Numeracy Higher November 2022 Unit 1 Q10
10. A rubber ball is dropped from a height of 8 m onto horizontal ground.
After each bounce, the ball reaches a maximum height that is 17% lower than the maximum height reached after its previous bounce.
The diagram below shows the path of the ball for the first few bounces.
Diagram not drawn to scale
Write a formula for the maximum height, \(H\), in metres, reached by the ball after \(n\) bounces. [3]
| Scheme | Marks | Comments |
|---|---|---|
| H = 8 × 0·83n or H = 8 × \(\left(\dfrac{83}{100}\right)^{n}\) or equivalent | B3 | B2 for 8 × (1 – 0.17)n or equivalent or H = 8 × \(\dfrac{83^{n}}{100}\) OR B1 for sight of 0·83n or equivalent, or B1 for H = (8 × 0·83)n or equivalent If no marks awarded: SC1 for H = 8 × 0.17n or equivalent |