Higher June 2018 Paper 1 Q6
6
Diagram NOT accurately drawn
\(M\), \(N\) and \(P\) are points on a circle, centre \(O\).
\(MON\) is a diameter of the circle.
\(MP\) = 3.5 cm
\(PN\) = 9.7 cm
Angle \(MPN\) = 90°
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(9.7^2 + 3.5^2\) (=106.34) | M1 |
| \(\sqrt{9.7^2 + 3.5^2}\) or \(\sqrt{\text{``}{106.34}\text{''}}\) (=10.3…) | M1 |
| π × “10.3…” or \(2 \times \pi \times \dfrac{\text{``}{10.3\ldots}\text{''}}{2}\) | M1 |
| 32.4 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: dep on M2
A1: for answer in range 32.3 – 32.41
M1 for the use of \(MN\) and a correct angle (70.1… or 70.2, 19.8…) in a correct trig statement
eg \(\cos 70.2 = \dfrac{3.5}{MN}\)
M1 for a complete method to find \(MN\)
eg \(MN = \dfrac{3.5}{\cos 70.2}\) (=10.3…)