Question 1
The diagram is a plan of the floor of Nikola’s room.
All the angles are right angles.
Nikola is going to lay flooring to cover the entire floor.
She can choose either carpet tiles or wood strips.
Carpet tiles come in packs of 32 and are square.
They measure 50 cm by 50 cm.
Wood strips come in packs of 10 and are rectangular.
They measure 2 m by 25 cm.
She only wants to use one type of flooring and buy as few
packs as she can.
Which type of flooring
should she choose?
Question 1
The diagram is a plan of the floor of Nikola’s room. All the angles are right
angles. Nikola is going to lay flooring to cover the entire floor. She can choose
either carpet tiles or wood strips.
Carpet tiles come in packs of 32 and are square. They measure 50 cm by 50 cm.
Wood strips come in packs of 10 and are rectangular. They measure 2 m by 25
cm. She only wants to use one type of flooring and buy as few packs as she can.
Which type of flooring should she choose?
Model Answer:

Calculate area of the room
= 4 × 8 + 4 × 6 = 56

Calculate area of a tile
= 0.5 × 0.5 = 0.25

Calculate number of tiles
= 56 ÷ 0.25 = 224

Calculate how many packs of tiles needed
224 ÷ 32 = 7

Calculate area of wood strips
= 2 x 0.25 = 0.5

Calculate number of wood strips
56 ÷ 0.5 = 112

Calculate how many packs of wood strips needed
112 ÷ 10 = 11.2
If Nikola used the wood strips she would need 12 packs so she
should use the carpet tiles as she will need 7 packs of those.
Question 2
Imran wants to work out how much tax he needs to pay.
Last year he earned £18 000
He does not pay Income tax on the first £6475 he
earned.
He pays tax of 20 pence for each pound he earned
above £6475
He pays the tax in two equal half-yearly instalments.
(a) How much Income tax does Imran have to pay in his
first half-yearly instalment?
Imran wants to know what percentage of his earnings he
pays in tax.
(b) Calculate the Income tax Imran has to pay as a
percentage of his earnings last year.
Question 2
Imran wants to work out how much tax he needs to pay.
Last year he earned £18 000
He does not pay Income tax on the first £6475 he earned.
He pays tax of 20 pence for each pound he earned above £6475
He pays the tax in two equal half-yearly instalments.
a)
How much Income tax does Imran have to pay in his first half-yearly instalment?
Imran wants to know what percentage of his earnings he pays in tax.
(b) Calculate the Income tax Imran has to pay as a percentage of his earnings last
year.
Model Answer:
a)

