WAEC - Mathematics (2019)

1
Express, correct to three significant figures, 0.003597.
إجابة
(C)
0.00360
2
Evaluate: (0.064)$^{-\frac{1}{3}}$

إجابة
(A)
$\frac{5}{2}$
3
Solve: $\frac{y + 1}{2} - \frac{2y - 1}{3}$ = 4
إجابة
(B)
y = -19
4
Simplify, correct to three significant figures, (27.63)$^2$ - (12.37)$^2$
إجابة
(D)
610
5
If 7 + y = 4 (mod 8), find the least value of y, 10 $\leq y \leq 30$
إجابة
(B)
13
6
If T = {prime numbers} and M = {odd numbers} are subsets of $\mu$ = {x : 0 < x ≤ 10} and x is an integer, find (T$^{\prime}$ n M$^{\prime}$).
إجابة
(A)
{4, 6, 8, 10}
7
Evaluate; $\frac{\log_3 9 - \log_2 8}{\log_3 9}$
إجابة
(D)
-$\frac{1}{2}$
8
If 23$_y$ = 1111$_{\text{two}}$, find the value of y
إجابة
(C)
6
9
If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.
إجابة
(B)
10
10
Evaluate: 2$\sqrt{28} - 3\sqrt{50} + \sqrt{72}$
إجابة
(C)
4$\sqrt{7} - 9 \sqrt{2}$
11
If m : n = 2 : 1, evaluate $\frac{3m^2 - 2n^2}{m^2 + mn}$

إجابة
(B)
$\frac{5}{3}$
12
H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.
إجابة
(C)
H = $\frac{p}{2y^2}$
13
Solve $4x^{2}$ - 16x + 15 = 0.
إجابة
(B)
x = 1$\frac{1}{2}$ or x = 2$\frac{1}{2}$
14
Simplify: $\log_{10}$ 6 - 3 log$_{10}$ 3 + $\frac{2}{3} \log_{10} 27$
إجابة
(B)
$\log_{10}^2$
15
Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00.
إجابة
(B)
10%
16
If 3p = 4q and 9p = 8q - 12, find the value of pq.
إجابة
(A)
12
17
If (0.25)$^y$ = 32, find the value of y.
إجابة
(A)
y = - $\frac{5}{2}$
18
There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
إجابة
(C)
$\frac{2}{3}$
19
Simplify: $\frac{x^2 - 5x - 14}{x^2 - 9x + 14}$
إجابة
(D)
$\frac{x + 2}{x - 2}$
20
Which of these values would make $\frac{3p - 1}{p^{2} - p}$ undefined?
إجابة
(A)
1
21
The total surface area of a solid cylinder 165cm$^2$. Of the base diameter is 7cm, calculate its height. [Take $\pi = \frac{22}{7}$]
إجابة
(C)
4.0 cm
22
If 2$^{a}$ = $\sqrt{64}$ and $\frac{b}{a}$ = 3, evaluate a$^2 + b^{2}$
إجابة
(C)
90
23

In XYZ, |YZ| = 32cm, < YXZ 53$^o$ and XZY = 90$^o$. Find, correct to the nearest centimetre, |XZ|
إجابة
(B)
25 cm
24
If log$_x$ 2 = 0.3, evaluate log$_x$ 8.
إجابة
(C)
0.9
25
An arc subtends an angle of 72$^o$ at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take $\pi = \frac{22}{7}$]
إجابة
(C)
4.4 cm
26
Make b the subject of the relation lb = $\frac{1}{2}$ (a + b)h
إجابة
(A)
$\frac{ah}{2l - h}$
27
Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?
إجابة
(B)
$128,000.00
28
Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm. [Take $\pi = \frac{22}{7}$]
إجابة
(B)
84$^o$
29
A rectangular board has a length of 15cm and width x cm. If its sides are doubled, find its new area.
إجابة
(A)
60x cm$^2$
30

In the diagram, POS and ROT are straight lines. OPQR is a parallelogram, |OS| = |OT| and ∠OST = 50°. Calculate the value of ∠OPQ.
إجابة
(A)
100$^o$
31
Factorize completely; (2x + 2y)(x - y) + (2x - 2y)(x + y)
إجابة
(A)
4(x - y)(x + y)
32
The interior angles of a polygon are 3x$^o$, 2x$^o$, 4x$^o$, 3x$^o$ and 6x$^o$. Find the size of the smallest angle of the polygon.
إجابة
(B)
60$^o$
33
A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?
إجابة
(D)
$\frac{12}{25}$
34
Find the equation of a straight line passing through the point (1, -5) and having gradient of $\frac{3}{4}$
إجابة
(D)
3x - 4y - 23 = 0
35
The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8m above the ground. How long is the ladder?
إجابة
(C)
10m
36
If tan x = $\frac{3}{4}$, 0 < x < 90$^o$, evaluate $\frac{\cos x}{2 sin x}$
إجابة
(D)
$\frac{2}{3}$
37
From the top of a vertical cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
إجابة
(D)
15$^o$
38

In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70$^o$, calculate the length of arc ZY. [Take $\pi = \frac{22}{7}$]

إجابة
(C)
44 cm
39

In the diagram, RT is a tangent to the circle at R, < PQR = 70$^o$, < QRT = 52$^o$, < QSR and < PRQ = x. Find the value of y.
إجابة
(C)
52$^o$
40

In the diagram, RT is a tangent to the circle at R, < PQR = 70$^o$, < QRT = 52$^o$, < QSR and < PRQ = x. Calculate the value of x.
إجابة
(B)
58$^o$
41
Calculate the variance of 2, 4, 7, 8 and 9
إجابة
(B)
6.8
42
The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.

إجابة
(C)
19
43

In the diagram, PQ is parallel to RS, < QFG = 105$^o$ and < FEG = 50$^o$. Find the value of m.
إجابة
(D)
55$^o$
44

In the diagram, PQ is parallel to RS, < QFG = 105$^o$ and < FEG = 50$^o$. Find the value of n
إجابة
(C)
75$^o$
45
A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?
إجابة
(C)
$\frac{1}{3}$