WAEC Mathematics 2010 past questions

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

Ten questions from the 2010 WAEC Mathematics paper, with answers and explanations. We hold 29 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2010 questions and answers

1. 1.A car uses one litre of petrol for every 14km. If one of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?
   1. A
      250 km
   2. B
      200 km
      Correct
   3. C
      100 km
   4. D
      150 km
   Show answerHide answer

   Answer: B

   Step 1: Find the number of litres purchasable.
   Litres = $\frac{900}{63} = \frac{100}{7}$

   Step 2: Calculate the distance.
   Distance = $\frac{100}{7} \times 14 = \frac{100 \times 14}{7} = 200$ km

2. 2.The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of the values of x
   1. A
      x ≤ 4
   2. B
      x ≤ 2
   3. C
      x ≤ 3
      Correct
   4. D
      x ≥ 3
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   Answer: C

   The mean of 2, 5, 2x and 7 is:

   $\frac{2 + 5 + 2x + 7}{4} \leq 5$

   $\frac{14 + 2x}{4} \leq 5$

   $14 + 2x \leq 20$

   $2x \leq 6$

   $x \leq 3$

3. 3.A rectangle has length xcm and width (x - 1)cm. If the perimeter is 16cm. Find the value of x
   1. A
      5.0
   2. B
      6.0
   3. C
      4.5
      Correct
   4. D
      3.5
   Show answerHide answer

   Answer: C

   Step 1: Write the perimeter formula.
   Perimeter = 2(length + width) = 2(x + x − 1) = 2(2x − 1)

   Step 2: Set equal to 16 and solve.
   2(2x − 1) = 16
   4x − 2 = 16
   4x = 18
   x = 4.5

4. 4.The sum of 6 and one-third of x is one more than twice x, find x
   1. A
      2
   2. B
      5
   3. C
      3
      Correct
   4. D
      4
   Show answerHide answer

   Answer: C

   Step 1: Translate into an equation.
   $6 + \frac{x}{3} = 1 + 2x$

   Step 2: Solve.
   $6 - 1 = 2x - \frac{x}{3}$
   $5 = \frac{6x - x}{3} = \frac{5x}{3}$
   $15 = 5x$
   $x = 3$

5. 5.Given that $\frac{5^{n +3}}{25^{2n -2}}$ = 5^o, find n
   1. A
      2
   2. B
      $\frac{7}{3}$
      Correct
   3. C
      1
   4. D
      $\frac{3}{7}$
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   Answer: B

   Step 1: Express 25 as a power of 5.
   $25^{2n-2} = (5^2)^{2n-2} = 5^{4n-4}$

   Step 2: Simplify the left side.
   $\frac{5^{n+3}}{5^{4n-4}} = 5^{(n+3)-(4n-4)} = 5^{-3n+7}$

   Step 3: Set equal to 5⁰ and solve.
   $-3n + 7 = 0$
   $n = \frac{7}{3}$

6. 6.What is the length of a rectangular garden whose perimeter is 32cm and area 39cm²?
   1. A
      9 cm
   2. B
      13 cm
      Correct
   3. C
      3 cm
   4. D
      16 cm
   Show answerHide answer

   Answer: B

   Let length = l and width = w.

   Perimeter: 2(l + w) = 32 → l + w = 16 → w = 16 − l

   Area: lw = 39

   Substituting: l(16 − l) = 39

   $l^2 - 16l + 39 = 0$

   $(l - 3)(l - 13) = 0$

   l = 3 or l = 13

   The length (longer side) = 13 cm (width = 3 cm).

7. 7.Factorize: x + y - ax = ay
   1. A
      (1 - a)(x + y)
      Correct
   2. B
      (a - 1)(x + y)
   3. C
      (1 - a)(x - y)
   4. D
      (1 + a)(x - y)
   Show answerHide answer

   Answer: A

   Step 1: Bring all terms to one side.
   x + y − ax − ay = 0

   Step 2: Group and factorise.
   x(1 − a) + y(1 − a) = 0
   (1 − a)(x + y) = 0

8. 8.

   $\begin{array}{c|c} \text{No. of pets} & 0 & 1 & 2 & 3 & 4 \\ \hline \text{No. of students} & 8 & 4 & 5 & 10 & 3\end{array}$

   The table shows the number of pets kept by 30 students in a class. If a student is picked at random from the class. What is the probability that he/she kept more than one pet?

   1. A
      $\frac{1}{2}$
   2. B
      $\frac{2}{5}$
   3. C
      $\frac{1}{3}$
   4. D
      $\frac{3}{5}$
      Correct
   Show answerHide answer

   Answer: D

   Step 1: Count students with more than 1 pet (i.e. 2, 3 or 4 pets).
   5 + 10 + 3 = 18 students

   Step 2: Calculate the probability.
   P = $\frac{18}{30} = \frac{3}{5}$

9. 9.The sum of 2 consecutive whole numbers is $\frac{5}{6}$ of their product, find the numbers
   1. A
      4 and 5
   2. B
      3 and 4
   3. C
      2 and 3
      Correct
   4. D
      1 and 2
   Show answerHide answer

   Answer: C

   Step 1: Set up the equation.
   Let the numbers be n and n + 1.
   $n + (n+1) = \frac{5}{6} \cdot n(n+1)$
   $2n + 1 = \frac{5}{6}n(n+1)$

   Step 2: Multiply through by 6.
   $12n + 6 = 5n(n+1) = 5n^2 + 5n$
   $5n^2 - 7n - 6 = 0$

   Step 3: Solve the quadratic.
   $(5n + 3)(n - 2) = 0$
   n = 2 (taking the positive whole-number root)

   Step 4: State the answer.
   The numbers are 2 and 3. Check: 2 + 3 = 5 and $\frac{5}{6}\times 2\times 3 = 5$. ✓

10. 10.The sum of the exterior of an n-sided convex polygon is half the sum of its interior angle. find n
    1. A
       6
       Correct
    2. B
       8
    3. C
       12
    4. D
       4
    Show answerHide answer

    Answer: A

    For any convex polygon:

    Sum of exterior angles = 360°

    Sum of interior angles = (n − 2) × 180°

    Setting exterior = ½ × interior:

    $360 = \frac{1}{2}(n-2) \times 180$

    $360 = 90(n-2)$

    $4 = n - 2$

    $n = 6$

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