Questions

Q1.

Jethro has sat 5 tests.

Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74

Jethro has to sit one more test that is also to be marked out of 100

Jethro wants his mean mark for all 6 tests to be at least 77

Work out the least mark that Jethro needs to get for the last test.

...........................................................

(Total for question = 3 marks)

(Q10 4MA1/1H, June 2021)

Q2.

The mean number of goals scored by a hockey team in 8 matches is 6

The team plays 2 more matches and scores k goals in each match.

The mean number of goals scored by the hockey team in the 10 matches is 7

Work out the value of k

k = ...........................................................
 (Total for question = 3 marks)

(Q08 4MA1/2H, Nov 2023)

Q3.

Ali uses a fitness tracker to count the number of steps he walks each day for 7 days.

For the first 4 days, his mean number of steps is 11 800

For the next 3 days, his mean number of steps is 13 207

Work out his mean number of steps for the 7 days.

...........................................................

(Total for question = 3 marks)

(QU12 4MA1/2H, June 2024)

Q4.

Kim puts 4 bananas in a bag.

The mean weight of the 4 bananas in the bag is 145 grams.

Andy puts one more banana into the bag.

The mean weight of the 5 bananas in the bag is 142 grams.

Work out the weight of the banana that Andy puts into the bag.
 ........................................................... grams

(Total for question = 3 marks)

(Q08 4MA1/2H, Nov 2024)

Q5.

A scientist is investigating the weight of 50 tigers.

Here is some information about these tigers.

The mean weight of all 50 tigers is 218 kg

Work out the mean weight of the Bengal tigers.

........................................................... kg

(Total for question = 3 marks)

(Q08 4MA1/2HR, Jan 2022)

Q6.

Team A and Team B take part in a quiz league.

After 11 rounds, Team A has a mean score per round of 17
After 9 rounds, Team B has a mean score per round of 18

Both teams take part in a further round.

After this round, both teams have a mean score per round of 18.5

In the further round, Team A scored more points than Team B.

How many more?

...........................................................

(Total for question = 4 marks)

(QU10 4MA1/2H, June 2023)

Q7.

There are 5 cocoa pods in a bag.

The mean weight of the 5 cocoa pods is 398 grams.

A sixth cocoa pod is put into the bag.

The mean weight of the 6 cocoa pods is 401 grams.

Work out the weight of the sixth cocoa pod that is put into the bag.
 ........................................................... grams

(Total for question = 3 marks)

(Q07 4MA1/2H, Jan 2021)

Q8.

15 students took an English test.

The same 15 students took a Maths test.
Both tests were marked out of 30

For the English test results

the median was 21
the interquartile range was 14
The Maths test results are shown below.

18 18 19 20 24 25 25 26 28 28 29 29 29 30 30

Use the information above to compare the English test results with the Maths test results.
Write down two comparisons.

1 ..........................................................................................................................................

.............................................................................................................................................

2 ..........................................................................................................................................

.............................................................................................................................................

(Total for question = 4 marks)

 (Q11 4MA1/1H/EAM, Specimen papers )

Q9.

The table gives information about the times taken, in minutes, for 80 taxi journeys.

(a) Complete the cumulative frequency table.

(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.
 (2)
(c) Use your graph to find an estimate for the median.

........................................................... minutes
(1)
(d) Use your graph to find an estimate for the interquartile range.

........................................................... minutes
(2)

(Total for question = 6 marks)

 (Q13 4MA1/2H, June 2019)

Q10.

The cumulative frequency table gives information about the distance, in kilometres, that each of 80
workers travel from home to work at Office A.

(a) On the grid below, draw a cumulative frequency graph for the information in the table.
 (2)
(b) Use your graph to find an estimate for the median distance travelled.

........................................................... km
(1)
(c) Use your graph to find an estimate for the interquartile range of the distances travelled.
 ........................................................... km
(2)
For Office B, the median distance workers travel from home to work is 15 km and the interquartile range is
5 km.

(d) Use the information above to compare the distances that workers at Office A and workers at Office B
travel from home
to work.
Write down two comparisons.

1 ..........................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

2 ..........................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................
(2)

(Total for question = 7 marks)

(Q12 4MA1/2H, June 2021)

Q11.

The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a
supermarket.
(a) Complete the cumulative frequency table.

(1)
(b) On the grid below, draw a cumulative frequency graph for your table.
 (2)
(c) Use your graph to find an estimate for the median time taken.

........................................................... minutes
(1)
One of the 80 customers is chosen at random.

