Foundation June 2025 Paper 2 Q26
26 The diagram shows a sector of a circle AOB and a circle with radius \(r\) cm.
Not to scale
The sector has radius 12 cm and angle AOB = \(120^\circ\).
The ratio of the area of the sector AOB to the area of the circle is 3 : 4.
Calculate the value of \(r\).
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 8 with correct working | 6 | Correct working requires evidence of at least M1 and M1dep If candidates use numerical values for \(\pi\), allow 3.1 or 3.14… or \(\dfrac{22}{7}\). If candidates use other values e.g. 3 they must state \(\pi = 3\) | |
| M2 for \(\dfrac{120}{360} \times \pi \times 12^2\) oe or M1 for \(\dfrac{120}{360}\) oe \(\times\ k\pi\) or \(\pi \times 12^2\) or \(k \times \pi \times 12^2\) A1 for \(48\pi\) | For M1 \(k\) must be numerical and > 0 M1 may be implied by \(144\pi\) Award M2 A1 if M1 A1 seen Award M and A marks for the area of sector even if not used to find final answer and not contradicted. | ||
| AND | |||
| M1dep for their \(48\pi \div 3 \times 4\) or for their \(48 \div 3 \times 4\) | Dependent on M1. Implied by \(64\pi\) implied by 64 | ||
| M1dep for \([\pi \times]\,r^2 = [\pi \times](\)their \(48 \div 3 \times 4)\) | e.g. \(\pi r^2 = 64\pi\) or \(r^2 = 64\) or \(r = \sqrt{64}\). Dependent on previous M1dep If candidates only use trials to find square root, they must obtain the correct answer. | ||
| If 0 or 1 scored instead award SC2 for \(r = 8\) with no/insufficient working or if 0 scored award SC1 for area of sector = \(48\pi\) | Do not award SC2 if clearly from wrong working Do not award SC1 if clearly from wrong working | ||