Mathematics past questions: WAEC SSCE 2024

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

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

1.
A car valued at $ 600,000.00 depreciates by 10% each year. What will be the value of the car at the end of two years?
1. A.$ 120,000.00
2. B.$ 480,000.00
3. C.$ 486,000.00
4. D.$ 540,000.00
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Answer: C $ 486,000.00
2.
A cliff on the bank of a river 87 m high. A boat on the river is 22 m away from the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
1. A.76 $^o$
2. B.64 $^o$
3. C.36 $^o$
4. D.24 $^o$
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Answer: A 76 $^o$
3.
A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?
1. A.5: 4
2. B.4: 3
3. C.3: 2
4. D.3: 4
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Answer: B 4: 3
4.
A cylindrical metallic barrel of height 2.5m and radius 0.245 is closed at one end. Find, correct to one decimal place, the total surface area of the barrel (Take π = $\frac{22}{7}$ )
1. A.2.1 m $^2$
2. B.3.5 m $^2$
3. C.4.0 m $^2$
4. D.9.4 m $^2$
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Answer: C 4.0 m $^2$
5.
A die is tossed once. Find the probability of getting a prime number.
1. A.$\frac{1}{2}$
2. B.$\frac{1}{6}$
3. C.$\frac{1}{3}$
4. D.$\frac{2}{3}$
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Answer: A $\frac{1}{2}$
6.
A ladder 15 m long leans against a vertical pole, making an angle of 72º with the horizontal. Calculate, correct to one decimal place, the distance between the foot of the ladder and the pole.
1. A.15.8 m
2. B.14.3 m
3. C.4.9 m
4. D.4.6 m
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Answer: D 4.6 m
7.
A number is added to both the numerator and the denominator of the fraction $\frac{1}{8}$ if the result is $\frac{1}{2}$ , find the number.
1. A.3
2. B.4
3. C.5
4. D.6
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Answer: D 6
8.
A piece of rod of length 44 m is cut to form a rectangular shape such that the ratio of the length to the breadth is 7: 4. Find the breath.
1. A.8m
2. B.14m
3. C.16m
4. D.24m
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Answer: A 8m
9.
A trader gave a change of # 540.00 instead of # 570.00 to a customer. Caculate the percentage error.
1. A.5 $\frac{5}{19}$ %
2. B.5 $\frac{5}{9}$ %
3. C.5 $\frac{7}{19}$ %
4. D.5 $\frac{7}{9}$ %
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Answer: A 5 $\frac{5}{19}$ %
10.
A variable W varies partly as M and Partly inversely as P. Which of the following correctly represents the relation with k $_1$ and k $_2$ constants?
1. A.W = $\frac{k_1M}{k_2P}$
2. B.W = ( $k_1 + k_2$ ) $\frac{\text{M}}{\text{P}}$
3. C.W = k $_1$ M + $\frac{k_2}{P}$
4. D.W = (k $_1 + k_2$ )M + P
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Answer: C W = k $_1$ M + $\frac{k_2}{P}$
11.
Consider the following statements: m = Edna is respectful n = Edna is brilliant, If m ⇒ n, which of the following is valid?
1. A.¬n ⇒ ¬m.
2. B.¬m ⇒ ¬n.
3. C.n ⇒ ¬m.
4. D.m ⇒ n.
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Answer: A ¬n ⇒ ¬m.
12.
Express in index form: log $_a^x$ + log $_a^y$ = 3
1. A.x + y = 3
2. B.xy = 3
3. C.xy = a $^3$
4. D.x + y = a $^3$
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Answer: C xy = a $^3$
13.
Factorize completely: 27x $^2$ - 48y $^2$
1. A.3(3x + 4y)(3x - 4y)
2. B.3(3x + 4y)(3x + 4y)
3. C.3(9x - 16y)(9x + 16y)
4. D.3(9x - 16y)(9x - 16y)
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Answer: A 3(3x + 4y)(3x - 4y)
14.
Find the quadratic equation whose roots are $\frac{2}{3}$ and - 1
1. A.3x $^2$ - x - 2 = 0
2. B.3x $^2$ + x + 2 = 0
3. C.3x $^2$ + x - 2 = 0
4. D.3x $^2$ + x - 1 = 0
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Answer: C 3x $^2$ + x - 2 = 0
15.
Find the range of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, and 25.
1. A.22
2. B.24
3. C.25
4. D.27
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Answer: B 24
16.
Find the sum for which $ 1,250.00 will amount to $ 2,031.25 at 12.5% per annum simple interest.
