4400 Higher November 2005 Paper 3 Q14
14
Diagram NOT accurately drawn
The diagram shows a circle of radius 4 cm inside a square \(ABCD\) of side 8 cm.
\(P\) is a point of intersection of the circle and the diagonal \(AC\) of the square.
(a) Show that \(AP = 1.66\) cm, correct to 3 significant figures. (4)
(b) Calculate the length of \(DP\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
| Scheme | Marks |
|---|---|
| \(8^2 + 8^2 = 64 + 64 = 128\) | M1 |
| \(\sqrt{\text{“}128\text{”}}\) | M1 |
| 11.3137… | A1 |
| \(\dfrac{11.3137\ldots - 8}{2}\) | B1 |
| (4) |
Notes
M1: for \(8^2 + 8^2\)
M1: (dep)
Alternative
| \(4^2 + 4^2 = 16 + 16 = 32\) | M1 |
| \(\sqrt{\text{“}32\text{”}}\) | M1 |
| 5.6568… | M1 |
| 5.6568… − 4 | B1 |
| Scheme | Marks |
|---|---|
| \(8^2 + 1.66^2 - 2 \times 8 \times 1.66\cos 45^\circ\) or \(8^2 + 9.66^2 - 2 \times 8 \times 9.66\cos 45^\circ\) | M1 |
| 47.974… | A1 |
| 6.93 | A1 |
| (3) | |
| (7 marks) |
Notes
A1: for 6.93 or better
Alternative
| \(PX = AX = 1.66\cos 45^\circ = 1.173\ldots\) | M1 |
| \((8 - \text{“}1.173\ldots\text{”})^2 + \text{“}1.173\text{”}^2\) | M1 |
| 6.93 | A1 |
M1: dep
A1: for 6.93 or better
Alternative
| \(OD = 4 + 1.66 = 5.66\) | M1 |
| \(5.66^2 + 4^2\) | M1 |
| 6.93 | A1 |
A1: for 6.93 or better