GCSE Sample Test
Paper 3
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Work out the square root of 100 million.

Circle your answer.

10 000
100 000
1 000 000
[1 mark]

a =  and   b =

Circle the vector a – b

[1 mark]

Circle the decimal that is closest in value to

[1 mark]

y is directly proportional to x.
Which graph shows this?

Choose the correct letter.

[1 mark]

In 1999 the minimum wage for adults was £3.60 per hour.
In 2013 it was £6.31 per hour.

Work out the percentage increase in the minimum wage.

% (to 1 d.p.) [3 marks]

A bag contains counters that are red, blue, green or yellow.

Number of counters93xx – 52x

A counter is chosen at random.
The probability it is red is

Work out the probability it is green.

[4 marks]

Use your calculator to work out 19.422 ÷ 4.95

Write down your full calculator display to 2 decimal places.

[1 mark]

The exterior angle of a regular polygon is 45°

Circle the name of the regular polygon.

[1 mark]

ABC is a triangle with AB = AC
BA is parallel to CD.

Work out angle x

x = ° [3 marks]

The pressure at sea level is 101 325 Pascals.

Any rise of 1 km above sea level decreases the pressure by 14%

For example,

at 3 km above sea level the pressure is 14% less than at 2 km

Work out the pressure at 4 km above sea level.

Give your answer to 2 significant figures.

Pascals [4 marks]

Tick whether each statement is true or false.


When x2 = 16 the only value that x can be is 4

[1 mark]

When n is a positive integer, the value of 2n is always a factor of the value of 20n.

[1 mark]

When y is positive, the value of y2 is always greater than the value of y.

[1 mark]

Here are the examination marks for 60 pupils.

Mark, m (%)Frequency
0 ≤ m < 208
20 ≤ m < 409
40 ≤ m < 6021
60 ≤ m < 8010
80 ≤ m < 10012

Molly drew this cumulative frequency graph to show the data.



How many pupils scored 50 marks or more

[2 marks]

The median mark

% [2 marks]

The nth term of a sequence is 2n + 2n – 1

Work out the 10th term of the sequence.

[1 mark]

The nth term of a different sequence is 4(2n + 2n – 1)

Circle the expression that is equivalent to 4(2n + 2n – 1)

2n + 2 + 2n + 1
22n + 22(n – 1)
8n + 8n – 1
2n + 2 + 2n – 1
[1 mark]

The diagram shows a design for a zipwire.

The zipwire will run between the top of two vertical posts, AB and CD.

Work out the distance AD.

m (to 1 d.p.) [4 marks]

During a game, players can win and lose counters.

At the start of the game

Rob, Tim and Zak share the counters in the ratio 5 : 6 : 7

At the end of the game

Rob, Tim and Zak share the same number of counters in the ratio 7 : 9 : 8

Work out Rob's counters at end of the game.

He has more counters
He has less counters
He has the same number of counters
Cannot tell
[3 marks]

Factorise 3x2 + 14x + 8

[2 marks]

Here is some information about the number of books read by a group of people in 2014

One of the frequencies is missing.

Number of booksFrequencyMidpoint
0 – 4162
5 – 97
10 – 142012
15 – 191017

Midpoints are used to work out an estimate for the mean number of books read.
The answer is 8.5

Work out the missing frequency.

[5 marks]

Here are two function machines, A and B.

Both machines have the same input.

Work out the range of input values for which

the output of A is less than the output of B.

Input value [4 marks]

In the triangle, angle y is obtuse.

Work out the size of angle y.

y = ° (to the nearest degree) [3 marks]

A box is a cuboid with dimensions 27 cm by 15 cm by 20 cm
These dimensions are to the nearest centimetre.

DVD cases are cuboids with dimensions 1.5 cm by 14.3 cm by 19.2 cm
These dimensions are to the nearest millimetre.


What is the maximum length of 16 DVDs packed as in the diagram?

cm [2 marks]

Will 17 DVDs definitely fit in the cuboid in this way?

[2 marks]

Bag X contains 9 blue balls and 18 red balls.
Bag Y contains 7 blue balls and 14 red balls.

Liz picks a ball at random from bag X.
She puts the ball into bag Y.
Mike now picks a ball at random from bag Y.

Work out

P (Liz picks a blue ball)

P (Mike picks a blue ball)

P (Liz picks a blue ball) =
P (Mike picks a blue ball) = [4 marks]

A container is filled with water in 5 seconds.
The graph shows the depth of water, d cm, at time t seconds.


The water flows into the container at a constant rate.

Which diagram represents the container?
Choose the correct letter.

[1 mark]

Use the graph to estimate the rate at which the depth of water is increasing at 3 seconds.

(to the nearest cm/s) [2 marks]

Amina and Ben had a cycle race.
Here is Amina’s speed-time graph from the start of the race.

The distance of the race was 400 metres.
Ben cycled the 400 metres in 64 seconds.

How many meters did Amina cycle in 64 seconds? Who won the race?

m, so won the race. [4 marks]

In triangle ABC

M is the midpoint of AC

N is the point on BC where BN : NC = 2 : 3

AC = 2a

AB = 3b


Work out MN in terms of a and b.
Give your answer in its simplest form.

[3 marks]

From your answer to part (a) which of these options is true:

MN is parallel to AB
MN is not parallel to AB
You cannot tell whether MN is parallel to AB or not parallel
[1 mark]

An approximate solution to an equation is found using this iterative process.

xn+1 = and x1 = −1


Work out the values of x2 and x3

x2 =

x3 =

[2 marks]

Work out the solution to 6 decimal places.

x3 = [1 mark]

The curve with equation y = x2 – 5x + 2 is reflected in the x-axis.

Circle the equation of the reflected curve.

y = x2 – 5x – 2
y = –x2 + 5x + 2
y = –x2 + 5x – 2
y = x2 + 5x + 2
[1 mark]

The diagram shows a line joining O to P.

The gradient of the line is 2

The length of the line is

Work out the coordinates of P.

P(, ) [4 marks]
Test check
Total: - of marks