November 2021 Paper 2 Q4
4 The equations of the two circles shown are
\[x^2 + y^2 = 100 \quad \text{and} \quad x^2 + y^2 = 36\]
Not drawn accurately
Work out the shaded area.
Give your answer as an integer multiple of \(\pi\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\pi \times 100\ (\div 4)\) or \(100\pi\ (\div 4)\) or \(25\pi\) or \(\pi \times 36\ (\div 4)\) or \(36\pi\ (\div 4)\) or \(9\pi\) | M1 | oe |
| \(\pi \times 100 \div 4 - \pi \times 36 \div 4\) | M1dep | oe eg \(\dfrac{100\pi - 36\pi}{4}\) or \(\dfrac{64\pi}{4}\) |
| \(16\pi\) | A1 | SC2 \(2176\pi\) |
Additional guidance
| Use of circumference instead of area throughout | M0M0A0 |
| Allow substitution of \(\pi = [3.14, 3.142]\) for M marks | |
| \(16\pi\) in working with eg 50.3 on answer line | M2A0 |
| SC2 is for using radii of 100 and 36 | |
| Omission of \(\pi\) in working must be recovered |