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5.2F Direct and Inverse Proportion: Foundation Tier Practice

EDEXCEL 1MA1 · Calculator allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A recipe uses 3 cups of flour to make 12 biscuits. Work out how many cups of flour are needed to make 4 biscuits.

(Total for Question 1 is 1 mark)

Sam can type 90 words in 3 minutes. At the same rate, how many words can Sam type in 1 minute?

(Total for Question 2 is 1 mark)

Direct proportion. If 5 pens cost 15 pounds, work out the cost of 8 pens.

(Total for Question 3 is 2 marks)

A car uses 6 litres of petrol to travel 30 miles. Work out how many litres the car will use to travel 50 miles at the same rate.

(Total for Question 4 is 2 marks)

Inverse proportion. 8 identical machines take 15 hours to complete a job. How many hours would 12 identical machines take to complete the same job, assuming they work at the same rate?

(Total for Question 5 is 3 marks)

A map scale says 1 cm represents 5 km. On the map, two towns are 7.2 cm apart. Work out the actual distance in kilometres.

(a)Find the actual distance in kilometres.(2)

(b)If a car travels at 60 km/h, how many minutes will it take to travel between the towns? Give your answer to the nearest minute.(2)

(Total for Question 6 is 4 marks)

Direct proportion with context. A small plant needs 150 ml of water every 5 days. How much water does it need in 14 days?

(a)Find the water needed in 14 days.(3)

(b)If the gardener has a 2 litre bottle, how many full bottles are needed for 14 days? Give your answer as a whole number of full bottles required.(1)

(Total for Question 7 is 4 marks)

Inverse proportion in a simple setting. 5 painters can paint a fence in 9 hours. How long would 3 painters take to paint the same fence, working at the same rate?

(a)Find the time in hours for 3 painters.(3)

(b)If each painter works 8 hours per day, how many whole days are needed to finish the job with 3 painters? Give your answer as a whole number of days.(2)

(Total for Question 8 is 5 marks)

Mark scheme · 5.2F Direct and Inverse Proportion: Foundation Tier Practice

Question 1

B1 1 cup cao
Answer: 1 cup of flour (cao). (3 cups for 12 biscuits means 0.25 cups per biscuit; for 4 biscuits 0.25 x 4 = 1.)

Question 2

B1 30 words cao
Answer: 30 words. (90 / 3 = 30.)

Question 3

M1 find unit cost 15/5 = 3 or scale 15 x 8/5
A1 24 pounds cao
Answer: 24 pounds. (Unit cost 15/5 = 3. 3 x 8 = 24.)

Question 4

M1 find litres per mile: 6/30 = 0.2 or scale 6 x 50/30
A1 10 litres cao
Answer: 10 litres. (6/30 = 0.2 litres per mile. 0.2 x 50 = 10.)

Question 5

M1 use inverse proportion: time proportional to 1/machines, or compute total machine-hours 8 x 15 = 120
M1 divide total machine-hours by 12 to find time for 12 machines
A1 10 hours cao
Answer: 10 hours. (Total work = 8 x 15 = 120 machine-hours. 120/12 = 10.)

Question 6

(a) M1 calculate 7.2 x 5 or equivalent scaling
(a) A1 36 km cao
(a) Answer: 36 km
(b) M1 time in hours = 36/60 = 0.6 hours or equivalent conversion to minutes
(b) A1 36 minutes awrt
(b) Answer: 36 minutes (awrt).

Question 7

(a) M1 find daily water or scale: 150/5 = 30 ml per day
(a) M1 30 x 14 or equivalent
(a) A1 420 ml cao
(a) Answer: 420 ml
(b) B1 1 bottle cao (2 litres = 2000 ml and 420 ml < 2000 ml, so 1 full 2 litre bottle is enough)
(b) Answer: 1 full bottle

Question 8

(a) M1 calculate total painter-hours: 5 x 9 = 45
(a) M1 divide total painter-hours by 3 to find time: 45/3
(a) A1 15 hours cao
(a) Answer: 15 hours
(b) M1 convert hours to days: 15/8 = 1.875
(b) A1 2 days cao
(b) Answer: 2 days

Direct and Inverse Proportion: Foundation Tier Practice - Worksheets, Questions and Revision