Lesson F1

F1 Exponential and natural logarithm functions and graphs Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F1, Exponential and natural logarithm functions and graphs: 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. Which statement describes the graph of y = a^x when a > 1?

    • It passes through (0, 1), increases for all x, and approaches 0 as x tends to minus infinity
    • It passes through (1, 0), decreases for all x, and approaches 0 as x tends to plus infinity
    • It has a vertical asymptote at x = 0 and takes only negative values for all x
    • It passes through (0, 0), is symmetric about the y-axis, and has no asymptote

  2. Which statement about y = e^x is correct?

    • It is periodic with period 2 pi and takes values between -1 and 1 inclusive
    • It is always negative, passes through (1, 0), and has the y-axis as an asymptote
    • It is always positive, passes through (0, 1), and has the x-axis as an asymptote as x tends to minus infinity
    • It passes through the origin and has gradient zero at x = 0

  3. For which range of a does y = a^x have a graph decreasing from left to right?

    • a > 1, so the graph rises from left to right with a steepening gradient
    • a < 0, so the graph is undefined for every real value of x
    • 0 < a < 1, so the graph falls as x increases from minus infinity to plus infinity
    • a = 1, so the graph is a horizontal line at y = 1 for all values of x

  4. What is the value of ln(e^3)?

    • 3
    • 1/3
    • ln 3
    • e^3

  5. What is the value of ln 1?

    • undefined
    • 1
    • e
    • 0

  6. Which is the domain of y = ln x?

    • x >= 0
    • All real values of x
    • x > 0
    • x < 0

  7. Where does the graph of y = ln x cross the x-axis?

    • At (1, 0)
    • At (0, 1)
    • It never crosses the x-axis
    • At (e, 0)

  8. Which point lies on the graph of y = e^x?

    • (2, ln 2)
    • (ln 2, 2)
    • (2, e^2)
    • (e, 2)

  9. Which point lies on the graph of y = 2^x?

    • (8, 3)
    • (3, 6)
    • (3, 8)
    • (3, 9)

  10. The graph of y = e^(-x) is a reflection of y = e^x in which line?

    • The x-axis
    • The line y = x
    • The y-axis
    • The line y = -x

  11. Solve e^x = 5, giving x to 3 decimal places.

    • 5.000
    • 1.609
    • 0.699
    • 2.322

  12. What is the value of e^(ln 7)?

    • e^7
    • 14
    • 7
    • ln 7

  13. The graph of y = ln x is reflected in the line y = x. Which function is the image?

    • y = e^x
    • y = ln(-x)
    • y = 1/ln x
    • y = x^e

  14. Which transformation maps y = e^x onto y = e^(x - 2)?

    • A translation of 2 units in the positive y direction
    • A translation of 2 units in the negative x direction
    • A translation of 2 units in the positive x direction
    • A stretch of scale factor 2 parallel to the y-axis

  15. Solve the inequality e^x > 10.

    • x > 10 ln e
    • x < ln 10
    • x > ln 10
    • x > 10/e

  16. For which values of x is ln(x^2 - 1) defined?

    • -1 < x < 1
    • All real x except x = 0
    • x < -1 or x > 1
    • x > 1 only

  17. At which point do the curve y = e^x and the line y = 1 meet?

    • (0, 1)
    • They do not meet
    • (1, e)
    • (1, 0)

  18. If (2, ln 2) lies on y = ln x, which point lies on y = e^x by reflection in the line y = x?

    • (e^2, 2)
    • (ln 2, 1/2)
    • (1/2, ln 2)
    • (ln 2, 2)

  19. The curve y = 2e^(-x) meets the y-axis at which y-value?

    • -2
    • 2
    • 0
    • e

  20. Which value of x makes y = ln(2x + 1) equal to zero?

    • x = 1/2
    • x = -1/2
    • x = 0
    • x = 1

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