Higher June 2017 Paper 3 Q8
8 A square, with sides of length \(x\) cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.
The area of the circle is 49 cm².
Work out the value of \(x\).
Give your answer correct to 3 significant figures. (4)
| Answer | Mark | Notes | |
|---|---|---|---|
| 5.59 | M1 | For use of \(\pi r^2 = 49\), where \(r\) is the radius or \(r = 3.9(49\ldots)\) or diameter \(= 7.8(9865\ldots)\) | |
| M1 | For use of Pythagoras to set up an equation in \(x^2\) e.g. \(x^2 + x^2 = (d)^2\) or \(x^2 = r^2 + r^2\) | For use of trigonometry to set up an equation in \(x\) eg \(\sin 45 = x \div d\) | |
| M1 | (dep on M2) Rearrange to \((x^2 =)\ 2 \times \text{``}3.949..\text{''}^2\) | Rearrange to \((x =)\ \text{``}7.898..\text{''} \times \sin 45\) oe | |
| A1 | 5.5 to 5.6 | ||