Higher November 2022 Paper 3 Q11
11 Part of a running track is the arc of a semicircle joined to a straight line.
The semicircle has diameter 45 metres.
The straight line has length 75 metres.
Abby runs once along this part of the track in 18 seconds.
Work out her average speed.
Give your answer to 2 significant figures. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.5 \times \pi \times 45\) or \(0.5 \times\) [141, 141.4] or [70.5, 70.7] or \(0.5 \times \pi \times 45 + 75\) or [145.5, 145.7] | M1 | oe eg \(22.5\pi\) |
| \((0.5 \times \pi \times 45 + 75) \div 18\) or their [145.5, 145.7] \(\div\) 18 | M1 | oe their [145.5, 145.7] can be any value |
| 8.08(…) or 8.09(…) | A1 | may be implied by 8.1 |
| 8.1 | B1ft | ft any answer seen with greater than 2 sf SC2 3.9 |
Additional guidance
| Up to M2 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts, B1ft may also be awarded | |
| \(\dfrac{120}{18} = 6.67\) answer 6.7 | M0M1A0B1ft |
| \(\dfrac{120}{18} = 6.7\) | M0M1A0B0ft |
| \(0.5 \times \pi \times 45\) and \(70.7 \div 18 = 3.93\) answer 3.9 | M1M1A0B1ft |
| SC2 for an answer of 3.9 without working is when 75 is not used |