Foundation June 2025 Paper 1 Q28
28 The shaded shape below is made from a right-angled triangle, ABC, and a semicircle. The length of AB is 20 cm and the diameter of the semicircle, BC, is of length 12 cm.
Not to scale
Calculate the perimeter of the shaded shape.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 62.16 to 62.18 or 62.2 with correct working or \(4\sqrt{34} + 6\pi + 20\) oe with correct working | 6 | Correct working requires at least the first M1 AND the second M1 | |
| M2 for \(\sqrt{20^2 + 12^2}\) or M1 for \(20^2 + 12^2\) maybe implied by 544 | Award M and A marks even if not used to find final answer and not contradicted | ||
| A1 for 23.3… or \(4\sqrt{34}\) or \(\sqrt{544}\) oe with correct working | Award M2 A1 if M1A1 seen | ||
| AND M2 for \(\dfrac{12\pi}{2}\) maybe implied by \(6\pi\) or by 18.84 to 18.852 or M1 for \(12\pi\) maybe implied by 37.68 to 37.704 | Award M marks even if not used to find final answer and not contradicted Their \(12\pi\) must not come from area calculation or from \(2 \times \pi \times 12 \div 2\) | ||
| If 0,1 or 2 scored, instead award SC3 for answer 62.16 to 62.18 or 62.2 or \(4\sqrt{34} + 6\pi + 20\) or \(\sqrt{544} + 6\pi + 20\) with no working or insufficient working If 0 or 1 scored, instead award SC2 for answer 42.16 to 42.18 or 42.2 or \(4\sqrt{34} + 6\pi\) or \(\sqrt{544} + 6\pi\) with no working or insufficient working If 0 scored, instead award SC1 for 23.3… or \(4\sqrt{34}\) or \(\sqrt{544}\) or 43.3… or \(4\sqrt{34} + 20\) or \(\sqrt{544} + 20\) with no working or insufficient working | Could be in working eg \(23.3 + 6\pi\) | ||