Calculate how much of his earnings Imran pays tax on.
18000 – 6475 = 11525


Calculate how much tax he pays on those earnings above
the tax threshold
Calculate the first half yearly tax instalment
2305 ÷ 2 = 1152.5
b)
 Calculate percentage of earnings that Imran pays tax on
Question 3
Tania went to Italy.
She changed £325 into euros (€).
The exchange rate was £1 = €1.68
(a)
Change £325 into euros (€).
When she came home she changed €117 into
pounds.
The new exchange rate was £1 = €1.50
(b)
Change €117 into pounds.
Question 3
Tania went to Italy.
She changed £325 into euros (€).
The exchange rate was £1 = €1.68
(a)
Change £325 into euros (€).
When she came home she changed €117 into pounds.
The new exchange rate was £1 = €1.50
(b)
Change €117 into pounds.
Model Answer:
a) Calculate how many euros Tania will get
for £325
£325 x €1.68 = €546
b) Calculate how many pounds Tania will
get for €117
€117 ÷ €1.5 = £78
Question 4
David buys some stamps.
Each stamp costs 25p.
The total cost of the stamps is £3
(a) Work out the number of stamps David buys.
(b) Adam, Barry and Charlie buy some stamps.
Adam buys x stamps.
Barry buys three times as many stamps as Adam.
Write down an expression, in terms of x, for the
number of stamps Barry buys.
(c) Charlie buys 5 more stamps than Adam.
Write down an expression, in terms of x, for the
number of stamps Charlie buys.
Question 4
David buys some stamps.
Each stamp costs 25p.
The total cost of the stamps is £3
(a) Work out the number of stamps David buys.
Adam, Barry and Charlie each buy some stamps.
Adam buys x stamps.
Barry buys three times as many stamps as Adam.
(b) Write down an expression, in terms of x, for the number of
stamps Barry buys.
Charlie buys 5 more stamps than Adam.
(c) Write down an expression, in terms of x, for the number of
stamps Charlie buys.
Model Answer:
a)
Calculate the amount of stamps bought.
300p ÷ 25p = 12 stamps
b)
Write an algebraic expression for the number of
stamps Barry bought.
3
c)
Write an algebraic expression for the number of
stamps Charlie buys.
Question 5
Mr and Mrs Jones are planning a holiday to the Majestic
Hotel in the Cape Verde Islands. The table gives
information about the prices of holidays to the Majestic
Hotel.
MAJESTIC HOTEL, Cape Verde Islands
Departures
1 Jan – 8 Jan
9 Jan – 28 Jan
29 Jan – 5 Feb
6 Feb – 18 Feb
19 Feb – 8 Mar
9 Mar – 31 Mar
1 Apr – 9 Apr
10 Apr – 30 Apr
Price per adult
7 nights
14 nights
£ 694
£ 825
£ 679
£ 804
£ 687
£ 815
£ 769
£ 835
£ 714
£ 817
£ 685
£ 805
£ 788
£ 862
£ 748
£ 802
Price per child: 95% of adult price for 7 nights or
85% of adult price for 14 nights.
Mr and Mrs Jones are thinking about going on holiday
on 20 February for 7 nights
or
on 10 April for 14 nights.
Mr and Mrs Jones have 2 children. Compare the costs
of these two holidays for the Jones family.
Question 5
Mr and Mrs Jones are planning a holiday to the Cape Verde Islands. The table gives
information about the prices of holidays to the Majestic Hotel.
MAJESTIC HOTEL, Cape Verde Islands
Departures
19 Feb – 8 Mar
10 Apr – 30 Apr
7 nights
£ 714
£ 748
Price per adult
14 nights
£ 817
£ 802
Price per child: 95% of adult price for 7 nights or 85% of adult price for 14 nights.
Mr and Mrs Jones are thinking about going on holiday on 20 February for 7 nights or on
10 April for 14 nights. Mr and Mrs Jones have 2 children. Compare the costs of these
two holidays for the Jones family
Model Answer:
 Calculate the cost of two adults for 20th February
714 × 2 = 1428
 Calculate the cost of two children for 20th February
714 × 0.95 = 678.30 (1 child)
678.30 × 2 = 1356.60 (2 children)
 Calculate the cost of two adults and 2 children for 20th February
1428 + 1356.60 = 2784.60
 Calculate the cost of two adults for 10th April
802 × 2 = 1604
 Calculate the cost of two children for 10th April
802 × 0.85 = 681.70 (1 child)
681.70 × 2 = 1363.40 (2 children)
 Calculate the cost of two adults and 2 children for 10th April
1604 + 1363.40 = 2967.40
 Compare the cost of 20th February and 10th April for one week
(allow marks for per day)
20th February = £2784.60
10th April = £1483.7, this is the cheapest option
Question 6
Kylie wants to invest £1000 for one year.
She considers two investments, Investment A and
Investment B.
Investment A
Investment B
£1000
£1000
Earns £2.39 per month
Earns £2.39 per annum
PLUS
Interest paid yearly by
£4.50 bonus for each
complete year
Cheque
Interest paid monthly by
cheque
Kylie wants to get the greatest return on
her investment.
Which of these investments should she
choose?
Question 6
Kylie wants to invest £1000 for one year.
She considers two investments, Investment A and Investment B.
Kylie wants to get the greatest return on her investment.
Which of these investments should she choose?
Model Answer:
 Calculate interest from Investment A
2.39 × 12 + 4.5 = 33.18
 Calculate interest from Investment B
3.29/100 × 1000 = 32.90
Investment A will pay out more than Investment B
so Kylie should choose Investment A.
Question 7
The diagram shows a wall in Jenny’s kitchen.
Jenny wishes to tile this wall in her kitchen.
She chooses between the two types of tile shown
below.
Which tiles should Jenny use to spend the least
amount of money on tiling the wall?
You must show all of your working.
Question 7
The diagram shows a wall in Jenny’s kitchen. Jenny wishes to tile this wall in her kitchen.
She chooses between the two types of tile shown below. Which tiles should Jenny use to
spend the least amount of money on tiling the wall?
Model Answer:

