Mathematics past questions: WAEC SSCE 2022

47 objective questions, with answers. Free to read and practise.

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47 questions, one at a time, marked as you go or at the end. No account needed.

1.
.Find the value of x such that $\frac{1}{x}$ + $\frac{4}{3x}$ - $\frac{5}{6x}$ + 1 = 0
1. A.$\frac{1}{6}$
2. B.$\frac{1}{4}$
3. C.$\frac{-3}{2}$
4. D.$\frac{-7}{6}$
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Answer: C $\frac{-3}{2}$
2.
A boy 1.4 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.
1. A.70º
2. B.47º
3. C.19º
4. D.8º
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Answer: B 47º
3.
A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area
1. A.126.5cm $^2$
2. B.165.0cm $^2$
3. C.212.0cm $^2$
4. D.214.5cm $^2$
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Answer: D 214.5cm $^2$
4.
A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?
1. A.3.611m
2. B.4.521m
3. C.4.792m
4. D.3.962m
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Answer: C 4.792m
5.
A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households. The Evening Dispatch is read by 60% of the households. Twenty percent of the households read both papers. What is the probability that a particular household reads at least one paper?
1. A.0.45
2. B.0.65
3. C.0.85
4. D.0.95
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Answer: C 0.85
6.
A rectangle with width $\frac{3}{4}$ cm and area 3 $\frac{3}{8}$ cm $^2$ . Find the length
1. A.6cm
2. B.4 $\frac{1}{2}$ cm
3. C.2 $\frac{5}{8}$ cm
4. D.12cm
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Answer: B 4 $\frac{1}{2}$ cm
7.
A trader made a loss of 15% when an article was sold. Find the ratio of the selling price : cost price
1. A.3:20
2. B.3:17
3. C.17:20
4. D.20:23
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Answer: C 17:20
8.
A weaver bought a bundle of grass for $ 50.00 from which he made 8 mats. If each mat was sold for $ 15.00, find the percentage profit.
1. A.240%
2. B.140%
3. C.120%
4. D.40%
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Answer: B 140%
9.
An exterior angle of a regular polygon is 22.5°. Find the number of sides.
1. A.13
2. B.14
3. C.15
4. D.16
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Answer: D 16
10.
Change 432 $_{five}$ to a number in base three.
1. A.10100 $_{three}$
2. B.11100 $_{three}$
3. C.11101 $_{three}$
4. D.10110 $_{three}$
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Answer: B 11100 $_{three}$
11.
Consider the statements: p: Stephen is intelligent q: Stephen is good at Mathematics If p⇒q, which of the following is a valid conclusion?
1. A.If Stephen is good at Mathematics, then he is intelligent
2. B.If Stephen is not good at Mathematics, then he is not intelligent
3. C.If Stephen is not intelligent, then he is not good at Mathematics
4. D.If Stephen is not good at Mathematics, then he is intelligent
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Answer: B If Stephen is not good at Mathematics, then he is not intelligent
12.
Evaluate 23 x 54 (mod 7)
1. A.2
2. B.3
3. C.5
4. D.6
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Answer: B 3
13.
Evaluate, correct to four significant figures, (573.06 x 184.25).
1. A.105600.00
2. B.105622.00
3. C.105500.00
4. D.105632.00
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Answer: A 105600.00
14.
Find ∠OSN
1. A.36º
2. B.42º
3. C.54º
4. D.72º
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Answer: A 36º
15.
Find the 17term of the Arithmetic Progression (A.P):-6,-1,4
1. A.-91
2. B.-86
3. C.74
4. D.79
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Answer: C 74
16.
Find the area of the sector OPSQ
1. A.15.40cm $^2$
2. B.17.64cm $^2$
3. C.23.10cm $^2$
4. D.32.34cm $^2$
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Answer: D 32.34cm $^2$
17.
Find the correct to two decimal places, the volume of a sphere whose radius is 3cm. [Take π = $\frac{22}{7}$ ]
1. A.72.57cm $^3$
2. B.88.12cm $^3$
3. C.10529cm $^3$
4. D.113.14cm $^3$
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Answer: D 113.14cm $^3$
18.
Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]
1. A.15.5cm $^3$
2. B.21.0cm $^3$
3. C.142cm $^3$
4. D.154cm $^3$
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Answer: D 154cm $^3$
19.
Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).
1. A.15
2. B.17
3. C.20
4. D.23
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Answer: B 17
20.
Given that log $_3$ 27 = 2x + 1, find the value of x.
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: B 1
21.
Given that sin (5x-28)° = cos (3x-50)", 0°≤ x ≤ 90°, find the value of x.
1. A.39
2. B.32
3. C.21
4. D.14
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Answer: C 21
22.
If √24 + √96 - √600 = y√6, find the value of y
1. A.4
2. B.2
3. C.-2
4. D.-4
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Answer: D -4
23.
If 4 $^{3x}$ = 16 $^{x+1}$ , find the value of x
1. A.2
2. B.3
3. C.4
4. D.5
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Answer: A 2
24.
