WAEC Mathematics 2021 past questions

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

Ten questions from the 2021 WAEC Mathematics paper, with answers and explanations. We hold 39 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2021 questions and answers

1. 1.The diagonal of a rhombus are 12cm and 5cm. calculate its perimeter
   1. A
      26 cm
      Correct
   2. B
      24 cm
   3. C
      30 cm
   4. D
      28 cm
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   Answer: A

   The diagonals of a rhombus bisect each other at right angles.

   Half-diagonals: 12/2 = 6 cm and 5/2 = 2.5 cm.

   Side of rhombus = √(6² + 2.5²) = √(36 + 6.25) = √42.25 = 6.5 cm

   Perimeter = 4 × 6.5 = 26 cm

2. 2.correct 0.007985 to three significant figures.
   1. A
      0.00799
      Correct
   2. B
      0.00798
   3. C
      0.00801
   4. D
      0.00800
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   Answer: A

   0.007985 — identify the significant figures:

   1st sig fig: 7, 2nd: 9, 3rd: 8, 4th: 5

   Rounding to 3 significant figures: the 4th digit (5) rounds the 3rd digit (8) up to 9.

   Result: 0.00799

3. 3.Simplify 2√7 - 14/√7 + 7/√21
   1. A
      √21
   2. B
      √7/3
   3. C
      2√7/3
   4. D
      √21/3
      Correct
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   Answer: D

   Rationalise each term:

   2√7 = 2√7

   14/√7 = 14√7/7 = 2√7

   7/√21 = 7√21/21 = √21/3

   So: 2√7 − 2√7 + √21/3 = √21/3

4. 4.The circumference of a circular track is 9km. A cyclist rides round it a number of times and stops after covering a distance of 302km. How far is the cyclist from the starting point?
   1. A
      9 km
   2. B
      7 km
   3. C
      3 km
   4. D
      5 km
      Correct
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   Answer: D

   Divide the total distance by the circumference:

   302 ÷ 9 = 33 remainder 5

   33 × 9 = 297 km (complete laps)

   302 − 297 = 5 km into the next lap.

   The cyclist is 5 km from the starting point.

5. 5.XY is a line segment with coordinates X(-8, -12) and Y(p, q). If the midpoint of XY is (-4, -2), find the coordinates of Y.
   1. A
      (0, -8)
   2. B
      (4, 10)
   3. C
      (0, 8)
      Correct
   4. D
      (-2, 5)
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   Answer: C

   Midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

   Given X(−8, −12), Y(p, q) and midpoint (−4, −2):

   x-coordinate: (−8 + p)/2 = −4 → −8 + p = −8 → p = 0

   y-coordinate: (−12 + q)/2 = −2 → −12 + q = −4 → q = 8

   Y = (0, 8)

6. 6.Factorize 6pq-3rs-3ps+6qr
   1. A
      3(p − r)(2q + s)
   2. B
      3(p + r)(2q − s)
      Correct
   3. C
      3(p − r)(2q − s)
   4. D
      3(p + r)(2q + s)
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   Answer: B

   Regroup the expression:

   6pq − 3rs − 3ps + 6qr

   = 6pq + 6qr − 3ps − 3rs

   = 6q(p + r) − 3s(p + r)

   = (p + r)(6q − 3s)

   = 3(p + r)(2q − s)

7. 7.The distance d between two villages is more than 18 km but not more than 23 km. Which of these inequalities represents the statement?
   1. A
      18 < d ≤ 23
      Correct
   2. B
      18 ≤ d ≤ 23
   3. C
      18 < d < 23
   4. D
      18 ≤ d < 23
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   Answer: A

   Translate the sentence into symbols:

   • "more than 18 km" → d > 18, i.e., strict inequality on the left.
   • "not more than 23 km" → d ≤ 23, i.e., inclusive on the right.

   Combined: 18 < d ≤ 23

8. 8.Given that sin x = 3/5, 0 ≤ x ≤ 90, evaluate (tan x + 2cos x)
   1. A
      13/4
   2. B
      7/4
   3. C
      47/20
      Correct
   4. D
      13/20
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   Answer: C

   Given sin x = 3/5 and 0 ≤ x ≤ 90°, use a 3-4-5 right triangle:

   Opposite = 3, Hypotenuse = 5, Adjacent = 4.

   cos x = 4/5

   tan x = 3/4

   tan x + 2cos x = 3/4 + 2(4/5) = 3/4 + 8/5

   LCM of 4 and 5 is 20: = 15/20 + 32/20 = 47/20

9. 9.Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?
   1. A
      5 years
      Correct
   2. B
      3 years
   3. C
      10 years
   4. D
      7 years
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   Answer: A

   Mensah's current age = 5 years. Joyce's current age = 3 × 5 = 15 years.

   Let n = number of years until Joyce is twice as old as Mensah:

   15 + n = 2(5 + n)

   15 + n = 10 + 2n

   5 = n

   In 5 years, Joyce will be 20 and Mensah will be 10.

10. 10.500 tickets were sold for a concert. Tickets for adults and children were sold at $4.50 and $3.00 respectively. If the total receipts were $1987.50, how many tickets for adults were sold?
    1. A
       275
    2. B
       250
    3. C
       325
       Correct
    4. D
       175
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    Answer: C

    Let the number of adult tickets = a, so children's tickets = 500 − a.

    Revenue equation: 4.50a + 3.00(500 − a) = 1987.50

    4.50a + 1500 − 3a = 1987.50

    1.5a = 487.50

    a = 325

    325 adult tickets were sold.

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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