Numeracy Higher November 2018 Unit 1 Q11
11. A group of pupils are taking turns to ride a zip wire.
Aled models the time it takes each rider to travel sections of the zip wire.
He uses the formula
where:
- t is the time taken, in seconds,
- s is the distance travelled, in metres,
- u is the starting velocity, in metres per second (ms−1),
- v is the final velocity, in metres per second (ms−1).
(a)
Vrishank is the first pupil to ride the zip wire.
The following values were recorded for a section of his ride:
- s = 195 m, measured correct to the nearest 5 m,
- u = 5 ms−1, measured correct to the nearest ms−1,
- v = 14 ms−1, measured correct to the nearest ms−1.
Using Aled’s model, calculate the least possible time it could have taken Vrishank to travel this section of the zip wire. [4]
(b)
Mari is the second pupil to ride the zip wire.
Values for a section of Mari’s ride were recorded:
- u = 8 ms−1, measured correct to the nearest ms−1,
- v = 21 ms−1, measured correct to the nearest ms−1,
- t = 14 s, measured correct to the nearest second.
Using Aled’s model, calculate the greatest possible distance that Mari could have travelled in this section of her ride. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Use of 192·5 | B1 | In their final calculation |
| Use of 5·5 and 14·5 | B1 | In their final calculation |
| \(\dfrac{2 \times 192{\cdot}5}{5{\cdot}5 + 14{\cdot}5}\) \(\left(= \dfrac{385}{20}\right)\) | M1 | FT ‘their 192·5’ provided 190 \(\leqslant\) s < 195, and ‘their 5·5’ provided 5 < u \(\leqslant\) 6, and ‘their 14·5’ provided 14 < v \(\leqslant\) 15 |
| = 19·25 (s) | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| Use of 14·5, 8·5 and 21·5 | B1 | In their final calculation |
| Use or sight of t(u + v) | B1 | In their final calculation Use of t = 14, u=8, v=21, ‘their upper bounds’ of t, u and v OR ‘their lower bounds of u, v and t in this expression implies this B1 mark |
| \(14{\cdot}5 \times \dfrac{(8{\cdot}5 + 21{\cdot}5)}{2}\) | M1 | FT ‘their 14·5’ provided 14 < t \(\leqslant\) 15 and ‘their 8·5’ provided 8 < u \(\leqslant\) 9, and ‘their 21·5’ provided 21 < v \(\leqslant\) 22 |
| = 217·5 (m) | A1 | CAO |