2026/2027 WAEC/GCE Further Mathematics Essay Questions and Answers

2026/2027 WAEC/GCE Further Mathematics/Mathematics OBJ and Essay Questions and Answers

PAPER 1 – OBJECTIVE TEST

Time: 1 Hour 30 Minutes
Instructions: Answer all questions. Choose the correct option A–D.

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OBJECTIVE QUESTIONS (1–60)

Algebra

1. If $2x+5=17$, find $x$.
A. 5
B. 6
C. 7
D. 8
Answer: B

2. Simplify $(x+3)(x-2)$.
A. x2+x−6x^2 + x – 6x2+x−6
B. x2−x−6x^2 – x – 6x2−x−6
C. x2+5x−6x^2 + 5x – 6x2+5x−6
D. x2−5x+6x^2 – 5x + 6x2−5x+6
Answer: A

3. Solve x2−9=0x^2 – 9 = 0x2−9=0.
A. ±2
B. ±3
C. ±9
D. 3 only
Answer: B

4. If log⁡101000=x\log_{10} 1000 = xlog10​1000=x, then x equals
A. 2
B. 3
C. 10
D. 100
Answer: B

5. The roots of x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0 are
A. 1 and 6
B. 2 and 3
C. -2 and -3
D. 3 and 5
Answer: B

Trigonometry

6. sin⁡30∘\sin 30^\circsin30∘ equals
A. 1
B. 0
C. 1/2
D. √3/2
Answer: C

7. The value of tan⁡45∘\tan 45^\circtan45∘ is
A. 0
B. 1
C. √2
D. √3
Answer: B

8. Convert $\pi$ radians to degrees.
A. 90°
B. 180°
C. 360°
D. 270°
Answer: B

9. The identity sin⁡2θ+cos⁡2θ=\sin^2\theta + \cos^2\theta =sin2θ+cos2θ=
A. 0
B. 1
C. 2
D. θ
Answer: B

10. If $\sin \theta =1$, then θ equals
A. 0°
B. 30°
C. 90°
D. 180°
Answer: C

2026/2027 WAEC/GCE Further Mathematics/Mathematics OBJ and Essay Questions and Answers

Calculus (Further Mathematics)

11. Differentiate x3x^3x3.
A. 3x
B. 3x²
C. x²
D. 2x
Answer: B

12. Integrate $2xdx$.
A. x² + C
B. 2x² + C
C. x + C
D. x³ + C
Answer: A

13. If y=5x2y = 5x^2y=5x2, find $dy/dx$.
A. 10x
B. 5x
C. x²
D. 25x
Answer: A

14. The derivative of a constant is
A. 1
B. 0
C. Constant
D. x
Answer: B

15. Find $\int 4dx$.
A. 4
B. x
C. 4x + C
D. 4x
Answer: C

Geometry

16. The sum of angles in a triangle is
A. 90°
B. 180°
C. 270°
D. 360°
Answer: B

17. Area of circle =
A. 2πr
B. πr²
C. πd
D. r²
Answer: B

18. Volume of cylinder =
A. πr²h
B. 2πr
C. πr²
D. r³
Answer: A

19. Pythagoras theorem states
A. a² + b² = c²
B. a + b = c
C. a² – b² = c²
D. ab = c²
Answer: A

20. An angle greater than 90° but less than 180° is
A. Acute
B. Right
C. Obtuse
D. Reflex
Answer: C

Statistics

21. Mean of 2, 4, 6 is
A. 3
B. 4
C. 5
D. 6
Answer: B

22. Median of 3, 5, 7, 9 is
A. 5
B. 6
C. 7
D. 8
Answer: B

23. Probability ranges from
A. 0 to 1
B. 1 to 10
C. 0 to 100
D. -1 to 1
Answer: A

24. Mode is
A. Highest number
B. Middle value
C. Most frequent value
D. Average
Answer: C

25. Variance measures
A. Central value
B. Spread of data
C. Total
D. Frequency
Answer: B

Further Mathematics (Matrices & Vectors)

26. Determinant of ∣1001∣\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix}​10​01​​ is
A. 0
B. 1
C. -1
D. 2
Answer: B

27. Order of matrix with 2 rows and 3 columns is
A. 3×2
B. 2×3
C. 2²
D. 3²
Answer: B

28. Two matrices can be added if
A. Same order
B. Same determinant
C. Same value
D. Same column only
Answer: A

29. Vector magnitude of (3,4) is
A. 5
B. 7
C. 12
D. 1
Answer: A

30. If A is 2×2, then A⁻¹ exists when determinant ≠
A. 0
B. 1
C. 2
D. -1
Answer: A

Number System

31. 1010₂ in decimal equals
A. 8
B. 10
C. 12
D. 14
Answer: B

32. LCM of 4 and 6 is
A. 10
B. 12
C. 24
D. 8
Answer: B

33. Prime number among these is
A. 9
B. 15
C. 17
D. 21
Answer: C

34. Standard form of 0.00045 is
A. 4.5×10⁻⁴
B. 45×10⁻⁴
C. 4.5×10⁻⁵
D. 0.45×10⁻⁵
Answer: A

35. 3! equals
A. 3
B. 6
C. 9
D. 12
Answer: B

2026/2027 WAEC/GCE Further Mathematics/Mathematics OBJ and Essay Questions and Answers

