1.
Grade 10 Extended Mathematics 2021-2022
Summative Criterion A- Unit 3
Name:_____________________________ Awarded Level:__________
Instructions and Information:
• You will have 5 minutes of reading time and 60 minutes to complete this test.
• You should show all the working and mathematical representations you have used in
order to answer the questions.
• Answers only will not necessarily be accredited with full understanding.
• Where appropriate answers can be given as exact or rounded to three significant figures.
• A calculator is allowed.
Level 1-2 3-4 5-6 7-8
Descriptor
Simple
Problems
More Complex and
Familiar Problems
Challenging and
Familiar Problems
Challenging and
Unfamiliar Problems

2.
Question Level 1-2:
Question 1:
State whether each of the following descriptions would generate discrete or continuous data.
a) A student’s grade on an IB mathematics examination.
b) The volume of water that a person uses when having a shower.
c) The length of time a person spends in the shower.
d) The number of emails that a person sends during the day.
Question 2:
A class of 20 students was asked “How many children are there in your household?” and the
following data was collected:
1, 2, 3, 3, 2, 4, 5, 4, 2, 3, 8,1 ,2, 1, 3, 2, 1, 2, 1, 2
a) What type of data is this? Discrete or continuous?
b) What is the mode of this data set?
c) What is the mean of this data set?
d) What is the median of this data set?

3.
Question Level 3-4:
Question 3:
A recruitment company tests the aptitude of 100 applicants applying for jobs in engineering.
Each applicant does a puzzle and the time taken, t, is recorded. The cumulative frequency
curve for these data is shown below.
Using the cumulative frequency curve,
(a) Write down the value of the median;
(b) Determine the interquartile range;

4.
(c) Complete the cumulative frequency table below.
Time to complete puzzle in seconds Frequency Cumulative Frequency
20 < t ≤ 30
30 < t ≤ 35
35 < t ≤ 40
40 < t ≤ 45
45 < t ≤ 50
50 < t ≤ 60
60 < t ≤ 80

5.
Question 3:
The 98th
Tour de France was made up by 21 stages and covered a total of 3450.5km. The distances
(in kilometers) for some of the stages are as follows. (All distances have been rounded to the
nearest whole number).
192 198 173 165 227 218
189 208 158 168 211 153
169 193 163 179 201 110
(a) Determine:
i. The five number summary.
ii. The interquartile range.
iii. The standard deviation.

6.
(b) Complete a box-and-whisker diagram representing all the stages in the Tour de
France.
(c) Comment on the overall distribution.

7.
Question Level 5-6:
Question 4:
The following table shows the rainfall in cm in Limerick from 2000 to 2008.
Below is the associated scatter plot for the above data.
(a) Find the mean point of the data.
Year
(𝒙)
2000 2001 2002 2003 2004 2005 2006 2007 2008
Rainfall
(𝒚)
42 51 39 44 31 33 30 28 21

8.
(b) Find the equation of the line of best fit.
(c) Use this equation and to predict the rainfall in 2022.
(d) Comment on your answer from part (e).

9.
Question 5:
The table shows some information about the weights of 32 rugby players.
Weight (w kg) Frequency
80 ≤ w < 90 5
90 ≤ w < 100 7
100 ≤ w < 110 6
110 ≤ w < 120 10
120 ≤ w < 130 4
(Data source: Rugby Football Union)
The incomplete histogram shows some of this data.
(a) Complete the histogram and label the axes.
(b) Work out an estimate of the mean weight of the 32 rugby players.

10.
Question Level 7-8:
Question 6:
There were 20 people in a figure-skating competition. The mark (𝑥) for each person was
recorded.
(a) Given that ∑ 𝑥 = 280, show that the mean mark (𝜇) is 14.
(b) Given that variance can be calculated by
𝜎!
=
∑ 𝑥!
𝑛
− 𝜇!
and ∑ 𝑥!
= 4220, show that the standard deviation (𝜎) of the marks is 3.9 to one decimal
place.

11.
(c) Use the variance formula given above to show that doubling the mark for each person
would result in the variance increasing by a factor of 4.

12.
Question 7:
A student who works at a restaurant recorded the meal cost and the tip left by
single diners.
(a) (i) Find the correlation coefficient.
(ii) Discuss the meaning of the value of the correlation coefficient.
(iii) Discuss the relationship between the cost of a meal and the tip left.

13.
(b) Calculate the equation of the y on x regression line.
(c) Use your regression line to estimate the tip left if the cost of the meal was $53.
(d) Is your answer in (c) sensible? Explain.