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KS3 · Ratio, Proportion and Rates of Change

KS3.M-R5 Direct Proportion and the Unitary Method

AQA KS3.M-R5 · Calculators not allowed · about 45 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the unit fraction for each quantity.

(a)What is 1 of 12 as a fraction of a whole?(1)

(b)What is 1 of 8 as a fraction of a whole?(1)

(c)What is 1 of 20 as a fraction of a whole?(1)

(d)What is 1 of 5 as a fraction of a whole?(1)

A recipe makes 6 pancakes using 300 g of flour. How much flour is needed for 1 pancake?

(2)

Scale the recipe amounts down to one portion.

(a)A soup recipe serves 4 and needs 800 ml of stock. How much stock for 1 serving?(1)

(b)A tray of muffins makes 12 and uses 360 g sugar. How much sugar per muffin?(1)

(c)A batch of 9 cookies uses 270 g butter. What is the butter for 1 cookie?(1)

Omar buys 5 apples for 2.50 pounds. What is the unit price for one apple?

(2)

Write as a ratio in simplest form: 300 g of flour to 2 cups of flour.

(2)

A drinks company makes 24 bottles using 3 litres of juice concentrate. How much concentrate is needed for 10 bottles?

(a)Find the amount of concentrate for 1 bottle.(1)

(b)Use your answer to find concentrate for 10 bottles.(2)

Which is better value: 6 cans for 3.30 pounds or 10 cans for 5.25 pounds? Show your working.

(3)

A cake recipe uses 250 g of sugar to serve 5. How much sugar is needed to serve 8 people?

(2)

Mark scheme · KS3.M-R5 Direct Proportion and the Unitary Method

Question 1

(a) B1 1/12 cao
(a) Answer: 1/12
(b) B1 1/8 cao
(b) Answer: 1/8
(c) B1 1/20 cao
(c) Answer: 1/20
(d) B1 1/5 cao
(d) Answer: 1/5

Question 2

M1 Divide 300 by 6 or show 300/6 method
A1 50 g cao
Answer: 50 g

Question 3

(a) B1 200 ml cao
(a) Answer: 200 ml
(b) B1 30 g cao
(b) Answer: 30 g
(c) B1 30 g cao
(c) Answer: 30 g

Question 4

M1 Divide 2.50 by 5 or 250p/5 shown
A1 0.50 pounds cao
Answer: 0.50 pounds

Question 5

M1 Divide both parts by 2 or show simplification method
A1 150:1 cao
Answer: 150:1

Question 6

(a) B1 0.125 litres or 125 ml cao
(a) Answer: 0.125 litres
(b) M1 Multiply 0.125 by 10 or equivalent method
(b) A1 1.25 litres cao
(b) Answer: 1.25 litres

Question 7

M1 Find unit price for 6 cans: 3.30/6 or equivalent shown
M1 Find unit price for 10 cans: 5.25/10 or equivalent shown
A1 State better value: 10 cans for 5.25 pounds cao
Answer: 10 cans for 5.25 pounds

Question 8

M1 Find sugar per person: 250/5 shown
A1 400 g cao
Answer: 400 g

Direct Proportion and the Unitary Method - Worksheets, Questions and Revision