GCSE · Graphs of functions

Real-life graphs (conversion, cost and travel graphs)Exam-style questions

Read real-life graphs both ways: change units with a conversion graph (and scale a reading beyond its edge only when the line starts at zero), read a fixed charge and a cost per hour off a cost graph, compare two tariffs where their lines cross, and turn a travel graph into a story: stops, speeds in km/h, the journey home, drawing the next part, and two journeys on one graph.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    Ria is timing a remote-control car that moves in a straight line at a constant speed.

    She starts her stopwatch when the car is already moving.

    The graph shows the distance of the car from Ria.12345624681012141618202224Time (seconds)Distance from Ria (metres)(a) How far from Ria was the car when she started the stopwatch?

    (1 mark)

    Ria says,

    "The speed of the car is 20÷620 \div 6, which is about 3.33.3 metres per second."
    (b) Explain why Ria is wrong.

    (1 mark)
    (c) Work out the speed of the car in metres per second.

    (2 marks)
    Level 4 · 4 marksTry it
  2. 2
    Ali cycles from her home to a lake.

    Her brother Ben leaves home 2020 minutes after Ali and drives to the lake along the same road.

    The graph shows their journeys. The time is measured from when Ali leaves home.10203040506024681012AliBenTime (minutes)Distance from home (km)(a) How many minutes after Ali leaves home does Ben overtake her?

    (1 mark)
    (b) How far from home are they when Ben overtakes Ali?

    (1 mark)
    (c) Work out Ben's speed.

    Give your answer in km/h.

    (2 marks)

    Ben waits at the lake until Ali arrives.
    (d) For how many minutes does Ben wait?

    (1 mark)
    Level 4 · 5 marksTry it
  3. 3
    The graph shows the charges of two plumbers, Ashby and Brook, for jobs of up to 44 hours.0.511.522.533.541020304050607080AshbyBrookNumber of hoursCharge (£)(a) Write down Ashby's fixed charge.

    (1 mark)

    Kate needs a plumber for a job that will take 77 hours.
    (b) Which plumber will be cheaper for Kate, and by how much?

    You must show all your working.

    (4 marks)
    Level 4 · 5 marksTry it
  4. 4
    Jess leaves home at 13 30 to go on a bike ride.

    The travel graph shows the first hour of her ride.0.511.522.533.5451015202530Time (hours)Distance from home (km)After the first hour, Jess
    • rests for 3030 minutes
    • then cycles a further 55 km, away from home, at 1010 km/h
    • then cycles straight home at 2020 km/h.
    (a) Complete the travel graph.

    (3 marks)
    (b) At what time does Jess get home?

    (1 mark)
    (c) Work out the total distance Jess cycles.

    (1 mark)
    Level 4 · 5 marksTry it