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GCSE · Ratio, Proportion and Rates of Change

3.4D Writing and Simplifying Ratio: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 85 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

There are 9 pens and 6 pencils in a pencil case. Write down the ratio of pens to pencils.

(Total for Question 1 is 1 mark)

In a car park there are 14 cars and 4 motorbikes. Write down the ratio of motorbikes to cars.

(Total for Question 2 is 1 mark)

Write the ratio 16:24 in its simplest form.

(Total for Question 3 is 1 mark)

Which of these ratios is equivalent to 3:4?

A) 6:8
B) 4:3
C) 3:8
D) 9:16

(Total for Question 4 is 1 mark)

Simplify the ratio 35:14.

(Total for Question 5 is 1 mark)

Simplify the ratio 45:60.

(Total for Question 6 is 1 mark)

Simplify the ratio 20:24:32 fully.

(Total for Question 7 is 2 marks)

Simplify the ratio 21:28:49 fully.

(Total for Question 8 is 2 marks)

Simplify the ratio 60 cm : 1.5 m, giving your answer in its simplest form.

(Total for Question 9 is 2 marks)

Simplify the ratio 900 m : 2 km, giving your answer in its simplest form.

(Total for Question 10 is 2 marks)

Simplify the ratio 2 hours : 50 minutes, giving your answer in its simplest form.

(Total for Question 11 is 2 marks)

Write the ratio 15:45 in the form 1:n.

(Total for Question 12 is 2 marks)

Write the ratio 45:18 in the form n:1.

(Total for Question 13 is 2 marks)

Write the ratio 5:9 in the form 1:n.

(Total for Question 14 is 2 marks)

In a choir the ratio of sopranos to altos is 7:5. Write down what fraction of the choir are altos.

(Total for Question 15 is 2 marks)

A fruit drink is made from concentrate and water in the ratio 1:4. Write down what fraction of the drink is concentrate.

(Total for Question 16 is 1 mark)

A fruit bowl contains 8 apples, 6 bananas and 10 oranges. Write the ratio apples : bananas : oranges in its simplest form.

(Total for Question 17 is 2 marks)

Ravi has £3.60 and his sister has 90p. Write the ratio of Ravi's money to his sister's money in its simplest form.

(Total for Question 18 is 3 marks)

A cafe sells squash. In Batch A the squash is diluted with water in the ratio 2:9. A jug from Batch B contains 150 ml of squash and 600 ml of water. Determine, showing your working, whether the jug from Batch B has been diluted in the same ratio as Batch A.

(Total for Question 19 is 3 marks)

Simplify fully: (3x + 6) : (5x + 10).

(Total for Question 20 is 3 marks)

At a school, the ratio of Year 10 students to Year 11 students is 4:5. The ratio of Year 11 students to Year 12 students is 3:2. Find the ratio Year 10 : Year 11 : Year 12 in its simplest form.

(Total for Question 21 is 4 marks)

A map is drawn using a scale where 4 cm represents 3 km. Write this scale as a ratio in the form 1:n.

(Total for Question 22 is 4 marks)

A coffee roastery blends Colombian and Kenyan beans. In Batch A the beans are blended in the ratio 7:3 (Colombian : Kenyan). Batch B is made using 630 g of Colombian beans and 260 g of Kenyan beans. Determine, showing your working, whether Batch B has been blended in the same ratio as Batch A.

(Total for Question 23 is 5 marks)

Simplify fully: (2x² - 8) : (x² + x - 6).

(Total for Question 24 is 4 marks)

The ratio a:b is equivalent to 5:8. The ratio b:c is equivalent to 6:11. Given that a, b and c are positive integers and that c - a = 58, find the ratio a : b : c in its simplest form and find the value of b.