(d) Use your graph to find an estimate for the probability that the time taken by this customer was more
than 42 minutes.
 ...........................................................
(2)

(Total for question = 6 marks)

(Q12 4MA1/1H, Jan 2022)

Q12.

The table gives information about the ages, in years, of 80 people in a train carriage.

(a) Complete the cumulative frequency table.

(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the median age of the 80 people.

........................................................... years
(1)

Of the people in the train carriage, 60% of those who are aged between 18 and 65 are going to work.
None of the other people in the train carriage are going to work.

(d) Use your graph to find an estimate for the number of people in the train carriage who are going to
work.

...........................................................
(3)

(Total for question = 7 marks)

 (QU13 4MA1/2H, June 2022)

Q13.

The cumulative frequency graph gives information about the times, in seconds, that 80 adults took to log
in to an online bank.

(a) Find an estimate for the median time.

........................................................... seconds
(1)
(b) Work out the percentage of these adults that took longer than 50 seconds to log in.
Show your working clearly.

........................................................... %
(3)

(Total for question = 4 marks)

(Q13 4MA1/1H, Nov 2023)

Q14.
The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.

(a) Write down the modal class.

...........................................................
(1)
(b) Work out an estimate for the mean frame size.

........................................................... cm
(4)

(Total for question = 5 marks)

(Q01 4MA1/1HR, Jan 2023)

Q15.

Here are some integers where a < b < c < d

a b c d d d
The mode of the integers is 9

The median of the integers is 8

The range of the integers is 4

Work out the value of a, the value of b, the value of c and the value of d

a = ...........................................................

b = ...........................................................

c = ...........................................................

d = ...........................................................

(Total for question = 3 marks)

(QU01 4MA1/2H, June 2022)

Q16.

A group of 60 students each sat an algebra test and a geometry test.

Each test was marked out of 110

The cumulative frequency graph gives information about the marks gained by the 60 students in the
algebra test.
(a) Use the graph to find an estimate for the median mark in the algebra test.

...........................................................
(1)
(b) Use the graph to find an estimate for the number of students who gained 58 marks or less in the
algebra test.

...........................................................
(1)
(c) Use the graph to find an estimate for the interquartile range of the marks gained in the algebra test.

...........................................................
(2)
The interquartile range of the marks gained in the geometry test is 9

Luis says
"The students' marks are more spread out in the algebra test than in the geometry test."
(d) Is Luis correct?
Give a reason for your answer.

.............................................................................................................................................

.............................................................................................................................................
(1)
To be awarded a grade A in the algebra test, a student had to gain a mark greater than 64

Two students are to be selected at random from the 60 students in the group.

(e) Use the graph to find an estimate for the probability that both of these students were awarded a grade
A in the algebra test.

...........................................................
(3)

(Total for question = 8 marks)

(Q14 4MA1/2HR, Jan 2022)

Q17.

Here are the numbers of aces that Rutger served in each of 11 tennis matches.

1 1 2 4 6 8 8 9 11 12 15

(a) Find the interquartile range of the numbers of aces.

Show your working clearly.

...........................................................
(2)
Kim also plays in 11 tennis matches.

For Kim
the median number of aces is 11
the interquartile range of the numbers of aces is 5
(b) State, giving a reason, whether Rutger or Kim
(i) served more aces on average,
.............................................................................................................................................

.............................................................................................................................................
.............................................................................................................................................
(1)
(ii) was more consistent with the number of aces served.
.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................
(1)

(Total for question = 4 marks)

(Q15 4MA1/2HR, Jan 2023)

Q18.

Here are five cards.

Each card has a number written on it.

The mean of the five numbers is 12

Work out the value of x

x = ...........................................................

(Total for question = 3 marks)

 (QU03 4MA1/1HR, June 2022)

Q19.

The frequency table gives information about the number of points scored by a player.

The mean number of points scored is 2

Work out the value of x

x = ...........................................................

(Total for question = 4 marks)

(Q09 4MA1/2H, Jan 2022)

Q20.

The table shows information about the heights, in cm, of 48 sunflowers in a garden centre.

Work out an estimate for the mean height of the sunflowers.

........................................................... cm

(Total for question = 4 marks)

(Q01 4MA1/2H, June 2019)

Q21.

80 students entered a dancing competition.

The table gives information about the length of time, in minutes, for which each student spent dancing.
Work out an estimate for the mean length of time the students spent dancing.

........................................................... minutes

(Total for question = 4 marks)

(Q01 4MA1/1H, Jan 2023)

Q22.

The frequency table gives information about the numbers of mice in some nests.

The mean number of mice in a nest is 7

Work out the value of x.

x=
 (Total for question = 4 marks)

(Q13 4MA1/2H, Jan 2019)

Q23.

