GCSE, 9-1 F, C2/3 online exam


Q1 - Sequence

Here are the first four terms of an arithmetic sequence

  –2    2     6     10     14

a) Write an expression, in terms of n, for the nth term of this sequence

The nth term of a different arithmetic sequence is 3n – 4

b) Is 104 a term of this sequence?
Show how you get your answer

What is the next number in this sequence
0,   1,   1,   2,   3,   5,   8,   13,   21,   34,   55,    89,   ?


Q2 Numbers and cubed root

a) Write down the value of the 2 in the number 9261

b) Find the cubed root of of 9361

Q3 Mean and speed

Henry measured how far some snails could crawl in 20 minutes.

Distance (cm)No. of snails
30 <t ≤ 34 4
34 <t ≤ 38 7
38 <t ≤ 42 16
42 <t ≤ 46 5
46 <t ≤ 50 2

a) Write down the modal class interval

b) Calculate an estimate for the mean distance to 1 decimal place.

c) Estimate the speed of the fastest snails.
Give your answer in metres per hour.


Q4 Calculation

a) Find the value of (3.9 – 0.36) + 3√6.7

David says √6 = √2 + √4 ,  Jess says √6 = √2 × √3.

b) Who is right?
Explain your answer


Q5 Decimals from fractions

In a class of 22 pupils 13 were boys. What fraction were girls.
Give your answer as a decimal to 2 significant figures


Q6 Symmetry

a) Shade in some squares to make the pattern below symmetrical


b) What order of rotational symmetry does this shape have?

rotational symmetry

Q7 Stem and Leaf

Speed signs were placed near a school to tell drivers to drive more slowly.
The stem-and-leaf diagrams show the speed of 19 cars before and after the sign was added.

stem leaf

How many mph did the median speed before and after fall by?


Q8 Pictogram

The pictogram shows how many cups of tea and cakes were sold in a tea shop in a week

a) How many teas were sold on Saturday?

Thirty teas and ten cakes were sold on Wednesday.
b) Complete the pictogram.

c) How many cakes were sold in the tea shop in the week?


Q9 Prime, square, odd numbers

Write each number in its correct place on the diagram

   21     23     25     36


Q10 Volume

A jug is partly filled with liquid.

A regular 3-D shape with dimensions shown in centimetres, is dropped into the jug.


a) What will be the new height of the liquid on the jug scale

b) What is the volume of the 3-D shape?
Give your answer in standard form in m3

c) The mass of the 3-D shape is 0.227kg
What is its density in grams per cm3

Q11 Graphs, equation line

Jane started an internet business selling socks.

In method 1, postage was £5 for any number of socks and socks cost £3 a pair.

a) Draw a line on the graph to represent this information


b) What is the equation of this line?

In method 2, she decided to increase the price of socks by ⅓ with free postage.

c) Draw a new line on the graph for method 2 and use your graph to work out how many pairs of socks cost the same for both methods

Q12 Exterior angle

a) Work out the value of y for this triangle.

find side angle

b) Work out the exterior angle marked y for this regular shape.

exterior angle

Q13 Algebra

a) Expand    (5z – 3)2

b) Factorise   10a3 – 15a2


Q14 Transformation

a) Rotate the shape A, 90° anti-clockwise about centre (– 1, 1)
Label the shape B

transformation - rotation

b) Reflect shape B in the line x = 1. Label it C.

c) Describe the transformation from shape C to shape A


Q15 Pythagoras and Bearings

A school S is directly 500m north of my house H

A cafe C is directly 600m East of my house H

a) How far is it from the school S to the cafe C?

Give your answer to the nearest metre

b) What is the bearing of the school from the cafe to 1 decimal place.

c) A tree T is directly West of my house. The distance from the tree to the school is 801m.

How far is the tree from my house. Give your answer to 2 significant figures.


Q16 Speed and distance

Poppy's house is 20 miles from David's house.

David drove 10 miles @ 30mph.

How fast will he have to drive the remaining distance to average 40mph for the trip.


Q17 Venn Diagram

Look at the Venn diagram for two sets.

a) Shade the region that represents P(A' B')

A' means NOT A

In a maths test for trainee teachers there was a mental part and a calculator part.
In a group of trainee teachers everyone passed at least one part.

85% passed the mental part and 90% passed the calculator part.

b) Show this information on a Venn diagram.


Q18 Exchange rate

Laura changed £250 into Euros. There was a fee of 1% and the exchange rate was £1 : €1.14

a) How much will she get to the nearest €?

She spent some euros and had €45 left. She exchanged that back into pounds.
There was no fee and the exchange rate was €1.15 : £0.76

b) How much will she get to the nearest £?


Q19 Ratio

Matt had 3 piles of penny coins.

In the 1st pile there was 49p, in the 2nd pile was 14p and in the 3rd pile was 35p.

What is the ratio for the money in the three piles.

Give your answer in its simplest form.


Q20 Truncation

a) Truncate 123.5 to a whole number

b) Truncate 25.599 to 1 dp

c) Truncate 2355.67 to the hundreds


Q21 Two way table

90 students were asked what subjects they liked - Art, PE or Drama.

42 of the 90 students were boys.
12 of the girls liked Drama.
6 boys liked Art.

⅔ of the 39 students who liked PE were boys.

Work out the total number of students who liked Art.


Q22 Equation line

Look at this line

equation line

Find the equation of another line that is perpendicular to the line shown and passes through the point (1 , 1)



What is the lowest common multiple of 56 and 72


Q24 Mode, mean and range

The modal age of three boys was 7 and the mean of their ages was 9

The age range of three girls was 7 and the mode of their ages was 7

Who was the oldest, a boy or a girl? Show your working.


Q25 Calculation

Calculate the value of

3.25 – 2.09  / 3.25 – 2.092

a) Write down your full calculator display

b) Give your answer to three significant figures.


Q26 Standard form

Work out

( 4 × 106 )2 ÷ (3.2 × 107)

Give your answer in standard form.


Q27 Directly proportional

The force F on a mass is directly proportional (∝) to the acceleration 'a' of the mass
When a = 250, F = 750

a) Find a formula for F in terms of a.
b) Find F when a = 140


Q28 Error Interval

a) Write the error interval for 33 kg, to the nearest kg

b) Write the error interval for 0.56 to 2 dp

c) Write the error interval of £2.50, to 2 sfs


Q29 Roots and turning points

Look at this graph of a quadratic equation.

turning points

a) Estimate the roots for x

b) Estimate the co-ordinates of the turning point of the curve


Q30 Trig ratios

a) Write the exact value of Cosine 30° [1]

b) Write the exact value of Sine 45° [1]

c) Write the exact value of Tan 60° [1]


Q31 Squared cubic reciprocal graphs

a) Sketch the graph y = x4

b) Sketch the graph y = x5

c) Sketch the graph y = 1/x