Higher June 2024 Paper 2 Q19
19 \(G = \dfrac{c}{2f - 3h}\)
| \(c = 8\) | correct to the nearest whole number |
| \(f = 6.62\) | correct to 2 decimal places |
| \(h = 1.2\) | correct to 1 decimal place |
Work out the lower bound for the value of \(G\)
Give your answer correct to 3 decimal places.
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
| 7.5, 8.5, 6.615, 6.625, 1.15, 1.25 | B1 |
| \((G =)\dfrac{7.5}{2 \times 6.625 - 3 \times 1.15}\left(= \dfrac{7.5}{13.25 - 3.45} = \dfrac{7.5}{9.8} = \dfrac{75}{98}\right)\) | M1 |
| working required Answer: 0.765 | A1 |
| (3) | |
| (3 marks) |
Notes
B1: For a correct upper or lower bound
Allow \(8.4\dot{9}\) for 8.5, \(6.624\dot{9}\) for 6.625, \(1.24\dot{9}\) for 1.25 (corrected from the printed mark scheme: “6.6249 for 6.5”)
M1: \(\dfrac{LB_c}{2 \times UB_f - 3 \times LB_h}\) where \(7.5 \leqslant LB_c \lt 8\)
\(6.62 \lt UB_f \leqslant 6.625\), \(1.15 \leqslant LB_h \lt 1.2\)
SCB1 for \(\dfrac{7.5}{6.625 - 1.15}\) (= 1.369(8...)) [in addition to the first B1]
A1: awrt 0.765 dep on completely correct bounds (0.7653061224…)
dep on M1