Mathematics past questions: WAEC SSCE 2021

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

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

1.
$\overline{XY}$ is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of $\overline{XY}$ is (-4,-2) find the coordinates of Y.
1. A.(-6,-2)
2. B.(0,8)
3. C.(4,10)
4. D.(0,4)
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Answer: B (0,8)
2.
Height(cm) 160 161 162 163 164 165
No. of players 4 6 3 7 8 9
the table shows the height of 37 players of a basketball team calculates correct to one decimal place the mean height of the players.
1. A.163.0
2. B.162.0
3. C.160.0
4. D.165.0
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Answer: A 163.0
3.
500 tickets were sold for a concert tickets for adults and children were sold at $4.50 and $3.00 respectively if the total receipts for the concerts was $1987.50 how many tickets for adults were sold?
1. A.325
2. B.235
3. C.175
4. D.400
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Answer: A 325
4.
A box contains 40 identical balls of which 10 are red and 12 are blue. if a ball is selected at random from the box what is the probability that it is neither red nor blue?
1. A.$\frac{9}{20}$
2. B.$\frac{3}{10}$
3. C.$\frac{1}{4}$
4. D.$\frac{11}{20}$
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Answer: A $\frac{9}{20}$
5.
A cone has a base radius of 8cm and height 11cm. calculate , correct to 2d.p, the curved surface area
1. A.341.98cm $^2$
2. B.276.57cm $^2$
3. C.201.14cm $^2$
4. D.477.71cm $^2$
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Answer: A 341.98cm $^2$
6.
A cyclist moved at a speed of Xkm/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours. If the total distance covered is 36 km, calculate his initials speed.
1. A.12km/h
2. B.3km/h
3. C.4km/h
4. D.6km/h
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Answer: D 6km/h
7.
A fair die is tossed twice what is the probability of get a sum of at least 10.
1. A.$\frac{5}{36}$
2. B.$\frac{2}{3}$
3. C.$\frac{5}{18}$
4. D.$\frac{1}{6}$
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Answer: D $\frac{1}{6}$
8.
A man will be (x+10)years old in 8years time. If 2years ago he was 63 years., find the value of x
1. A.55
2. B.63
3. C.57
4. D.67
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Answer: B 63
9.
A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.
1. A.r = h
2. B.r = √ $\frac{3h^2}{π}$
3. C.r = πh
4. D.r = h √ $\frac{3}{h}$
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Answer: B r = √ $\frac{3h^2}{π}$
10.
A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of #22,800.00 was paid as import duty, calculate the cost of the engine.
1. A.#60,000.00
2. B.#120,000.00
3. C.#24,000.00
4. D.#18,000.00
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Answer: A #60,000.00
11.
A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. calculate the area of the region not covered by the trapezium. π = $\frac{22}{7}$
1. A.84cm $^2$
2. B.80cm $^2$
3. C.30cm $^2$
4. D.94cm $^2$
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Answer: C 30cm $^2$
12.
consider the statements: P = All students offering Literature(L) also offer History(H); Q = Students offering History(H) do not offer Geography(G). Which of the Venn diagram correctly illustrate the two statements?
1. A.A
2. B.B
3. C.C
4. D.D
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Answer: C C
13.
correct 0.007985 to three significant figures.
1. A.0.0109
2. B.0.0800
3. C.0.00799
4. D.0.008
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Answer: C 0.00799
14.
Factorize 6pq-3rs-3ps+6qr
1. A.3(r -p)(2q + s)
2. B.3(p + r)( 2q - 2q - s)
3. C.3(2q - s)(p + r)
4. D.3(r - p)(s - 2q)
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Answer: C 3(2q - s)(p + r)
15.
Find the 5th term of the sequence 2,5,10,17....?
1. A.22
2. B.24
3. C.36
4. D.26
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Answer: D 26
16.
find the first quartile of 7,8,7,9,11,8,7,9,6 and 8.
1. A.8.5
2. B.7.0
3. C.7.5
4. D.8.0
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Answer: B 7.0
17.