Here is a list of six numbers written in order of size.

4 7 x 10 y y

The numbers have

a median of 9
a mean of 11
Find the value of x and the value of y.

x = ...........................................................

y = ...........................................................

(Total for question = 4 marks)

(Q04 4MA1/1H, Nov 2020)

Q24.

Gemara works as a taxi driver.

Last week, he recorded the following information about the distances he drove.

For the 5 days from Monday to Friday, the mean number of kilometres he drove was 104

For the 7 days from Monday to Sunday, the mean number of kilometres he drove was 127

On Saturday, Gemara drove 132 kilometres.

Work out the number of kilometres he drove on Sunday.

........................................................... kilometres

(Total for question = 3 marks)

(QU10 4MA1/2HR, June 2023)

Q25.

Twenty students took a Science test and a Maths test.

Both tests were marked out of 50

The table gives information about their results.

Use this information to compare the Science test results with the Maths test results.
Write down two comparisons.

2.

(Total for question = 2 marks)

 (Q11 4MA1/2H, Jan 2019)

Q26.

Alberto, Bill, Candela and Diana are four friends.

Here is some information about the height of each of these friends.

Alberto's height is 158 cm.
Bill's height is 175 cm.
Candela's height is greater than Diana's height.
The median height of these four friends is 160 cm.
The range of the heights of these four friends is 21 cm.

Work out Candela's height and Diana's height.

Candela ........................................................... cm

Diana ........................................................... cm

(Total for question = 3 marks)

(QU03 4MA1/2HR, June 2022)

Q27.

Jenny has six cards.

Each card has a whole number written on it so that

the smallest number is 5
the largest number is 24
the median of the six numbers is 14
the mode of the six numbers is 8
Jenny arranges her cards so that the numbers are in order of size.
(a) For the remaining four cards, write on each dotted line a number that could be on the card.

(3)
A basketball team plays 6 games.
After playing 5 games, the team has a mean score of 21 points per game.
After playing 6 games, the team has a mean score of 23 points per game.

(b) Work out the number of points the team scored in its 6th game.

...........................................................
(3)

(Total for question = 6 marks)

(Q05 4MA1/1H, Jan 2022)

Q28.

Here is a list of six numbers written in order of size.

x 5 y z 10 12

The numbers have

a range of 9
 a median of 8
a mode of 10
Find the value of x, the value of y and the value of z

x = ...........................................................

y = ...........................................................

z = ...........................................................

(Total for question = 3 marks)

(Q03 4MA1/1HR, Jan 2023)

Q29.

Ava writes down five whole numbers.

For these five numbers

the median is 7
the mode is 8
the range is 5
Find a possible value for each of the five numbers that Ava writes down.
 ...........................................................

(Total for question = 3 marks)

(Q02 4MA1/2H, Jan 2021)

Q30.

Here are eight numbers written in order of size

h 6 7 8 j 16 k k

where h, j and k are integers.

The median of the eight numbers is 10

The mode of the eight numbers is 18

The range of the eight numbers is 13

Work out the value of h, the value of j and the value of k

h = ...............................

j = ...............................

k = ...............................

(Total for question = 3 marks)

 (QU01 4MA1/2H, June 2024)

Q31.

The table shows some information about the hourly rates of pay of 60 workers.

(a) Write down the modal class.

...........................................................
(1)
(b) Work out an estimate for the mean hourly rate of pay of the 60 workers.

........................................................... dollars
(4)

(Total for question = 5 marks)

(Q01 4MA1/1H, Nov 2024)

Q32.
The table shows information about the weights, in kilograms, of 40 babies.

(a) Write down the modal class.

...........................................................
(1)
(b) Work out an estimate for the mean weight of the 40 babies.

........................................................... kg
(4)
One of the 40 babies is going to be chosen at random.

(c) Find the probability that this baby has a weight of more than 5 kg.

...........................................................
(2)

(Total for question = 7 marks)

 (Q04 4MA1/1H, Jan 2020)

Q33.

The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass
under a bridge.

(a) Write down the modal class.

...........................................................
(1)
(b) Work out an estimate for the mean speed of the motorbikes as they pass under the bridge. Give your
answer correct to 3
significant figures.

........................................................... kilometres per hour

(4)

(Total for question = 5 marks)

(Q02 4MA1/1H, Jan 2021)

Q34.

The table shows information about the lengths, in minutes, of 50 telephone calls.

(a) Write down the modal class.

...........................................................
(1)
(b) Work out an estimate for the total length, in minutes, of these telephone calls.

