WAEC - Mathematics (2019)

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

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

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

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

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

پاسخ دهید
(C)
19
43

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

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