Calculate how many Type A tiles are needed for large area
330 ÷ 10 = 33 A tiles per long row
40 ÷ 10 = 4 long rows
33 × 4 = 132 tiles
 Calculate how many Type A tiles are
needed for small area
90 ÷ 10 = 9 tiles per short row
30 ÷ 10 = 3 short rows
9 × 3 = 27 tiles

Calculate total cost of Type A tiles
132 + 27 = 159 tiles
No of boxes needed
= 8 (20 × 8 = 160 tiles)
£9.99 × 8 = £79.92

Calculate how many Type B tiles are needed for large area
330 ÷ 15 = 22 B tiles per long row
40 ÷ 15 = 3 long rows (1 row of tiles will be cut)
22 × 3 = 66 A tiles

Calculate how many Type B tiles are needed for small area
90 ÷ 15 = 6 tiles per short row
30 ÷ 15 = 2 short rows
6 × 2 = 12 tiles

Calculate total cost of Type B tiles
66 + 12 = 78 tiles
No of boxes needed
= 7 (12 × 7 = 84 tiles)
£11.49 × 7 = £80.43
Jenny should use Type A
tile (£79.92) as they are
cheaper than the Type B
tiles ( £80.43)
Question 8
Mrs White wants to buy a new washing machine.
Three shops sell the washing machine she wants.
Clean Machines
Washing
Machine
Buy now pay
later!
Electrics
Washing
Machine
Wash ‘n’ Go
Washing
Machine
off the usual
£280
price
£50 deposit plus
of
Plus
10 equal
payments of £27
£420
VAT at 17.5%
Mrs White wants to buy the cheapest one.
She decides to buy her washing machine from one of
these 3 shops.
From which of these shops should she buy her washing
machine?
You must show how you decided on your answer.
Question 8
Mrs White wants to buy a new washing machine. Three shops sell the washing
machine she wants.
Clean Machines
Washing Machine
Buy now pay later!
Electrics Washing
Machine
off the usual price
Wash ‘n’ Go Washing
Machine
£280
£50 deposit plus
Of
Plus
10 equal payments of
£27
£420
VAT at 17.5%
Mrs White wants to buy the cheapest one. She decides to buy her washing
machine from one of these 3 shops. From which of these shops should she buy
her washing machine? You must show how you decided on your answer.
Model Answer:
 Calculate the cost from clean machines
50 + (10 × 27) = 320
 Calculate the cost from Electrics
420 ÷ 4 = 105
420 - 105 = 315
 Calculate the cost of Wash ‘n’ Go
280 × 0.175 = 49
49 + 280 = 329
Mrs White should buy her washing machine from Electrics as it is the
cheapest at £315.
Question 9
Jason earns £50 000 a year.
He has to pay income tax.
He is allowed to earn £6500 before paying
tax.
He pays 20% tax on the next £37 400.
He then pays 40% tax on the rest.
His employer deducts the income tax each
month.
How much income tax does Jason get
deducted each month?
Question 9
Jason earns £50 000 a year.
He has to pay income tax.
He is allowed to earn £6500 before paying tax.
He pays 20% tax on the next £37 400.
He then pays 40% tax on the rest.
His employer deducts the income tax each month.
How much income tax does Jason get deducted each month?
Model Answer:
 Calculate the 20% tax on £37400
20% of £37 400 = £7480
 Calculate the earnings Jason pays 40% tax on
50 000 – 37 400 – 6500 = £6100
 Calculate 40% tax on £6100
40% of 6100 = £2440
 Calculate how much tax he pays in total each year
7480 + 2440 = 9920
 Calculate how much tax Jason pays each month
9920 ÷ 12 = 826.666666
Jason pays £826.67 each month in tax.
Question 10
Alan bought 20 melons for £15.
of the melons were bad so he threw
them away.
He sold the remaining melons for £1.50
each.
Work out Alan’s profit.
Question 10
Alan bought 20 melons for £15.
of the melons were bad so he threw them away.
He sold the remaining melons for £1.50 each.
Work out Alan’s profit.
Model Answer:
 Calculate how many melons Alan threw away
20 ÷ 5 = 4 bad melons
 Calculate how many melons Alan sold
20 – 4 = 16 melons sold
 Calculate total income of sold melons
16 × 1.50 = 24
 Calculate profit of melons
