Paper 1

Question 1

The price of a computer was £750. In a sale it gets reduced by 20%.

On the final day of the sale it gets reduced by a further 12%.

How much is saved in total buying the computer on the day of the sale?

Answer 1

Find 20% of 750 = 600

0.2 x 750= 150
750-150=600

Then find 12% of 600 = 528
0.12 x 600 = 72
600-72= 528

Final sale price : 750-528 = £222

Question 2

R hires a car.
It costs £150, plus 85p for each mile he travels.
When he hires the car, its mileage is 27612 miles.
When he returns the car, its mileage is 28361 miles.

How much did R pay to hire the car?

Answer 2

85p =0.85

Subtract the mileage : 28361-27612= 749 miles

He drive 749 miles.
Mileage cost : 0.85(749) = 636.65

Total cost ; 150+636.65= 786.65

Question 3

Mia puts £6400 in each account

NSB: 2.5% per year compound interest.
CAB: 2.7% per year simple interest.

Calculate the difference in value between the two accounts after 8 years (correct to the nearest penny).

Answer 3

NSB:
6400 x 1.025 ^8 = 7797. 778544

CAB: Simple interest

Find 2.7% of 6400 - 0.027(6400)= 172.8

Multiply 172.8 by 8 = 1382.4 .
Add 1382.4 to 6400 = 7782.4

7797.778544- 7782.4= 15.38

Question 4

Martin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
Find the cost of one crayon.

Answer 4

7R+15C = £7.

R= 0.12+C

7R+15C(0.12) multiply 7R by 0.12; =0.84

22C= 7-0.84= 6.16 C= 0.28

Question 5

Students deliver catalogues and leaflets to houses.

One day they have to deliver 360 catalogues and 1440 leaflets. Each student can either deliver 15 catalogues or 80 leaflets in 1 hour.

Each student can only work for 8 hours. Work out the minimum number of students needed.

Answer 5

360/15 = 24. 1440/80= 18.

24+18= 42. 42/8= 5.25. Can’t have ‘5.25 students’ so round up ~ 6

Question 6

Leo, Kush, and Mali share money in the ratio 3:5:8. Kush receives £750 more than Leo.
Calculate the amount of money that the shared.

Answer 6

Leo: 3. Kush : 5. 5-3=2

Divide 750 by 2 to find one part = £375

375(3) = 1125. 375(5)=1875. 375(8)= 3000

3000+1125+1875= 6000

Question 7

Derek has £10000 that he wants to invest.

Account A: 3% per year compound interest.

Account B: 4% for the first year .
3% for the second year.
2% for the third year.

Calculate the account which would give him the most money and calculate the difference to the nearest penny after 3 years

Answer 7

Account A: 10000 x 1.03^3 = 10927.27

Account B: 0.04% of 10000 = 10400

0. 03% of 10400= 10712.
1. 02% of 10712= 10926.24

10927.27-10926.24= 103

Question 8

Ali is y years old.
Bhavara is twice as old as Ali.

Ceri is 3 years younger than Ali.
The total of their ages is 125 years. Find the age of each person

Answer 8

Ali = y
Bhavara = 2y 
Ceris = y-3 

4Y-3 = 125
+3
4Y = 128. Y= 32

Ali = 32, Bhavara = 64, Ceris = 29

Question 9

Additi, Becky, and Calli collect coins. Additi has 6 more coins than Becky. Calli has one less than Aditi. Altogether they have 71 coins. How many coins do they each have?

Answer 9

B = X
A = X+6 
C= X+6 - 1 = X+5 
C= X+5

3X + 11 = 71
3X = 60 X = 20
B= 20, A = 26, C = 25

Question 10

Mr and Mrs Thomas buy tickets for themselves and their four children. The cost of an adult ticket is £7 more than the cost of a child ticket. The total cost of the six tickets is £86.

Work out the cost of an adult ticket.

Answer 10

Child = X Adult = X+7
4X 2X + 14

6X + 14 = £86

-14

6X = 72   X = 12
12+7 = 19

Adult £19

Question 11

Mr and Mrs W have five children who are all different ages.

The mean age is 6.4
The range is 9
The median is 6
The oldest child is 12.

