Paper 2

Question 1

There’s a total of 250 women,men, and children on the train. The ratio of men to women is 4:5. The ratio of women to children is 10:7.

How many men are on the train?

Answer 1

Make the amount of women the same

M:W. W:C
4:5 10:7

Times ratio one by 2&raquo_space; 8:10

M:W:C
8:10: 7 Add 8+10+7= 25 parts. Divide 250 by 25 =10
Men= 8(10) = 80 men

Question 2

Floor plan of a rectangular room - 4.5m by 3m

Each square is measuring 50 by 50cm. The tiles are only sold in packets of 10. Each packet costs £20.Tim pays a fitting rate at 7.50 which each square metre rounded up.

Work out the cost of fitting and tiles.

Answer 2

Turn m into cm > multiply by 100

Divide 450cm and 300cm by 50 = 9 and 6.
Multiply 9 and 6 = 54. Packets only come in 10 so round up to 60 = 6 packets.

6(20) £120. Tiles = £120.

Find the cost of fitting : find the area of a rectangle = 4.5(3) = 13.5
Round up to 14. 14(7.50) = £105.
£105+120= £225

Question 3

3(2x+D) + C(X+5) = 10X+17

Find the value of C and D

Answer 3

6X+3D +CX +5C = 10X+17.

6X+CX=10. 6+C =10. -6. C= 4.

5C +3D =17. 5(4)+3D = 17. 20+3D = 17. -20.
3D=-3. D=-1

C=4 D=-1

Question 4

Owen weighs 6 stones and 4 pounds. There are 14 pounds in a stone. Convert Owen’s weight into kilograms.

Answer 4

6(14) = 84 pounds. Add on the 4 pounds = 88 pounds.

To convert into kg»

88(10)= 880

880/22= 40 KG

Question 5

The ratio of flour to butter is 5:4
The ratio of butter to sugar is 2:1

The total weight is 770g. Work out the weight of each ingredient.

Answer 5

F:B. B:S

5: 4. 2:1 Multiply the second ratio by 2
4: 2

F:B:S
5:4:2. 5+4+2= 11 parts per person

770/11= 70g per ingredient.

Flour: 350g, Butter: 280g, Sugar: 140g

Question 6

A water company charged the following:

£2.00 for each m^3 of water used plus a fixed charge of £45.
Jenny uses 110m^3 of water.
For the 12 months of 2017 she paid £20 per month to the water company. How much more does she need to pay to the water company?

Answer 6

Cost of water used: 2.00(110) = £220.
Fixed charge: 220+45 = £265.

1 year cost: 20(12)= £240.

Fixed charge- yearly charge
265 - 240 = 25

£25

Question 7

The depth of water in a garden pond is 57.8cm. The depth increases by 0.3 cm per day.

Assuming that the depth continues to decrease at the same rate.

After how many days will the depth reach 54.2 cm?

Answer 7

57.8- 54.2 =

Question 8

Emily spent £2400 on holiday in 2017.
This was 20% more than she spent on holiday in 2016.

Calculate the amount she spent on holiday in 2016.

Answer 8

100+20 = 120%

120%= 2400 
1% = 20 
100%= 2000

Question 9

Nutritional information for a 110g serving of cereal.

Carbohydrates: 99.4g
Proteins: 9.5
Fats:1.1g

Emily says that more than 90% of this serving is carbohydrates. Is she correct?

Answer 9

Find 90% of 110g = 99

Emily is correct

Question 9

Liam is 0.83m tall. William is 1.31m tall.

Jacob is taller than Liam by half the difference between Liam’s height and William’s height. How tall is Jacob?

Answer 9

Find the difference between Liam and William’s height

1.31m- 0.83m = 0.48m

Find 1/2 of 0.48 = 0.24

Jacob is taller by half the distance so add Liam’s height
0.24+ 0.48 = 1.07

Question 10

The width of a rectangle is (x+5) cm.

The ratio width: length of the rectangle is 48cm.

Calculate the area.

Answer 10

To find the length double X+5 = 2X+ 10.

X+5, X+5, 2X+10, 2X+10 = 6X +30

6X+ 30 = 48cm
- 30

6X = 18 
X = 3 

Width ; X+5 (3+5) = 8
Length : 8 (2) = 16

16 x 8 = 128 cm

Question 11

A circle with centre O and radius 6cm, contains another circle, with centre O and radius X cm.

Write down an expression, in terms of x and π, for the shaded area in cm^2

Answer 11

Area of big circle: six squared = 36 π

Area of small circle: x squared = x^2 π

Takeaway= 36 π - πx^2

Question 12

Work out 2 x 10^2 x 4 x 10^5

Answer 12

2(4) = 8

10^2 + 10^5 = 10^7<

8 x 10^7

Question 13

Solve by factorising X^2- 7X+10 = 0

Answer 13

X^2 -7x + 10 = 0

Two minuses make a positive ten and - 7

(X-5) (X-2)

X+5 X+2

Question 14

Three regular polygons meet at a point.
60 X X

Find the number of sides of each of the three regular polygons in the diagram.

Answer 14

2X + 60 = 360
2X = 300 X = 150.

180-150= 30

360/30 = 12

Question 15

Football teams get 3 points for a win, 1 point for a draw and no points for a loss.

United have played 32 games and have a total of 57 points. They’ve drawn 6 of their games.

How many games have they lost?

Answer 15

Drawn : 6(1) = 6.

32- 6= 26 games remaining.

57-6= 51 points for winning.

51/3 = 17 games of winning.

26-17 = 9 games remaining.

Question 16

(3X+2) (X-4)

Answer 16

3X^2-12x+2X-8

3X^2 -10x - 8

Question 17

Four friends buy a cinema ticket using this offer.