1. A.2 years
2. B.3 years
3. C.4 years
4. D.5 years
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Answer: D 5 years
17.
Find the value of x in the diagram above.
1. A.120º
2. B.100º
3. C.60º
4. D.150º
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Answer: A 120º
18.
Find, correct to the nearest whole number, the value of h in the diagram above.
1. A.15 m
2. B.22 m
3. C.23 m
4. D.18 m
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Answer: C 23 m
19.
For what values of x is $\frac{x - 3}{4}$ + $\frac{x + 1}{8}$ $\geq$ 2 ?
1. A.x $\geq$ 5
2. B.x $\geq$ 6
3. C.x $\geq$ 7
4. D.x $\geq$ 8
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Answer: C x $\geq$ 7
20.
For what values of y is $\frac{y + 2}{8y^2 - 10y + 3}$ not defined?
1. A.$\frac{-3}{4}$ , $\frac{1}{2}$
2. B.$\frac{-3}{4}$ , $\frac{-1}{2}$
3. C.$\frac{3}{4}$ , $\frac{1}{2}$
4. D.$\frac{3}{4}$ , $\frac{-1}{2}$
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Answer: C $\frac{3}{4}$ , $\frac{1}{2}$
21.
Four of the angles of a hexagon sum up to 420º. If the remaining angles are equal, find the value of each of the angles.
1. A.60 $^O$
2. B.100 $^O$
3. C.120 $^O$
4. D.150 $^O$
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Answer: D 150 $^O$
22.
Gifty, Justina, and Frank shared 60 oranges in the ratio 5: 3: 7 respectively. How many oranges did Justina receive?
1. A.16
2. B.12
3. C.20
4. D.28
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Answer: B 12
23.
Given that P = {p: 1< p < 20}, where p is an integer and R = {r : 0 $\leq$ r $\leq$ 25, where r is a multiple of 4}. Find P ∩ R
1. A.{4, 8, 10, 16}
2. B.{4, 8, 12, 16}
3. C.{4, 8, 12, 16, 20}
4. D.{4, 8, 12, 16, 20, 24}
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Answer: B {4, 8, 12, 16}
24.
Given that P is 25 m on a bearing of 330º from Q, how far south of P is Q?
1. A.25.2 m
2. B.21.7 m
3. C.19.8 m
4. D.18.5 m
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Answer: B 21.7 m
25.
If (3 - 4 $\sqrt{2}$ )(1 + 3 $\sqrt{2}$ ) = a + b $\sqrt{2}$ , find the value of b
1. A.-5
2. B.5
3. C.-21
4. D.21
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Answer: B 5
26.
If 3x - 2y = - 5 and x + 2y = 9, find the value of $\frac{x - y}{x + y}$
1. A.$\frac{5}{3}$
2. B.$\frac{3}{5}$
3. C.$\frac{-3}{5}$
4. D.$\frac{-5}{3}$
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Answer: C $\frac{-3}{5}$
27.
If log $_3^{2x - 1}$ = 5, find the value of x
1. A.8
2. B.16
3. C.64
4. D.122
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Answer: D 122
28.
In the diagram $\overline{TU}$ is a tangent to the circle SPQR at P. If $\angle$ PTS = 44º, $\angle$ SQP = 35º, find $\angle$ PST
1. A.101º
2. B.125º
3. C.130º
4. D.135º
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Answer: A 101º
29.
In the diagram above, $\overline{MN} || \overline{KL}$ , $\overline{ML}$ and $\overline{KN}$ intersect at X. | $\overline{MN}$ | = 12cm, | $\overline{MX}$ | = 10cm and | $\overline{MN}$ | = 9cm. If the area of $\triangle$ MXN is 16cm $^2$ , calculate the area of $\triangle$ LXK
1. A.9cm $^2$
2. B.8cm $^2$
3. C.10cm $^2$
4. D.12cm $^2$
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Answer: A 9cm $^2$
30.
In the diagram above, $\overline{PQ}$ || $\overline{RS}$ , $\angle$ WYZ = 44º and $\angle$ WXY = 50º. Find $\angle$ WTX
1. A.65º
2. B.68º
3. C.86º
4. D.90º
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Answer: C 86º
31.
In the diagram above, < SQR = 52º and < PRT = 16º. Find the value of the angle marked y
1. A.64 $^0$
2. B.68 $^0$
3. C.112 $^0$
4. D.128 $^0$
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Answer: C 112 $^0$
32.
In the diagram above, JKL is a tangent to the circle GHIK at K. Find the value of the angle marked x
1. A.93º
2. B.55º
3. C.42º
4. D.23º
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Answer: B 55º
33.