24 – 15 = 9
Alan made £9 profit
Question 11
Jennie’s council has a target of for
households to recycle their waste.
In January, Jennie recycled
household waste.
of her
In February, she recycled 15 kg of her 120
kg of household waste.
Her result for March was 13% recycled out
of 112 kg of household waste.
Has Jennie met the council’s target?
Which was her best month for recycling?
Show clearly how you got your answers.
Question 11
Jennie’s council has a target of
for households to recycle their waste.
In January, Jennie recycled
of her household waste.
In February, she recycled 15 kg of her 120 kg of household waste.
Her result for March was 13% recycled out of 112 kg of household waste.
Has Jennie met the council’s target?
Which was her best month for recycling?
Show clearly how you got your answers.
Model Answer:
Fraction
In January she
recycled
Decimal
%
kg
0.1
10%
Not
known
0.125
12.5%
15 kg
0.13
13%
14.56 kg
In February she
recycled
(equivalent fractions)
In March she
recycled
So Jennie has NOT met the target of
(20%)
Her best month for recycling was March (13%)
Question 12
Last year Sasha was paid £15400 after
deductions from her gross salary.
She was paid 70% of her gross salary.
This year Sasha’s gross salary increased
by 2%.
Work out the increase in Sasha’s gross
salary.
Give your answer in pounds.
Question 12
Last year Sasha was paid £15400 after deductions from her gross salary.
She was paid 70% of her gross salary.
This year Sasha’s gross salary increased by 2%.
Work out the increase in Sasha’s gross salary. Give your answer in pounds.
Model Answer:
 Calculate last years total earnings
15400 ÷ 70 × 100 = £22000
 Calculate 2% of last years total earnings
22000 × 2 ÷ 100 = £440
Question 13
There are some sweets in a bag.
18 of the sweets are toffees.
12 of the sweets are mints.
(a)
Write down the ratio of the number of
toffees to the number of mints.
Give your ratio in its simplest form.
(b) There are some oranges and apples in a box.
The total number of oranges and apples is 54.
The ratio of the number of oranges to the
number of apples is 1 : 5.
Work out the number of apples in the box.
Question 13
There are some sweets in a bag.
18 of the sweets are toffees.
12 of the sweets are mints.
(a) Write down the ratio of the number of toffees to the number of mints.
Give your ratio in its simplest form.
(b) There are some oranges and apples in a box.
The total number of oranges and apples is 54.
The ratio of the number of oranges to the number of apples is 1 : 5.
Work out the number of apples in the box.
Model Answer:
a)
Calculate the ratio of toffees to mints.
Both 18 and 12 divide by 6 so the ratio is 3:2
18 ÷ 6:12 ÷ 6
3:2
b)
Calculate the total number of shares in
the ratio
5+1=6
Calculate the amount of those shares which will fit
into 54
54 ÷ 6 = 9
Multiply the amount of shares by the ratio
5 × 9 = 45 apples
Question 14
A tin of cat food
costs 40p.
A shop has a
special offer on
the cat food.
Julie wants 12 tins of cat food.
(a) Work out how much she pays.
(b) 9 of the 12 tins are tuna.
Write 9 out of 12 as a percentage.
(c) The normal price of a cat basket is £20.
In a sale, the price of the cat basket is
reduced by 15%.
Work out the sale price of the cat basket.
Question 14
A tin of cat food costs 40p. A shop has a special offer on the
cat food. Julie wants 12 tins of cat food.
(a) Work out how much she pays.
(b) 9 of the 12 tins are tuna. Write 9 out of 12 as a
percentage.
(c) The normal price of a cat basket is £20. In a sale, the price of the cat basket is
reduced by 15%. Work out the sale price of the cat basket.
Model Answer:
a) Calculate how many tins Julia has to pay for
12 ÷ 3 = 4 sets of cans on special offer x 2 = 8 cans
