GCSE, H, NC online test 1

Q1 Area

Two walls of a bathroom need tiling. The walls are shown below.


One wall is 3 metres by 3 metres.
The other wall is 3 metres by 4 metres with a window which is 1 metre by ½ metre.

a) Work out the area that needs tiling

Tiles are squares measuring 25cm by 25 cm. They cost £3.00 each
b) Calculate the costs of tiling the bathroom


Q2 Algebra

a) Expand y (y – 5)

b) Expand and simplify (5x – 2)( x + 3)

c) Simplify 10a2 – 6b – 3a2 + 3b - b

d) Factorise 9x2 – 4

e) Solve 21a2 +5a = 4


Q3 Number

Given that

 543 × 21 = 11403

find the value of

a) 54.3 × 2.1

b) 0.543 × 0.21

c) 1140.3 ÷ 5.43


Q4 Fractions

For a qualification 2/5 of the marks were given for coursework.
The rest of the marks were given for a written paper of which 3/8 were given for a mental test.
Total marks were out of 120.
How many marks were given for the mental test.


Q5 Similar shapes

Two mathematically similar cylinders are shown .

The volume of the smaller cylinder is 50 cm3 Calculate the volume of the larger cylinder.


Q6 Probability

Cyril had a pack of playing cards.
Each card in the pack was either green or blue with a circle, square, triangle or rectangle symbol. The table shows the probability of picking different cards.

Cyril picked two cards at random without replacement.

a) What is the probability of picking a blue card and a green card.

Cyril put the cards back, then picked two cards at random without replacement.
b) What is the probability of not picking a card with the square symbol


Q6b Probability

A bag contained some blue and green balls. Two balls are picked at random without replacement

The probability of picking a blue ball on the first selection is
The probability of picking two blue balls is

How many blue balls were in the bag



What is the Lowest Common Multiple of 420 and 540


Q8 Straight line graph

Poppy had an internet business selling socks. She starts by charging £5.00 for each pair plus postage of £3 for each order.

a) Get some graph paper and plot the equation  y = 5x + 3

In a special offer, Poppy reduced the price for a pair of socks to £4, but increased postage to £6. On the same graph plot the equation for this special offer.

b) Use the graphs to compare both offers and work out for how many pairs of socks they charge the same.


Q9 Payslip calculations

Matt looked at his yearly income statement and noticed some missing values.
Copy the statement and use the formula below to complete it


His taxable pay is worked out using the tax code 747L.
This means, he doesn't pay tax on £7475 of his gross pay.

a) Taxable Pay = Gross Pay – £7475.
Work out Matt's Taxable Pay.

b) Matt's Income tax = 20% of Taxable Pay.
Work out Matt's Income tax.

c) Matt's Total Deductions = Income Tax + NI (national Insurance)
Work out Matt's Total Deductions.

d) Net Pay = Gross pay – Total deductions.
Work out Matt's Net Pay.


Q10 Proportions

Peter made some bricklaying mortars using the proportions:

1 part cement
¼ part lime
3 parts sand

He made 34 kg of mortar. Work out the proportions in kg for each.


Q11 Using formula

The formula

v2 = u2 + 2as

gives the velocity v of an object dropped from a height.

u is the starting velocity of an object
v is the final velocity of an object
a is the acceleration due to gravity. a = 9.8 on Earth.
s is the height dropped in metres.

a) An object is dropped from rest and reaches a final velocity of 10m/s
Calculate the height dropped to 1 decimal place.

Another object has an initial velocity of 20 m/s and falls 25m
u = 20m/s; s = 25m

b) Calculate the final velocity v to 1 decimal place.


Q12 Best value

Chantelle wants to buy two pairs of trainers.
Three shops sell the trainers she wants, as shown below

DW ShoesCB SportJoggers
Normally £40

1/5th off
Normally £38

15% off
Normally £43

Buy one pair
get 2nd pair
half price

Calculate which shop is the cheapest for two pairs of trainers


Q13 Algebra

a) Make y the subject of the formula .

algebra fraction

b) Simplify subject formula

c) Simplify simplify

d) Solve the simultaneous equations


Q14 Transformation

Enlarge triangle A by scale factor of – 1½ , centre O.



Q15 Reverse Percentage

The sale price for a coat was £108.
The normal price was reduced by 20%.
Work out the normal price for the coat.


Q16 Complete the square

Given that x2 – 8x – 4 = (x – a)2 + b 
find a and b

Hence solve x2 – 8x – 4 = 0

Give your answer in the form    c ± d√5


Q17 Proportion

The amount of energy (E) released when matter is converted to energy is proportional to mass of that object (m).

When E = 9 × 1013 Joules, m = 1 × 10–3 kg
a) Find a formula for E in terms of m giving your answer in standard form

b) Calculate the mass, in kg when E = 1.8 × 1015 Joules
Give your answer in standard form

c) Calculate the energy, in joules when m = 0.00000015 kg
Give your answer in standard form


Q18 Vectors

ACDE is a rectangle with:
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


Q19 Cumulative Frequency

A survey of 100 trainee teachers was made to see how long they spent revising for their QTS numeracy test
The table below shows how long in hours the trainee teachers spent.

Time (t hours)Frequency
0 ≤ t ≤ 48
4 ≤ t ≤ 823
8 ≤ t ≤ 1237
12 ≤ t ≤ 1625
16 ≤ t ≤ 207

a) Complete the cumulative frequency table

Time (t hours)Cumulative
0 ≤ t ≤ 48
0 ≤ t ≤ 8 
0 ≤ t ≤ 12 
0 ≤ t ≤ 16 
0 ≤ t ≤ 20 

Get some graph paper and use your completed table to draw a cumulative frequency graph

c) One quarter of the trainee teachers spent x hours or more revising.
Using the cumulative frequency graph estimate the value of x.


Q20 Recurring decimal

Prove that the recurring decimal


Q21 Graph transformation

The diagram shows a sketch of y = f(x).
graph transformation

a) For a graph of y = f(2x) what are the co-ordinates of points A and B.

b) For a graph of y = –2f(x) what are the co-ordinates of points A and B.