Find The quadratic Equation Whose Roots Are -2q And 5q.
1. A.3x $^2$ + 3qx - 10q $^2$
2. B.x $^2$ + 3qx + 10q $^2$
3. C.x $^2$ - 3qx + 10q $^2$
4. D.x $^2$ - 3qx - 10q $^2$
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Answer: D x $^2$ - 3qx - 10q $^2$
18.
find the value of (x+y)
1. A.215°
2. B.70°
3. C.135°
4. D.145°
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Answer: A 215°
19.
Find, correct to two decimal, the mean of 1 $\frac{1}{2}$ , 2 $\frac{2}{3}$ , 3 $\frac{3}{4}$ , 4 $\frac{4}{5}$ , and 5 $\frac{5}{6}$ .
1. A.3.71
2. B.3.70
3. C.3.69
4. D.3.72
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Answer: A 3.71
20.
For what value of x is $\frac{4 - 2x}{x + 1}$ undefined.
1. A.2
2. B.-1
3. C.1
4. D.-2
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Answer: B -1
21.
From a point T, a man moves 12km due west and then moves 12km due south to another point Q. Calculate the bearing of T from Q.
1. A.225°
2. B.315°
3. C.045°
4. D.135°
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Answer: C 045°
22.
Given that sin x = $\frac{3}{5}$ , 0 ≤ x ≤ 90, evaluate (tan x + 2cosx)
1. A.2 $\frac{11}{20}$
2. B.2 $\frac{7}{20}$
3. C.$\frac{11}{20}$
4. D.$\frac{1}{20}$
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Answer: B 2 $\frac{7}{20}$
23.
If $\frac{2}{x-3}$ - $\frac{3}{x-2}$ = $\frac{p}{(x-3)(x -2)}$ , find p.
1. A.5 - x
2. B.- (x + 5)
3. C.13 - x
4. D.- (5x - 13)
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Answer: A 5 - x
24.
If 16 * 2 $^{(x + 1)}$ = 4 $^x$ * 8 $^{(1 - x)}$ , find the value of x.
1. A.-4
2. B.4
3. C.1
4. D.-1
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Answer: D -1
25.
If 4x+2y=16 and 6x-2y=4 , find the value of (y-x).
1. A.8
2. B.2
3. C.4
4. D.6
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Answer: B 2
26.
If log $_{10}$ 2 = m and log $_{10}$ 3 = n, find log $_{10}$ 24 in terms of m and n.
1. A.3m + n
2. B.m + 3n
3. C.4mn
4. D.3mn
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Answer: A 3m + n
27.
if p = {-3<x<1} and Q = {-1<x<3}, where x is a real number, find P n Q.
1. A.0
2. B.-3, -2, -1, 0 and 1
3. C.-2, -1 and 0
4. D.-1, 0 and 1
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Answer: A 0
28.
if tanθ = $frac{3}{4}$ , 180° < θ < 270°, find the value of cosθ.
1. A.$\frac{4}{5}$
2. B.$\frac{3}{5}$
3. C.- $\frac{4}{5}$
4. D.- $\frac{3}{5}$
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Answer: C - $\frac{4}{5}$
29.
In △LMN, |LM| = 6cm, ∠LNM = x and sin x = sin x = $\frac{3}{5}$ . Find the area of △LMN
1. A.60cm $^2$
2. B.48cm $^2$
3. C.24cm $^2$
4. D.30cm $^2$
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Answer: C 24cm $^2$
30.
In the diagram, $\overline{MP}$ is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | $\overline{RQ}$ | = | $\overline{RN}$ |. Find the angle market t.
1. A.130°
2. B.115°
3. C.58°
4. D.68°
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Answer: C 58°
31.
In the diagram, ∠ABC and ∠BCD are right angles, ∠BAD = t and ∠EDF = 70°. Find the value of t.
1. A.70°
2. B.165°
3. C.140°
4. D.110°
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Answer: D 110°
32.
In the diagram, △XYZ is produced to T. if |XY| = |ZY| and ∠XYT = 40°, find ∠XZT
1. A.110°
2. B.130°
3. C.140°
4. D.180°
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Answer: A 110°
33.
