Lesson H4

H4 Integration as a limit of a sum Quiz: AQA Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson H4, Integration as a limit of a sum: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. In the limit of a sum, a definite integral represents the limit of what sums?

    • Geometric sums
    • Binomial sums
    • Riemann sums
    • Arithmetic sums

  2. As the number of equal-width rectangles n tends to infinity, what does their sum tend to?

    • Derivative function
    • Gradient of curve
    • Indefinite integral
    • Definite integral

  3. An interval [0, 2] is split into 4 equal strips. What is the width of each strip?

    • 2
    • 0.4
    • 0.5
    • 0.25

  4. The sum of (r/n)² × (1/n) from r = 1 to n as n → ∞ represents which integral?

    • ∫₀¹ x² dx
    • ∫₀¹ x dx
    • ∫₀² x² dx
    • ∫₀¹ x³ dx

  5. What is the limit as n tends to infinity of (1/n) times the sum from r = 1 to n of (r/n)^2?

    • 2/3
    • 1/3
    • 1
    • 1/2

  6. What is the limit as n tends to infinity of (1/n) times the sum from r = 1 to n of (1 + r/n)?

    • 1
    • 1/2
    • 3/2
    • 2

  7. In the definite integral notation ∫ f(x) dx, what does dx represent?

    • Upper boundary
    • Number of strips
    • Function height
    • Strip width limit

  8. Using right endpoints, 2 rectangles of width 1 approximate the area under y = x^2 on [0, 2]. What is the total area of the rectangles?

    • 3
    • 8
    • 5
    • 4

  9. Using left endpoints, 2 rectangles of width 1 approximate the area under y = x^2 on [0, 2]. What is the total area of the rectangles?

    • 5
    • 4
    • 1
    • 2

  10. What is the limit as n tends to infinity of the sum from r = 1 to n of (2r/n)(2/n)?

    • 4
    • 2
    • 8
    • 1

  11. For the integral from 1 to 5 of f(x) dx split into n = 4 equal strips, what is the strip width?

    • 2
    • 4
    • 0.25
    • 1

  12. What is the limit as n tends to infinity of (1/n^2) times the sum from r = 1 to n of r?

    • 1/3
    • 1
    • 1/2
    • 2

  13. What is the limit as n tends to infinity of the sum from r = 1 to n of (3 + 2r/n)(2/n)?

    • 8
    • 6
    • 4
    • 10

  14. What is the limit as n tends to infinity of (1/n) times the sum from r = 1 to n of e^(r/n)?

    • e + 1
    • e - 1
    • 1/e
    • e

  15. Using n equal strips and right endpoints for the integral from 0 to 3 of x dx, what is the Riemann sum?

    • (9/2)(1 - 1/n)
    • 3(1 + 1/n)
    • (9/2)(1 + 1/n)
    • (9/2)(1 + 1/n^2)

  16. What is the limit as n tends to infinity of the sum from r = 1 to n of 1/(n + r)?

    • ln 3
    • 1/2
    • 1
    • ln 2

  17. What is the limit as n tends to infinity of (1/n) times the sum from r = 1 to n of (r/n)^3?

    • 1
    • 1/4
    • 1/3
    • 1/2

  18. What is the limit as n tends to infinity of (1/n) times the sum from r = 1 to n of sin(pi r/n)?

    • 0
    • 1
    • 2/pi
    • pi/2

  19. The sum of (1 + 2r/n)(2/n) from r = 1 to n as n → ∞ represents which integral?

    • ∫₀¹ (1 + x) dx
    • ∫₀² (1 + x) dx
    • ∫₀² (1 + 2x) dx
    • ∫₀¹ (1 + 2x) dx

  20. What is the limit as n tends to infinity of (1/n) times the sum from r = 1 to n of sqrt(r/n)?

    • 2/3
    • 1
    • 1/2
    • 3/2

All AQA Maths quizzes