WAEC Mathematics 2020 past questions

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

Ten questions from the 2020 WAEC Mathematics paper, with answers and explanations. We hold 38 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2020 questions and answers

1. 1.

   Find the sum of the interior angle of a pentagon.

   1. A
      480°
   2. B
      720°
   3. C
      360°
   4. D
      540°
      Correct
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   Answer: D

   The sum of interior angles of a polygon with n sides is given by:

   Sum = (n − 2) × 180°

   For a pentagon, n = 5:

   Sum = (5 − 2) × 180° = 3 × 180° = 540°

2. 2.

   The interquartile range of distribution is 7. If the 25th percentile is 16, find the upper quartile.

   1. A
      25
   2. B
      9
   3. C
      23
      Correct
   4. D
      27
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   Answer: C

   The 25th percentile is the lower quartile (Q₁).

   Given:

   • IQR = Q₃ − Q₁ = 7
   • Q₁ = 16

   Therefore: Q₃ = Q₁ + IQR = 16 + 7 = 23

3. 3.

   If 101$_{\text{two}}$ + 12y = 3.3$_{\text{five}}$. Find the value of y

   1. A
      9
   2. B
      11
      Correct
   3. C
      7
   4. D
      8
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   Answer: B

   Convert 101₂ to decimal:
   101₂ = 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 = 5

   Convert 33₅ to decimal (interpreting 3.3₅ as 33₅):
   33₅ = 3×5¹ + 3×5⁰ = 15 + 3 = 18

   The number 12ᵧ (12 in base y) = 1×y + 2 = y + 2

   Setting up the equation:
   5 + (y + 2) = 18
   y + 7 = 18
   y = 11

4. 4.

   A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the son's age is y, express the product of their ages in terms of y.

   1. A
      5y² + 20y + 16
   2. B
      y(5y + 4) + 16
   3. C
      5y² + 24y + 20
   4. D
      (y + 4)(5y + 4)
      Correct
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   Answer: D

   Current ages: Son = y, Man = 5y

   In four years: Son = y + 4, Man = 5y + 4

   Product of their ages in four years:

   (y + 4)(5y + 4) = 5y² + 4y + 20y + 16 = 5y² + 24y + 16

   The product expressed in terms of y is (y + 4)(5y + 4).

5. 5.

   The dimensionof a rectangular base of a right pyramid is 9 cm by 5cm. If the volume of the pyramid is 105 cm$^3$, how high is the pyramid?

   1. A
      9 cm
   2. B
      6 cm
   3. C
      8 cm
   4. D
      7 cm
      Correct
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   Answer: D

   Volume of a pyramid: V = (1/3) × base area × height

   Base area = 9 × 5 = 45 cm²

   105 = (1/3) × 45 × h

   105 = 15h

   h = 105 / 15 = 7 cm

6. 6.

   Solve $\frac{1}{3}$(5 - 3x) < $\frac{2}{5}$(3 - 7x)

   1. A
      x < 7/27
   2. B
      x < -7/27
      Correct
   3. C
      x > -7/27
   4. D
      x > 7/27
   Show answerHide answer

   Answer: B

   (1/3)(5 − 3x) < (2/5)(3 − 7x)

   Multiply both sides by 15 (LCM of 3 and 5):
   5(5 − 3x) < 6(3 − 7x)
   25 − 15x < 18 − 42x

   Rearrange:
   25 − 18 < −42x + 15x
   7 < −27x

   Divide both sides by −27 (inequality sign flips when dividing by a negative):
   x < −7/27

7. 7.

   Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart?

   1. A
      11:00 am
      Correct
   2. B
      10:00 am
   3. C
      11:30 am
   4. D
      10:30 am
   Show answerHide answer

   Answer: A

   Since the buses travel in opposite directions, their speeds add up.

   Combined speed = 72 + 48 = 120 km/h

   Time to be 240 km apart:
   Time = Distance ÷ Speed = 240 ÷ 120 = 2 hours

   They start at 9:00 am, so after 2 hours they will be 240 km apart at 11:00 am.

8. 8.

   Find the quadratic equation whose roots are $\frac{1}{2}$ and -$\frac{1}{3}$

   1. A
      6x² - x + 1 = 0
   2. B
      6x² + x - 1 = 0
   3. C
      6x² - x - 1 = 0
      Correct
   4. D
      6x² + x + 1 = 0
   Show answerHide answer

   Answer: C

   For roots α = 1/2 and β = −1/3:

   Sum of roots = α + β = 1/2 + (−1/3) = 3/6 − 2/6 = 1/6

   Product of roots = αβ = (1/2)(−1/3) = −1/6

   Using the formula x² − (sum)x + (product) = 0:
   x² − (1/6)x + (−1/6) = 0
   x² − x/6 − 1/6 = 0

   Multiply through by 6:
   6x² − x − 1 = 0

9. 9.

   Given that $\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}$

   = x + y$\sqrt{15}$, find the value of (x + y)

   1. A
      4/5
   2. B
      7/5
   3. C
      1/5
   4. D
      6/5
      Correct
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   Answer: D

   Simplify (√3 + √5)/√5 by splitting the fraction:

   = √3/√5 + √5/√5
   = √3/√5 + 1

   Rationalise √3/√5:
   = (√3 × √5)/(√5 × √5)
   = √15/5
   = (1/5)√15

   So: (√3 + √5)/√5 = 1 + (1/5)√15

   Comparing with x + y√15:
   x = 1, y = 1/5

   Therefore: x + y = 1 + 1/5 = 6/5

10. 10.

    The diameter of a sphere is 12 cm. Calculate, correct of the nearest cm$^3$, the volume of the sphere, [Take $\pi = \frac{22}{7}$]

    1. A
       905 cm³
       Correct
    2. B
       910 cm³
    3. C
       904 cm³
    4. D
       900 cm³
    Show answerHide answer

    Answer: A

    Diameter = 12 cm, so radius r = 6 cm.

    Volume of a sphere: V = (4/3)πr³

    V = (4/3) × (22/7) × 6³

    V = (4/3) × (22/7) × 216

    V = (4 × 22 × 216) / (3 × 7)

    V = 19008 / 21

    V ≈ 904.857 ≈ 905 cm³ (to the nearest cm³)

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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