Revision NotesExam QuestionsFlashcardsPast Papers
GCSEMathsEdexcelHigherExam Questions3. Ratio, Proportion & Rates of ChangeDirect & Inverse Proportion

Direct & Inverse Proportion (Edexcel GCSE Maths: Higher): Exam Questions

Exam code: 1MA1

3 hours51 questions
Medium
Hard
Very Hard
1
Sme Calculator3 marks

Yesterday it took 5 cleaners 4 1 half  hours to clean all the rooms in a hotel.

There are only 3 cleaners to clean all the rooms in the hotel today.

Each cleaner is paid £8.20 for each hour or part of an hour they work.

How much will each cleaner be paid today?

How did you do?

2
Sme Calculator3 marks

p spaceis inversely proportional to t.

When space t space equals space 4 comma space p space equals space 12

Find the value of space p space when  t space equals space 6

How did you do?

3
Sme Calculator3 marks

d is inversely proportional to c

When c space equals space 280 comma space space d space equals space 25

Find the value of d when c space equals space 350

How did you do?

4
Sme Calculator3 marks

y is inversely proportional to x

Whenspace x equals space 1.5 comma space y space equals space 36 space

Find the value of y when x space equals space 6

How did you do?

5a
Sme Calculator3 marks

At a depth of x metres, the temperature of the water in an ocean is T to the power of ring operator C. At depths below space 900 spacemetres, T is inversely proportional tospace x.

T is given by

            T space equals space 4500 over x

Work out the difference in the temperature of the water at a depth of space 1200 space metres and the temperature of the water at a depth of space 2500 spacemetres.

How did you do?

5b1 mark

Here are four graphs.

q5b-medium-3-4-direct-and-inverse-proportional-edexcel-gcse-maths

One of the graphs could show that T is inversely proportional to x.

Choose the letter corresponding to this graph.

    Choose your answer

    6a
    Sme Calculator    3 marks

    T is directly proportional to the cube of  r

    T space equals space 21.76 when r space equals space 4

    Find a formula for T in terms of r

    How did you do?

    6b
    Sme Calculator    1 mark

    Work out the value of T when r space equals space 6

    How did you do?

    7
    Sme Calculator    2 marks

    y spaceis inversely proportional to x.

    Complete the table.

    x

    12

    6

     

    y

     

    4

    8

    How did you do?

    8
    Sme Calculator    4 marks

    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°

    q9-1-paper-2h-nov-2018-aqa-gcse-maths

    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°

    q9-2-paper-2h-nov-2018-aqa-gcse-maths

    The water flows into a tank with a capacity of 79.8 litres. Will it take less than 7 1 half minutes to fill the tank?

    You must show your working.

    How did you do?

    9a
    Sme Calculator    3 marks

    To complete a task in 15 days a company needs

    4 people each working for 8 hours per day.

    The company decides to have

    5 people each working for 6 hours per day.

    Assume that each person works at the same rate.

    How many days will the task take to complete? You must show your working.

    How did you do?

    9b1 mark

    Comment on how the assumption affects your answer to part (a).

    How did you do?

    101 mark

    y is directly proportional to x.

    Which graph shows this?

    q4-paper3h-specimen2015-aqa-gcse-maths

      Choose your answer

      11
      Sme Calculator      5 marks

      Carol makes birthday cards. Each card takes the same amount of time to make.

      She makes 3 cards in 48 minutes.
      She has an order for 80 cards.

      Can she complete this order in 3 days if she works 8 hours each day?
      Show how you decide.

      ..................... because .................................................................................................

      How did you do?

      12
      Sme Calculator      3 marks

      y is inversely proportional to x.
      y = 0.04 when x = 80.

      Find the value of y when x = 32.

      y = ...................

      How did you do?

      13
      Sme Calculator      2 marks

      The table shows values of x and y.

      x

      4

      16

      36

      y

      6

      3

      2

      Show that these values fit the relationship that y is inversely proportional to begin mathsize 16px style square root of x end style .

