Higher June 2025 Paper 2 Q8
8 Here is a circle, centre \(O\).
Not drawn accurately
(a) The circle has a circumference of 20 cm
Assume that angle \(x\) is \(90^\circ\)
Work out the shaded area.
Give your answer as a decimal. [3 marks]
(b) In fact, angle \(x\) is smaller than \(90^\circ\)
What does this mean about the shaded area?
Tick one box. [1 mark]
- It is smaller than the answer to part (a)
- It is the same as the answer to part (a)
- It is larger than the answer to part (a)
- It could be any of the above
| Answer | Mark | Comments |
|---|---|---|
| \(20 \div \pi\) or [6.36, 6.37] or 6.4 or \(20 \div 2\pi\) or [3.18, 3.185] or 3.2 | M1 | oe |
| \(\pi \times (20 \div 2\pi)^2 \times \dfrac{90}{360}\) or \(\dfrac{100}{\pi} \times \dfrac{90}{360}\) or \(\dfrac{25}{\pi}\) | M1dep | oe full method |
| [7.93, 7.97] | A1 |
Additional guidance
Accept [3.14, 3.142] for \(\pi\) throughout
Ignore subsequent rounding after answer [7.93, 7.97] seen in working
| Answer | Mark | Comments |
|---|---|---|
| It is smaller than the answer to part (a) | B1 |