Calculate how much those 8 tins cost
8 × 40p = 320p or £3.20
An alternative method
Calculate how much 3 tins cost
3 tins = 40p × 2 = 80p
Multiply this by 4 to calculate the cost of 12 tins
12 tins = 80p × 4 = 320p or £3.20
b)
can be simplified into
which is equal to 75%
c) Calculate 10% and 5% of £20 and add together
10% = 20 ÷ 10 = 2
5%=2÷2=1
15% = 2 + 1 = 3
Calculate sale price of cat basket
20 – 3 = £17
An alternative method
Calculate how much of the total cost the sale price is (85%)
20 x 0.85 = £17
Question 15
Here are the ingredients for making cheese pie
for 6 people.
Cheese pie for 6 people
180 g flour
240 g cheese
80 g butter
4 eggs
160 ml milk
Bill makes a cheese pie for 3 people.
(a) Work out how much flour he needs.
Jenny makes a cheese pie for 15 people.
(b)
Work out how much milk she needs.
Question 15
Cheese pie for 6 people
Here are the ingredients for making cheese pie for 6
people.
240 g cheese
Bill makes a cheese pie for 3 people.
(a)
Work out how much flour he needs.
180 g flour
80 g butter
4 eggs
160 ml milk
Jenny makes a cheese pie for 15 people.
(b)
Work out how much milk she needs.
Model Answer:
a) Calculate how much flour Bill needs
180 ÷ 2 = 90g of flour
b) Calculate how many times Jenny
must use this recipe for 15 people
15 ÷ 6 = 2.5
Calculate how much milk Jenny
needs for 15 people
160 x 2.5 = 400ml
Question 16
The table shows the cost of two
different models of the Eiffel Tower.
Small £2.40
Large £4.50
(a) Pierre buys 10 Small models, and 5 Large
models. He pays with a £50 note.
Work out how much change he should get.
(b) A different model of the Eiffel Tower is
made to a scale of 2 millimetres to 1 metre.
The width of the base of the real Eiffel
Tower is 125 metres.
Work out the width of the base of the
model. Give your answer in millimetres.
(c) The height of the model is 648
millimetres. Work out the height of the real
Eiffel Tower. Give your answer in metres.
Question 16
The table shows the cost of two different models of the Eiffel Tower.
Small
£2.40
Large
£4.50
(a) Pierre buys 10 Small models, and 5 Large
models. He pays with a £50 note.
Work out how much change he should get.
(b) A different model of the Eiffel Tower is made to a scale of 2 millimetres
to 1 metre. The width of the base of the real Eiffel Tower is 125 metres.
Work out the width of the base of the model. Give your answer in
millimetres.
(c) The height of the model is 648 millimetres. Work out the height of the real Eiffel
Tower. Give your answer in metres.
Model Answer:
a) Calculate how much Pierre has spent in total and deduct
this from £50.
Small model costs £2.40 x 10 = £24.00
Large model costs £4.50 x 5 = £22.50
Total spent = £24.00 + £22.50 = £46.50
£50.00 - £46.50 = £3.50
b) Calculate the base width of the model
1 m = 2 mm
125m = (2 x 125) = 250mm
c) Calculate the height of the model
2mm = 1m
648mm = (648 ÷ 2) = 324m
Question 17
Chris owns a clothes shop.
He bought 50 shirts at £12 for each shirt.
He chose the selling price of each shirt so that
he would make a profit of 30% on each shirt.
He sold 20 shirts at this price.
Chris then reduced the selling price of each
shirt by 15%.
He then sold the remaining shirts at this
reduced selling price.
Has Chris made a profit or loss?
You must explain your answer clearly.
Question 17
Chris owns a clothes shop.
He bought 50 shirts at £12 for each shirt.
He chose the selling price of each shirt so that he would make a profit of
30% on each shirt.
He sold 20 shirts at this price.
Chris then reduced the selling price of each shirt by 15%.
He then sold the remaining shirts at this reduced selling price.
Has Chris made a profit or loss?
You must explain your answer clearly.
Model Answer:

