GCSE Sample Test
Paper 2
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Which sequence is a geometric progression?

Circle your answer.

1 2 3 4
1 2 4 7
1 2 4 8
1 2 3 5
[1 mark]

Which of these is not used to prove that triangles are congruent?

Circle your answer.

[1 mark]

Circle the expression that is equivalent to 2a + 5a × 4aa

a + 20a2
2a + 15a2
[1 mark]

Circle the equation of a line that is parallel to y = 5x – 2

y = 2x – 5
y = 5x + 2
y = 3x – 2
y = –x – 2
[1 mark]

In a sale, the original price of a bag was reduced by
The sale price of the bag is £29.40

Work out the original price.

£ [3 marks]

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

S = square numbers

E = even numbers


Complete the Venn diagram.

[3 marks]

One of the numbers is chosen at random.
Write down P(S ∩ E)

[1 mark]

A coin is rolled onto a grid of squares.
It lands randomly on the grid.
To win, the coin must land completely within one of the squares.

Meera and John each roll the coin a number of times and record their results.

Number of winsNumber of losses

Work out two different estimates for the probability of winning.

and [2 marks]

Which of your estimates is the better estimate for the probability of winning?

[1 mark]

Here is the graph of 4x – 3y = 12 for values of x from 0 to 4

By drawing a second graph on the grid, work out an approximate solution to the simultaneous equations

4x – 3y = 12   and   3x + 2y = 6

x =

y = [3 marks]


Written as the product of its prime factors

672 = 25 × 3 × 7


Write 252 as the product of its prime factors.

[2 marks]

Work out the value of the highest common factor of 672 and 252

[1 mark]

At a school

number of boys : number of girls = 9 : 7

There are 116 more boys than girls.

Work out the total number of students at the school.

[3 marks]

Circle the equation with roots 4 and −8

4x(x – 8) = 0
(x – 4)(x + 8) = 0
x2 – 32 = 0
(x + 4)(x – 8) = 0
[1 mark]

R =

x = 3.6 × 105

y = 7.5 × 104

Work out the value of R.

Give your answer in standard form to an appropriate degree of accuracy.

R = × 10 [3 marks]

Two spheres have radii in the ratio 5 : 3

Circle the ratio of their volumes.

5 : 3
15 : 9
25 : 9
125 : 27
[1 mark]

A pattern is made from two similar trapeziums.

Work out the area of the shaded part.

cm2 [4 marks]

The pattern has one line of symmetry.

Work out the size of angle x.

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

Ann picks a 4-digit number.

The first digit is not zero.

The 4-digit number is a multiple of 5

How many different 4-digit numbers could she pick?

[3 marks]

c is a positive integer.

Prove that is an even number.

Which of these options is true

The expression is even
The expression is odd
You cannot tell whether the expression is even or odd
[3 marks]

The distance from the Earth to the Sun is 93 million miles.


it takes 365 days for the Earth to travel once around the Sun

the Earth travels in a circle with the Sun at the centre.


Work out the average speed of the Earth in miles per hour.

× 10 miles per hour [4 marks]

It actually takes 365 days for the Earth to travel once around the Sun.

How does this affect your answer to part (a)?

[1 mark]

In the formula T = (n − 6)2 + 1   n is a positive integer.


Kim says,

“The value of T is always greater than 1

because (n − 6)2 is always greater than 0”

Comment on her statement.

[1 mark]

What is the only value of T that is a square number?

[1 mark]

f(x) = 3x

Circle the expression for f−1(x)

[1 mark]

y is directly proportional to


Work out the value of a.

a = [4 marks]

A company makes boxes of cereal.
A box usually contains 450 grams of cereal.

Here are two options for a special offer.

Which option is the better value for the customer?

[3 marks]

The histogram shows the ages, in years, of members of a chess club.

There are 22 members with ages in the range 40 ≤ age < 65

Work out the number of members with ages in the range 25 ≤ age < 40

[4 marks]

A bowl is a hemisphere with radius 6 cm. Water fills two-fifths of the volume of the bowl.

The water is poured into a hollow cone. The depth of the water in the cone is 12 cm

Volume of a sphere = πr3   where r is the radius.

Volume of a cone = πr2 h   where r is the radius and h is the perpendicular height

Work out the radius of the surface of the water in the cone.

r = (to 1 d.p.) [4 marks]

A Big Wheel is modelled as a circle with centre O and radius 15 metres.
The wheel turns in an anticlockwise direction.
The lowest point on the wheel is always 2 metres above horizontal ground.


C is a point on the wheel, h metres above horizontal ground.
Angle COB = x°

Find an expression of h in terms of x.

h = ° [2 marks]

D is a point on the wheel.
Angle DOB = 120°

Work out the height of D above horizontal ground.

[2 marks]

2x2 − 6x + 5 can be written in the form a(xb)2 + c
where a, b and c are positive numbers.


Work out the values of a, b and c.

a =

b =

c =

[3 marks]

Using your answer to part (a), or otherwise, solve 2x2 – 6x + 5 = 8.5

x = and [3 marks]

Two boxes are made with card.
The boxes are similar cuboids.
The smaller box has height 32 cm

It takes 44% more card to make the larger box.

Work out the height, h, of the larger box.

h = cm [4 marks]
Test check
Total: - of marks