Further Calculus & Series

36. If f(x)=x²+2x, find f’(1).
A. 2
B. 4
C. 6
D. 8
Answer: B

37. Sum of first n natural numbers =
A. n²
B. n(n+1)/2
C. 2n
D. n+1
Answer: B

38. Common difference in AP 2,5,8 is
A. 2
B. 3
C. 4
D. 5
Answer: B

39. Sum of GP formula =
A. a/(1-r)
B. a+r
C. ar
D. r-a
Answer: A

40. If r = 1 in GP, sum becomes
A. Undefined
B. Infinite
C. 0
D. 1
Answer: A

Miscellaneous

41. Perimeter of square =
A. 4a
B. a²
C. 2a
D. a³
Answer: A

42. 25% of 200 is
A. 25
B. 40
C. 50
D. 75
Answer: C

43. If log a + log b =
A. log(a+b)
B. log(ab)
C. a+b
D. ab
Answer: B

44. The gradient of horizontal line is
A. 1
B. -1
C. 0
D. Undefined
Answer: C

45. Equation of straight line is
A. y = mx + c
B. x² + y²
C. ax²
D. xy
Answer: A

46. Probability of sure event =
A. 0
B. 1
C. ½
D. -1
Answer: B

47. Cos 0° =
A. 0
B. 1
C. -1
D. ½
Answer: B

48. If matrix A = I, then A is
A. Zero matrix
B. Unit matrix
C. Diagonal only
D. Singular
Answer: B

49. The inverse of multiplication is
A. Addition
B. Subtraction
C. Division
D. Square
Answer: C

50. In statistics, Σ means
A. Product
B. Division
C. Summation
D. Mode
Answer: C

51. Differentiate sin x
A. cos x
B. -cos x
C. tan x
D. sec x
Answer: A

52. Integral of cos x
A. sin x + C
B. cos x
C. -sin x
D. tan x
Answer: A

53. If determinant = 0, matrix is
A. Singular
B. Identity
C. Unit
D. Diagonal
Answer: A

54. Vector dot product gives
A. Scalar
B. Vector
C. Matrix
D. Determinant
Answer: A

55. The area under curve is found by
A. Differentiation
B. Integration
C. Factorization
D. Expansion
Answer: B

56. Binomial expansion applies to
A. (a+b)ⁿ
B. a+b
C. ab
D. a²
Answer: A

57. Standard deviation is square root of
A. Mean
B. Median
C. Variance
D. Mode
Answer: C

58. Angle in semicircle is
A. 30°
B. 45°
C. 60°
D. 90°
Answer: D

59. If sin θ = 0, θ equals
A. 0°
B. 90°
C. 45°
D. 30°
Answer: A

60. Limit of constant is
A. 0
B. 1
C. Infinity
D. The constant
Answer: D

PAPER 2 – ESSAY (THEORY)

Time: 2 Hours 30 Minutes
Answer Five Questions Only

QUESTION 1 (Compulsory)

Solve the quadratic equation x2−7x+10=0x^2 – 7x + 10 = 0x2−7x+10=0.

Answer:
Factorization:
$(x-5)(x-2)=0$
x = 5 or x = 2

2026/2027 WAEC/GCE Further Mathematics/Mathematics OBJ and Essay Questions and Answers

QUESTION 2

(a) Differentiate y=3×3−5×2+4y = 3x^3 – 5x^2 + 4y=3x3−5x2+4.
(b) Find gradient at x = 2.

Answer:
dy/dx = 9x² – 10x
At x=2: 9(4) – 20 = 36 – 20 = 16

QUESTION 3

Given matrix
A=(2132)A = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}A=(23​12​)

Find determinant and inverse.

Answer:
Det = (2×2)-(1×3)=4-3=1
Inverse exists since det ≠ 0

QUESTION 4

A class has scores: 10, 15, 20, 25, 30
Find mean and variance.

Answer:
Mean = 20
Variance = 50

QUESTION 5

Prove that sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1sin2θ+cos2θ=1.

Answer:
Using unit circle identity, sum of squares equals 1.

QUESTION 6

Find sum of first 20 terms of AP: 3, 7, 11, …

Answer:
a=3, d=4
Sₙ = n/2[2a+(n-1)d]
= 20/2[6+76]
=10×82 = 820

QUESTION 7

Solve using integration:
Find area under curve y = 2x from x=0 to x=3.

Answer:
∫2x dx = x²
Area = 3² – 0 = 9 units²