Ratio, Proportion and Rates of Change - Worksheets, Questions and Revision

20 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Ratio and Proportion

KS3.M-R1 Ratio, Proportion and Rates of Change

AQA KS3.M-R1 · Calculator allowed · about 65 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Simplify the ratio 42 : 56 fully.
(1)
2
A jar contains 8 red counters and 12 blue counters.
(a)Write the ratio of red counters to blue counters in its simplest form.(1)
(b)What fraction of the counters in the jar are red? Give your answer in its simplest form.(1)
3
Priya and Tom share £420 in the ratio 3 : 4. Work out how much each person receives.
(2)
4
Amara, Ben and Chidi share 720 kg of gravel in the ratio 2 : 3 : 4 for a building project. Work out the mass each person receives.
(3)
5
A recipe uses 300 ml of stock and 1.5 litres of water. Write the ratio of stock to water in its simplest form.
(2)
6
Shampoo A costs £2.75 for 250 ml. Shampoo B costs £4.20 for 400 ml. Which shampoo is better value for money? You must show your working.
(3)
7
A recipe for 6 people uses 450 g of rice and 3 eggs.
(a)Work out how much rice is needed to serve 8 people.(2)
(b)Work out how many eggs are needed to serve 15 people. Give a sensible whole number of eggs.(2)
8
It takes 5 builders 12 days to build a wall, all working at the same constant rate. Assuming the same rate of work, how many days would it take 8 builders to build an identical wall?
(3)
9
A train travels 210 km in 2 hours 30 minutes at a constant speed.
(a)Calculate the average speed of the train in km/h.(2)
(b)Assuming the same average speed, find the time taken to travel 350 km. Give your answer in hours and minutes.(2)
10
A metal block has a mass of 540 g and a volume of 60 cm3.
(a)Calculate the density of the metal in g/cm3.(1)
(b)A second block made from the same metal has a volume of 85 cm3. Calculate its mass.(2)
11
The exchange rate is £1 = $1.28.
(a)Convert £250 to dollars.(1)
(b)Convert $192 to pounds sterling. Give your answer to the nearest penny.(2)
12
A sofa has a price of £680 before VAT. VAT is charged at 20%.
(a)Calculate the total price of the sofa including VAT.(2)
(b)In a sale, the total price (including VAT) is reduced by 15%. Calculate the sale price.(2)
13
A map has a scale of 1 : 25000.
(a)The distance between two villages on the map is 8.4 cm. Calculate the real-life distance in kilometres.(2)
(b)A field has an area of 12 cm2 on the map. Calculate the real-life area of the field in km2.(3)
14
A water tank is filled at a constant rate. After 4 minutes it contains 60 litres of water. After 10 minutes it contains 150 litres of water.
(a)Find the rate at which the tank is being filled, in litres per minute.(2)
(b)Find how much water was in the tank at the start, when time = 0 minutes.(2)
15
A shade of paint is made by mixing blue and white paint. Batch 1 mixes blue and white in the ratio 3 : 7. Batch 2 mixes blue and white in the ratio 1 : 4. Grace mixes 400 g of Batch 1 with 500 g of Batch 2 to make a new batch of paint. Find the ratio of blue to white paint in the new mixture, in its simplest form.
(5)
16
A population of rabbits increases by 20% each year. The starting population is 150.
(a)Find the population after 2 years.(2)
(b)Find the single multiplier that could be used to calculate the population after 3 years directly from the starting population.(2)
17
The ratio of Ali's age to Beth's age is 3 : 5. In 4 years' time, the ratio of their ages will be 2 : 3. Find their current ages.
(4)
18
A car uses fuel at a rate of 1 litre per 14 km. Petrol costs £1.48 per litre.
(a)How many litres of fuel are needed for a 420 km journey?(1)
(b)Find the total cost of the fuel for this journey.(2)
19
The braking distance, d metres, of a car is directly proportional to the square of its speed, v mph. When v = 30 mph, d = 15 m. Find the braking distance when v = 60 mph.
(4)
20
Nadia is baking and uses flour, sugar and butter in the ratio 5 : 2 : 3 by mass. She has 600 g of flour, 300 g of sugar and 150 g of butter, and cannot buy any more of any ingredient. Find the maximum total mass of mixture she can make, and find how much of each ingredient will be left over.
(6)
Mark scheme · KS3.M-R1 Ratio, Proportion and Rates of Change

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20