(Total for Question 25 is 5 marks)

Mark scheme · 3.4D Writing and Simplifying Ratio: Fluency and Exam Drill

Question 1

B1 9:6 oe (simplifying is not required)
Answer: 9:6

Question 2

B1 4:14 oe (order must be motorbikes then cars; simplifying is not required)
Answer: 4:14

Question 3

B1 2:3 cao
Answer: 2:3

Question 4

B1 A cao
Answer: A) 6:8

Question 5

B1 5:2 cao
Answer: 5:2

Question 6

B1 3:4 cao
Answer: 3:4

Question 7

M1 identify a common factor of 20, 24 and 32 (e.g. divide by 4) oe
A1 5:6:8 cao
Answer: 5:6:8

Question 8

M1 identify a common factor of 21, 28 and 49 (e.g. divide by 7) oe
A1 3:4:7 cao
Answer: 3:4:7

Question 9

M1 convert 1.5 m to 150 cm oe
A1 2:5 cao
Answer: 2:5

Question 10

M1 convert 2 km to 2000 m oe
A1 9:20 cao
Answer: 9:20

Question 11

M1 convert 2 hours to 120 minutes oe
A1 12:5 cao
Answer: 12:5

Question 12

M1 divide both parts by 15 oe
A1 1:3 cao
Answer: 1:3

Question 13

M1 divide both parts by 18 oe
A1 2.5:1 oe (accept 5/2 : 1)
Answer: 2.5:1

Question 14

M1 divide both parts by 5 oe
A1 1:1.8 oe (accept 1 : 9/5)
Answer: 1:1.8

Question 15

M1 total parts = 7+5=12 oe
A1 5/12 oe
Answer: 5/12

Question 16

B1 1/5 oe
Answer: 1/5

Question 17

M1 identify a common factor of 8, 6 and 10 (e.g. 2) oe
A1 4:3:5 cao
Answer: 4:3:5

Question 18

M1 convert £3.60 to 360p oe
M1 form the ratio 360:90 and begin to simplify
A1 4:1 cao
Answer: 4:1

Question 19

M1 scale Batch A's ratio so the squash matches 150 ml, e.g. 2:9 x 75 = 150:675 oe
M1 compare 675 ml (water needed for Batch A's ratio) with Batch B's actual 600 ml of water
A1 correct conclusion with valid reason, e.g. 'No - Batch B is not diluted in the same ratio; it needs 675 ml of water to match Batch A but only has 600 ml, so Batch B's squash is more concentrated' oe cao
Answer: No - Batch B is not in the same ratio as Batch A (Batch B is more concentrated).

Question 20

M1 factorise 3x+6 = 3(x+2) oe
M1 factorise 5x+10 = 5(x+2) oe
A1 3:5 cao
Answer: 3:5

Question 21

M1 find a common value for the Year 11 parts, e.g. LCM of 5 and 3 = 15 oe
M1 scale Year10:Year11 = 4:5 by 3 to get 12:15
M1 scale Year11:Year12 = 3:2 by 5 to get 15:10
A1 12:15:10 cao
Answer: 12:15:10

Question 22

M1 convert 3 km to 300000 cm oe
M1 form the ratio 4:300000
M1 divide both parts by 4
A1 1:75000 cao
Answer: 1:75000

Question 23

M1 find the scale factor for Batch A's ratio using the Colombian mass, 630/7=90 oe
M1 use the scale factor to find the Kenyan mass Batch A's ratio requires, 3x90 oe
A1 270 g cao
M1 compare 270 g with Batch B's actual 260 g of Kenyan beans
A1 correct conclusion with valid reason, e.g. 'No - Batch B is not blended in the same ratio; it has less Kenyan beans (260 g) than the 270 g Batch A's ratio requires, so Batch B is relatively more Colombian' oe cao
Answer: No - Batch B is not in the same ratio as Batch A (Batch B has relatively more Colombian beans).

Question 24

M1 factorise the numerator, 2x²-8 = 2(x-2)(x+2) oe
M1 factorise the denominator, x²+x-6 = (x+3)(x-2) oe
M1 cancel the common factor (x-2)
A1 2(x+2):(x+3) oe (accept (2x+4):(x+3)) cao
Answer: 2(x+2) : (x+3), i.e. (2x+4):(x+3)

Question 25

M1 find a common value for b, e.g. LCM of 8 and 6 = 24 oe
M1 scale both ratios to combine: a:b:c = 15:24:44
M1 set up c-a in terms of a scale factor k, e.g. 44k-15k=29k=58
M1 solve to find k=2
A1 b=48 cao (with ratio a:b:c=15:24:44 stated)
Answer: a:b:c = 15:24:44; b = 48

Writing and Simplifying Ratio: Fluency and Exam Drill - Worksheets, Questions and Revision