Calculate total expenditure
50 shirts at £12 each = £600

Calculate selling price of one shirt (for profit of 30%)
£12 × 1.3 = £15.60

Calculate total income from 20 shirts
20 shirts at £15.60 = £312

Calculate reduced selling price (for profit of 15%)
£15.60 × 0.85 = £13.26
 Calculate total income from 30 shirts at reduced price
30 shirts at £13.26 = £397.80

Calculate total income
£397.80 + £312 > £600
Chris made a total profit of £109.80
Question 18
CEAY and BDAX are straight lines.
XY, ED and CB are parallel.
AE = 5 cm.
AX = 9 cm.
AD = 4 cm.
BC = 4 cm.
BD = 2 cm.
CE = x cm.
XY = y cm.
Find the value of x and the value of y.
Question 18
CEAY and BDAX are straight lines.
XY, ED and CB are parallel.
AE = 5 cm.
AX = 9 cm.
AD = 4 cm.
BC = 4 cm.
BD = 2 cm.
CE = x cm.
XY = y cm.
Find the value of x and the value of y.
Model Answer:
Calculate x
Calculate y
Question 19
ABCD is a rectangle.
X is the midpoint of AB.
Y is the midpoint of BC.
Z is the midpoint of CD.
What fraction of the total area
of ABCD is shaded?
Show clearly how you get your answer.
Question 19
ABCD is a rectangle.
X is the midpoint of AB.
Y is the midpoint of BC.
Z is the midpoint of CD.
What fraction of the total area
of ABCD is shaded?
Show clearly how you get your answer.
Model Answer:
 Write an expression for area of whole rectangle
Let AB = x, AD = y
Area of rectangle =xy
 Calculate unshaded area AXD
Area AXD =
(this is ¼ of the whole rectangle)
 Calculate unshaded area CYZ
Area CYZ =
(this is ¼ of the whole rectangle)
 Calculate shaded area of rectangle
Shaded area =
=
Question 20
Mr Smith had his car
serviced.
He had to pay for a 15 000
mile service, 3 litres of oil
and 4 spark plugs.
Complete his bill, and work
out the total amount to
pay.
Item
Costs (£)
Motor oil 1L
2.50
Wiper blades 1
8.75
Brake Pads 1
14.85
Antifreeze 1L
3.99
Hydraulic Fluid 1L
5.99
Spark Plugs
1.75
Question 20
Mr Smith had his car serviced.
He had to pay for a 15 000 mile service, 3 litres
of oil and 4 spark plugs.
Complete his bill, and work out the total amount
to pay.
Model Answer:
Item
Costs (£)
Motor oil 1L
2.50
Wiper blades 1
8.75
Brake Pads 1
14.85
Antifreeze 1L
3.99
Hydraulic Fluid 1L
5.99
Spark Plugs
1.75