Work out the ages of the children from youngest to eldest.

Answer 11

3rd number = 6

To find the youngest age : 12-9 = 3 years old

First three numbers : 3,6, 12.

3+6+12 / 5
21/5 = 6.4. 6.4(5)= 32.
32-21 = 11.

Trial and error: missing numbers = 4 and 7

Question 12

Jack and Alex take rubbish to be recycled.
Jack takes 520 kg, 87% of which can be recycled.
Alex takes 750 kg, 61% of which can be recycled.

Calculate the greatest amount of rubbish that can be recycled and by how much.

Answer 12

0. 87 (520) = 452.4
1. 61 (750) = 457.5

457.5-452.4= 5.1kg

Alex by 5.1 kg

Question 13

Anna and Paddy take part in the same fun run.
Anna completed the fun run in 2 hours.
Her average speed was 6 KM per hour.

Paddy completed the fun run in 90 minutes.

Work out his average speed in kilometres per hour.

Answer 13

Speed x Time

6 x 2 = 12

90 mins = 1 hr 30 = 1.5

12/1.5 = 8

8 KM / H

Question 14

Anne, Barry, and Colin share a prize in the ratio 3:4:5.

Colin gives 1/3 of his share to charity.

What fraction of the whole prize does Colin give to charity?

Answer 14

3+4+5 = 12

Coin = 5/12 x 1/3 = 5/36

Question 15

Claudia invests £25000 at a rate of 2% per year compound interest.

Calculate the total amount of interest she will have earned after 5 years. Give your answer correct to the nearest penny.

Answer 15

25,000 x 1.02^5 = £27602.02

£25602.02-£25000 = £2,602.02

Question 16

James and Elizabeth buy clothes.

James buys 5 shirts and 4 jumpers he pays £163.
Elizabeth buys 3 shirts and 2 jumpers she pays £89.

Work out the cost of one shirt and one jumper

Answer 16

Simultaneous equations

1. 5S+4J=£163
2. 3S+2J=£89

15S+12J=£489
15S+10J=£445

2J=44 J=22

5S+4J=163
5S+4(22)=163
5S+88=163

5S=75. S=15.
Shirt £15. Jumper £22

Question 17

A bus following route T leaves for the train station every 20 minutes.

A bus following route A leaves the airport every 18 minutes.

A bus following route T and a bus following route A both leave at 8:37am.

What is the next time one of each bus is timetabled to leave at the same time?

Answer 17

HCF of 18 and 20 =180
180 mins = 3 hours
8:37am+3hrs =11:37

11:37am

Question 18

Delia, Edwin, and Freya share money in the ratio 5:7:8.

Freya’s share is £1600. How much money did they share?

Answer 18

1600/8 = 200. 200 per part

200(5)= 1000
200(7)=1400

1400+1000+1600 =4000

Question 19

Mike drinks 2/5 of a litre of juice everyday.
Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.

He buys enough juice to last 7 days.

What’s the lowest price that he can pay for this juice?

Answer 19

2/5 = 0.4

0.4 (7)= 2.8. 2.8~3

He needs a 3 litre carton

£2.60+4.40

£7.00

Question 20

The perimeter of a pentagon is equal to the perimeter of a square and has the sides : 5X+3, 7X+4, 9X-10, 2X+3, 5X+8.

Give the answers in terms of X in its simplest form

Answer 20

Collect like terms

28X+8

Divide by 4

7X+2

Question 21

A rectangle has the length :
5X-Y-8 and 3X+5Y-4.

&width : 3X+Y-4 and 2X-6Y-3

Work out the length and width of the rectangle

Answer 21

Opposite sides are equal.
5X-Y-8= 3X+5Y+4

2X-6Y=12

3X+Y-4=2X-6Y-3

X-5Y=1

Simplify ‘2X-6Y=12’ = X-3Y=6

X-7Y=1
X-3Y=6
10Y = -5
Y=-0.5

sub ‘Y=-0.5’ into X-3Y=6
X-3(-0.5)=6. X=4.5

To find the length sub ‘4.5’ and ‘-0.5’into ‘3X+5Y+4’. 3(4.5)+ 5(-0.5)+4= 15.

