4MA0 Higher June 2014 Paper 3 Q13
13
Diagram NOT accurately drawn
The diagram shows a square ABCD drawn inside a circle, centre O.
A, B, C and D are points on the circle.
The lengths of the sides of the square are 10 cm.
AC is a diameter of the circle.
Calculate the circumference of the circle.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \((AC^2 =)\ 10^2 + 10^2\) (=200) or \((AO^2 =)\ 5^2 + 5^2\) (= 50) | M1 |
\((AC =)\sqrt{10^2 + 10^2}\) (= 14.1...) or \((AO =)\sqrt{5^2 + 5^2}\) (=7.07..) | M1 |
\(\pi \times \sqrt{10^2 + 10^2}\) oe or \(14.1\pi\) or \(2\pi \times 7.07\) or \(2 \times \pi \times \sqrt{5^2 + 5^2}\) | M1 |
| 44.4 | A1 |
| (4 marks) |
Notes
M1: dep
M1: dep
A1: awrt 44.3 or 44.4
Alternative method
| Scheme | Marks |
|---|---|
| \(\cos 45 = \dfrac{10}{x}\) or \(\sin 45 = \dfrac{10}{x}\) | M1 |
| \((x =)\ \dfrac{10}{\cos 45}\) or \((x =)\ \dfrac{10}{\sin 45}\) oe (= 14.1..) | M1dep |
| \(\pi \times \dfrac{10}{\cos 45}\) or \(\pi \times \dfrac{10}{\sin 45}\) oe | M1 dep |
| 44.4 | A1 |
Notes
A1: awrt 44.3 or 44.4