Higher June 2023 Paper 4 Q8
8 The diagram shows a circle inside a square of side 12 cm.
Work out the percentage of the square that is shaded.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5.36 to 5.4 and correct working | 6 | B5 for the correct answer in the wrong format with correct working e.g. 0.0536 OR M5 for \(\frac{12^2 - \pi \times 6^2}{12^2 \times 4}\) [× 100] oe OR Square M1 for \(12^2\) or 144 or \(6^2\) or 36 (must be consistent with \(\frac{1}{4} \times \pi \times 6^2\)) and Circle M2 for \(\pi \times 6^2\) or \(\frac{1}{4} \times \pi \times 6^2\) or M1 for radius of 6 may be implied e.g. 2×π×6 (with \(\pi\)) and M1 for (their \(12^2\) – their (\(\pi \times 6^2\))) [÷4] or their (\(\pi \times 6^2\)) ÷ their \(12^2\) or their (\(6^2\) – their (\(\frac{1}{4} \times \pi \times 6^2\))) [÷their \(12^2\)] or their (\(\frac{1}{4} \times \pi \times 6^2\)) ÷ \(\frac{their\ 12^2}{4}\) If 0 or M1 or M2 scored, instead award SC3 for answer 5.36 to 5.4 with no or insufficient working If 0 or M1 scored, instead award SC2 for 30.88 to 31 or 7.72 to 7.75 or 0.785 to 0.786 with no or insufficient working | “Correct working” requires evidence of at least M1 AND M2 AND M1 their 144 must come from attempt at area of a square M2 implied by 113.04 to 113.12 or 28.26 to 28.28 6 [cm] could be on diagram FT their incorrect 6 identified as radius implied by 30.88 to 31 or 7.72 to 7.75 implied by 0.785 to 0.786 implied by 7.72 to 7.75 implied by 0.785 or 0.7852 to 0.7856 their area of the circle has to be an attempt at \(\pi r^2\) not \(2\pi r\) so that, if they do not, the most they can be awarded is M1 for 144 and M1 for radius = 6 cm |