      How did you do?

      14a
      Sme Calculator      2 marks

      Sam and two friends put letters in envelopes on Monday.
      The three of them take two hours to put 600 letters in envelopes.

      On Tuesday Sam has three friends helping.

      Working at the same rate, how many letters should the four of them be able to put in envelopes in two hours?

      How did you do?

      14b
      Sme Calculator      4 marks

      Working at the same rate, how much longer would it take four people to put 1000 letters in envelopes than it would take five people?

      How did you do?

      14c2 marks

      Sam says

      It took two hours for three people to put 600 letters in envelopes.

      If I assume they work all day, then in one day three people will put 7200 letters in envelopes because 600 × 12 = 7200.

      Why is Sam’s assumption not reasonable? What effect has Sam’s assumption had on her answer?

      How did you do?

      15a
      Sme Calculator      5 marks

      Donald swims 3 lengths of a swimming pool in 93 seconds.

      i) Use this information to show that he could swim 100 lengths in under 55 minutes.

      [4]

      ii) What assumption did you make in part (i)?

      [1]

      How did you do?

      15b1 mark

      Donald tries to swim the 100 lengths in under 55 minutes.

      Suggest one reason why he might not achieve this.

      How did you do?

      1
      Sme Calculator      4 marks

      y is directly proportional to the square of x.

      When x space equals space 3 comma space y space equals space 36

      Find the value of y when x space equals space 5

      How did you do?

      2
      Sme Calculator      3 marks

      h is inversely proportional to the square of r.

      When space r equals 5 comma space h equals 3.4

      Find the value of h when r space equals space 8

      How did you do?

      3
      Sme Calculator      4 marks

      Given that y space proportional to space 1 over x squared, complete this table of values.

      x

      1

      2

      5

      10

      y

       

       

       

      1

      How did you do?

      4
      Sme Calculator      3 marks

      The intensity of the sound, I watts/m2, received from a loudspeaker is inversely proportional to the square of the distance, d metres, from the loudspeaker.

      When d space equals space 2 comma space I space equals space 30

      Work out the value of I when d space equals space 10

      How did you do?

      5
      Sme Calculator      3 marks

      T is inversely proportional to d squared
      T space equals space 12 spacewhen d space equals space 8

      Find the value of T when d space equals space 0.5

      How did you do?

      62 marks
      LJeW5o9-_q6-hard-3-3-direct-and-inverse-proportional-edexcel-gcse-maths

      The graphs of y against x represent four different types of proportionality.

      Match each type of proportionality in the table to the correct graph.

      Type of proportionality

      Graph letter

      y space proportional to space x

       

      y space proportional to space x squared

       

      y space proportional to space square root of x

       

      y space proportional to space 1 over x

       

      How did you do?

      7
      Sme Calculator      3 marks

      A company has to make a large number of boxes.

      The company has 6 machines.
      All the machines work at the same rate.
      When all the machines are working, they can make all the boxes in 9 days.

      The table gives the number of machines working each day.

       

      day 1

      day 2

      day 3 

      all other days

      Number of machines working

      3

      4

      5

      6

      Work out the total number of days taken to make all the boxes.

      How did you do?

      8
      Sme Calculator      3 marks

      A is inversely proportional to C squared
      A = 40 when C = 1.5
      Calculate the value of C when A = 1000

      C space= ...................................................

      How did you do?

      9a
      Sme Calculator      3 marks

      R is proportional to t squared
      The graph shows the relationship between R and t for 0 space less-than or slanted equal to space t space less-than or slanted equal to space 4

      q16-paper2h-june2018-edexcel-igcse-maths

      Find a formula for R in terms of t.

      How did you do?

      9b
      Sme Calculator      2 marks

      Given also that R space equals fraction numerator 8 over denominator 5 x end fraction
      show that t is inversely proportional to square root of x for t space greater than space 0

      How did you do?

      10
      Sme Calculator      3 marks

      F is inversely proportional to the square of v.

