WAEC - Mathematics (2020)

1
Evaluate and correct to two decimal places, 75.0785 - 34.624 + 9.83
إجابة
(C)
50.28
2
If X = {x : x < 7} and Y = {y:y is a factor of 24} are subsets of $\mu$ = {1, 2, 3...10} find X $\cap$ Y.
إجابة
(B)
{1, 2, 3, 4, 6}
3
Simplify; [($\frac{16}{9}$)$^{\frac{-3}{2}}$ x 16$^{\frac{-3}{4}}$]$^{\frac{1}{3}}$
إجابة
(C)
$\frac{3}{8}$
4
Express 1 + 2 log10$^3$ in the form log10$^9$
إجابة
(A)
log10$^{90}$
5
If 101$_{\text{two}}$ + 12$_y$ = 23$_{\text{five}}$. Find the value of y
إجابة
(C)
6
6
An amount of N550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x
إجابة
(D)
N500,000.00
7
Given that $\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}$

= x + y$\sqrt{15}$, find the value of (x + y)
إجابة
(C)
1$\frac{1}{5}$
8
If x = 3 and y = -1, evaluate 2(x$^2$ - y$^3$)
إجابة
(C)
20
9
Solve 3x - 2y = 10 and x + 3y = 7 simultaneously
إجابة
(D)
x = 4 and y = 1
10
The implication x $\to$ y is equivalent to?
إجابة
(A)
~ y $\to$ ~ x
11
The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio.
إجابة
(A)
2
12
Solve $\frac{1}{3}$(5 - 3x) < $\frac{2}{5}$(3 - 7x)
إجابة
(D)
x < $\frac{-7}{27}$
13
Make m the subject of the relation k = $\sqrt{\frac{m - y}{m + 1}}$
إجابة
(B)
m = $\frac{y + k^2}{1 - k^2}$
14
Find the quadratic equation whose roots are $\frac{1}{2}$ and -$\frac{1}{3}$
إجابة
(D)
6x$^2$ - x - 1 = 0
15
Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z
إجابة
(A)
x = $\frac{6y}{z}$
16
Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart?
إجابة
(C)
11:00 am
17
A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area.
إجابة
(B)
166 cm$^2$
18
In the diagram, PQ // SR. Find the value of x

إجابة
(B)
46
19
Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3)
إجابة
(C)
y = $\frac{3}{2} x$
20
The expression $\frac{5x + 3}{6x (x + 1)}$ will be undefined when x equals
إجابة
(B)
{0, -1}
21
A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the son's age is y, express the product of their ages in terms of y.
إجابة
(D)
5y$^2 + 24y - 324 = 0$
22
Simplify; $\frac{a}{b} - \frac{b}{a} - \frac{c}{b}$
إجابة
(D)
$\frac{a^2 - b^2 - ac}{ab}$
23

In the diagram, XYZ is an equilateral triangle of side 6cm and Y is the midpoint of $\overline{XY}$. Find tan (< XZT)
إجابة
(A)
$\frac{1}{\sqrt{3}}$
24
A fence 2.4 m tall, is 10m away from a tree of height 16m. Calculate the angle of elevation of the top of the tree from the top of the fence.
إجابة
(B)
53.67$^o$
25
Fati buys milk at ₦x per tin sells each at a profit of ₦y. If she sells 10 tins of milk, how much does she receives from the sales?
إجابة
(D)
₦10(x + y)
26
If tan y is positive and sin y is negative, in which quadrant would y lie?
إجابة
(C)
Third only
27
The dimension of a rectangular base of a right pyramid is 9 cm by 5cm. If the volume of the pyramid is 105 cm$^3$, how high is the pyramid?
إجابة
(D)
7cm
28
Each interior angle of a regular polygon is 168$^o$. Find the number of sides of the polygon
إجابة
(A)
30
29

In the diagram, $\overline{MN}$//$\overline{PQ}$, < MNP = 2x, and < NPQ = (3x - 50)°. Find the value of < NPQ
إجابة
(B)
100$^o$
30
The length of an arc of a circle of radius 3.5 cm is 1$\frac{19}{36}$ cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take $\pi = \frac{22}{7}$]
إجابة
(C)
25$^o$
31

In the diagram, $\overline{PU}$/$\overline{SR}$, $\overline{PS}$/$\overline{TR}$, $\overline{QS}$/$\overline{UR}$, $\overline{UR}$ = 15cm, $\overline{SR}$ = 8 cm, $\overline{PS}$ = 10 cm and area of △SUR = 24 cm$^2$. Calculate the area of PTRS.
إجابة
(C)
80 cm$^2$
32

In the diagram, PQR is a circle with center O. If ∠OPQ = 48°, find the value of M.

إجابة
(A)
96$^o$
33

The pie chart shows the population of men, women, and children in a city. If the population of the city is 1,800,000, how many men are in the city?
إجابة
(C)
355,000
34
The mean of the numbers 15, 21, 17, 26, 18, and 29 is 21. Calculate the standard deviation
إجابة
(C)
5
35
Find the sum of the interior angle of a pentagon.
إجابة
(C)
540$^o$
36
The diameter of a sphere is 12 cm. Calculate, correct of the nearest cm$^3$, the volume of the sphere, [Take $\pi = \frac{22}{7}$]
إجابة
(C)
905 cm$^3$
37
A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If a ball is selected at random from the box, what is the probability that it is green?
إجابة
(D)
$\frac{1}{4}$
38
A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If two balls are selected at random one after the other with replacement, what is the probability that both are red?
إجابة
(A)
$\frac{25}{144}$
39

In the diagram, PQ is a straight line. If m = $\frac{1}{2}$ (x + y + z), find value of m.
إجابة
(B)
60$^o$
40

x 6.20 6.85 7.50

y 3.90 5.20 6.50

The points on a linear graph are as shown in the table. Find the gradient (slope) of the line.
إجابة
(B)
2
41

In the diagram, O is the center of the circle. $\overline{PQ}$ and $\overline{RS}$ are tangents to the circle. Find the value of (M + N).
إجابة
(B)
90$^o$
42
Which of the following is not a sufficient condition for two triangles to be congruent?
إجابة
(D)
SSA
43
A woman received a discount of 20% on a piece of cloth she purchased from a shop. If she paid $525.00, what was the original price?
إجابة
(C)
$656.25
44
The interquartile range of distribution is 7. If the 25th percentile is 16, find the upper quartile.
إجابة
(C)
23
45

The graph of the equations y = 2x + 5 and y = 2x$^2$ + x - 1 are shown. Use the information above to answer this question.

Find the point of intersection of the two graphs.
إجابة
(A)
(2.0, 9.0) and (-1.5, 2.0)

x	6.20	6.85	7.50
y	3.90	5.20	6.50