AQA GCSE Maths
Topic questions Ratio, proportion and rates of change Direct and inverse proportion
39 questions · 110 marks · about 2 hours
Here is a list of ingredients for lentil soup.
| Lentil soup for 4 people | |
| Lentils | 170 g |
| Water | 600 ml |
| Onion | 50 g |
How many grams of lentils are needed to make this soup for 10 people?
d represents the number of days to complete a job.
w represents the number of workers needed.
Assume the job needs completing in 20 days.
How many workers are needed?
In fact, the job needs completing in fewer than 20 days.
What does this mean about the number of workers that are needed? Tick one box.
4 apples cost £2.20
Work out the cost of 7 of these apples.
A study suggests a student’s exam mark, m, is directly proportional to the cube root of total revision time, t hours.
A student doubles their total revision time.
Work out the percentage increase in their exam mark.
In this part, assume that each person works at the same rate. 10 people can complete a job in 9 hours.
If 15 people work on the same job, how many hours will it take to complete the job?
In fact, of the 15 people 6 work at a slower rate 9 work at a faster rate.
What does this mean about the number of hours it will take to complete the job? Tick one box.
Also involves Proportion
In this part, assume that each person works at the same rate. 10 people can complete a job in 9 hours.
If 15 people work on the same job, how many hours will it take to complete the job?
In fact, of the 15 people 6 work at a slower rate 9 work at a faster rate.
What does this mean about the number of hours it will take to complete the job? Tick one box.
X is inversely proportional to Y.
Circle the correct statement.
X is directly proportional to Y X is directly proportional to 
X is inversely proportional to Y.
Circle the correct statement.
X is directly proportional to Y X is directly proportional to
A stone falls vertically from 300 metres above ground.
The stone falls d metres in t seconds.
d is directly proportional to the square of t.
The stone falls 20 metres in the first 2 seconds.
Work out the total time taken for the stone to reach the ground.
One lettuce costs £1.29
How much do seven of these lettuces cost?
Five cucumbers cost £6.40 in total.
How much do two of these cucumbers cost?
A chef has a tub of blueberries. She wants to use all the blueberries put the same number of blueberries on each dessert.
D is the number of desserts. b is the number of blueberries on each dessert.
What does the constant k represent? Tick the correct box.
Complete the table.
| b | 2 | 6 | |
| D | 120 | 30 |
A chef has a tub of blueberries. She wants to use all the blueberries put the same number of blueberries on each dessert.
D is the number of desserts. b is the number of blueberries on each dessert.
What does the constant k represent? Tick the correct box.
Complete the table.
| b | 2 | 6 | |
| D | 120 | 30 |
P, Q, and R have positive values. P is directly proportional to Q When P = 8, Q = 2
When R = 10, Q = 3
Work out the value of R when P = 0.5
Salma is raising money for charity. Her mum says, “Whatever amount you raise, I will add double that amount.”
Show this information by drawing a graph on each grid below.
The graph below is used to convert between pounds (£) and Norwegian krone (kr).
Convert 720 krone into pounds.
Convert £500 into krone.
A is directly proportional to B4 The value of B is doubled.
Pete thinks that the value of A will be 8 times bigger because 4 × 2 is 8
Is he correct? Tick a box.
Give a reason for your answer.
The total cost of broadband for 5 months is £99.20
At the same monthly rate, work out the total cost of broadband for 2 years.
The graph shows the values of D and E for 2 
D 
6
Choose one point on the graph and state if Sunil’s equation is correct for that point.
G is directly proportional to the square root of H. G: H = 3: 2 when H = 16 Work out G: H when H = 100
m = pr p is halved and r is multiplied by 3 What happens to m ? Circle your answer.
Circle the equation where c is inversely proportional to d.
Also involves Proportion
H is inversely proportional to the cube root of L. H = 7 when L = 64
Work out an equation connecting H and L.
Work out the value of H when L = 2744
4 y = 5 x Which statement is correct? Tick one box.
4 y = 5 x Which statement is correct? Tick one box.
L is directly proportional to D2 L = 85 when D = 10
Work out an equation connecting L and D.
Work out the value of L when D = 5
Also involves Proportion
y is directly proportional to x3 y = 17 when x = 4 Work out an equation connecting y and x.
The value of r is multiplied by 4 Circle what happens to the value of m. × 2 × 16 ÷ 2 ÷ 16
Which two statements are correct? Tick two boxes.
Which two statements are correct? Tick two boxes.
P, Q and R have positive values. P is directly proportional to the square of Q. When P = 1.25, Q = 0.5 Q is inversely proportional to R. When Q = 0.5, R = 6 Work out the value of R when P = 0.8
d is directly proportional to the square of v. d = 6 when v = 20
Work out an equation connecting d and v.
Work out the value of d when v = 30
Also involves Compound measures
The diagrams show the position of a tap when off and fully on. The tap is fully on when the angle of turn is 180°
When fully on, water flows out of the tap at 14 litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned 135°
The water flows into a tank with a capacity of 79.8 litres. Will it take less than 7 
minutes to fill the tank? You must show your working.
y = 4 when x = 9
Work out an equation connecting y and x.
Work out the value of y when x = 25
y is inversely proportional to x. Complete the table.
| x | 12 | 6 | |
| y | 4 | 8 |
y is inversely proportional to x. Complete the table.
| x | 12 | 6 | |
| y | 4 | 8 |
The mass of an ornament is m grams. The height of the ornament is h centimetres. m is directly proportional to the cube of h. m = 1600 when h = 8
Work out an equation connecting m and h.
Work out the mass of an ornament of height 12 centimetres.
4
If the value of x doubles, what happens to the value of y ? Circle your answer. ÷ 2 × 2 ÷ 5 × 5
A stone is thrown upwards with a speed of v metres per second. The stone reaches a maximum height of h metres.
When v = 10, h = 5 Work out the maximum height reached when v = 24
y is inversely proportional to x and k is a constant. Circle the correct equation.
A ball, dropped vertically, falls d metres in t seconds. d is directly proportional to the square of t. The ball drops 45 metres in the first 3 seconds. How far does the ball drop in the next 7 seconds?
xy = c where c is a constant. Circle the correct statement.
y is directly proportional to x y is directly proportional to 
y is inversely proportional to 
x is directly proportional to y
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