Direct and Inverse Proportion - Worksheets, Questions and Revision

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GCSE · Ratio, Proportion and Rates of Change

5.2 Direct and Inverse Proportion

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A recipe for 4 people uses 300 g of flour and 120 g of butter. Farah wants to make the recipe for 10 people. Work out how much butter she needs.
(Total for Question 1 is 2 marks)
2
Tom changes 150 pounds sterling into US dollars. The exchange rate is 1 pound = 1.28 dollars.
(a)Work out how many dollars Tom gets.(2)
(b)Tom's friend changes some pounds into dollars at the same rate and receives 96 dollars. Work out how many pounds she changed.(2)
(Total for Question 2 is 4 marks)
3
A supermarket sells apple juice in two sizes:
Small bottle: 750 ml for 1.35 pounds
Large bottle: 2 litres for 3.20 pounds
Determine which bottle is the better value for money. You must show your working.
(Total for Question 3 is 3 marks)
4
The cost, C pounds, of petrol is directly proportional to the number of litres, n, bought.
n (litres): 10, 25, 40
C (pounds): 14.20, ?, ?
(a)Work out the missing value of C when n = 25.(2)
(b)Work out the missing value of C when n = 40.(1)
(Total for Question 4 is 3 marks)
5
It takes 6 workers 8 hours to build a wall, all working at the same constant rate. Work out how long it would take 4 workers, working at the same rate, to build the same wall.
(Total for Question 5 is 3 marks)
6
Three tables of values are shown.
Table A
x: 1 2 5
y: 4 8 20
Table B
x: 1 2 5
y: 20 10 4
Table C
x: 1 2 5
y: 3 5 11
(a)State which table shows y directly proportional to x. Give a reason for your answer.(2)
(b)State which table shows y inversely proportional to x. Give a reason for your answer.(2)
(c)Explain why Table C shows neither direct nor inverse proportion between x and y.(1)
(Total for Question 6 is 5 marks)
7
y is directly proportional to x. When x = 8, y = 20.
(a)Find a formula for y in terms of x.(2)
(b)Work out the value of y when x = 14.(1)
(c)Work out the value of x when y = 100.(2)
(Total for Question 7 is 5 marks)
8
y is inversely proportional to x. When x = 5, y = 12.
(a)Find a formula for y in terms of x.(2)
(b)Work out the value of y when x = 15.(1)
(c)Work out the value of x when y = 24.(2)
(Total for Question 8 is 5 marks)
9
The cost, C pounds, of tiling a floor is directly proportional to the area, A m2, of the floor. It costs 187.50 pounds to tile a floor with area 25 m2.
(a)Find a formula for C in terms of A.(3)
(b)Work out the cost of tiling a floor with area 34 m2.(2)
(Total for Question 9 is 5 marks)
10
A car being driven at a constant average speed takes 3 hours to complete a journey when its average speed is 60 mph. The time taken, T hours, for the journey is inversely proportional to the average speed, S mph.
(a)Find a formula for T in terms of S.(3)
(b)Work out the time taken for the same journey if the average speed is 40 mph. Give your answer in hours and minutes.(3)
(Total for Question 10 is 6 marks)
11
Three graphs, P, Q and R, show relationships between x and y.
Graph P: a straight line passing through the origin.
Graph Q: a curve that decreases as x increases, getting closer and closer to both axes but never touching them.
Graph R: a straight line that does not pass through the origin.
(a)Which graph could represent y directly proportional to x?(1)
(b)Which graph could represent y inversely proportional to x?(1)
(c)Explain why graph R cannot represent a proportional relationship between x and y.(1)
(Total for Question 11 is 3 marks)
12
y is directly proportional to x2. When x = 3, y = 45.
(a)Find a formula for y in terms of x.(3)
(b)Work out the value of y when x = 6.(2)
(Total for Question 12 is 5 marks)
13
P is directly proportional to Q2. Q is increased by 50%. Work out the percentage increase in P.
(Total for Question 13 is 3 marks)
14
y is inversely proportional to x2. When x = 2, y = 15.
(a)Find a formula for y in terms of x.(3)
(b)Work out the value of x when y = 2.4, given that x is positive.(3)
(Total for Question 14 is 6 marks)
15
y is directly proportional to √x. When x = 16, y = 20.
(a)Find a formula for y in terms of x.(3)
(b)Work out the value of y when x = 25.(2)
(Total for Question 15 is 5 marks)
16
z is directly proportional to x and inversely proportional to y. When x = 6 and y = 4, z = 27.
(a)Find a formula for z in terms of x and y.(3)
(b)Work out the value of z when x = 10 and y = 5.(2)
(Total for Question 16 is 5 marks)
17
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 200 cm3, the pressure is 350 pascals.
(a)Find a formula for P in terms of V.(3)
(b)The gas is compressed so that its volume becomes 125 cm3. Work out the new pressure.(2)
(c)For safety reasons, the pressure must not exceed 800 pascals. Find the minimum volume, in cm3, that the gas can be compressed to.(2)
(Total for Question 17 is 7 marks)
18
y is directly proportional to x3. x is increased by 20%. Work out the percentage increase in y.
(Total for Question 18 is 3 marks)
19
The cost, C pounds, of painting a fence is directly proportional to the length, L metres, of the fence and inversely proportional to the number of painters, n, working on it. It costs 60 pounds to paint a 20 m fence using 4 painters.
(a)Find a formula for C in terms of L and n.(3)
(b)Work out the cost of painting a 45 m fence using 6 painters.(2)
(c)A different fence costs 100 pounds to paint using 8 painters. Work out the length of this fence, in metres. Give your answer correct to 1 decimal place.(3)
(Total for Question 19 is 8 marks)
20
y is directly proportional to x2. x is first doubled, and then the new value of x is trebled. Show that the overall effect is that y is multiplied by 36.
(Total for Question 20 is 3 marks)
Mark scheme · 5.2 Direct and Inverse Proportion

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