Direct and Inverse Proportion: Fluency and Exam Drill - Worksheets, Questions and Revision

20 original exam-style questions - 9 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Ratio, Proportion and Rates of Change

5.2D Direct and Inverse Proportion: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 95 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
y is directly proportional to x. When x = 5, y = 15.
(a)Work out the value of y when x = 8.(2)
(b)Work out the value of x when y = 39.(2)
(Total for Question 1 is 4 marks)
2
A shop sells pens in packs. The cost of pens is directly proportional to the number of pens bought. 6 pens cost £4.20.
(a)Work out the cost of 10 pens.(2)
(b)Rhys has £6. Work out the greatest number of pens he can buy.(2)
(Total for Question 2 is 4 marks)
3
On a certain day, the amount received in pounds sterling, P, when exchanging euros is directly proportional to the number of euros exchanged, E. Grace exchanges 250 euros and receives £215.
(a)Work out the exchange rate, in pounds sterling received per euro, giving your answer to 3 significant figures.(2)
(b)Prisha exchanges 460 euros. Work out how many pounds sterling she receives.(2)
(Total for Question 3 is 4 marks)
4
The time, T hours, taken by a train to travel a fixed distance is inversely proportional to its average speed, S mph. When S = 50, T = 4.
(a)Find a formula for T in terms of S.(2)
(b)Work out T when S = 80.(2)
(Total for Question 4 is 4 marks)
5
A cake recipe for 8 people uses 240 g of caster sugar and 200 g of butter. The amounts of each ingredient needed are directly proportional to the number of people.
(a)Work out the mass of caster sugar needed to make the recipe for 6 people.(2)
(b)Nadia has 620 g of butter. Work out the maximum number of people she can make the recipe for.(3)
(Total for Question 5 is 5 marks)
6
y is directly proportional to x2. When x = 4, y = 32.
(a)Find a formula for y in terms of x.(2)
(b)Work out the value of y when x = 5.(2)
(c)Work out the positive value of x when y = 98.(2)
(Total for Question 6 is 6 marks)
7
y is inversely proportional to x. When x = 4, y = 9.
(a)Find a formula for y in terms of x.(2)
(b)Work out the value of x when y = 6.(2)
(Total for Question 7 is 4 marks)
8
The table shows some corresponding values of x and y.
x: 1, 2, 4
y: 48, 24, 12
(a)Show that y is inversely proportional to x.(2)
(b)Write down a formula for y in terms of x.(1)
(Total for Question 8 is 3 marks)
9
The table shows values of x and y, where y is directly proportional to x2.
x: 1, 3, 5
y: 4, 36, 100
(a)Find the value of k in y = kx2.(1)
(b)Hence find the value of y when x = 10.(2)
(Total for Question 9 is 3 marks)
10
y is directly proportional to √x. When x = 9, y = 15.
(a)Find a formula for y in terms of x.(2)
(b)Work out the value of y when x = 16.(2)
(c)Work out the value of x when y = 17.5.(2)
(Total for Question 10 is 6 marks)
11
y is inversely proportional to x2. When x = 3, y = 10.
(a)Find a formula for y in terms of x.(2)
(b)Work out the value of y when x = 5, giving your answer as a decimal.(2)
(Total for Question 11 is 4 marks)
12
The pressure, P pascals, of a fixed mass of gas at constant temperature is inversely proportional to its volume, V cm3. When the volume is 150 cm3, the pressure is 240 pascals.
(a)Find a formula for P in terms of V.(2)
(b)Work out the pressure when the volume is decreased to 100 cm3.(2)
(c)The volume is increased so that the pressure drops to 90 pascals. Work out the new volume.(2)
(Total for Question 12 is 6 marks)
13
It takes 5 taps 22 minutes to fill a tank, with all taps flowing at the same constant rate. Work out how many minutes it would take 7 taps, flowing at the same rate, to fill an identical tank. Give your answer correct to 1 decimal place.
(Total for Question 13 is 3 marks)
14
y is directly proportional to x and inversely proportional to z. When x = 4 and z = 2, y = 10.
(a)Find a formula for y in terms of x and z.(3)
(b)Work out the value of y when x = 9 and z = 3.(2)
(Total for Question 14 is 5 marks)
15
The intensity of light, I lux, from a lamp is inversely proportional to the square of the distance, d metres, from the lamp. At a distance of 3 m, the intensity is 20 lux.
(a)Find a formula for I in terms of d.(2)
(b)Work out the intensity at a distance of 5 m. Give your answer to 3 significant figures.(2)
(c)For safe reading, the intensity must be at least 8 lux. Find the maximum distance, to 1 decimal place, at which this is possible.(3)
(Total for Question 15 is 7 marks)
16
The braking distance, D metres, of a car is directly proportional to the square of its speed, v mph. A car travelling at 30 mph has a braking distance of 13.5 m.
(a)Find a formula for D in terms of v.(2)
(b)A car is travelling at 50 mph. Investigators find that its actual braking distance is 3 times the value predicted by the formula in part (a), due to a wet road surface. Work out the actual braking distance of the car at 50 mph.(3)
(Total for Question 16 is 5 marks)
17
V is directly proportional to L3. When L = 2, V = 40.
(a)Find a formula for V in terms of L.(2)
(b)Work out V when L = 5.(2)
(c)Work out the value of L when V = 200, giving your answer to 3 significant figures.(3)
(Total for Question 17 is 7 marks)
18
y is directly proportional to x2. Work out the percentage increase in y when x is increased by 20%.
(Total for Question 18 is 3 marks)
19
y is inversely proportional to x3. Work out the percentage decrease in y when x is increased by 50%.
(Total for Question 19 is 3 marks)
20
y is directly proportional to x2. z is inversely proportional to y. When x = 2, y = 12 and z = 3.
(a)Find a formula for y in terms of x.(2)
(b)Find a formula for z in terms of x.(3)
(c)Find the positive value of x for which y = z.(3)
(Total for Question 20 is 8 marks)
Mark scheme · 5.2D Direct and Inverse Proportion: Fluency and Exam Drill

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