4MA0 Higher June 2017 Paper 4 Q11
11
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on a circle.
\(ABCD\) is a square of side 7 cm.
Work out the total area of the shaded regions.
Give your answer correct to the nearest whole number.
(5)
| Scheme | Marks |
|---|---|
eg \((d^2 =)\;7^2 + 7^2\) or \(r^2 + r^2 = 7^2\) or \(\cos 45 = \dfrac{7}{d}\) or \(\sin 45 = \dfrac{7}{d}\) or \(\cos 45 = \dfrac{r}{7}\) or \(\sin 45 = \dfrac{r}{7}\) | M1 |
eg \((d =)\sqrt{98}\) (9.899..) or \((r =)\sqrt{\dfrac{49}{2}}\) (=4.9...) or \(d = \dfrac{7}{\cos 45}\) or \(d = \dfrac{7}{\sin 45}\) or \(r^2 = 24.5\) or \(r = 7\cos 45\) or \(r = 7\sin 45\) | M1 |
| eg. \(\pi \times \text{“}4.9..\text{”}^2\) (=76.969...) | M1 |
| eg. \(\pi \times \text{“}4.9..\text{”}^2 - 7^2\) | M1 |
| 28 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: Start of method to find radius or diameter of circle
M1: complete method to find radius or diameter or \(r^2\)
(if method to find radius or diameter shown then allow use of radius = 5 for method marks only)
M1: For method to find area of circle or semi-circle or quarter circle – use of radius from correct working
M1: for complete method
A1: 27.9 – 28