Lesson R13

R13 Equations and graphs for direct and inverse proportion Quiz: AQA Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson R13, Equations and graphs for direct and inverse proportion: 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. Which equation represents direct proportion between y and x?

    • y = 3x
    • y = 3 + x
    • y = x²
    • y = 3/x

  2. Which equation represents inverse proportion?

    • y = 12/x
    • y = 12x
    • y = 12 + x
    • y = 12x²

  3. If y is directly proportional to x, which equation expresses this with constant k?

    • y = k/x
    • y = kx
    • y = x²k
    • y = x + k

  4. Given y = 7/x, what is y when x = 0.5?

    • 3.5
    • 70
    • 14
    • 0.07

  5. Given y = 2.5x, what value of x gives y = 35?

    • 87.5
    • 12.5
    • 14
    • 0.07

  6. Which point lies on the graph of y = 4/x?

    • (4, 4)
    • (2, 8)
    • (2, 2)
    • (1, 2)

  7. What is the equation of the direct proportion graph through the point (3, 12)?

    • y = 4/x
    • y = 4x
    • y = x + 9
    • y = 9x

  8. A straight line passes through (0, 0) and (4, 10). Which equation describes it?

    • y = 2.5 + x
    • y = 2.5x
    • y = 6x
    • y = 0.4x

  9. For the equation y = 6/x, what is the value of x when y = 2?

    • 0.33
    • 8
    • 12
    • 3

  10. Which description matches the graph of an inverse proportion relationship?

    • A straight line that slopes downwards and crosses both axes
    • A curve that decreases steadily and crosses the x-axis at zero
    • A curve that increases from the origin, getting steeper all the time
    • A curve that decreases, approaching both axes but never meeting them

  11. For y = kx, x = 2 gives y = 5. What is y when x = 6?

    • 17
    • 3.33
    • 12
    • 15

  12. Which property is true for the graph of a direct proportion relationship y = kx?

    • The graph is a curve bending upwards
    • The gradient of the line equals the constant k
    • The line always has a y-intercept equal to k
    • The gradient of the line is zero

  13. A point on the graph of y = k/x is (5, 7). What is the value of k?

    • 2/35
    • 35
    • 12
    • 1.4

  14. Is y = 3x + 2 a direct proportion relationship?

    • Yes, because the constant term 2 only shifts the line upwards
    • No, because the line does not pass through the origin
    • Yes, because it is a straight line with a constant gradient
    • No, because the gradient of 3 is not a whole number

  15. (H) Given y = k/x² with y = 10 when x = 2, find y when x = 5.

    • 25
    • 0.4
    • 1.6
    • 4

  16. (H) Which equation shows y directly proportional to the cube of x?

    • y = 3kx²
    • y = kx³
    • y = kx + 3
    • y = k³x

  17. For y = 9/x, what is the value of y when x = −3?

    • −27
    • 3
    • −3
    • 27

  18. A line passes through (0, 0) and (3, 4.5). Which is its equation?

    • y = 4.5x
    • y = 3x
    • y = 1.5x
    • y = 0.67x

  19. An inverse proportion curve y = k/x passes through (4, 3). What is k?

    • 0.75
    • 12
    • 1.33
    • 7

  20. In a table, y doubles every time x doubles. Which equation fits this pattern?

    • y = kx²
    • y = k/x
    • y = k + x
    • y = kx

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