Lesson H2

H2 Indefinite integration Quiz: AQA Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson H2, Indefinite integration: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. Which expression is an integral of x^n with n not equal to -1, up to a constant?

    • x^(n+1)/(n+1) + C
    • x^n ln x + C
    • n x^(n-1) + C
    • x^(n+1) + C

  2. What is the integral of e^(kx) with respect to x, for k not zero?

    • k e^(kx) + C
    • e^(x/k) + C
    • e^(kx)/x + C
    • (1/k) e^(kx) + C

  3. What is the integral of 1/x with respect to x, for x > 0?

    • ln x + C
    • 1/ln x + C
    • ln x^2 + C
    • -1/x^2 + C

  4. What is the integral of sin(kx) with respect to x?

    • -k cos(kx) + C
    • -(1/k) cos(kx) + C
    • (1/k) cos(kx) + C
    • k cos(kx) + C

  5. What is the integral of cos(kx) with respect to x?

    • -k sin(kx) + C
    • -(1/k) sin(kx) + C
    • (1/k) sin(kx) + C
    • k sin(kx) + C

  6. Which is the integral of 6x^5 - 4x^3 + 2 with respect to x?

    • x^6 - x^4 + 2 + C
    • x^6 - x^4 + 2x + C
    • 30x^4 - 12x^2 + C
    • x^6 - x^4 + C

  7. What does the general solution of dy/dx = f(x) contain?

    • Only the values where f(x) is zero
    • A separate value of x for each solution
    • A single fixed curve only
    • An arbitrary constant C, giving a family of curves

  8. Find y given dy/dx = 3x^2 - 2x + 1 and y = 4 when x = 0.

    • y = x^3 - x^2 + x + 4
    • y = x^3 - x^2 + 4
    • y = x^3 - x^2 + x - 4
    • y = 6x - 2 + 4

  9. Given dy/dx = 4 sin(2x) and y = 0 when x = 0, which expression gives y?

    • y = 2 - 2cos(2x)
    • y = 2cos(2x) + 2
    • y = 2 + 2cos(2x)
    • y = -2cos(2x)

  10. A curve has dy/dx = 1/x + 2 and passes through (1, 5). Which equation describes the curve?

    • y = ln x + 2x + 3
    • y = ln x + 2x + 2
    • y = ln x + 2x + 5
    • y = 1/x^2 + 2x + 2

  11. A particle has velocity v = 6t^2 - 4 m/s, and s = 1 when t = 0. What is s when t = 2 s?

    • 9 m
    • 13 m
    • 5 m
    • 1 m

  12. Given dy/dx = e^(3x) and y = 1 when x = 0, which expression gives y?

    • y = e^(3x) + 2/3
    • y = 3e^(3x) - 2
    • y = e^(3x)/3 + 2/3
    • y = e^(3x)/3 + 1

  13. Which is an integral of (2x + 1)^2 with respect to x, found by expanding it to 4x^2 + 4x + 1 first?

    • 8x^3 + 4x^2 + x + C
    • 4x^3/3 + 2x^2 + x + C
    • 4x^3/3 + 2x^2 + C
    • 2x^3 + 2x^2 + x + C

  14. Which is an integral of ln x with respect to x?

    • 1/x + C
    • (ln x)/x + C
    • x ln x + C
    • x ln x - x + C

  15. What is the integral of (x + 1)/x with respect to x, for x > 0?

    • x - 1/x^2 + C
    • x + 1/x + C
    • x + ln x + C
    • 1 + ln x + C

  16. A function satisfies f''(x) = 6x with f'(0) = 2 and f(0) = 1. What is f(x)?

    • x^3 + 2x + 1
    • x^3 + 2x
    • 6x^2 + 2x + 1
    • 3x^2 + 2x + 1

  17. A curve has dy/dx = 4x^3 - 6x and passes through (2, 3). Which equation describes the curve?

    • y = x^4 - 3x^2 - 1
    • y = x^4 - 3x^2 + 3
    • y = x^4 - 3x^2 + 1
    • y = 4x^4 - 3x^2 - 1

  18. What is the integral of (3x^2 - 2)/x^2 with respect to x, for x not zero?

    • x^3 - 2 ln x + C
    • 3x - 2/x + C
    • 3x + 2/x + C
    • 3x + 2 ln x + C

  19. A curve has gradient 3 sin(3x) and passes through (0, 1). What is y when x = pi/3?

    • 2
    • -1
    • 1
    • 3

  20. Which is the general solution of dy/dx = 2/x + 3x^2?

    • y = 2 ln|x| + x^3 + C
    • y = -2/x^2 + x^3 + C
    • y = 2 ln|x| + 3x^3 + C
    • y = 2/x + x^3 + C

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