      Given that F space equals space 6.5 when v space equals space 4

      find a formula for F in terms of v.

      How did you do?

      11a
      Sme Calculator      3 marks

      T is inversely proportional to m squared

      T space equals space 30 when m space equals space 0.5

      Find a formula for T in terms of m.

      How did you do?

      11b
      Sme Calculator      1 mark

      Work out the value of T when m space equals space 0.1

      How did you do?

      12a
      Sme Calculator      3 marks

      The following table gives values of space x spaceand y where y is inversely proportional to the square of space x space.

      x

      1.5

      2

      3

      4

      y

      16

      9

      4

      2.25

      Find a formula for y in terms of x.

      How did you do?

      12b
      Sme Calculator      2 marks

      Given that x greater than0

      find the value of x when y space equals space144

      How did you do?

      13a
      Sme Calculator      3 marks

      P  is inversely proportional to square root of space q space end root
      P  = 10 when q space equals 0.0064

      Find a formula for space P space in terms of q.

      How did you do?

      13b
      Sme Calculator      2 marks

      Find the value of space q space when  P = 20

      How did you do?

      14a
      Sme Calculator      3 marks

      y is inversely proportional to square root of x

            y space equals space 4     when     x space equals space 9

      Work out an equation connecting y and x.

      How did you do?

      14b
      Sme Calculator      2 marks

      Work out the value of y when x space equals space 25

      How did you do?

      15
      Sme Calculator      3 marks

      15 machines work at the same rate.
      Together, the 15 machines can complete an order in 8 hours.

      3 of the machines break down after working for 6 hours.
      The other machines carry on working until the order is complete.

      In total, how many hours does each of the other machines work?

      ............................hours

      How did you do?

      16
      Sme Calculator      1 mark

      V equals k over H  where k is a constant. Which two statements are correct?

      Tick two boxes.

      square

      V is directly proportional to H

      square

      V is inversely proportional to H

      square

      V is directly proportional to 1 over H

      size 26px square

      V is inversely proportional to 1 over H

      How did you do?

      171 mark

      x y space equals space c where c is a constant.
      Choose the correct statement.

      • y is directly proportional to x

      • y is directly proportional to 1 over x

      • y is inversely proportional to 1 over x

      • x is directly proportional to y

      Choose your answer

      18
      Sme Calculator      4 marks

      Three people take 2 begin inline style 1 half end style hours to deliver leaflets to space 270 spacehouses.

      Assuming all people deliver leaflets at the same rate, how long will it take five people to deliver leaflets to 405 houses?
      Give your answer in hours and minutes.

      ................. hours ................. minutes

      How did you do?

      19
      Sme Calculator      3 marks

      y is inversely proportional to the square root of x.
      y is 40 when x is 9.

      Find a formula linking x and y.

      How did you do?

      20
      Sme Calculator      3 marks

      The graph shows the speed, v metres per second (m/s), of a car at time t seconds.

      q15-paper4-june2017-ocr-gcse-maths

      The speed of this car is directly proportional to the square of the time.

      Find a formula linking v and t.

      How did you do?

      1a
      Sme Calculator      2 marks

      The table shows a set of values for x and y.

      x

      1

      2

      3

      4

      y

      9

      2 1 fourth

      1

      9 over 16

      y is inversely proportional to the square of x.

      Find an equation for y in terms of x.

      How did you do?

      1b
      Sme Calculator      2 marks

      Find the positive value of x when y equals 16

      How did you do?

      2
      Sme Calculator      3 marks

      y is directly proportional to cube root of x

      y space equals space 1 1 over 6 when  x equals 8

      Find the value of y when x equals 64

      How did you do?

      3
      Sme Calculator      5 marks

      y is inversely proportional to d squared
      When d space equals space 10 comma space y equals 4

      d is directly proportional to x squared
      When x space equals space 2 comma space d space equals space 24

      Find a formula for y in terms of x.
      Give your answer in its simplest form.