In the diagram above, O is the centre of the circle. If | $\overline{OA}$ = 25 cm and | $\overline{AB}$ = 40 cm, find | $\overline{OH}$ |
1. A.15 cm
2. B.20 cm
3. C.25 cm
4. D.30 cm
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Answer: A 15 cm
34.
Make R the subject of the relation V = πl(R $^2$ - r $^2$ )
1. A.R = $\sqrt{\frac{V}{πl} + r^2}$
2. B.R = $\sqrt{\frac{V}{πl} - r^2}$
3. C.R = $\sqrt{V - πlr^2}$
4. D.R = $\sqrt{V + πlr^2}$
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Answer: A R = $\sqrt{\frac{V}{πl} + r^2}$
35.
Multiply 3.4 x 10 $^{-5}$ by 7.1 x 10 $^8$ and leave the answer in standard form.
1. A.2.414 x 10 $^2$
2. B.2.414 x 10 $^3$
3. C.2.414 x 10 $^4$
4. D.2.414 x 10 $^5$
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Answer: C 2.414 x 10 $^4$
36.
Simplify: (2p - q) $^2$ - (p + q) $^2$
1. A.3p(p - 2q)
2. B.2p(p - 3q)
3. C.3p(2p - q)
4. D.2p(3p - q)
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Answer: A 3p(p - 2q)
37.
The area of a sector of a circle with radius 7cm is 51.3 cm $^2$ . Calculate, correct to the nearest whole number, the angle of the sector. (Take $\pi$ = $\frac{22}{7}$ )
1. A.60 $^0$
2. B.120 $^0$
3. C.150 $^0$
4. D.150 $^0$
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Answer: B 120 $^0$
38.
The first term of an Arithmetic Progression (A.P) is 2 and the last term is 29. If the common difference is 3, how many terms are in the A.P.?
1. A.8
2. B.9
3. C.10
4. D.11
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Answer: C 10
39.
The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 57, 40, 48, and 50. Calculate the mean mass.
1. A.44 kg
2. B.50 kg
3. C.40 kg
4. D.53 kg
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Answer: B 50 kg
40.
The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 57, 40, 48, and 50. Calculate the variance of the distribution.
1. A.35
2. B.36
3. C.40
4. D.50
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Answer: A 35
41.
The fourth and eighth terms of an Arithmetic Progression are 16 and 40 respectively. Find the common difference.
1. A.- 6
2. B.6
3. C.-2
4. D.2
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Answer: B 6
42.
The gradient of the line joining the points P(2, -8) and Q(1, y) is -4. Find the value of y
1. A.2
2. B.4
3. C.-4
4. D.-3
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Answer: C -4
43.
The interior angle of a regular polygon is 168º. Find the number of sides of the polygon.
1. A.24
2. B.30
3. C.15
4. D.12
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Answer: B 30
44.
The length and breadth of a cuboid are 15 cm and 8 cm respectively. If the volume of the cuboid is 1560 cm $^3$ , calculate the total surface area.
1. A.976cm $^2$
2. B.838cm $^2$
3. C.792cm $^2$
4. D.746cm $^2$
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Answer: B 838cm $^2$
45.
The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.
1. A.Seven
2. B.Eight
3. C.Nine
4. D.Ten
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Answer: A Seven
46.
The perimeter of a rectangular garden is 90 m. If the width is 7 m less than the length, find the length of the garden.
1. A.19 m
2. B.23 m
3. C.24 m
4. D.26 m
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Answer: D 26 m
47.
The population of a town increases by 3% every year. In the year 2000, the population was 3000. Find the population in the year 2003.
1. A.3,182
2. B.3,278
3. C.6,591
4. D.7,515
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Answer: B 3,278
48.
The probability that Amaka will pass an examination is $\frac{3}{7}$ and that Bala will pass is $\frac{4}{9}$ . Find the probability that both will pass the examination.
1. A.$\frac{2}{21}$
2. B.$\frac{4}{21}$
3. C.$\frac{5}{21}$
4. D.$\frac{9}{21}$
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Answer: B $\frac{4}{21}$
49.
Two opposite sides of a rectangle are (5x + 3) m and (2x + 9) m. If an adjacent side is (6x - 7) m, find in m $^2$ , the area of the rectangle.
1. A.45
2. B.65
3. C.125
4. D.165
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Answer: B 65
50.
Which of the following points lies on the line 3x - 8y = 11?
1. A.(1, 1)
2. B.(1, -1)
3. C.(-1, 1)
4. D.(-1, -1)
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Answer: B (1, -1)

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