If 5x + 3y=4 and 5x-3y= 2, what is the value of (25x $^2$ -9y $^2$ )?
1. A.20
2. B.16
3. C.2
4. D.8
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Answer: D 8
25.
If a = 3 and b = -7, find the value of $\frac{5b+(a+b)^2}{(a-b)^2}$
1. A.0.51
2. B.0.91
3. C.-0.19
4. D.-0.51
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Answer: C -0.19
26.
If the equations x $^2$ - 5x + 6 = 0 and x $^2$ + px + 6 = 0 have the same roots, find the value of p.
1. A.5
2. B.6
3. C.-5
4. D.-6
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Answer: C -5
27.
In the diagram, ∠POQ = 150 and the radius of the circle PSQR is 4.2cm. [take π = 22/7] What is the length of the minor arc?
1. A.11cm
2. B.15.4cm
3. C.17.64cm
4. D.23.10cm
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Answer: A 11cm
28.
In the diagram, ∠ZWZY and WYX are right angles. Find the perimeter of WXYZ.
1. A.30cm
2. B.32cm
3. C.35cm
4. D.37cm
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Answer: B 32cm
29.
In the diagram, MNR is a tangent to the circle centre O at N and ∠NOS = 108°. Find ∠OSN
1. A.72°
2. B.32°
3. C.36°
4. D.18°
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Answer: C 36°
30.
In the diagram, triangle MNR is inscribed in circle MNR, and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR
1. A.39º
2. B.80º
3. C.110º
4. D.141º
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Answer: B 80º
31.
M varies directly as n and inversely as the square of p. If M= 3 when n = 2 and p = 1, find M in terms of n and p.
1. A.$\frac{3n}{2p^2}$
2. B.$\frac{2n}{3p^2}$
3. C.$\frac{2n}{3p}$
4. D.$\frac{3n^2}{2p^2}$
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Answer: A $\frac{3n}{2p^2}$
32.
Make t the subject of k = $m \sqrt \frac{t-p}{r}$
1. A.$\frac{k^2r + p}{m^2}$
2. B.$\frac{k^2r + pm^2}{m^2}$
3. C.$\frac{k^2r - p}{m^2}$
4. D.$\frac{k^2r + p^2}{m^2}$
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Answer: B $\frac{k^2r + pm^2}{m^2}$
33.
Mary has $ 3.00 more than Ben but $ 5.00 less than Jane. If Mary has $ x, how much does Jane and Ben have altogether?
1. A.$(2x-8)
2. B.$(2x+8)
3. C.$(2x-2)
4. D.$(2x+2)
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Answer: D $(2x+2)
34.
Mrs Gabriel is pregnant. The probability that she will give birth to a girl is 1/2 and with blue eyes is 1/4. What is the probability that she will give birth to a girl with blue eyes?
1. A.1
2. B.$\frac{3}{4}$
3. C.$\frac{1}{8}$
4. D.$\frac{1}{4}$
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Answer: C $\frac{1}{8}$
35.
Simplify $\frac{2-18m^2}{1+3m}$
1. A.2[1+3m]
2. B.2[1-3m]
3. C.2[1-3m $^2$ ]
4. D.2[1+3m $^2$ ]
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Answer: B 2[1-3m]
36.
Solve $\frac{y+2}{4}$ - $\frac{y-1}{3}$ > 1
1. A.y < -10
2. B.y < -2
3. C.y < 2
4. D.y < 10
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Answer: B y < -2
37.
Solve 6x $^2$ = 5x - 1
1. A.x = 2,3
2. B.x = 0,3
3. C.x = $\frac{1}{2}$ , $\frac{1}{3}$
4. D.x = $\frac{1}{2}$ , $\frac{-1}{3}$
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Answer: C x = $\frac{1}{2}$ , $\frac{1}{3}$
38.
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the lower quartile
1. A.12
2. B.13
3. C.15
4. D.20
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Answer: C 15
39.
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the mean
1. A.33.35
2. B.35.54
3. C.34.45
4. D.36.44
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Answer: C 34.45
40.
The length of a piece of stick is 1.75 m. A boy measured it as 1.80 m. Find the percentage error
1. A.4 $\frac{4}{7}$
2. B.2 $\frac{6}{7}$
3. C.2 $\frac{7}{9}$
4. D.4 $\frac{7}{9}$
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Answer: B 2 $\frac{6}{7}$
41.
The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area
1. A.30cm $^2$
2. B.40cm $^2$
3. C.60cm $^2$
4. D.80cm $^2$
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Answer: B 40cm $^2$
42.
The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm $^2$ , find the perpendicular distance between the parallel sides.
1. A.5cm
2. B.7cm
3. C.10cm
4. D.15cm
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Answer: C 10cm
43.
The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.
1. A.75
2. B.65
3. C.55
4. D.45
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Answer: B 65
44.
The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y
1. A.2
2. B.4
3. C.6
4. D.8
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Answer: C 6
45.
The straight line y = mx - 4 passes through the point(-4,16). Calculate the gradient of the line
1. A.-5
2. B.-3
3. C.3
4. D.5
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Answer: A -5
46.
Three boys shared D 10,500.00 in the ratio 6:7:8. Find the largest share.
1. A.4000
2. B.5000
3. C.4500
4. D.3500
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Answer: A 4000
47.
What value of p will make (x $^2$ - 4x + p) a perfect square?
1. A.-2
2. B.16
3. C.4
4. D.-8
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Answer: C 4

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