Exam Body

Year

Subject

Paper Type

WAEC 2022 Mathematics | Essay

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Question 1

Question Parts

(a)

Given that $ (7-2 x), 9,(5 x+17) $ are consecutive terms of a Geometric Progression (G.P.) with common ratio, $ r $ > 0, find the values of $ x $.

(b)

Two positive numbers are in the ratio 3:4. The sum of thrice the first number and twice the second is 68. Find the smaller number.

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Question 2

Question Parts

(a)

Given that $ y=\left(\frac{p r}{m}-p^{2} r\right)^{\frac{-3}{2}} $, make $ r $ the subject.

(b)

Find the value of $ r $ when $ y=-8, m=1 $ and $ p=3 $.

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Question 3

A chord subtends an angle of $ 72^{\circ} $ at the centre of a circle of radius 24.5 m. Calculate the perimeter of the minor segment. $ \left[\right. $ Take $ \left.\pi=\frac{22}{7}\right] $.

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Question 4

In the diagram, $ B C D E $ is a circle with centre $ A $. $ \angle B C D=(2 x+40)^{\circ}, \angle B A D =(5 + x35)^{\circ}, \angle B E D=(2 y+10)^{\circ} $ and $ \angle A D C=40^{\circ} $, find:

Question Parts

(a)

the values of $ x $ and $ y $.

(b)

$ \angle A B C $.

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Question 5

Question Parts

(a)

Given that $ m=\tan 30^{\circ} $ and $ n=\tan 45^{\circ} $, simplify, without using calculator; $ \frac{m-n}{m n} $, leaving the answer in the form $ p+\sqrt{q} $.

(b)

There are 20 women in a bus. 15 of them wear glasses and 10 wear wrist watches. If a woman is chosen at random from the bus, find the probability that she wears both glasses and wrist watch.

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Question 6

The graph shows the relation of the Form $ y=m x^{2}+m x+r $, where $ m, n $ and $ r $ are constants. Using the graph:

Question Parts

(a)

state the scale used on both axes;

(b)

find the values of $ m, n $ and $ r $;

(c)

find the gradient of the line through P and Q;

(d)

state the range of values of $ x $ for which $ y>0 $.

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Question 7

Question Parts

(a)

A man purchased 180 copies of a book at N 250.00 each. He sold $ y $ copies at N300.00 each and the rest at a discount of 5 kobo in the Naira of the cost price. If he made a profit of $ \mathrm{N} 7,125.00 $, find the value of $ y $.

(b)

A trader bought $ x $ bags of rice at a cost, $ c=24 x+103 $ and sold them at a price, $ s=33 x-\frac{x^{2}}{20} $.

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Question 8

$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text{Item} & \text{Food and drinks} & \text{Fuel} & \text{Rent} & \text{Building Project} & \text{Education} & \text{Savings} \\ \hline \text{Percentage } (\%) & 35 & 7.5 & 10 & 15 & 17.5 & x \\ \hline \end{array} $ The table shows the monthly expenditure (in percentage) of Mr. Okafor's salary.

Question Parts

(a)

Calculate the percentage of Okafor's salary that was put into savings.

(b)

Illustrate the information on a pie chart.

(c)

If Mr. Okafor's annual gross salary is $28,800.00 and he pays tax of 12%, calculate:

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Question 9

Question Parts

(a)

Copy and complete the table of values for $ y=3 \sin x+7 \cos x $ for $ \theta^{\circ}<x< 180^{\circ} $ $ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 0^\circ & 20^\circ & 40^\circ & 60^\circ & 80^\circ & 100^\circ & 120^\circ & 140^\circ & 160^\circ & 180^\circ \\ \hline y & 7.0 & & & & 4.2 & & -0.9 & & & \\ \hline \end{array} $.

(b)

Using a scale of 2 cm to $ 20^{\circ} $ on the $ x $-axis and $ 2 cm $ to 2 unit on the $ y $-axis, draw the graph of $ y=3 \sin x+7 \cos x $ for $ 0<x<180^{\circ} $.

(c)

Using the graph, find the:

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Question 10

$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Age (years)} & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text{Number of Children} & 2 & 6 & 5 & x & 6 & 9 & 8 & 5 \\ \hline \end{array} $ The table shows the distribution of ages of a number of children in a school. If the mean of the distribution is 7, find the:

Question Parts

(a)

value of $ x $;

(b)

standard deviation of their ages.

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Question 11

Question Parts

(a)

The exterior angles of a polygon are $ 42^{\circ}, 38^{\circ}, 57^{\circ}, x^{\circ},(x+y)^{\circ},(2 x-15)^{\circ} $ and $ (3 x-y)^{\mathrm{c}} $. If $ x $ is $ 7^{\mathrm{o}} $ less than $ y $, find the values of $ x $ and $ y $.

(b)

In the diagram, $ O $ is the centre of the circle $ X Y Z, \angle Z X O=34^{\circ} $ and $ \angle X O Y= 146^{\circ} $. Find $ \angle O Y Z $.

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Question 12

Question Parts

(a)

The probability that an athlete will not win any of the three races is $ \frac{1}{4} $. If the athlete runs in all the races, what is the probability that the athlete will win:$ (i) $ only the second race;

(ii)

All the three races;

(iii)

Only two of the races?

(c)

A cone with perpendicular height 24 cm has a volume of $ 1200 \mathrm{~cm}^{3} $. Find the volume of a cone with same base radius and height 84 cm. [Take $ \pi=22 / 7 $].

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Question 13

Question Parts

(a)

The diameter of a cylinder closed at both ends is 7 cm. If the total surface area is $ 209 \mathrm{~cm}^{2} $, calculate the height. [Take $ \pi=22 / 7 $ ].

(b)

The points $ X $ and $ Y, 19 \mathrm{~m} $ apart are on the same side of a tree. The angles of elevation of the top, $ T $, of the tree from $ X $ and $ Y $ on the horizontal ground with the foot of the tree are $ 43^{\circ} $ and $ 38^{\circ} $ respectively; $ (i) $ Illustrate the information in a diagram.

(ii)

Find correct to one decimal place, the height of the tree.

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