J1 Mid-ordinate and Simpson's rules Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Where is the function evaluated in each strip when using the mid-ordinate rule?

   • Left boundary
   • Strip midpoint
   • Right boundary
   • Both endpoints

2. In the mid-ordinate rule, what factor multiplies the sum of the mid-ordinates?

   • h / 3
   • 2h
   • h
   • h / 2

3. What condition must the number of strips n satisfy to apply Simpson's rule?

   • Must be even
   • Must be zero
   • Must be prime
   • Must be odd

4. In Simpson's rule with n strips of width h, which weight multiplies the interior ordinates with odd index?

   • 4
   • 2
   • 3
   • 1

5. In numerical integration rules, what quantity does h represent?

   • Function midpoint
   • Interval length
   • Number of strips
   • Strip width

6. What maximum degree of polynomial can be integrated exactly using Simpson's rule?

   • Degree 2
   • Degree 1
   • Degree 3
   • Degree 4

7. Which functions are integrated exactly by the mid-ordinate rule?

   • No functions exactly
   • Linear functions
   • Cubic functions
   • Constant functions only

8. Use Simpson's rule with n = 2 to estimate the integral of x^2 from 0 to 2.

   • 2
   • 2.5
   • 8/3
   • 3

9. Use Simpson's rule with n = 2 to estimate the integral of x^3 from 0 to 2.

   • 4.5
   • 4
   • 3
   • 5

10. Use the mid-ordinate rule with n = 2 to estimate the integral of 1/(1 + x) from 0 to 1, to 3 decimal places.

    • 0.693
    • 0.750
    • 0.686
    • 0.861

11. Use Simpson's rule with n = 2 to estimate the integral of 1/(1 + x) from 0 to 1, to 3 decimal places.

    • 0.693
    • 0.686
    • 0.861
    • 0.750

12. Use the mid-ordinate rule with n = 2 to estimate the integral of x^2 from 0 to 2.

    • 2
    • 8/3
    • 2.5
    • 3

13. Use Simpson's rule with n = 2 to estimate the integral of e^x from 0 to 2, to 2 decimal places.

    • 7.39
    • 6.39
    • 6.00
    • 6.42

14. Use the mid-ordinate rule with n = 2 to estimate the integral of x^2 from 0 to 1.

    • 5/16
    • 1/4
    • 1/3
    • 3/8

15. Use Simpson's rule with n = 2 to estimate the integral of x^3 from 0 to 1.

    • 1/3
    • 0.5
    • 1/4
    • 3/16

16. Use Simpson's rule with n = 4 to estimate the integral of x^2 from 0 to 1.

    • 1/3
    • 0.375
    • 0.25
    • 0.3125

17. A table gives f(0) = 1, f(1) = 3 and f(2) = 5. Estimate the integral from 0 to 2 using Simpson's rule.

    • 5
    • 9
    • 4.5
    • 6

18. Strips of width 0.5 cover [0, 1.5], with mid-ordinate values 2, 3 and 4. Estimate the integral using the mid-ordinate rule.

    • 4.5
    • 9
    • 5.5
    • 3

19. How many ordinates are needed when Simpson's rule uses 4 strips?

    • 6
    • 5
    • 4
    • 3

20. Use Simpson's rule with n = 2 to estimate the integral of 1/x from 1 to 3, as an exact fraction.

    • 4/3
    • 10/9
    • 1.5
    • ln 3

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