Foundation November 2018 Paper 2 Q23
23 Two identical quarter circles are cut from a rectangle as shown.
Not drawn accurately
Work out the shaded area. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(12 \times 6\) or 72 | M1 | oe area of rectangle |
| \(\pi \times 6^2\) or \(36\pi\) or [113, 113.112] | M1 | oe may be implied eg \(\pi \times 6^2 \div 4\) or \(9\pi\) or [28.2, 28.3] |
| \(\pi \times 6^2 \div 2\) or \(18\pi\) or [56.4, 56.6] | M1dep | oe dep on 2nd M1 |
| [15.4, 15.5] or \(72 - 18\pi\) | A1 |
Additional guidance
| \(72 - 18\pi = 54\pi\) | M1M1M1A0 |
| \(\pi \times 6^2 \div 2\) scores 2nd and 3rd M1 | |
| \(12 \times 6 = 72\) \(72 \div 2 = 36\) (unless identified as half of rectangle) | (1st) M0 |
| \(\pi \times 6^2\) scores 2nd M1 even if subsequently used incorrectly eg \(\pi \times 6^2 = 36\pi\) \(36\pi \times 2 = 72\pi\) | (2nd) M1 |
| Ignore units throughout |