WAEC Mathematics 2011 past questions

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

Ten questions from the 2011 WAEC Mathematics paper, with answers and explanations. We hold 29 questions from this paper, and the Skolra app has all of them.

WAEC Mathematics 2011 questions and answers

1. 1.

   Simplify $10\frac{2}{5} - 6 \frac{2}{3} + 3$

   1. A
      $6\frac{11}{15}$
      Correct
   2. B
      $7\frac{1}{15}$
   3. C
      $6\frac{7}{15}$
   4. D
      $5\frac{4}{15}$
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   Answer: A

   Step 1: Convert to improper fractions.

   $10\frac{2}{5} = \frac{52}{5},\quad 6\frac{2}{3} = \frac{20}{3}$

   Step 2: LCM of 5 and 3 is 15. Convert all terms:

   $\frac{52}{5} = \frac{156}{15},\quad \frac{20}{3} = \frac{100}{15},\quad 3 = \frac{45}{15}$

   Step 3: Combine: $\frac{156 - 100 + 45}{15} = \frac{101}{15} = 6\frac{11}{15}$

2. 2.Given that n(P) = 19, n(P $\cup$ Q) = 38 and n(P $\cap$ Q) = 7, find n(Q)
   1. A
      32
   2. B
      26
      Correct
   3. C
      19
   4. D
      20
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   Answer: B

   Step 1: Apply the inclusion-exclusion formula:

   $n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)$

   Step 2: Substitute known values:

   $38 = 19 + n(Q) - 7$

   Step 3: $n(Q) = 38 - 19 + 7 = 26$

3. 3.A rectangular garden measures 18.6m by 12.5m. Calculate, correct to three significant figures, the area of the garden
   1. A
      233 m²
      Correct
   2. B
      232 m²
   3. C
      235 m²
   4. D
      230 m²
   Show answerHide answer

   Answer: A

   Step 1: Area = length × breadth:

   $18.6 \times 12.5 = 232.5\,\text{m}^2$

   Step 2: To 3 significant figures the digits kept are 2, 3, 2. The next digit is 5, so round up the third digit:

   $232.5 \rightarrow 233\,\text{m}^2$

4. 4.What must be added to (2x - 3y) to get (x 0 2y)?
   1. A
      -x - 5y
   2. B
      x + 5y
   3. C
      3x - y
   4. D
      -x + 5y
      Correct
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   Answer: D

   Step 1: Let the required expression be k:

   $(2x - 3y) + k = x + 2y$

   Step 2: Solve for k:

   $k = (x + 2y) - (2x - 3y) = x + 2y - 2x + 3y = -x + 5y$

5. 5.Esther was facing S 20^o W. She turned 90^o in the clock wise direction. What direction is she facing?
   1. A
      N 70° W
      Correct
   2. B
      N 20° W
   3. C
      N 20° E
   4. D
      S 70° W
   Show answerHide answer

   Answer: A

   Convert to three-figure bearings, add the clockwise turn, then convert back.

   1. S 20° W = bearing 180° + 20° = 200°
   2. Turn 90° clockwise: 200° + 90° = 290°
   3. 290° lies between W (270°) and N (360°): 290° − 270° = 20° past West toward North.
   4. In compass notation: starting from North, rotate 90° − 20° = 70° toward West → N 70° W.
6. 6.in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?
   1. A
      8
   2. B
      15
   3. C
      10
      Correct
   4. D
      12
   Show answerHide answer

   Answer: C

   Step 1: Total = (number of questions) × (amount per question):

   $n(n + 50) = 600$

   Step 2: Expand and rearrange: $n^2 + 50n - 600 = 0$

   Step 3: Factorise: $(n + 60)(n - 10) = 0$

   Taking the positive root: n = 10.

7. 7.One of the factors of (mn - nq - n2 + mq) is (m - n). The other factor is
   1. A
      (m + q)
   2. B
      (m − q)
   3. C
      (n − q)
   4. D
      (n + q)
      Correct
   Show answerHide answer

   Answer: D

   Factor by grouping: mn − nq − n² + mq.

   1. Rearrange: mn + mq − nq − n²
   2. Group: m(n + q) − n(q + n)
   3. = (m − n)(n + q)
   4. Since one factor is (m − n), the other factor is (n + q).
8. 8.Solve the equation; 3x - 2y = 7, x + 2y = -3
   1. A
      x = 1, y = −2
      Correct
   2. B
      x = −1, y = 2
   3. C
      x = 2, y = −1
   4. D
      x = −2, y = 1
   Show answerHide answer

   Answer: A

   Solve the simultaneous equations by elimination.

   1. Equation (1): 3x − 2y = 7
   2. Equation (2): x + 2y = −3
   3. Add (1) and (2): 4x = 4, so x = 1
   4. Substitute x = 1 into (2): 1 + 2y = −3 → 2y = −4 → y = −2
   5. Solution: x = 1, y = −2
9. 9.If N112.00 exchanges for D14.95, calculate the value of D1.00 in naira
   1. A
      N8.00
   2. B
      N7.49
      Correct
   3. C
      N7.50
   4. D
      N7.95
   Show answerHide answer

   Answer: B

   Find the naira equivalent of D1.00 using direct proportion.

   1. D14.95 = N112.00
   2. D1.00 = N(112.00 ÷ 14.95)
   3. 112 ÷ 14.95 ≈ 7.491...
   4. Value of D1.00 = N7.49 (to the nearest kobo).
10. 10.a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window
    1. A
       11°
    2. B
       10°
       Correct
    3. C
       13°
    4. D
       80°
    Show answerHide answer

    Answer: B

    Step 1: The vertical height from window to ground is 9 m; the horizontal distance from the foot of the building to the mango is 50 m.

    Step 2: The angle of depression θ satisfies:

    $\tan\theta = \frac{9}{50} = 0.18$

    Step 3: $\theta = \tan^{-1}(0.18) \approx 10.2°$

    Correct to the nearest degree: 10°.

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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