WAEC - Mathematics (2019)

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

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

Одговорити
(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.
Одговорити
(C)
H = $\frac{p}{2y^2}$
13
Solve $4x^{2}$ - 16x + 15 = 0.
Одговорити
(B)
x = 1$\frac{1}{2}$ or x = 2$\frac{1}{2}$
14
Simplify: $\log_{10}$ 6 - 3 log$_{10}$ 3 + $\frac{2}{3} \log_{10} 27$
Одговорити
(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.
Одговорити
(B)
10%
16
If 3p = 4q and 9p = 8q - 12, find the value of pq.
Одговорити
(A)
12
17
If (0.25)$^y$ = 32, find the value of y.
Одговорити
(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?
Одговорити
(C)
$\frac{2}{3}$
19
Simplify: $\frac{x^2 - 5x - 14}{x^2 - 9x + 14}$
Одговорити
(D)
$\frac{x + 2}{x - 2}$
20
Which of these values would make $\frac{3p - 1}{p^{2} - p}$ undefined?
Одговорити
(A)
1
21
The total surface area of a solid cylinder 165cm$^2$. Of the base diameter is 7cm, calculate its height. [Take $\pi = \frac{22}{7}$]
Одговорити
(C)
4.0 cm
22
If 2$^{a}$ = $\sqrt{64}$ and $\frac{b}{a}$ = 3, evaluate a$^2 + b^{2}$
Одговорити
(C)
90
23

In XYZ, |YZ| = 32cm, < YXZ 53$^o$ and XZY = 90$^o$. Find, correct to the nearest centimetre, |XZ|
Одговорити
(B)
25 cm
24
If log$_x$ 2 = 0.3, evaluate log$_x$ 8.
Одговорити
(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 $\pi = \frac{22}{7}$]
Одговорити
(C)
4.4 cm
26
Make b the subject of the relation lb = $\frac{1}{2}$ (a + b)h
Одговорити
(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?
Одговорити
(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 $\pi = \frac{22}{7}$]
Одговорити
(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.
Одговорити
(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.
Одговорити
(A)
100$^o$
31
Factorize completely; (2x + 2y)(x - y) + (2x - 2y)(x + y)
Одговорити
(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.
Одговорити
(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?
Одговорити
(D)
$\frac{12}{25}$
34
Find the equation of a straight line passing through the point (1, -5) and having gradient of $\frac{3}{4}$
Одговорити
(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?
Одговорити
(C)
10m
36
If tan x = $\frac{3}{4}$, 0 < x < 90$^o$, evaluate $\frac{\cos x}{2 sin x}$
Одговорити
(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.
Одговорити
(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 $\pi = \frac{22}{7}$]

Одговорити
(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.
Одговорити
(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.
Одговорити
(B)
58$^o$
41
Calculate the variance of 2, 4, 7, 8 and 9
Одговорити
(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.

Одговорити
(C)
19
43

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

In the diagram, PQ is parallel to RS, < QFG = 105$^o$ and < FEG = 50$^o$. Find the value of n
Одговорити
(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?
Одговорити
(C)
$\frac{1}{3}$