WAEC Mathematics 2015 past questions

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

Ten questions from the 2015 WAEC Mathematics paper, with answers and explanations. We hold 30 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2015 questions and answers

1. 1.If m = 4, n = 9 and r = 16., evaluate $\frac{m}{n}$ - 1$\frac{7}{9}$ + $\frac{n}{r}$
   1. A
      −37/48
      Correct
   2. B
      13/36
   3. C
      37/48
   4. D
      −13/36
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   Answer: A

   Step 1: Substitute the values.

   m/n = 4/9, n/r = 9/16, 1 7/9 = 16/9

   Step 2: Compute.

   4/9 − 16/9 + 9/16 = −12/9 + 9/16 = −4/3 + 9/16

   Step 3: Use LCD = 48.

   −64/48 + 27/48 = −37/48

2. 2.A farmer uses $\frac{2}{5}$ of his land to grow cassava, $\frac{1}{3}$ of the remaining for yam and the rest for maize. Find the part of the land used for maize
   1. A
      4/15
   2. B
      2/5
      Correct
   3. C
      3/5
   4. D
      1/5
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   Answer: B

   Work through each allocation step by step.

   1. Cassava = 2/5
   2. Remaining after cassava = 1 − 2/5 = 3/5
   3. Yam = 1/3 of remaining = 1/3 × 3/5 = 1/5
   4. Maize = remaining − yam = 3/5 − 1/5 = 2/5
3. 3.The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students
   1. A
      32°
      Correct
   2. B
      40°
   3. C
      36°
   4. D
      30°
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   Answer: A

   Sectoral angle = (class frequency ÷ total) × 360°

   1. Sectoral angle = (72/810) × 360°
   2. = 72 × 360 / 810
   3. = 25920 / 810
   4. = 32°
4. 4.Which of the following is used to determine the mode of a grouped data?
   1. A
      Cumulative frequency curve
   2. B
      Frequency polygon
   3. C
      Pie chart
   4. D
      Histogram
      Correct
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   Answer: D

   The mode of grouped data is estimated graphically from a histogram.

   1. Draw a histogram for the frequency distribution.
   2. Identify the tallest bar — this is the modal class.
   3. Draw a line from the top-right corner of the modal bar to the top-right corner of the preceding bar, and another from the top-left corner of the modal bar to the top-left corner of the following bar.
   4. The x-value at the intersection of these two lines is the estimated mode.
   5. Hence, a histogram is used to determine the mode of grouped data.
5. 5.Make K the subject of the relation T = $\sqrt{\frac{TK - H}{K - H}}$
   1. A
      H(T − 1) / T
   2. B
      H(T + 1) / T
      Correct
   3. C
      HT / (T − 1)
   4. D
      HT / (T + 1)
   Show answerHide answer

   Answer: B

   Square both sides, then collect terms in K.

   1. T² = (TK − H) / (K − H)
   2. T²(K − H) = TK − H
   3. T²K − T²H = TK − H
   4. T²K − TK = T²H − H
   5. K(T² − T) = H(T² − 1)
   6. K = H(T² − 1) / (T² − T) = H(T−1)(T+1) / [T(T−1)]
   7. K = H(T + 1) / T
6. 6.Ada draws the graph of y = x² - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?
   1. A
      x² + 3x + 1 = 0
   2. B
      x² − 3x − 1 = 0
      Correct
   3. C
      x² + 3x − 1 = 0
   4. D
      x² − 3x + 1 = 0
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   Answer: B

   Step 1: Equate the two expressions at their intersection.

   x² − x − 2 = 2x − 1

   Step 2: Rearrange to standard form.

   x² − x − 2x − 2 + 1 = 0

   x² − 3x − 1 = 0

   The graphs intersect where x² − 3x − 1 = 0, which is the equation being solved.

7. 7.Simplify: $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}$
   1. A
      (4x − 5y) / (2xy)
   2. B
      (4x − 5y + xy) / (2xy)
      Correct
   3. C
      (4x − 5y − xy) / (2xy)
   4. D
      (4x + 5y + xy) / (2xy)
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   Answer: B

   Combine all three fractions using the common denominator 2xy.

   1. (3x−y)/(xy) = 2(3x−y)/(2xy) = (6x−2y)/(2xy)
   2. Note that 1/2 = xy/(2xy) since xy/(2xy) = 1/2
   3. Expression = [(6x−2y) − (2x+3y) + xy] / (2xy)
   4. Numerator = 6x−2y−2x−3y+xy = 4x−5y+xy
   5. Result = (4x − 5y + xy) / (2xy)
8. 8.The volume of a cone of height 3cm is 38$\frac{1}{2}$cm³. Find the radius of its base. [Take $\pi = \frac{22}{7}$]
   1. A
      3.5 cm
      Correct
   2. B
      7 cm
   3. C
      4.5 cm
   4. D
      2.5 cm
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   Answer: A

   Step 1: Write the volume formula for a cone.

   V = (1/3)πr²h

   Step 2: Substitute the known values.

   38½ = (1/3) × (22/7) × r² × 3

   77/2 = (22/7)r²

   Step 3: Solve for r².

   r² = (77/2) × (7/22) = 539/44 = 12.25

   r = √12.25 = 3.5 cm

9. 9.Adding 42 to a given positive number gives the same result as squaring the number. Find the number
   1. A
      9
   2. B
      6
   3. C
      8
   4. D
      7
      Correct
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   Answer: D

   Step 1: Set up the equation.

   Let the positive number be x. Then: x + 42 = x²

   Step 2: Rearrange into a quadratic.

   x² − x − 42 = 0

   Step 3: Factorise.

   (x − 7)(x + 6) = 0 → x = 7 or x = −6

   Since x must be positive, x = 7.

10. 10.If $\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1$, find the value of x.
    1. A
       2
    2. B
       1
    3. C
       −1/2
    4. D
       1/2
       Correct
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    Answer: D

    Step 1: Express all bases as powers of 3.

    27^x = 3^3x, 9^2x = 3^4x

    Step 2: Combine the numerator.

    3^3x × 3^(1−x) = 3^{(3x + 1 − x)} = 3^(2x+1)

    Step 3: Divide and set equal to 3⁰.

    3^(2x+1) / 3^4x = 3^(2x+1−4x) = 3^(1−2x) = 3⁰

    1 − 2x = 0 → x = 1/2

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