WAEC Mathematics 2014 past questions

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

Ten questions from the 2014 WAEC Mathematics paper, with answers and explanations. We hold 37 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2014 questions and answers

1. 1.

   If x varies inversely as y and y varies directly as z, what is the relationship between x and z?

   1. A
      x varies inversely as z²
   2. B
      x varies directly as z
   3. C
      x varies directly as z²
   4. D
      x varies inversely as z
      Correct
   Show answerHide answer

   Answer: D

   x varies inversely as y means x = k/y (for some constant k).

   y varies directly as z means y = mz (for some constant m).

   Substituting: x = k/(mz) = c/z, where c = k/m is a constant.

   Therefore x varies inversely as z.

2. 2.

   The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.

   1. A
      2√5
      Correct
   2. B
      2√3
   3. C
      √8
   4. D
      2√6
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   Answer: A

   Using the distance formula:
   PQ = √[(x₂ − x₁)² + (y₂ − y₁)²]
   = √[(4 − 2)² + (3 − (−1))²]
   = √[2² + 4²]
   = √[4 + 16]
   = √20 = 2√5

3. 3.

   Given that cos x = $\frac{12}{13}$, evaluate $\frac{1 - \tan x}{\tan x}$

   1. A
      7/5
      Correct
   2. B
      12/5
   3. C
      5/7
   4. D
      7/12
   Show answerHide answer

   Answer: A

   Given cos x = 12/13, use the Pythagorean triple (5, 12, 13): sin x = 5/13.

   tan x = sin x / cos x = (5/13) ÷ (12/13) = 5/12

   (1 − tan x) / tan x = 1/tan x − 1 = cot x − 1 = 12/5 − 1 = 12/5 − 5/5 = 7/5

4. 4.

   In what modulus is it true that 9 + 8 = 5?

   1. A
      mod 12
      Correct
   2. B
      mod 10
   3. C
      mod 7
   4. D
      mod 6
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   Answer: A

   In ordinary arithmetic, 9 + 8 = 17. In modular arithmetic, we need 17 ≡ 5 (mod m).

   This means m divides (17 − 5) = 12.

   The suitable modulus is m = 12, because 17 ÷ 12 = 1 remainder 5, i.e. 17 mod 12 = 5.

5. 5.

   If $\frac{2}{x - 3} - \frac{3}{x - 2}$ is equal to $\frac{p}{(x - 3)(x - 2)}$, find p

   1. A
      x-5
   2. B
      x+5
   3. C
      5-x
      Correct
   4. D
      2x+5
   Show answerHide answer

   Answer: C

   Combine the fractions using the common denominator (x − 3)(x − 2):

   2/(x−3) − 3/(x−2) = [2(x−2) − 3(x−3)] / [(x−3)(x−2)]

   Expand the numerator:
   2(x−2) − 3(x−3) = 2x − 4 − 3x + 9 = 5 − x

   So p = 5 − x

6. 6.

   If a number is selected at random from each of the sets p = {1, 2, 3} and Q = {2, 3, 5}, find the probability that the sum of the numbers is prime

   1. A
      1/3
   2. B
      5/9
   3. C
      2/3
   4. D
      4/9
      Correct
   Show answerHide answer

   Answer: D

   List all 9 equally likely pairs and their sums:

   (1,2)→3 (prime), (1,3)→4, (1,5)→6
   (2,2)→4, (2,3)→5 (prime), (2,5)→7 (prime)
   (3,2)→5 (prime), (3,3)→6, (3,5)→8

   Prime sums: 3, 5, 7, 5 — that is 4 favourable outcomes out of 9.

   Probability = 4/9

7. 7.

   If 23_x = 32₅, find the value of x

   1. A
      8
   2. B
      5
   3. C
      7
      Correct
   4. D
      6
   Show answerHide answer

   Answer: C

   Step 1: Convert 32₅ to base 10.
   32₅ = 3 × 5¹ + 2 × 5⁰ = 15 + 2 = 17.

   Step 2: Express 23ₓ in base 10.
   23ₓ = 2 × x¹ + 3 × x⁰ = 2x + 3.

   Step 3: Equate and solve.
   2x + 3 = 17
   2x = 14
   x = 7.

8. 8.

   If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x : 0 $\geq$ x $\geq$ 6}, find x $\cap$ (Y' $\cup$ Z)

   1. A
      {2, 4}
   2. B
      {4, 6}
   3. C
      {0, 6}
      Correct
   4. D
      {0, 2}
   Show answerHide answer

   Answer: C

   Step 1: Identify U.
   U = {0, 1, 2, 3, 4, 5, 6} (integers from 0 to 6).

   Step 2: Find Y′ (complement of Y in U).
   Y = {1, 2, 3, 4}, so Y′ = U − Y = {0, 5, 6}.

   Step 3: Find Y′ ∪ Z.
   Y′ = {0, 5, 6}, Z = {1, 3}
   Y′ ∪ Z = {0, 1, 3, 5, 6}.

   Step 4: Find X ∩ (Y′ ∪ Z).
   X = {0, 2, 4, 6}
   {0, 2, 4, 6} ∩ {0, 1, 3, 5, 6} = {0, 6}.

9. 9.

   A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.

   1. A
      135°
   2. B
      045°
      Correct
   3. C
      225°
   4. D
      315°
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   Answer: B

   The ship travels x km due East then x km due North. The final displacement from the starting point has equal eastward (x) and northward (x) components.

   The bearing is measured clockwise from North:
   tan(bearing from N) = East/North = x/x = 1 → angle = 45°

   Bearing of F from start = N45°E = 045°

10. 10.

    In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years?

    1. A
       40%
    2. B
       35%
    3. C
       65%
       Correct
    4. D
       60%
    Show answerHide answer

    Answer: C

    The lower quartile (Q₁) = 18 years means 25% of the distribution is at most 18 years.

    The 60th percentile = 48 years means 60% of the distribution is at most 48 years, so 40% is greater than 48 years.

    Since these two groups cannot overlap (no value can be both ≤18 and >48 at the same time):

    Percentage at most 18 or greater than 48 = 25% + 40% = 65%

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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