Mathematics (Syllabus D) 4024/21 — October/November 2018

Cambridge O-Level · Calculator · worked solutions for every part, with the mark scheme

questions

100

marks

150

minutes

Topics Number · Algebra and Graphs · Trigonometry · Probability · Geometry · Coordinate Geometry · +3 more

Q1StatisticsProbabilityNumberFree sample

(a)

The table shows the distances 10 people drive to work and the times they take.

Distance (km)	12	32	18	54	26	36	29	15	20	42
Time (minutes)	20	40	25	62	35	34	32	18	32	50

(i)

On the grid, complete the scatter diagram to show this information.
The first four points have been plotted for you.

Fig. 1

(ii)

What type of correlation does the scatter diagram show?

______

(iii)

One of these 10 people is selected at random.

Find the probability that this person drove less than $30\,\text{km}$ to work.
Give your answer as a fraction in its simplest form.

______

(iv)

Ateeq drives $48\,\text{km}$ to work.

By drawing a line of best fit on the scatter diagram, estimate the time Ateeq takes to travel to work.

______ $\text{minutes}$

(b)

The table summarises the times taken by the 120 employees in a company to travel to work.

Time ( $t$ minutes)	$0 < t \leq 20$	$20 < t \leq 40$	$40 < t \leq 60$	$60 < t \leq 80$	$80 < t \leq 100$
Frequency	29	38	26	21	6

(i)

Write down the modal class.

______

(ii)

Calculate an estimate of the mean time.

______ $\text{minutes}$

(iii)

Work out the percentage of employees who took more than 1 hour to travel to work.

______ %

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