A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2017 · Q25 Marks

The time taken by a car to accelerate from 0 to 30 metres per second was measured correct to the nearest second. The results from 48 cars are summarised in the following table. Time (seconds) | 3–5 | 6–8 | 9–11 | 12–16 | 17–25 Frequency | 10 | 15 | 17 | 4 | 2

(i)On the grid, draw a cumulative frequency graph to represent this information.[3]
(ii)35 of these cars accelerated from 0 to 30 metres per second in a time more than t seconds. Estimate the value of t.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] (i) Correct cfs values seen listed, in or by table or on graph, 0 not required
[1] (i) Axes labelled “cumulative frequency” (or cf) and "time [or t etc.] (in) seconds (or sec etc.)". Linear scales - cf 0–48, time 2.5 – 25.5 (ignore <2.5 on time.) At least 3 values stated on each axis, but (0,0) can be implied without stating.
[1] (i) All points plotted accurately, (5, 10) etc. scores B0. Curve or line segments drawn starting at (5.5,10) and passing within '1 scale unit' vertically and horizontally of plotted points
[1] (ii) Subt 35 (checked ±1 mm on graph) from 48 or 50,
[1] (ii) 6 ≤ Ans < 7

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