GCSE, 9-1 H, NC online exam


Q1 Algebra, pythagoras

The perimeter of this isosceles triangle is 16cm

area triangle

What is the area of the triangle


Q2 Venn Diagram

A group of 55 pupils were asked if they owned a phone or a tablet.

11 said they owned both

18 said they only owned a tablet

34 said they owned a phone

a) Draw a Venn diagram to show the information.

b) A student is chosen at random from the group.
What is the probability that the student doesn't have a phone or tablet


Q3 Ratio

Matt had 3 piles of coins, A, B and C.
Altogether there was 72p.
Pile B had twice as much as pile A.
Pile C had three times as much as pile B.

How long was each pile of coins


Q4 Angles

Work out the size of the angle marked x.


Q5 Fractions

Work out

a) 3 ½ – 2 ⅓
Give your answer as a mixed number in its simplest form

b) 2 ½ + 3 ½ × 4 ½
Give your answer as a fraction


Q6 Equation line
equation line

Find the equation of the line on the graph above


Q7 Prime factors

Write 252 as a product of its prime factors


Q8 Distance-time graph

Look at the distance time graph.

distance time

Q: Calculate the speed for parts A, B, C and D of the graph.


Q9 Probability tree

Laura is going to play one game of chess and one game of draughts.

The probability that she will win the game of chess is ⅗

The probability that she will win the game of draughts is ⅜

probability tree

(a) Complete the probability tree diagram.

(b) Work out the probability that Laura will win exactly one game.


Q10 Standard form

Work out

( 4 × 103 )2 + 3.5 × 107

Give your answer in standard form.


Q11 Volume

A spherical ball has a diameter of 10.4cm.

Volume of sphere = 4/3 πr3

a) Estimate the volume of the ball.

b) Is your answer to part a an underestimate or an overestimate.
Explain why.


Q12 Percentage

In a test out of 25 marks David got 32%

In another test out of 32 marks Jane got 75%

What was the difference between their marks


Q13 Bisect

Construct the bisector of the angle ABC



Q14 Cumulative Frequency

A survey of 100 adults was made to see how many hours they spent watching TV each week.
The table below shows how long in hours the adults spent.

Complete the cumulative frequency table

TimeFreqTimeCum Freq
0<t≤5 80<t≤5 
5<t≤10 180<t≤10
10<t≤15 260<t≤15
15<t≤20 280<t≤20
20<t≤25 140<t≤25
25<t≤30 60<t≤30

b) On the grid draw a cumulative frequency graph for your table

cum freq

c) Use your graph to find the median time spent watching TV

d) Estimate how many adults watched more than 17 hours TV per week.


Q15 Powers





Q16 Recurring decimals

Express this recurring decimal as a fraction


Q17 Similar shapes

Q: Two cones, A and B, are mathematically similar.
The total surface area of A is 18 cm2
The total surface area of cone B is 162 cm2
The height of cone A is 8 cm.

Work out the height of cone B.


The volume of cone B is 135cm3

Work out the volume of cone A


Q18 Subject of formula

Make y the subject of the formula.

subject formula


Q19 Proof

Prove algebraically that

 (3n + 1)2 – (3n + 1)

 is an even number for all positive integer values of n.


Q20 Vectors

ACDE is a rectangle with = 4b, = 5a and = 8b
M is the midpoint of AC
ABC is a right angled triangle


Write each of the following vectors in terms of a and b



c) Show that M is the midpoint of the line BE


Q21 Circle Theorem
circle theorem

A and B are points on the circumference of a circle, centre O.

CB is a tangent to the circle.
COA is a straight line.
Angle OCB = 34°.

Work out the size of the angle marked x.

Give reasons for your answer.


Q22 Algebra - quadratics


x2 + 4x – 21 / 2x2 – 5x – 3


Q23 Surds

Simplify by rationalising the denominator.

7 – √5 / 9 + √5


Q24 functions and inverse function

Functions f and g are such that f(x) = x2 and g(x) = x – 3

Solve the equation gf(x) = g–1(x).