WAEC Mathematics 2018 past questions

Checked by the Skolra question team · Last updated 15 October 2026

Ten questions from the 2018 WAEC Mathematics paper, with answers and explanations. We hold 37 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2018 questions and answers

1. 1.

   The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot of the tree is 30$^o$. Find the height of the tree.

   1. A
      9√3 m
      Correct
   2. B
      9 m
   3. C
      27 m
   4. D
      27√3 m
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   Answer: A

   Let h = height of the tree. The horizontal distance = 27 m and the angle of elevation = 30°.

   tan(30°) = h / 27

   h = 27 × tan(30°) = 27 × (1/√3) = 27/√3 = 27√3/3 = 9√3 m

2. 2.

   M and N are two subsets of the universal set (U). If n(U) = 48, n(M) = 20, n(N) = 30 and n(MUN) = 40, find n(M $\cap$ N)

   1. A
      15
   2. B
      12
   3. C
      10
      Correct
   4. D
      8
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   Answer: C

   Use the inclusion-exclusion formula: n(M ∪ N) = n(M) + n(N) − n(M ∩ N)

   Substitute: 40 = 20 + 30 − n(M ∩ N)

   40 = 50 − n(M ∩ N)

   n(M ∩ N) = 50 − 40 = 10

3. 3.

   Expression 0.612 in the form $\frac{x}{y}$, where x and y are integers and y $\neq$ 0

   1. A
      68/111
      Correct
   2. B
      34/55
   3. C
      153/250
   4. D
      204/333
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   Answer: A

   Let x = 0.612612612... (recurring). Multiply both sides by 1000:

   1000x = 612.612612...

   Subtract: 1000x − x = 612 → 999x = 612

   x = 612/999. Divide by GCD (9): x = 68/111

4. 4.

   Solved the equation $2x^2 - x - 6$ = 0

   1. A
      x = 3 or x = −2
   2. B
      x = −3 or x = 2
   3. C
      x = −3/2 or x = 2
      Correct
   4. D
      x = 3/2 or x = −2
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   Answer: C

   Factorise 2x² − x − 6 = 0.

   Find two numbers that multiply to 2 × (−6) = −12 and add to −1: those are −4 and 3.

   2x² − 4x + 3x − 6 = 0 → 2x(x − 2) + 3(x − 2) = 0 → (2x + 3)(x − 2) = 0

   x = −3/2 or x = 2

5. 5.

   Simplify; $\frac{2 - 18m^2}{1 + 3m}$

   1. A
      2(3m − 1)
   2. B
      2(1 − 3m)
      Correct
   3. C
      2(1 + 3m)
   4. D
      2(9m + 1)
   Show answerHide answer

   Answer: B

   Factor the numerator: 2 − 18m² = 2(1 − 9m²)

   Use difference of squares: 1 − 9m² = (1 − 3m)(1 + 3m)

   So: 2(1 − 3m)(1 + 3m) / (1 + 3m) = 2(1 − 3m)

6. 6.

   A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take $\pi = \frac{22}{7}$]

   1. A
      173°
   2. B
      177°
      Correct
   3. C
      180°
   4. D
      175°
   Show answerHide answer

   Answer: B

   Perimeter of sector = 2r + arc length

   21.4 = 2(4.2) + arc → arc = 21.4 − 8.4 = 13 cm

   Arc length formula: arc = (θ/360) × 2πr

   13 = (θ/360) × 2 × (22/7) × 4.2 = (θ/360) × 26.4

   θ = (13 × 360) / 26.4 = 4680 / 26.4 ≈ 177°

7. 7.

   If M and N are the points (-3, 8) and (5, -7) respectively, find |MN|

   1. A
      19
   2. B
      15
   3. C
      17
      Correct
   4. D
      13
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   Answer: C

   Using the distance formula: |MN| = √[(x₂ − x₁)² + (y₂ − y₁)²]

   = √[(5 − (−3))² + (−7 − 8)²]

   = √[8² + (−15)²]

   = √[64 + 225] = √289 = 17

8. 8.

   If x : y : z = 3 : 3 : 4, evaluate $\frac{9x + 3y}{6z - 2y}$

   1. A
      2
      Correct
   2. B
      3
   3. C
      1
   4. D
      4
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   Answer: A

   Let x = 3k, y = 3k, z = 4k.

   Numerator: 9x + 3y = 9(3k) + 3(3k) = 27k + 9k = 36k

   Denominator: 6z − 2y = 6(4k) − 2(3k) = 24k − 6k = 18k

   Result = 36k / 18k = 2

9. 9.

   If F = $\frac{9}{5}$C + 32, find C when F = 98.6

   1. A
      32
   2. B
      35
   3. C
      40
   4. D
      37
      Correct
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   Answer: D

   Substitute F = 98.6: 98.6 = (9/5)C + 32

   (9/5)C = 98.6 − 32 = 66.6

   C = 66.6 × 5/9 = 333/9 = 37

10. 10.

    Simplify: $\sqrt{108} + \sqrt{125} - \sqrt{75}$

    1. A
       $\sqrt{3} - 5\sqrt{5}$
    2. B
       $6\sqrt{3} + 5\sqrt{5}$
    3. C
       $11\sqrt{3}$
    4. D
       $\sqrt{3} + 5\sqrt{5}$
       Correct
    Show answerHide answer

    Answer: D

    Step 1: Simplify each surd by finding the largest perfect-square factor.

    • $\sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3}$
    • $\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}$
    • $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$

    Step 2: Substitute and collect like surds.

    $6\sqrt{3} + 5\sqrt{5} - 5\sqrt{3} = (6 - 5)\sqrt{3} + 5\sqrt{5} = \sqrt{3} + 5\sqrt{5}$

The questions come from past JAMB, WAEC and NECO papers. We use software to help write the answer options and explanations, and every answer is checked twice before it goes on the site. How we check

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