........................................................... minutes
(3)

(Total for question = 4 marks)

(Q01 4MA1/2H, Nov 2023)

Q35.

Yusuf sat 8 examinations.

Here are his marks for 5 of the examinations.

68 72 75 77 80

For his results in all 8 examinations

the mode of his marks is 80
the median of his marks is 74
the range of his marks is 16
Find Yusuf's marks for each of the other 3 examinations.

.....................

.....................

.....................

(Total for question = 4 marks)

(Q05 4MA1/1HR, Jan 2022)

Q36.

30 students in a class sat a Mathematics test.

The mean mark in the test for the 30 students was 26.8

13 of the 30 students in the class are boys.

The mean mark in the test for the boys was 25

Find the mean mark in the test for the girls.

Give your answer correct to 3 significant figures.

...........................................................

(Total for question = 3 marks)

(Q07 4MA1/2H, June 2019)

Q37.

60 students sat a Mathematics exam.

The mean mark for the 32 students in Class A was 55
The mean mark for the 28 students in Class B was 52

Find the mean mark for all 60 students.

...........................................................

(Total for question = 3 marks)

(Q08 4MA1/2HR, Jan 2023)

Q38.

Ian plays 7 games of cricket.

His mean score per game for these 7 games is 42 runs.

Ian is going to play one more game of cricket.

He wants his mean score per game for the 8 games to be exactly 50 runs.

How many runs must he score in his 8th game?

 ...........................................................

(Total for question = 3 marks)

(Q07 4MA1/1H/EAM, Specimen papers )

Q39.

Larry is a delivery man.

He has 7 parcels to deliver.

The mean weight of the 7 parcels is 2.7 kg

Larry delivers 3 of the parcels.

Each of these 3 parcels has a weight of W kg

The mean weight of the other 4 parcels is 3.3 kg

Work out the value of W

 W = ...........................................................

(Total for question = 3 marks)

(QU12 4MA1/2H, June 2022)

Mark Scheme
Q1.

(Q10 4MA1/1H, June 2021)

Q2.
 (Q08 4MA1/2H, Nov 2023)

Q3.

(QU12 4MA1/2H, June 2024)

Q4.
 (Q08 4MA1/2H, Nov 2024)

Q5.

(Q08 4MA1/2HR, Jan 2022)

Q6.
 (QU10 4MA1/2H, June 2023)

Q7.

(Q07 4MA1/2H, Jan 2021)

Q8.
 (Q11 4MA1/1H/EAM, Specimen papers )

Q9.
 (Q13 4MA1/2H, June 2019)

Q10.
 (Q12 4MA1/2H, June 2021)

Q11.
 (Q12 4MA1/1H, Jan 2022)

Q12.
 (QU13 4MA1/2H, June 2022)

Q13.
 (Q13 4MA1/1H, Nov 2023)

Q14.
 (Q01 4MA1/1HR, Jan 2023)

Q15.
 (QU01 4MA1/2H, June 2022)

Q16.
 (Q14 4MA1/2HR, Jan 2022)

Q17.
 (Q15 4MA1/2HR, Jan 2023)

Q18.
 (QU03 4MA1/1HR, June 2022)

Q19.

(Q09 4MA1/2H, Jan 2022)

Q20.
 (Q01 4MA1/2H, June 2019)

Q21.
 (Q01 4MA1/1H, Jan 2023)

Q22.

(Q13 4MA1/2H, Jan 2019)

Q23.
 (Q04 4MA1/1H, Nov 2020)

Q24.

(QU10 4MA1/2HR, June 2023)

Q25.
 (Q11 4MA1/2H, Jan 2019)

Q26.

(QU03 4MA1/2HR, June 2022)

Q27.
 (Q05 4MA1/1H, Jan 2022)

Q28.

(Q03 4MA1/1HR, Jan 2023)

Q29.

(Q02 4MA1/2H, Jan 2021)

Q30.
 (QU01 4MA1/2H, June 2024)

Q31.
 (Q01 4MA1/1H, Nov 2024)

Q32.
 (Q04 4MA1/1H, Jan 2020)

Q33.
 (Q02 4MA1/1H, Jan 2021)

Q34.
 (Q01 4MA1/2H, Nov 2023)

Q35.

(Q05 4MA1/1HR, Jan 2022)

Q36.
 (Q07 4MA1/2H, June 2019)

Q37.

(Q08 4MA1/2HR, Jan 2023)

Q38.
 (Q07 4MA1/1H/EAM, Specimen papers )

Q39.

(QU12 4MA1/2H, June 2022)