Width: sub ‘4.5 and 0.5’ into 3X+Y-4
3(4.5)+(-0.5)-4=9

Question 22

Kieran, Chris , and Jermaine play football. Kieran has scored 8 more goals than Chris. Jermaine has scored 5 more than Kieran. Altogether they’ve scored 72 goals. How many goals did they each score?

Answer 22

Chris = X
Kieran= X+8
Jermaine= X+13

3X+21=72
3X= 51. X=17.

Chris= 17, Kieran= 25, Jermaine= 30

Question 23

Some children arrive at the nursery by car.
40% of the children at the nursery are boys.
70% of the boys at the nursery arrive by car.
60% of the girls at the nursery arrive by car.

What’s the probability that a child chosen at random from the nursery arrives by car?

Answer 23

Frequency trees.

1. Boy 0.6. Girl 0.4.
2. Car 0.7. No car 0.3
3. Car 0.6. No car 0.4

Probability of arriving by car = P(B) + P(G)
0.4x 0.7+0.6+0.6
=0.64

Question 24

Kim is paid £9.40 per hour for the first 35 hours she works each week. After 35 hours she is paid 1 1/4 times the hourly rate.

One week Kim works 42 hours.

Calculate how much she’s paid for that week.

Answer 24

£9.40 x 35= £329.

42-35= 7 extra hours.

1/4 x £9.40= £11.75 per hour.

£11.75 x 7= £82.25

Total pay: £329+82.25= £411.25

Question 25

James works from 2pm until 8:30pm on Thursday and Friday. He’s paid £12 per hour and on Saturday he’s paid 1/2 times this hourly pay.

He works 5H on Saturday.

Calculate how much he earns in total for these three days.

Answer 25

2–> 8:30= 6 hours 30 mins = 6.5 hours .

One day pay : £12 x 6.5= £78

Thursday and Friday pay= £156

Saturday: 1/2 x £12= £18
£18 per hour.

5x£18= £90. Total pay= £156+90
£246

Question 26

Hector can run 400 metres in 66 seconds. Use this information to show that he could run 5KM in less than 14 minutes.

Answer 26

Turn 5KM into M (x1000)= 5000M

5000M/400M= 12.5.
12.5 x 66= 825

400M:66 seconds
5000M: 825 seconds

825 s into minutes (divide by 60)

=13.75

Question 27

The volume of a piece of wood is 620cm. Its density is 0.85 cm.

Work out it’s mass

Answer 27

Mass = DxV

620x 0.85= 527

Question 28

P chooses four numbers.

The mode is 8, the range is 7, and the mean is 11. Find the four numbers.

Answer 28

Mode: 8,8,

Range: 8+7 = 15.

Finding the mean : the sum of all numbers/ amount of numbers.

8+8+15/4 = 11

31+ X / 4 = 11. ( multiply by 4).

31+ X = 44. Minus 31
X= 13

8,8, 13, 15

Question 29

Donald swims 3 lengths of a swimming pool in 93 seconds. Use this information to show that he could swim 100 lengths in under 55 minutes.

Answer 29

Divide the lengths - 100/3 = 33.3

33. 3 x 93= 3069.9 seconds
34. 9/60= 51.6 minutes

Question 30

Maria mixes white and red paint in the ratio 2:3. She mixes a total of 15L of paint.

How much more red paint does she need to add to the mixture so that the ratio of white paint to red paint becomes 1:5?

Answer 30

3+2= 5 parts

15/5 = 3 per part.
W:R
2:3 
White :2(3)= 6L.  Red: 3(3)=9L.
W:R is = to 1:5
White : 6, Red = 5(6)=30.

30-9= 21.

There’s 20L of red paint.

Question 31

Trish and Marc both cycled the same distance. Trish completed the distance in 2 hours.
Her average speed was 16 miles per hour. Marc completed the distance in 4 hours.
Find Marc’s average speed for the journey.

Answer 31

16(2)= 32

32/4= 8

8 mph

Question 32

The scale on a map is 1:25000.

How many kilometres on the ground is represented by 6 cm on the map?

Answer 32

1cm = 25000m

6cm : 25000(6)= 150000m

150000/100= 1500.

1500m (km divide by 1000)

1.5 km