Higher June 2019 Paper 3 Q28
28 Leo runs for 12 seconds.
The graph shows his speed.
(a) Show that the distance he runs is less than 67.5 metres. [4 marks]
(b) Work out his average acceleration for the first 9 seconds.
State the units of your answer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{2} \times 5 \times 8\) or 20 or \(\dfrac{1}{2} \times (8 + 9) \times (9 - 5)\) or 34 | M1 | oe eg \(\dfrac{1}{2} \times 4\ (\times 1)\) and \(4 \times 8\) or 2 and 32 |
| \(\dfrac{1}{2} \times 5 \times 8\) or 20 and \(\dfrac{1}{2} \times (8 + 9) \times (9 - 5)\) or 34 | M1dep | \(\dfrac{1}{2} \times 4\ (\times 1)\) and \(4 \times 8\) or 2 and 32 |
| \(\dfrac{1}{2} \times (9 + 4.6) \times 1\) \(+\ \dfrac{1}{2} \times (4.6 + 2) \times 1\) \(+\ \dfrac{1}{2} \times 1 \times 2\) or 6.8 + 3.3 + 1 or 11.1 or \(\dfrac{1}{2} \times (9 + 4.6) \times 1 + \dfrac{1}{2} \times 2 \times 4.6\) or 6.8 + 4.6 or 11.4 or \(\dfrac{1}{2} \times (9 + 2) \times 2 + \dfrac{1}{2} \times 1 \times 2\) or 11 + 1 or 12 or \(\dfrac{1}{2} \times 3 \times 9\) or 13.5 | M1 | correct attempt to estimate the full area below curve using trapezia, a trapezium and a triangle or a triangle |
| Correctly evaluates 20 + 34 + their correct estimate for the full area below curve, which must sum to an answer which is less than or equal to 67.5 | A1 | M3 must be awarded |
Additional guidance
If first two marks are awarded, the third area must not come from 67.5 minus their two areas
If a concluding statement is made do not award A mark if it contains an error
| Answer | Mark | Comments |
|---|---|---|
| 1 | B1 | |
| m/s2 or ms–2 or metres per second per second | B1 | oe allow mps2 or m/s/s |
Additional guidance
| Do not accept fractions | |
| m/s–2 | B0 |