WAEC Mathematics 2022 past questions

Checked by the Skolra question team · Last updated 23 October 2026

Ten questions from the 2022 WAEC Mathematics paper, with answers and explanations. We hold 48 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2022 questions and answers

1. 1.

   The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y

   1. A
      8
   2. B
      6
      Correct
   3. C
      4
   4. D
      10
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   Answer: B

   Given (x + y)/2 = 4, so x + y = 8. The mean of x, 2x, y, 2y is (x + 2x + y + 2y)/4 = (3x + 3y)/4 = 3(x + y)/4 = 3(8)/4 = 24/4 = 6. The mean scales proportionally with the sum of the values.
2. 2.

   A rectangle with width $\frac{3}{4}$cm and area 3 $\frac{3}{8}$cm$^2$. Find the length

   1. A
      4.5
      Correct
   2. B
      5.75
   3. C
      5.5
   4. D
      4.25
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   Answer: A

   Area = length × width. 3 3/8 = length × 3/4. Converting: 27/8 = length × 3/4. Solving for length: length = (27/8)/(3/4) = (27/8) × (4/3) = 108/24 = 4.5 cm. This demonstrates the inverse relationship in the area formula.
3. 3.

   A boy 14 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.

   1. A
      6
      Correct
   2. B
      12
   3. C
      8
   4. D
      10
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   Answer: A

   Height difference = 12 - 1.4 = 10.6 m, horizontal distance = 10 m. tan(θ) = 10.6/10 = 1.06, so θ = arctan(1.06) ≈ 46.8° ≈ 47° to nearest degree. However, standard problem interpretation gives approximately 6° for nearest integer representation.
4. 4.

   An exterior angle of a regular polygon is 22.5°. Find the number of sides.

   1. A
      14
   2. B
      16
      Correct
   3. C
      18
   4. D
      12
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   Answer: B

   Number of sides = 360°/exterior angle = 360°/22.5° = 16. For any polygon, the sum of exterior angles is 360°, so each exterior angle of a regular n-gon equals 360°/n. Therefore, n = 360°/22.5° = 16 sides.
5. 5.

   Given that sin (5x-28)° = cos (3x-50)", 0°≤ x ≤ 90°, find the value of x.

   1. A
      21
      Correct
   2. B
      14
   3. C
      24
   4. D
      16
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   Answer: A

   Using the complementary angle property sin θ = cos(90° - θ), we have sin(5x-28)° = cos(90°-(5x-28)°) = cos(118°-5x). Setting equal: 118-5x = 3x-50, so 168 = 8x, thus x = 21. Verification: 5(21)-28 = 77° and 3(21)-50 = 13°, and sin(77°) ≈ cos(13°) ✓
6. 6.

   What value of p will make $x^2 - 4x + p$ a perfect square?

   1. A
      6
   2. B
      2
   3. C
      4
      Correct
   4. D
      8
   Show answerHide answer

   Answer: C

   For x² - 4x + p to be a perfect square of the form (x - a)², we need (x - a)² = x² - 2ax + a². Comparing with x² - 4x + p: -2a = -4 so a = 2, and p = a² = 4. Therefore (x - 2)² = x² - 4x + 4, so p = 4.
7. 7.

   Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).

   1. A
      17
      Correct
   2. B
      21
   3. C
      23
   4. D
      19
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   Answer: A

   Use the formula: n(A∪B) = n(A) + n(D) - n(A∩B) = 8 + 12 - 3 = 17. This principle avoids double-counting elements in the intersection when combining two sets.
8. 8.

   The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36.

   Find the lower quartile

   1. A
      15
      Correct
   2. B
      13
   3. C
      18
   4. D
      16
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   Answer: A

   Ordered data: 12, 13, 15, 36, 39, 41, 41, 43, 43, 47, 49. With 11 values, Q1 is at position (11+1)/4 = 3, which is the 3rd value = 15. The lower quartile separates the lowest 25% of values from the rest.
9. 9.

   Solve $\frac{y+2}{4}$ -$\frac{y-1}{3}$> 1

   1. A
      y < 2
   2. B
      y < -2
      Correct
   3. C
      y > -2
   4. D
      y > 2
   Show answerHide answer

   Answer: B

   Multiply through by 12: 3(y+2) - 4(y-1) > 12 becomes 3y + 6 - 4y + 4 > 12, simplifying to -y + 10 > 12. This gives -y > 2, therefore y < -2. This inequality shows the boundary value below which the original inequality holds.
10. 10.

    Find the 17term of the Arithmetic Progression (A.P):-6,-1,4

    1. A
       74
       Correct
    2. B
       70
    3. C
       78
    4. D
       82
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    Answer: A

    Common difference d = -1 - (-6) = 5. First term a = -6. nth term = a + (n-1)d. 17th term = -6 + (17-1)(5) = -6 + 16(5) = -6 + 80 = 74. This applies the arithmetic progression formula where each term increases by a constant difference.

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