WAEC Mathematics 2017 past questions

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

Ten questions from the 2017 WAEC Mathematics paper, with answers and explanations. We hold 40 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2017 questions and answers

1. 1.

   The ages of Tunde and Ola are in the ratio 1:2. If the ratio of Ola's age to Musa's age is 4:5, what is the ratio of Tunde's age to Musa's age?

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

   Answer: C

   Step 1: Tunde : Ola = 1 : 2

   Step 2: Ola : Musa = 4 : 5

   Step 3: Make Ola's value the same in both ratios. The LCM of 2 and 4 is 4.
   Multiply the first ratio by 2: Tunde : Ola = 2 : 4

   Step 4: Combine into a three-way ratio:
   Tunde : Ola : Musa = 2 : 4 : 5

   Step 5: Extract Tunde : Musa = 2 : 5

2. 2.

   The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres

   1. A
      9.1 litres
   2. B
      4.55 litres
      Correct
   3. C
      45.5 litres
   4. D
      2.275 litres
   Show answerHide answer

   Answer: B

   Step 1: Calculate the full volume of the tank:
   V = 13 × 10 × 70 = 9100 cm³

   Step 2: Half-filled volume:
   V_half = 9100 / 2 = 4550 cm³

   Step 3: Convert to litres (1 litre = 1000 cm³):
   4550 / 1000 = 4.55 litres

3. 3.

   If M = {x : 3 $\leq$ x < 8} and N = {x : 8 < x $\leq$ 12}, which of the following is true?

   i. 8 $\in$ M $\cap$ N

   ii. 8 $\in$ M $\cup$ N

   iii. M $\cap$ N = $\varnothing$

   1. A
      i and ii only
   2. B
      i only
   3. C
      ii only
   4. D
      iii only
      Correct
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   Answer: D

   Analyse the sets:
   M = {x : 3 ≤ x < 8} — includes 3 but excludes 8
   N = {x : 8 < x ≤ 12} — includes 12 but excludes 8

   Check each statement:

   • i. 8 ∈ M∩N? — 8 ∉ M and 8 ∉ N, so FALSE
   • ii. 8 ∈ M∪N? — 8 is in neither set, so 8 ∉ M∪N: FALSE
   • iii. M∩N = ∅? — M contains values up to (but not including) 8, and N contains values greater than 8; they share no element: TRUE

   Only statement iii is true.

4. 4.

   A stationary boat is observed from a height of 100m. If the horizontal distance between the observer and the boat is 80m, calculate, correct to two decimal places, the angles of depression of the boat from point of observation

   1. A
      38.66°
   2. B
      51.34°
      Correct
   3. C
      45.00°
   4. D
      53.13°
   Show answerHide answer

   Answer: B

   Step 1: Set up the right triangle.
   The angle of depression θ is measured from the horizontal down to the line of sight to the boat.
   Opposite side (vertical) = 100 m
   Adjacent side (horizontal) = 80 m

   Step 2: Apply trigonometry.
   tan θ = opposite/adjacent = 100/80 = 1.25

   Step 3: Find the angle.
   θ = tan⁻¹(1.25) ≈ 51.34°

5. 5.

   In a class of 45 students, 28 offer chemistry and 25 offer Biology. If each student offers at least one of the two subjects, calculate the probability that a student selected at random from the class offers chemistry only.

   1. A
      8/45
   2. B
      17/45
   3. C
      5/9
   4. D
      4/9
      Correct
   Show answerHide answer

   Answer: D

   Step 1: Find students offering both subjects.
   Using the union formula: |C ∪ B| = |C| + |B| − |C ∩ B|
   45 = 28 + 25 − |C ∩ B|
   |C ∩ B| = 53 − 45 = 8

   Step 2: Find students offering chemistry only.
   Chemistry only = 28 − 8 = 20

   Step 3: Calculate probability.
   P(chemistry only) = 20/45 = 4/9

6. 6.

   Three exterior angles of a polygon are 30$^o$, 40$^o$ and 60$^o$. If the remaining exterior angles are 46$^o$ each, name the polygon.

   1. A
      Heptagon
   2. B
      Nonagon
   3. C
      Hexagon
   4. D
      Octagon
      Correct
   Show answerHide answer

   Answer: D

   Step 1: Sum of exterior angles of any polygon = 360°.

   Step 2: Find remaining angles.
   Known angles: 30° + 40° + 60° = 130°
   Remaining sum = 360° − 130° = 230°
   Number of remaining angles = 230° / 46° = 5

   Step 3: Total number of sides.
   Total sides = 3 (given angles) + 5 (remaining) = 8
   A polygon with 8 sides is an Octagon

7. 7.

   A circular pond of radius 4m has a path of width 2.5m round it. Find, correct to two decimal places, the area of the path. [Take 22/7]

   1. A
      65.36 m²
   2. B
      75.43 m²
   3. C
      82.50 m²
      Correct
   4. D
      90.25 m²
   Show answerHide answer

   Answer: C

   Step 1: Identify inner and outer radii.
   Inner radius r₁ = 4 m
   Outer radius r₂ = 4 + 2.5 = 6.5 m

   Step 2: Area of path = area of outer circle − area of inner circle.
   Area = π(r₂² − r₁²) = (22/7)(6.5² − 4²)
   = (22/7)(42.25 − 16)
   = (22/7)(26.25)
   = 22 × 26.25 / 7
   = 577.5 / 7
   = 82.50 m²

8. 8.

   If the total surface area of a solid hemisphere is equal to its volume, find the radius

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

   Step 1: Total surface area of a solid hemisphere = curved surface + flat circular base
   = 2πr² + πr² = 3πr²

   Step 2: Volume of a solid hemisphere = (2/3)πr³

   Step 3: Set them equal:
   3πr² = (2/3)πr³

   Step 4: Divide both sides by πr²:
   3 = (2/3)r

   Step 5: Solve for r:
   r = 3 × (3/2) = 9/2 = 4.5 cm

9. 9.

   Simplify; 3x - (p - x) - (r - p)

   1. A
      4x - r
      Correct
   2. B
      2x - r
   3. C
      2x + r
   4. D
      4x + r
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   Answer: A

   Step 1: Expand the brackets (distributing the minus signs):
   3x - (p - x) - (r - p) = 3x - p + x - r + p

   Step 2: Collect like terms:
   x terms: 3x + x = 4x
   p terms: -p + p = 0
   r terms: -r

   Result: 4x - r

10. 10.

    Evaluate $\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}$

    1. A
       26/15
    2. B
       2/5
    3. C
       1/2
    4. D
       13/15
       Correct
    Show answerHide answer

    Answer: D

    Step 1: Convert mixed numbers to improper fractions:
    3¼ = 13/4; 1⅗ = 8/5; 11⅓ = 34/3; 5⅓ = 16/3

    Step 2: Compute the numerator:
    (13/4) × (8/5) = 104/20 = 26/5

    Step 3: Compute the denominator:
    34/3 - 16/3 = 18/3 = 6

    Step 4: Divide:
    (26/5) ÷ 6 = 26/30 = 13/15

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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