Higher June 2024 Paper 3 Q17
17 A ball is thrown upwards and reaches a maximum height.
The ball then falls and bounces repeatedly.
After the \(n\)th bounce, the ball reaches a height of \(h_n\)
After the next bounce, the ball reaches a height given by \(h_{n + 1} = 0.55h_n\)
After the 1st bounce, the ball reaches a height of 8 metres.
What height does the ball reach after the 4th bounce? (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 1.331 | M1 | for method to find height after 2nd bounce, eg \(0.55 \times 8\ (= 4.4)\) |
| M1 | for method to find height after 3rd bounce, eg \(0.55 \times \text{``}4.4\text{''}\ (= 2.4(2))\) or for method to find height after 4th bounce, eg \(0.55^3 \times 8\) or for method to find height after 5th bounce, eg \(0.55^4 \times 8\ (= 0.73(205))\) | |
| A1 | for 1.331, accept 1.33, 1.3 oe mixed number |
Additional guidance
Award this mark for \(0.55^n \times 8\) where \(n \gt 1\)
If a correct answer is shown and then incorrectly rounded award full marks