Lesson 1.06h

1.06h Reduction to linear form Quiz: OCR Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.06h, Reduction to linear form: 20 multiple choice questions for the OCR Maths (H240), Unit 6: Exponentials and Logarithms, written with Revision Ninja.

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The 20 questions

  1. When y = ax^n is plotted as log y against log x, what does the gradient represent?

    • x
    • n
    • a
    • log a

  2. For y = k b^x, what is the gradient of log y plotted against x?

    • k
    • log b
    • b
    • log k

  3. For y = a x^n, what is the intercept of log y against log x?

    • n
    • a
    • log n
    • log a

  4. Which operation converts the power equation y = ax^n into a linear form?

    • Take logarithms
    • Integrate both sides
    • Differentiate both sides
    • Square both sides

  5. A log10-log10 graph has gradient 2.5 and intercept 0.6. What is a for y = a x^n?

    • 1.60
    • About 3.98
    • 0.6
    • 6.00

  6. A log10 y against x graph of y = k b^x has intercept 0.5. What is k?

    • 1.50
    • About 3.16
    • 5.00
    • 0.5

  7. A log10 y against x graph of y = k b^x has gradient 0.2. What is b to 3 significant figures?

    • 2.00
    • About 1.58
    • 0.2
    • 5.01

  8. The curve y = a x^n passes through (1, 2) and (2, 8). What is n?

    • 2
    • 1/2
    • 3
    • 4

  9. The curve y = k b^x passes through (0, 2) and (1, 8). What is b?

    • 6
    • 2
    • 3
    • 4

  10. Which plot gives a straight line for y = 4 x 3^x?

    • log y against log x
    • y against x^2
    • y against x
    • log y against x

  11. Given log10 y = 0.8x + 1.2, which expression describes y?

    • y is about 1.2 x 10^(0.8x)
    • y is about 15.85 x 0.8^x
    • y is about 6.31 x 15.85^x
    • y is about 15.85 x 6.31^x

  12. A straight line of gradient 1.5 and intercept 0 on log-log axes corresponds to which relation?

    • y = 10^1.5 x
    • y = 1.5x
    • y = x^1.5
    • y = 1.5^x

  13. For y = k e^(mx), what is the gradient of ln y against x?

    • m
    • e^m
    • ln m
    • k

  14. For y = k b^x, what is the intercept of ln y against x?

    • ln b
    • ln k
    • k
    • b

  15. If the intercept of log10 y against log10 x is 0, what is a in y = a x^n?

    • e
    • 0
    • 10
    • 1

  16. For y = 3x^(-2), what is the gradient of log10 y against log10 x?

    • -1/2
    • 3
    • 2
    • -2

  17. For y = 5 x 2^x, what is the gradient of log10 y against x?

    • About 0.301
    • 0.693
    • 2
    • 5

  18. In experimental data fitting, what shape does a logarithmic transformation produce for exponential models?

    • Hyperbola
    • Parabola
    • Straight line
    • Sine wave

  19. A log10-log10 graph is a straight line with gradient 2 and intercept log10 3. Which relation is shown?

    • y = 3x^2
    • y = 2x^3
    • y = 3 x 2^x
    • y = 3x^(1/2)

  20. A natural-log graph of ln y against x for y = k b^x has gradient 0.7. Which estimates b?

    • 10^0.7, about 5.01
    • e^(0.7^2), about 1.63
    • e^0.7, about 2.01
    • ln 0.7, about -0.36

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