100)\) \((= 7.4285..\% - 5\%)\) | M2 | Award M2 for \(\dfrac{170 - 8.5}{170}(\times 100) - \dfrac{175 - 13}{175}(\times 100)\) \((= 95 - 92.57..)(\%)\) M1 for either \(\dfrac{8.5}{170}(\times 100)\) OR \(\dfrac{13}{175}(\times 100)\) provided unambiguous or used to obtain the final answer May be seen as \(170 \times 0.05 = 8.5\) If B0, FT for M2 or M1 provided unambiguous or used to obtain the final answer provided: for M2: \(8 \leqslant\) ‘their 8.5’ \(\lt 9\) AND \(12 \lt\) ‘their 13’ \(\leqslant 14\). for M1: \(8 \leqslant\) ‘their 8.5’ \(\lt 9\) OR \(12 \lt\) ‘their 13’ \(\leqslant 14\). Award M1 for \(\dfrac{170 - a}{170}(\times 100) - \dfrac{175 - b}{175}(\times 100)\) provided \(8 \leqslant a \lt 9\) OR \(12 \lt b \leqslant 14\) |
| \(= 2.4(2\ldots)\) or \(2\frac{3}{7}\) (%) oe | A1 | CAO Allow 2(%) from correct working. If no marks, award SC1 for an answer of 0.697(5..)% or 0.7% from: \(\dfrac{11}{175}(\times 100) - \dfrac{9.5}{170}(\times 100)\) \((= 6.286...\% - 5.588\ldots\%)\) |
| (4) |
Corrected by Westie's Workshop
- The board's mark scheme printed “their 8.5’”. Changed to “‘their 8.5’” because the opening quotation mark was missing (in both the M2 and M1 lines).
Original: see the board's mark scheme PDF (link above).