In the diagram, line $\overline{EC}$ is a diameter of the circle ABCDE. If angle ABC equals 158°, find ∠ADE
1. A.112
2. B.90
3. C.68
4. D.22
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Answer: C 68
34.
In the diagram, O is the centre of the circle PQRS, ∠PQR = 72° and OR is parallel to PS. Find ∠ OPS.
1. A.18°
2. B.108°
3. C.54°
4. D.36°
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Answer: D 36°
35.
In the diagram, PQRS is a circle. find the value of x.
1. A.50°
2. B.30°
3. C.80°
4. D.100°
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Answer: A 50°
36.
make u the subject in x = $\frac{2u-3}{3u + 2}$
1. A.u = $\frac{2x + 3}{3x - 2}$
2. B.u = $\frac{2x - 3}{3x - 2}$
3. C.u = $\frac{2x + 3}{2 - 3x}$
4. D.u = $\frac{2x + 3}{3x + 2}$
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Answer: C u = $\frac{2x + 3}{2 - 3x}$
37.
Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?
1. A.3 years
2. B.10 years
3. C.5 years
4. D.15 years
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Answer: C 5 years
38.
Simplify 2√7- $\frac{14}{√7} + \frac{7}{√21}$
1. A.$\frac{√21}{21}$
2. B.7 $\frac{√21}{21}$
3. C.$\frac{√21}{3}$
4. D.3√21
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Answer: C $\frac{√21}{3}$
39.
Simplify: (11 $_{two}$ ) $^2$
1. A.1001 $_2$
2. B.1101 $_2$
3. C.101 $_2$
4. D.10001 $_2$
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Answer: A 1001 $_2$
40.
Solve: 2 $^{\sqrt{2x + 1}}$ = 32
1. A.13
2. B.24
3. C.12
4. D.11
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Answer: C 12
41.
The circumference of a circular track is 9km. A cyclist rides round it a number of times and stops after covering a distance of 302km. How far is the cyclist from the starting point?
1. A.5km
2. B.6km
3. C.7km
4. D.3km
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Answer: A 5km
42.
The diagonal of a rhombus are 12cm and 5cm. calculate its perimeter
1. A.26cm
2. B.24cm
3. C.17cm
4. D.34cm
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Answer: A 26cm
43.
The distance d between two villages east more than 18 KM but not more than 23KM. which of these inequalities represents the statements?
1. A.18 ≤ d ≤ 23
2. B.18 < d < 23
3. C.18 ≤ d < 23
4. D.18 < d ≤ 23
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Answer: D 18 < d ≤ 23
44.
The equation of a line is given as 3 x - 5y = 7. Find its gradient (slope)
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: B $\frac{3}{5}$ .
45.
The height of an equilateral triangle of side is 10 $\sqrt{3}$ cm. Calculate its perimeter.
1. A.20cm
2. B.60cm
3. C.40cm
4. D.30cm
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Answer: B 60cm
46.
The pie chart represents the distribution of fruits on display in the shop if there are 60 apples on display how many oranges are there?
1. A.80
2. B.270
3. C.120
4. D.90
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Answer: D 90
47.
The sum of the interior angles of a regular polygon with k sides is (3k-10) right angles. Find the size of the exterior angle?
1. A.60°
2. B.40°
3. C.90°
4. D.120°
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Answer: A 60°
48.
What number should be subtracted from the sum of 2 $\frac{1}{6}$ and 2 $\frac{7}{12}$ to give 3 $\frac{1}{4}$ ?
1. A.$\frac{1}{3}$
2. B.1 $\frac{1}{2}$
3. C.1 $\frac{1}{6}$
4. D.$\frac{1}{2}$
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Answer: B 1 $\frac{1}{2}$
49.
Which of the following is not an exterior angle of a regular polygon?
1. A.66°
2. B.72°
3. C.24°
4. D.15°
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Answer: A 66°

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Height(cm)	160	161	162	163	164	165
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