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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.

1.

GCSE Higher

A survey is carried out by asking people questions as they come out of a coffee bar.

A section of the questionnaire is shown below.

Put a tick ☑ into the box in front of your chosen answer.

1. How often do you visit a coffee bar?

☐ Every day; ☐ Once or twice each week; ☐ Never.

2. What is your gender?

☐ Female; ☐ Male.

3. What is your age group?

☐ Under 10; ☐ 10-20; ☐ 20-30; ☐ 31-40.

(a) Explain why this is a biased survey.

(b) State two criticisms of the questions or the options given for answers.


2.

GCSE Higher

Jimmy is ordering the t-shirts for the community choir which has 240 members.

He asks a sample of 36 members what colour the t-shirts should be. Each members chooses one colour.

The table shows information about his results.

Colour Number of members
Blue 6
Red 3
Green 7
Yellow 5
Purple 2
Black 6
White 7

(a) Work out how many of the 240 members you think will want black t-shirts.

(b) State any assumption you made and explain how this may affect your answer.


3.

GCSE Higher

Donna is in a class of 25 students, 5 of whom have a pet dog.

There are 2200 students in the school.

(a) Use this information to estimate how many students in the school have pet dogs.

Dogs

(b) Luka is at a different school.

She is in a class of 28 students, 7 of whom have pet dogs.

Luka and Donna have an idea. They think "In our two classes there are 53 students, 12 of whom have a pet dog. We can use this bigger sample to improve the estimate for Donna's school."

What assumption have they made?

(c) Use this idea to estimate how many students in Donna's school have pet dogs.


4.

GCSE Higher

Poppy Pringle recorded the heights in centimetres of the sunflowers growing in her brother's and sister's gardens.

Sunflower

Here are the heights of the 19 sunflowers in her brother's garden:

$$94, 103, 110, 111, 123, 143, 150, 150, 151, 156, 157, 160, 170, 182, 201, 220, 250, 255, 231$$

(a) Complete the table below to show information about this data.

Median        
Lower quartile 
Upper quartile 
Shortest 
Tallest 

Here is some information about the sunflowers in Poppy's sister's garden:

Median160
Lower quartile143
Upper quartile172
Shortest110
Tallest199

Poppy says that the sunflowers in her brother's garden are shorter that those in her sister's garden.

(b) Is Poppy correct?

You must give a reason for your answer.

Poppy says that the sunflowers in her brother's garden vary more in height than those in her sister's garden.

(c) Is Poppy correct?

You must give a reason for your answer.


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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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