4MA0 Higher January 2014 Paper 3 Q12
12
Diagram NOT accurately drawn
The diagram shows a shape made from triangle \(ABC\) and a semicircle with diameter \(BC\).
Triangle \(ABC\) is right-angled at \(B\).
\(AB = 7.6\) cm and \(AC = 9.5\) cm.
Calculate the area of the shape.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
\(\sqrt{9.5^2 - 7.6^2}\) or \(\sqrt{90.25 - 57.76}\) or \(\sqrt{32.49}\) or \(\sqrt{32.5}\) | M1 |
| (BC = ) 5.7 | A1 |
| \(\frac{1}{2} \times 7.6 \times \text{“}5.7\text{”}\) or 21.6(6) or 21.7 | M1 |
| \(\dfrac{1}{2} \times \pi \times \left(\dfrac{\text{“}5.7\text{”}}{2}\right)^2\) or 12.7(587...) or 12.8 | M1 |
| 34.4 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: dep on first M1
or eg. \(ACB = \sin^{-1}\left(\dfrac{7.6}{9.5}\right)\) (= 53.1...)
and
\(\dfrac{1}{2} \times 9.5 \times \text{“}5.7\text{”} \times \sin \text{“}53.1\text{”}\)
M1: dep on first M1
A1: for answer rounding to 34.4
(\(\pi \to\) 34.4187... 3.14 \(\to\) 34.4123...)