Foundation November 2017 Paper 2 Q26
26 A ball is thrown from a height of 15 metres.
It bounces to height \(h_1\), then to height \(h_2\) as shown.
Not drawn accurately
\(h_1\) is three quarters of the original height.
(a) Jack expects \(h_2\) to be three quarters of \(h_1\)
Work out the value of \(h_2\) that he expects. [2 marks]
(b) In fact, \(h_2\) is two thirds of \(h_1\)
How does this affect the answer to part (a)?
Tick a box.
- The ball bounced higher than he expected
- The ball bounced lower than he expected
Show working to support your answer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{3}{4} \times \dfrac{3}{4} \times 15\) or \(\dfrac{3}{4} \times 15\) or 11.25 and \(\dfrac{3}{4} \times\) their 11.25 | M1 | oe |
| 8.4(375) or 8.44 or 8.438 or \(\dfrac{135}{16}\) or \(8\dfrac{7}{16}\) | A1 |
Additional guidance
| 8.43 or 8.437 | M1A1 |
| 8.4 seen, answer 8 | M1A1 |
| \(\dfrac{3}{4}\) of 11.25 (unless correctly evaluated) | M0 |
| \(\dfrac{3}{4} \times 8.4375\), answer 6.328 (further work) | M1A0 |
| 11.25 + 8.4375, answer 19.6875 (further work) | M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Ticks second box and [7.425, 7.5375] or Ticks second box and correctly evaluates \(\dfrac{2}{3} \times\) their 11.25 | B2ft | ft correct box ticked for comparing with their answer to (a) B1ft [7.425, 7.5375] with no or incorrect decision or Correctly evaluates \(\dfrac{2}{3} \times\) their 11.25 with no or incorrect decision |
| Alternative method 2 | ||
| Ticks second box and valid comparison | B2 | eg \(\dfrac{8}{12}\) and \(\dfrac{9}{12}\) 0.66… or 0.67 and 0.75 66.(...)% or 67% and 75% \(\dfrac{9}{16}\) and \(\dfrac{8}{16}\) clear diagrams showing \(\dfrac{2}{3}\) and \(\dfrac{3}{4}\) B1 Ticks second box and incomplete comparison eg \(\dfrac{8}{12}\) and \(\dfrac{3}{4}\) two thirds is less than three quarters \(\dfrac{3}{4} \times \dfrac{3}{4} = \dfrac{9}{16}\) and \(\dfrac{3}{4} \times \dfrac{2}{3} = \dfrac{6}{12}\) or Valid comparison (that would score B2) with no or incorrect decision |
Additional guidance
| In Alt 1 only follow through their answer to (a) for the comparison, the working for \(\dfrac{2}{3}\) of their 11.25 must be correct | |
| (a) answer 6.5 (b) Ticks first box and 7.5 seen | B2ft |
| Accept 0.66... or 0.67 for \(\dfrac{2}{3}\) | |
| Using 0.6 for \(\dfrac{2}{3}\) | B0 |