Higher June 2025 Paper 2 Q22
22 The diagram shows a square inside rectangle \(ABCD\)
Diagram NOT accurately drawn
The total area of the region shown shaded in the diagram is \(X\) cm2
\(AB = 11.5\) cm correct to the nearest 0.5 cm
\(BC = 9.2\) cm correct to 2 significant figures
side of square = 4.1 cm correct to 2 significant figures
By considering bounds, work out the value of \(X\) to a suitable degree of accuracy.
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| 11.25, 11.75, 9.15, 9.25, 4.05, 4.15 | B1 |
| \(11.75 \times 9.25 - 4.05^2\) (= 92.285) | M1 |
| \(11.25 \times 9.15 - 4.15^2\) (= 85.715) | M1 |
| Working required Answer: 90 | A1 |
| (4) | |
| (4 marks) |
Notes
B1: for a correct bound
Accept
\(11.74\dot{9}\) for 11.75 or \(11.74\overline{9}\) for 11.75
\(9.24\dot{9}\) for 9.25 or \(9.24\overline{9}\) for 9.25
\(4.14\dot{9}\) for 4.15 or \(4.14\overline{9}\) for 4.15
M1: for a correct method to find the UB of \(X\), allow
\((11.5 \lt AB \leqslant 11.75) \times (9.2 \lt BC \leqslant 9.25) - \left((4.05 \leqslant s \lt 4.1)^2\right)\)
M1: for a correct method to find the LB of \(X\), allow
\((11.25 \leqslant AB \lt 11.5) \times (9.15 \leqslant BC \lt 9.2) - \left((4.1 \lt s \leqslant 4.15)^2\right)\)
A1: dep on M2
90 and both UB and LB correct using correct values 11.25, 11.75, 9.15, 9.25, 4.05 and 4.15