Lesson F6

F6 Logarithmic graphs to estimate parameters Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F6, Logarithmic graphs to estimate parameters: 20 multiple choice questions for the AQA Maths (7357), Unit 6: Exponentials and logarithms, written with Revision Ninja.

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The 20 questions

  1. For y = a x^n, which plot gives a straight line?

    • y against log x
    • y against x squared
    • log y against x
    • log y against log x

  2. For y = k b^x, which plot gives a straight line?

    • y against x
    • y against log x
    • log y against log x
    • log y against x

  3. On a graph of log y against x for y = k b^x, what does the gradient equal?

    • b
    • k
    • log b
    • log k

  4. On a graph of log y against log x for y = a x^n, what does the gradient represent?

    • The value of log a
    • The square of n
    • The constant a
    • The power n

  5. What is the vertical intercept of a straight line of log y against x for y = k b^x?

    • k
    • log k
    • log b
    • 0

  6. Which logarithm base can be used when plotting these graphs?

    • Only base 2 can be used, since powers of 2 are the only valid values
    • Any base works, since changing the base only scales the gradient and intercept
    • Only base 10 can be used for these graphs
    • Only base e can be used because the gradient is always 1

  7. What relationship does a straight line on a log y against x graph indicate?

    • An exponential relationship y = k b^x
    • A power law y = a x^n
    • A quadratic relationship y = a x^2
    • A linear relationship y = mx + c

  8. Points (x, log_10 y) = (0, 1.0) and (2, 1.6) lie on a straight line. What is its gradient?

    • 1.6
    • 0.3
    • 0.6
    • 1.0

  9. A straight line of log_10 y against x has equation log_10 y = 1.0 + 0.3x. What is k in y = k b^x?

    • k = 1
    • k = 10
    • k = 1.6
    • k = 0.3

  10. A line of log_10 y against x has equation log_10 y = 0.3x + 1. Which value is b?

    • b = 10
    • b is approximately 3
    • b is approximately 2.0
    • b is approximately 0.3

  11. A log_10 y against log_10 x graph is a straight line with gradient 2 and intercept log_10 5. Which relationship fits?

    • y = 5x^2
    • y = 5x^(1/2)
    • y = 2 x 5^x
    • y = 2x^5

  12. A log_10 y against x graph has gradient 0.5 and intercept 0. Which relationship fits?

    • y = 10^(0.5x)
    • y = x^10
    • y = 0.5^x
    • y = 0.5x

  13. Data satisfy y = 3x^2. On a log-log graph, what is the gradient?

    • 1/2
    • log 3
    • 2
    • 3

  14. Data satisfy y = 4(1.5)^x. On a log_10 y against x graph, what is the gradient to 3 decimal places?

    • 1.5
    • 0.176
    • 0.405
    • 0.6

  15. On a graph of log_10 y against log_10 x, the line passes through the points (log_10 x, log_10 y) = (0, 2) and (1, 4). What is the gradient?

    • 0.5
    • 6
    • 4
    • 2

  16. Points (1, 3) and (10, 300) lie on a log-log graph of y = a x^n. What is n?

    • n = 2
    • n = 0.5
    • n = 100
    • n = 3

  17. The points (0, 2) and (3, 16) lie on the curve y = k b^x. What is b?

    • b = 3
    • b = 16
    • b = 2
    • b = 4

  18. Why can a straight line on a log y against x graph reveal exponential behaviour?

    • Because log y stays constant for exponential data
    • Because log y = log k + x log b is linear in x
    • Because log y equals x for every exponential function
    • Because exponential graphs are always straight lines when plotted

  19. A log-log plot has gradient 1.5 and intercept log 4. Which relationship is implied?

    • y = 4x^(2/3)
    • y = 1.5 x 4^x
    • y = 4x^1.5
    • y = 10^1.5 x^4

  20. Data follow y = 10(0.8)^x. What is the gradient of log_10 y against x, to 3 decimal places?

    • -1.250
    • 0.097
    • -0.8
    • -0.097

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