Buy 3 tickets and get one free. They each pay £6.45. How much does one ticket cost?

Answer 17

6.45 (4) = £25.80

3 tickets : 25.80/3 = £8.60

1 ticket = £8.60

Question 18

Two numbers are in the ratio 5:7

The difference between the numbers is 12.

Work out the two numbers

Answer 18

7-5 = 2

12/2 =6

6(5) = 30 6(7)=42

Question 19

A group of people had a driving test. 40 of this group were men and the rest were women.

3/5 of the men and 2/3 of the women passed the driving test. The number of men and women that passed the driving test was the same.

Work out the number of women that took the driving test that day.

Answer 19

3/5 of 40 = 24 men passed.

Number of men passed = number of women passed. 24 men and 24 women passed.

2/3 of women =24

1/3= 12

24 +12=36. -36 women

Question 20

Adam buys some theatre tickets in a sale.

The normal prices are :
£80 for each adult.
£40 for each child.

In the sale, the prices are reduced by 15%. Adam buys 2 adult tickets and 1 child ticket at the sale price. A 2% booking fee is then added to the total cost of the tickets. Calculate the amount that Adam must pay.

Answer 20

Find 15% of £80 and £40.

10% of 80= 8
5%= 4
12. £80-12= £68. 68(2)= £136. Adults =£136.

10% of 40= 4
5%= 2
6. £40-6= £34. Child =£34.

Adult + child = £170.

2% booking fee: 10% of 170= 17

1%=1.70. 2%= 3.40

£173.40

Question 21

Kate is 5 feet 2 inches tall. Alice is 1.7m tall. Alice says that she’s taller than Kate.

12 inches = 1 foot.
1 inch= 2.5 cm.
Use the conversions to decide if Alice is correct.

Answer 21

5 feet 2: 12(5) + 2 = 62 inches.

62 x 2.5. 62(2)=124. 62(5)=31

124+31=155m

Alice is correct

Question 22

Andrew is thinking of a number. It’s between 1 and 150. It’s one more than a square number, three less than a cube number, and it’s not a prime number. What’s his number?

Answer 22

Square numbers: 1, 4, 9 ,16, 25, 36, 49, 64, 81, 100, 121, 144.

Cube numbers: 1, 8, 27, 64, 125.

Square numbers +1

2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145.

Cube numbers : -3
-2, 5, 24, 61, 122

Answer = 122

Question 23

A 100g packet of tea costs £4.16
A 25g packet of tea costs £1.05.

Which packet is better value for money?

Answer 23

25g : £1.05
X4

100g: £4.20

You can get a cheaper 100g packet for £4.16

Question 24

Weight in pounds - x30- +20- time in minutes.

Use the rule to work out the time needed to roast lamb which weighs 4 pounds.

Answer 24

4x30 =120

120+20 =140

Question 25

Another lamb takes 95 minutes to roast. Work out the weight of the lamb.

Weight in pounds- x 30- +20 - Time in minutes

Answer 25

W x 30+20= 95.

30W+20 = 95
-20

30W=75. W= 2.5

Question 26

Jenny plays four games of golf. Her modal score was 76 and her mean score was 75. Her range was 10. Work out the scores for her four games.

Answer 26

Multiply the mean by the number of games

75(4) = 300.

Mode = 76.   76+76=152.
300-152= 148.

X+Y= 148
X-Y = 10
2X = 158.  X =79.

79 is the highest score. To find the last missing number : 79-10= 69

69, 76, 79, 79.

Question 27

The population of a village is in the following ratios.
Men : Children = 11:3
Women: Children = 5:2
Find the ratio of M:W

Answer 27

M: C = 11/3. W:C = 5/2

Multiply 11 by 2 and 5 by 3.

= 22:15

Question 28

There are 36 children in the village. Find the total population of the village.

Men: Children. Women: Children
11: 3. 5:2

Answer 28

11: 3
36. 36/3= 12

132:36 .

5: 2
36. 36/12= 18
90: 36

Total: 132+36+90= 258

Question 29

There are 20p coins in a pot. The coins are 1p, 5p, 2p, and 10p. A coin is taken at random from the pot.

The probability that it’s a 1p coin is 3/10
The probability that it’s a 2p coin is 2/5.

The total value of the coins in the pot is 57p. Work out how many of each type of coin there is in the pot.

Answer 29

3/10 of 20 = 6 = 6 1p coins = 6p

2/5 of 20= 8= 8 2p coins = 16p.

Remaining coins: 57p-22p= 35p left over.

Split 35p into 10p and 5p.
3 10ps and 1 5p.

6 1p, 8 2p, 1 5p, 3 10p.

Question 30

The farmer has a field that is in the shape of a Trapezium. The trapezium has a length of 180m and 220m and a height of 150m.

The field produces 6400 kilograms of wheat per hectare. One hectare is 10000m^2.

Work out how many kilograms of wheat the field produced?

Answer 30

1/2 (a+b) h.

180+220= 400.
400(150)= 60000.   60000/2= 30,000. 

30,000/10,000=3

6400 kg (3)= 19200kg

Question 31

Ed’s profit on cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.

Work out his profit in 2017.

Answer 31

100-20= 80%

80%=360.
1%= 4.5
100%= 450

£450

Question 32

Isaac and Maya eat part of a pizza.
Isaac eats 1/6 of the pizza.
Maya then eats 3/5 of the remaining pizza.

What fraction of the original pizza is left?

Answer 32

1/6 = 5/6 of the pizza is left.

3/5 of 5/6 = 3/5 multiplied by 5/6= 15/30= 1/2.

1/2= half of the remaining pizza. 
1-1/6= 5/6.    5/6-1/2= 4/12=1/3.

1/3