Lesson 1.09f

1.09f Numerical integration Quiz: OCR Maths, Unit 9

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.09f, Numerical integration: 20 multiple choice questions for the OCR Maths (H240), Unit 9: Numerical Methods, written with Revision Ninja.

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The 20 questions

  1. What is the trapezium rule approximation for n strips of width h?

    • (h/2)[y0 + 2(y1 + ... + y(n-1)) + yn]
    • (h/2)[y0 + yn]
    • h[y0 + y1 + ... + yn]
    • (h/2)[2y0 + y1 + yn]

  2. What shape approximates the area under a curve in each strip of the trapezium rule?

    • Rectangle
    • Trapezium
    • Triangle
    • Parallelogram

  3. For a concave up function on [a, b], the trapezium rule gives what type of estimate?

    • Lower bound
    • Overestimate
    • Underestimate
    • Exact value

  4. For a concave down curve, the trapezium rule gives which kind of estimate?

    • An underestimate
    • A negative estimate
    • The exact value
    • An overestimate

  5. When integrating from a to b with n strips, what is the strip width h?

    • (a + b)/n
    • n/(b - a)
    • (b - a)/n
    • b/n

  6. For a strictly decreasing function, left-endpoint rectangles give what kind of estimate for the area?

    • Underestimate
    • Exact value
    • Overestimate
    • Lower bound

  7. The area of one trapezium strip with parallel sides y and z and width h is?

    • (y + z)/(2h)
    • h(y + z)/2
    • h(y + z)
    • h(y - z)/2

  8. Using the trapezium rule with 2 strips, what is the estimate of the integral of x^2 from 0 to 2?

    • 2
    • 4
    • 3
    • 8/3

  9. Using the trapezium rule with 4 strips, what is the estimate of the integral of x^2 from 0 to 2?

    • 2.5
    • 2.25
    • 2.75
    • 3.0

  10. Why does the trapezium rule overestimate the integral of f(x) = x^2 on [0, 2]?

    • Concave up curve
    • Decreasing curve
    • Concave down curve
    • Linear curve

  11. Using the trapezium rule with 2 strips, what is the estimate of the integral of 1/x from 1 to 3?

    • 1.0986
    • 1.5
    • 4/3 (about 1.333)
    • 7/6 (about 1.167)

  12. For f(x) = 1/x on [1, 3] with 2 strips of width 1, what are the rectangle bounds for the integral?

    • Lower 1, upper 2
    • Lower 3/2, upper 5/6
    • Lower 5/6 (about 0.833), upper 3/2 (1.5)
    • Lower 7/6, upper 4/3

  13. Speeds at t = 0, 2, 4 and 6 seconds are 0, 3, 5 and 4 m/s. What is the trapezium estimate of the distance travelled?

    • 20 m
    • 16 m
    • 12 m
    • 24 m

  14. Using the trapezium rule with 2 strips, the integral of e^x from 0 to 1 is approximately?

    • 1.500
    • 2.000
    • 1.718
    • 1.754

  15. For which type of function is the trapezium rule always exact?

    • Exponential function
    • Linear function
    • Quadratic function
    • Logarithmic function

  16. Using 2 rectangles of width 0.5 for the integral of x^2 from 0 to 1, which bounds are valid?

    • 0.125 < integral < 0.625
    • 0.2 < integral < 0.3
    • 0.5 < integral < 0.625
    • 0.4 < integral < 0.5

  17. Why does the trapezium rule underestimate the integral of sin(x) from 0 to pi?

    • Symmetric curve
    • Increasing curve
    • Concave down curve
    • Concave up curve

  18. Values of f at x = 0, 1, 2 and 3 are 2, 3, 5 and 8. What is the trapezium estimate with 3 strips?

    • 13
    • 14
    • 12
    • 26

  19. What happens to the error in numerical integration as the number of strips increases?

    • It increases
    • It stays constant
    • It reaches zero
    • It decreases

  20. For an increasing function, which rectangle sum gives a lower bound for the integral?

    • Right-endpoint rectangles
    • Left-endpoint rectangles
    • Midpoint rectangles
    • Trapezium rule

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