A recipe makes 5 cakes using 250 g of butter. How much butter is needed for 1 cake?
(1)
2
8 identical books cost 32 pounds together. Find the cost of 1 book.
(1)
3
A car travels 180 miles in 3 hours at a constant speed. What distance does it travel in 1 hour?
(1)
4
6 identical pens cost 3.60 pounds. Find the cost of 1 pen.
(1)
5
9 identical tiles cover 4.5 m2. Find the area covered by 1 tile.
(1)
6
A factory makes 480 toys in 8 hours at a constant rate. Find how many toys are made in 1 hour.
(1)
7
A recipe for 4 people needs 320 g of rice. How much rice is needed for 7 people?
(2)
8
5 identical calculators cost 22.50 pounds. Find the cost of 9 calculators.
(2)
9
A machine fills 150 bottles in 6 minutes at a constant rate. How many bottles does it fill in 10 minutes?
(2)
10
12 identical chairs cost 300 pounds. Find the cost of 5 chairs.
(2)
11
A car uses 8 litres of fuel to travel 96 km. How far can it travel using 20 litres of fuel, assuming the same rate?
(2)
12
3 workers can pack 234 boxes in a shift. At the same rate, how many boxes can 5 workers pack in one shift?
(2)
13
A recipe for 6 people uses 900 ml of stock. Find the amount of stock needed for 10 people.
(2)
14
9 litres of paint cover 45 m2 of wall. How many litres of paint are needed to cover 60 m2, assuming the same rate of coverage?
(2)
15
A recipe for 8 servings requires 640 g of pasta and 400 ml of sauce, both in direct proportion to the number of servings. Amara wants to make enough for 5 servings. Work out the mass of pasta and the volume of sauce she needs.
(3)
16
A printer prints 45 pages in 6 minutes at a constant rate. Work out how long it will take to print 100 pages, giving your answer in minutes and seconds.
(3)
17
A shop sells fabric at a constant price per metre. 5 metres cost 22.50 pounds. Sara buys some fabric and pays 40.50 pounds. Work out how many metres she bought, then work out how much 12 metres would cost.
(3)
18
A car uses fuel at a constant rate of 15 km per litre. Its fuel tank holds 40 litres. If the tank is currently 3/4 full, how far can the car travel before running out of fuel?
(3)
19
A stall sells apples at a fixed price per kilogram. 3.5 kg of apples costs 5.60 pounds. Work out the cost of 6 kg of apples, and state how many kilograms could be bought for 12.80 pounds.
(3)
20
Stretch question. A recipe for 12 muffins requires 4 eggs and 360 g of flour, with both amounts in direct proportion to the number of muffins made. Fatima wants to make 18 muffins but only has 480 g of flour. Work out how many eggs she needs for 18 muffins, and determine whether she has enough flour, showing your working.
(3)
Mark scheme · KS3.M-R5D Direct Proportion and the Unitary Method: Fluency and Exam Drill
Question 1
B1 50 g cao
Answer: 50 g
Question 2
B1 4 pounds cao
Answer: 4 pounds
Question 3
B1 60 miles cao
Answer: 60 miles
Question 4
B1 0.60 pounds cao
Answer: 0.60 pounds
Question 5
B1 0.5 m2 cao
Answer: 0.5 m2
Question 6
B1 60 toys cao
Answer: 60 toys
Question 7
M1 rice per person = 320/4 = 80
A1 560 g cao
Answer: 560 g
Question 8
M1 cost per calculator = 22.50/5 = 4.50
A1 40.50 pounds cao
Answer: 40.50 pounds
Question 9
M1 bottles per minute = 150/6 = 25
A1 250 bottles cao
Answer: 250 bottles
Question 10
M1 cost per chair = 300/12 = 25
A1 125 pounds cao
Answer: 125 pounds
Question 11
M1 distance per litre = 96/8 = 12
A1 240 km cao
Answer: 240 km
Question 12
M1 boxes per worker = 234/3 = 78
A1 390 boxes cao
Answer: 390 boxes
Question 13
M1 stock per person = 900/6 = 150
A1 1500 ml cao
Answer: 1500 ml
Question 14
M1 paint per m2 = 9/45 = 0.2
A1 12 litres cao
Answer: 12 litres
Question 15
M1 pasta per serving = 640/8 = 80
M1 sauce per serving = 400/8 = 50
A1 400 g pasta and 250 ml sauce cao
Answer: 400 g pasta and 250 ml sauce
Question 16
M1 rate = 45/6 = 7.5 pages per minute
M1 time = 100/7.5 = 13 and 1/3 minutes
A1 13 minutes 20 seconds cao
Answer: 13 minutes 20 seconds
Question 17
M1 unit price = 22.50/5 = 4.50
M1 metres bought = 40.50/4.50 = 9
A1 9 metres; 12 metres cost 54 pounds cao
Answer: 9 metres bought; 12 metres would cost 54 pounds
Question 18
M1 fuel in tank = 3/4 x 40 = 30 litres
M1 distance = 30 x 15
A1 450 km cao
Answer: 450 km
Question 19
M1 unit price = 5.60/3.5 = 1.60 pounds per kg
M1 6 kg costs 6 x 1.60, and 12.80/1.60 gives the mass
A1 9.60 pounds and 8 kg cao
Answer: 9.60 pounds for 6 kg; 8 kg for 12.80 pounds
Question 20
M1 eggs needed = (4/12) x 18 = 6
M1 flour needed = (360/12) x 18 = 540 g
A1 6 eggs; 540 g flour needed, so 480 g is not enough cao
Answer: 6 eggs; she needs 540 g of flour but only has 480 g, so she does not have enough