WAEC - Mathematics (2022)

1
Evaluate, correct to four significant figures, (573.06 x 184.25).
Svar
(A)
105600.00
2
Change 432$_{five}$ to a number in base three.
Svar
(B)
11100$_{three}$
3
Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).
Svar
(B)
17
4
If √24 + √96 - √600 = y√6, find the value of y
Svar
(D)
-4
5
Evaluate 23 x 54 (mod 7)
Svar
(B)
3
6
If 4$^{3x}$ = 16$^{x+1}$, find the value of x
Svar
(A)
2
7
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.
Svar
(B)
140%
8
Find the 17term of the Arithmetic Progression (A.P):-6,-1,4
Svar
(C)
74
9
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.
Svar
(A)
$\frac{3n}{2p^2}$
10
If a = 3 and b = -7, find the value of $\frac{5b+(a+b)^2}{(a-b)^2}$
Svar
(C)
-0.19
11
Three boys shared D 10,500.00 in the ratio 6:7:8. Find the largest share.
Svar
(A)
4000
12
The length of a piece of stick is 1.75 m. A boy measured it as 1.80 m. Find the percentage error
Svar
(B)
2$\frac{6}{7}$
13
If 5x + 3y=4 and 5x-3y= 2, what is the value of (25x$^2$ -9y$^2$)?
Svar
(D)
8
14
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?
Svar
(D)
$(2x+2)
15
Consider the statements:

p: Stephen is intelligent

q: Stephen is good at Mathematics

If p⇒q, which of the following is a valid conclusion?

Svar
(B)
If Stephen is not good at Mathematics, then he is not intelligent
16
What value of p will make (x$^2$ - 4x + p) a perfect square?
Svar
(C)
4
17
.Find the value of x such that $\frac{1}{x}$ +$\frac{4}{3x}$ - $\frac{5}{6x}$ + 1 = 0
Svar
(C)
$\frac{-3}{2}$
18
Make t the subject of k = $m \sqrt \frac{t-p}{r}$
Svar
(B)
$\frac{k^2r + pm^2}{m^2}$
19
An exterior angle of a regular polygon is 22.5°. Find the number of sides.
Svar
(D)
16
20

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?
Svar
(A)
11cm
21

Find the area of the sector OPSQ
Svar
(D)
32.34cm$^2$
22
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?
Svar
(C)
4.792m
23
A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area
Svar
(D)
214.5cm$^2$
24

In the diagram, ∠ZWZY and WYX are right angles. Find the perimeter of WXYZ.
Svar
(B)
32cm
25

The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area
Svar
(B)
40cm$^2$
26
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.
Svar
(B)
47º
27
Given that sin (5x-28)° = cos (3x-50)", 0°≤ x ≤ 90°, find the value of x.
Svar
(B)
32
28

In the diagram, MNR is a tangent to the circle centre O at N and ∠NOS = 108°. Find ∠OSN
Svar
(C)
36°
29

Find ∠OSN
Svar
(A)
36º
30
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?
Svar
(C)
$\frac{1}{8}$
31
The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.
Svar
(B)
65
32
Simplify $\frac{2-18m^2}{1+3m}$
Svar
(B)
2[1-3m]
33

In the diagram, triangle MNR is inscribed in circle MNR, and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR

Svar
(B)
80º
34
Solve $\frac{y+2}{4}$ - $\frac{y-1}{3}$ > 1
Svar
(B)
y < -2
35
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
Svar
(C)
15
36
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
Svar
(C)
34.45
37
Find the correct to two decimal places, the volume of a sphere whose radius is 3cm. [Take π = $\frac{22}{7}$]
Svar
(D)
113.14cm$^3$
38
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.
Svar
(C)
10cm
39
Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]
Svar
(D)
154cm$^3$
40
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?
Svar
(C)
0.85
41
A rectangle with width $\frac{3}{4}$cm and area 3 $\frac{3}{8}$cm$^2$. Find the length
Svar
(B)
4$\frac{1}{2}$cm
42
The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y
Svar
(C)
6
43
The straight line y = mx - 4 passes through the point(-4,16). Calculate the gradient of the line
Svar
(A)
-5
44
If the equations x$^2$ - 5x + 6 = 0 and x$^2$ + px + 6 = 0 have the same roots, find the value of p.
Svar
(C)
-5
45
A trader made a loss of 15% when an article was sold. Find the ratio of the selling price : cost price
Svar
(C)
17:20