WAEC: MATHEMATICS
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2021 Mathematics WAEC Objective Past Questions

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2014 Mathematics WAEC Theory Past Questions
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Question 1 of 50
1. Question
Simplify: √108 + √125 − √75
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Question 2 of 50
2. Question
Evaluate:\(\left(\scriptsize 64^{\frac{1}{2}} + 125^{\frac{1}{3}}\right)^2\)
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Question 3 of 50
3. Question
Given that y varies inversely as the square of x. If x = 3 when y = 100, find the equation connecting x and y.
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Question 4 of 50
4. Question
Find the value of x for which 32_{four} = 22_{x}
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Question 5 of 50
5. Question
Simplify; \(\scriptsize 2\frac{1}{4} \: \times \: 3\frac{1}{2} \: \div \: 4 \frac{3}{8}\)
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Question 6 of 50
6. Question
There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football, what percentage of the school play football?
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Question 7 of 50
7. Question
If log_{10}(6x – 4) – log_{10}2 = 1, solve for x.
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Question 8 of 50
8. Question
If F = ^{9}/_{5}C + 32, find C when F = 98.6
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Question 9 of 50
9. Question
If y + 2x = 4 and y – 3x = 1, find the value of (x + y)
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Question 10 of 50
10. Question
If x : y : z = 2 : 3 : 4, evaluate \(\frac{9x \:+\: 3y}{6z \: \:2y}\)
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Question 11 of 50
11. Question
Simplify; \(\frac{2 \: – \: 18m^2}{1\: + \: 3m}\)
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Question 12 of 50
12. Question
A curve is such that when y = 0, x = 2 or x = 3. Find the equation of the curve.
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Question 13 of 50
13. Question
The volume of a cylindrical tank, 10m high is 385 m^{2}. Find the diameter of the tank. [Take π=^{22}/_{7}]
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Question 14 of 50
14. Question
The surface area of a sphere is \( \frac{792}{7} \scriptsize cm^2 \). Find, correct to the nearest whole number, its volume. [Take π=^{22}/_{7}]
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Question 15 of 50
15. Question
A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take π=^{22}/_{7}]
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Question 16 of 50
16. Question
In the diagram, which of the following ratios is equal to \(\frac{PN}{PQ}\)?
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Question 17 of 50
17. Question
In the diagram, PS and RS are tangents to the circle centre O, ∠PSR = 70º, ∠POR = m and ∠PQR = n, find (m + n)
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Question 18 of 50
18. Question
Find the value of t in the diagram
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Question 19 of 50
19. Question
In the diagram, PR is a tangent to the circle at Q, QT//RS, <SQR = 35^{0} and <RSQ = 50^{0. }Find the value of <QST.
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Question 20 of 50
20. Question
The angles of a polygon are x, 2x, 2x, (x + 30^{o}), (x + 20^{o}) and (x – 10^{o}). Find the value of x
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Question 21 of 50
21. Question
If M and N are the points (3, 8) and (5, 7) respectively, find MN
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Question 22 of 50
22. Question
The equation of the line through the points (4,2) and (8, 2) is 3y = px + q, where p and q are constants. Find the value of p.
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Question 23 of 50
23. Question
The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot of the tree is 30^{o}. Find the height of the tree.
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Question 24 of 50
24. Question
If tan x = \( \frac{4}{3}\normalsize, \)
0^{o} < x < 90^{o}, find the value of sin x – cos x
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Question 25 of 50
25. Question
Given that Y is 20cm on a bearing of 30oº from x, how far south of y is x?
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Question 26 of 50
26. Question
The mean of 1, 3, 5, 7 and x is 4. Find the value of x
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Question 27 of 50
27. Question
Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2
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Question 28 of 50
28. Question
Number of goals 1 2 3 4 5 6 7 Number of teams 3 1 6 6 4 2 3 The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at random scored at most 3 goals.
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Question 29 of 50
29. Question
Number of goals 1 2 3 4 5 6 7 Number of teams 3 1 6 6 4 2 3 The table shows the distribution of goals scored by 25 teams in a football competition.
Calculate the probability that a team selected at random scored either 4 or 7 goals.
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Question 30 of 50
30. Question
In the diagram, WXYZ is a rectangle with dimensions 8cm by 6cm. P, Q, R, and S are the midpoints of the sides of the rectangle as shown.
Using this information, what type of quadrilateral is the shaded region?
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Question 31 of 50
31. Question
In the diagram, WXYZ is a rectangle with dimension 8cm by 6cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown.
Using this information calculate the area of the part of the rectangle that is not shaded
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Question 32 of 50
32. Question
The total surface area of a hemispher is 75πcm^{2}. Find the radius.
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Question 33 of 50
33. Question
Find the value of x for which \(\frac{x – 5}{x(x – 1)}\) is defined
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Question 34 of 50
34. Question
Solve the equation 2x^{2 }− x − 6 = 0
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Question 35 of 50
35. Question
Factorise completely the expression (x+2)^{2} – (2x+1)^{2}
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Question 36 of 50
36. Question
Find the nth term of the sequence 2 × 3, 4 × 6, 8 × 9, 16 × 12…
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Question 37 of 50
37. Question
If 3x = 4(mod 5), find the least value of x
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Question 38 of 50
38. Question
The solution of x + 2 ≥ 2x + 1 is illustrated on the number line as
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Question 39 of 50
39. Question
If P and Q are two statements, under what condition would pq be false?
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Question 40 of 50
40. Question
The diagram shows a trapezium inscribed in a semicircle. If O is the midpoint of WZ and WX = XY = YZ, calculate the value of m
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Question 41 of 50
41. Question
Find the interquartile range of 1, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16
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Question 42 of 50
42. Question
No. of envelopes 4 7 20 9 4 5 3 1 2 Amount (N) 5000 2000 1000 700 500 100 50 2 10 Donations during the launching of a church project were sent in sealed envelopes.
The table shows the distribution of the amount of money in the envelopes.
How much was the total donation?
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Question 43 of 50
43. Question
In the diagram, PQ is a straight line, (m + n) = 110^{o} and (n + r) = 130^{o} and (m + r) = 120^{o}. Find the ratio of m : n : r
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Question 44 of 50
44. Question
If x : y = ^{1}/_{4 }: ^{3}/_{8} and y : z = ^{1}/_{3 }: ^{4}/_{9}, find x : z
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Question 45 of 50
45. Question
Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45
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Question 46 of 50
46. Question
M and N are two subsets of the universal set (U). If n(U) = 48, n(M) = 20, n(N) = 30 and n(M U N) = 40, find n(M ∩ N)’
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Question 47 of 50
47. Question
Express 0.612 in the form ^{x}/_{y}, where x and y are integers and y ≠ 0
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Question 48 of 50
48. Question
In the diagram, PQ//RS. Find x in terms of y and z
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Question 49 of 50
49. Question
The diagonals of a rhombus WXYZ intersect at M. If MW = 5cm and MX = 12cm, calculate its perimeter
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Question 50 of 50
50. Question
The graph of y = x^{2} and y = x intersect at which of these points?
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