JAMB and WAEC Further Mathematics questions

267 questions with answers and explanations. Tap an option to check yourself.

1. Question 61· Functions and rational functions· WAEC

   If f(x) = 3x − 2, find f⁻¹(x).

   • A(x + 2)/3
   • B(x − 2)/3
   • C3x + 2
   • D1/(3x − 2)

   Show answer

   Explanation and discussion

2. Question 62· Functions and rational functions· WAEC

   A function f is one-to-one if

   • Aits graph is a horizontal line
   • Bevery input gives the same output
   • Cit has no inverse
   • Ddifferent inputs always give different outputs

   Show answer

   Explanation and discussion

3. Question 63· Functions and rational functions· WAEC

   If f(x) = x² − 1, the range of f for real x is

   • Aall real numbers
   • Bf(x) ≥ 0
   • Cf(x) ≥ −1
   • Df(x) ≤ −1

   Show answer

   Explanation and discussion

4. Question 64· Functions and rational functions· WAEC

   The function f(x) = 1/(x − 2) is undefined at

   • Ax = 1
   • Bx = 0
   • Cx = −2
   • Dx = 2

   Show answer

   Explanation and discussion

5. Question 65· Integration· WAEC

   Find the area bounded by the curve y = 4 − x² and the x-axis.

   • A8 square units
   • B16/3 square units
   • C32/3 square units
   • D16 square units

   Show answer

   Explanation and discussion

6. Question 66· Integration· WAEC

   Find the integral of (2x + 3)² with respect to x.

   • A(2x + 3)³/6 + c
   • B(2x + 3)³/3 + c
   • C2(2x + 3)³ + c
   • D(2x + 3)³ + c

   Show answer

   Explanation and discussion

7. Question 67· Integration· WAEC

   Integrate (4x³ − 6x) with respect to x.

   • A12x² − 6 + c
   • Bx⁴ − 3x² + c
   • C4x⁴ − 6x² + c
   • Dx⁴ − 6x² + c

   Show answer

   Explanation and discussion

8. Question 68· Integration· WAEC

   Find the integral of sin x with respect to x.

   • Acos x + c
   • B−cos x + c
   • C−sin x + c
   • Dtan x + c

   Show answer

   Explanation and discussion

9. Question 69· Integration· WAEC

   Evaluate the integral of (3x² + 2x) with respect to x from x = 0 to x = 2.

   • A10
   • B16
   • C12
   • D8

   Show answer

   Explanation and discussion

10. Question 70· Integration· WAEC

    ∫ (4x + 1) dx is

    • A4x² + x + c
    • B2x² + x + c
    • C4 + c
    • D2x + c

    Show answer

    Explanation and discussion

11. Question 71· Integration· WAEC

    Find the area under the curve y = 3x² from x = 0 to x = 2.

    • A8
    • B12
    • C6
    • D4

    Show answer

    Explanation and discussion

12. Question 72· Integration· WAEC

    A particle moves with velocity v = 3t² + 2 m/s. Find the distance it covers from t = 0 to t = 2 s.

    • A10 m
    • B14 m
    • C12 m
    • D6 m

    Show answer

    Explanation and discussion

13. Question 73· Integration· WAEC

    ∫ cos x dx is

    • Asin x + c
    • B−sin x + c
    • Ccos x + c
    • D−cos x + c

    Show answer

    Explanation and discussion

14. Question 74· Integration· WAEC

    The area under y = x² from x = 0 to x = 3 is

    • A6 square units
    • B27 square units
    • C3 square units
    • D9 square units

    Show answer

    Explanation and discussion

15. Question 75· Integration· WAEC

    Find the integral of (x² − 4)/(x − 2) with respect to x.

    • Ax²/2 − 2x + c
    • Bx² + 2x + c
    • Cx³/3 − 4x + c
    • Dx²/2 + 2x + c

    Show answer

    Explanation and discussion

16. Question 76· Integration· WAEC

    The integral of cos x with respect to x is

    • Asin x + c
    • B−sin x + c
    • Ccos x + c
    • D−cos x + c

    Show answer

    Explanation and discussion

17. Question 77· Integration· WAEC

    Evaluate the integral of (2x + 1) from x = 1 to x = 2.

    • A6
    • B4
    • C5
    • D3

    Show answer

    Explanation and discussion

18. Question 78· Integration· WAEC

    Evaluate ∫ from 1 to 3 of 3 dx.

    • A9
    • B6
    • C3
    • D12

    Show answer

    Explanation and discussion

19. Question 79· Integration· WAEC

    The integral of 3x² with respect to x is

    • Ax³ + c
    • B6x + c
    • C3x³ + c
    • Dx² + c

    Show answer

    Explanation and discussion

20. Question 80· Integration· WAEC

    Evaluate ∫ from 0 to 2 of 2x dx.

    • A8
    • B2
    • C4
    • D0

    Show answer

    Explanation and discussion