      How did you do?

      4
      Sme Calculator      3 marks

      A pendulum of length space L space cm has time period T seconds.
      T is directly proportional to the square root of L.

      The length of the pendulum is increased by 40%.

      Work out the percentage increase in the time period.

      How did you do?

      51 mark

      D is directly proportional to the cube of n.
      Mary says that when n is doubled, the value of D is multiplied by 6

      Mary is wrong.
      Explain why.

      How did you do?

      62 marks

      These graphs show four different proportionality relationships between y and x.

      q6-hard-3-3-direct-and-inverse-proportional-edexcel-gcse-maths

      Match each graph with a statement in the table below.

      Proportionality relationship

      Graph letter

      y is directly proportional to x

       

      y is inversely proportional to x

       

      y is proportional to the square of x

       

      y is inversely proportional to the square of x

       

      How did you do?

      7
      Sme Calculator      4 marks

      h is inversely proportional to p
      p is directly proportional to square root of t

      Given that h space equals space 10 and t space equals space 144 when p space equals space 6
      find a formula for h in terms of t

      How did you do?

      8
      Sme Calculator      4 marks

      y is inversely proportional to square root of x
      x is directly proportional to T cubed

      Given thatspace y space equals space 8 space when T space equals space 25
      find the exact value of space T spacewhen y space equals space 27

      T space equals space.......................................................

      How did you do?

      9a
      Sme Calculator      3 marks

      y is directly proportional to the cube of x

      y space equals space 20 space h spacewhen x space equals space h space space space space space space left parenthesis h space not equal to space 0 right parenthesis

      Find a formula for y in terms of space x spaceand h

      y = .....................

      How did you do?

      9b
      Sme Calculator      2 marks

      Find x in terms of h when y space equals space 67.5 space h
      Give your answer in its simplest form.

      x space=.......................

      How did you do?

      10a
      Sme Calculator      3 marks

      A is inversely proportional to the square of r.
      space A space equals space 5 spacewhen r space equals space 0.3.

      Find a formula for A in terms of r.

      How did you do?

      10b
      Sme Calculator      3 marks

      Find the value of A whenspace r space equals space 7.5 A

      A space equals space..............................................

      How did you do?

      11
      Sme Calculator      4 marks

      Beth and Mia translate documents from Spanish into English.
      A set of documents that would take Beth 8 days would take Mia 10 days.

      Beth starts to translate the documents.
      After 2 days Beth and Mia both work on translating the documents.

      How many more days will it take to complete the work?
      You must show your working.

      ......................days

      How did you do?

      12a
      Sme Calculator      3 marks

      y is directly proportional to x cubed

      y space equals space 17   when   x space equals space 4

      Work out an equation connecting y and x.

      How did you do?

      12b1 mark

      m is inversely proportional to square root of r.

      The value of space r spaceis multiplied by 4.

      Select what happens to the value of m.

      • cross times 2

      • cross times 16

      • divided by 2

      • divided by 16

      Choose your answer

      13
      Sme Calculator      5 marks

      P comma space Q and space R spacehave positive values.

      P is directly proportional to the square of Q.
      When P space equals space 1.25 comma space Q space equals space 0.5
      Q is inversely proportional to R.
      When Q space equals space 0.5 comma space R space equals space 6

      Work out the value of R when P space equals space 0.8

      How did you do?

      14
      Sme Calculator      4 marks

      y is directly proportional to the square of x.

      Find the percentage increase in y when x is increased by 15%.

      How did you do?

      15
      Sme Calculator      4 marks

      At a constant temperature, the volume of a gas V is inversely proportional to its pressure p.
      By what percentage will the pressure of a gas change if its volume increases by 25%?

      How did you do?

      16
      Sme Calculator      4 marks

      x is directly proportional to y. y is directly proportional to z.

      When x = 10, y = 60.
      When y = 8, z = 1.6.

      Find a formula for z in terms of x.

      How did you do?