Lesson R14

R14 Gradient as a rate of change and proportion graphs Quiz: AQA Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson R14, Gradient as a rate of change and proportion graphs: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 3: Ratio, proportion and rates of change, written with Revision Ninja.

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The 20 questions

  1. On a distance-time graph, the gradient of a straight line is 4. What does this gradient represent?

    • The speed is 4 metres per second
    • The time is 4 seconds
    • The acceleration is 4 m/s²
    • The distance is 4 metres

  2. What is the gradient of the line joining (2, 5) and (6, 25)?

    • 20
    • 5
    • 0.2
    • 4

  3. On a graph of cost in pounds against litres, the gradient is 1.20. What does this gradient represent?

    • The total cost of one litre plus £1.20
    • The cost per litre, £1.20
    • The number of litres per pound
    • The fixed charge, £1.20

  4. A tank graph of volume in litres against time in minutes has gradient 15. What is the rate of filling?

    • 0.067 minutes per litre
    • 15 minutes per litre
    • 15 litres
    • 15 litres per minute

  5. Which graph shows direct proportion?

    • A curve through (1, 1) and (2, 4)
    • A horizontal straight line
    • A straight line with a positive y-intercept
    • A straight line through the origin

  6. For inverse proportion, what is true about the rectangle formed by a point (x, y) on the graph and the two axes?

    • Its area halves whenever y doubles, from k to k/2
    • Its area is always the same, equal to k
    • Its area doubles when x doubles, equal to 2k
    • Its area equals x plus y, so it grows as x grows

  7. A straight-line graph passes through the origin, (4, 10) and (8, 20). What is its gradient?

    • 2
    • 6
    • 2.5
    • 0.4

  8. What does a gradient of zero on a graph tell you?

    • The quantity doubles every second
    • The line is vertical
    • The quantity is increasing at a constant rate
    • The quantity is not changing

  9. A straight line passes through (1, 3) and (3, 9). What is its gradient?

    • 3
    • 0.33
    • 2
    • 6

  10. A direct proportion graph has gradient 2.5. What is y when x = 12?

    • 4.8
    • 30
    • 14.5
    • 2.5

  11. A graph of water depth in cm against time in minutes has gradient 0.8. How much does the depth rise in 15 minutes?

    • 1.2 cm
    • 0.053 cm
    • 18.75 cm
    • 12 cm

  12. For a direct proportion graph y = kx, what does k tell you about the line?

    • y decreases by k for each unit increase in x
    • y equals k for every value of x
    • y increases by x for each unit increase in k
    • y increases by k for each unit increase in x

  13. What is the gradient of the line segment from (−2, 1) to (2, 9)?

    • −2
    • 2
    • 0.5
    • 8

  14. On a distance-time graph, what quantity does the gradient describe?

    • Time taken
    • Acceleration
    • Speed
    • Total distance

  15. A graph of cost in pounds against number of tickets is a straight line through the origin with gradient 7.50. What is the cost of 6 tickets?

    • £1.25
    • £45
    • £7.50
    • £13.50

  16. A line passes through (0, 3) and (5, 13). What are its gradient and y-intercept?

    • Gradient 2, intercept 3
    • Gradient 5, intercept 3
    • Gradient 3, intercept 2
    • Gradient 2, intercept 13

  17. A straight-line graph of pressure in kPa against depth in m has gradient 9.8. What is the pressure at 3 m?

    • 29.4 kPa
    • 3.27 kPa
    • 12.8 kPa
    • 98 kPa

  18. A line with gradient −4 passes through (0, 12). Where does it cross the x-axis?

    • (12, 0)
    • (−3, 0)
    • (3, 0)
    • (0, 3)

  19. A direct proportion graph y = kx passes through (6, 18). What is the gradient?

    • 108
    • 3
    • 0.33
    • 12

  20. Two lines pass through the origin, one with gradient 2 and one with gradient 5. Which statement is correct?

    • The line with gradient 2 is steeper by 3 times
    • The line with gradient 2 is steeper
    • Both lines are equally steep
    • The line with gradient 5 is steeper

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