WAEC 2023 Mathematics | Essay

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Question 1
A car travels a distance of 112 km at an average speed of \( 70 \mathrm{~km} / \mathrm{h} \). It then travels further for 60 km at an average speed of \( 50 \mathrm{~km} / \mathrm{h} \). Calculate, the entire journey, the total time taken.
Question Parts
(a)
If \( \frac{x}{y}=2 \) and \( \frac{y}{z}=3 \), find the value of \( \frac{x+y}{y+z} \)
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Question 2
In a football match, the tickets for children and adults were sold at D 3.00 and \( D 5.00 \) respectively. If 400 people attended the football match and \( D 1,700.00 \) was collected in ticket sales,
Question Parts
(a)
How many tickets were sold to adults?
(b)
Mr. Sonko sold 250 tickets. If 175 of the tickets were for adults, how much sales did he make altogether?
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Question 3
In the diagram, \( P Q R \) is an equilibrium triangle of side \( 18 \mathrm{~cm} \). M is the midpoint of \( \overline{Q R} \). An arc of a circle with centre \( P \), touches \( \overline{Q R} \) at \( M \) and meets \( \overline{P Q} \) at \( A \) and \( \overline{P R} \) at \( B \). Calculate, the correct to two decimal places, the area of the shaded region. \( \left[\right. \) Take \( \left.\pi=\frac{22}{7}\right] \)
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Question 4
In the diagram, \( P, Q, R \) and \( S \) are points on the circle centre \( K \). \( \overline{K R} \) is a bisector of \( \angle S R Q, \angle K S P=41^{\circ} \) and \( \angle S K R= 80^{\circ} \). Find:
Question Parts
(a)
\( \angle R Q P \);
(b)
\( \angle S P Q \).
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Question 5
A boy stands at a point \( M \) on the same horizontal level as the foot, \( T \), of a vertical building. He observes an object on the top, \( P \) of the building at angle of elevation of \( 66^{\circ} \). He moves directly backwards to a new point \( C \) and observes the same object at an angle of elevation of \( 53^{\circ} \). If \( |\overline{M T}|=50 \mathrm{~m} \),
Question Parts
(a)
illustrate the information in a diagram;
(b)
calculate, correct to one decimal place:
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Question 6
\( M=\{n: 2 n-3 \leq 37\} \), where \( n \) is a counting number.
Question Parts
(a)
(i) Write down all the elements in \( M \).
(ii)
If a number is selected at random from \( M \), what is the probability that it is a;
(b)
A shop owner gave an end-of-year bonus to two of his attendants, Kontor and Gapson in the ratio of their ages. Kontor's age is one and half times that of Kontor who is 20 years old. If Kontor received Le 200,000.00, find:
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Question 7
Question Parts
(a)
The sum of three numbers is 81. The second number is twice the first. Given that the third number is 6 more than the second, find the numbers.
(b)
Given the points P(3, 5) and Q(-5, 7) on the cartesian plane such that R(x, y) is the midpoint of \( \overline{PQ} \), find the equation of the line that passes through R and perpendicular to \( \overline{PQ} \).
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Question 8
\( \begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & 17 & & & -4 & & & \\ \hline \end{array} \)
Question Parts
(a)
Copy and complete the table of values for \( y=2 x^{2}-x-4 \) for \( -3 \leq x \leq 3 \).
(b)
Using a scale of 2 cm to 1 unit on the \( x \)-axis and 2 cm to 2 units on the \( y \)-axis, draw the graph of \( y=2 x^{2}-x-4 \) for \( -3 \leq x \leq 3 \).
(c)
Use the graph to find the;
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Question 9
\( \begin{array}{|l|c|c|c|c|c|c|} \hline \text{Height } (m) & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text{Number of trees} & 4 & 6 & 4 & 5 & 6 & 2 \\ \hline \end{array} \) The table shows the height of teak trees harvested by a farmer.
Question Parts
(a)
Find the median height.
(b)
Calculate, correct to one decimal place, the;
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Question 10
In a town, Chief \( X \) resides \( 60 m \) away on a bearing of \( 057^{\circ} \) from the palace \( P \) while Chief \( Y \) resides on a bearing \( 150^{\circ} \) from the same palace \( P \). The residence of \( X \) and \( Y \) are \( 180 m \) apart.
Question Parts
(a)
Illustrate the information in a diagram.
(b)
Find, correct to three significant figures, the;
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Question 11
Question Parts
(a)
Two regular polygons \( P \) and \( Q \) such that the number of sides of \( P \) is twice the number of sides of \( Q \). The difference between the exterior angle of \( Q \) and \( P \) is \( 45^{\circ} \). Find the number of sides of \( P \).
(b)
The area of a semi-circle is \( 32 \pi \mathrm{~cm}^{2} \). Find, in terms of \( \pi \), the circumference of the semi-circle.
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Question 12
Question Parts
(a)
In the diagram, \( P, Q, R \) and \( S \) are points on the circle with centre \( O \). \( \overline{Q R} \parallel \overline{O S} \), \( \angle Q O R=2 m, \angle Q P R=n \) and \( \angle S O R= 54^{\circ} \). Find the values of \( m \) and \( n \).
(b)
The length of a rectangle is 4 cm more than the width. If the perimeter is 40 \( cm \), find the area.
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Question 13
Question Parts
(a)
In the diagram, the radius of the sector of circle centre \( O \), is 7 cm and \( \angle M O N \) is \( 60^{\circ} \). Find, correct to one decimal place, the area of the shaded portion. Take \( \left.\pi=\frac{22}{7}\right] \)
(b)
The \( x \) and \( y \) intercepts of a straight line are \( -\frac{3}{4} \) and \( \frac{2}{7} \) respectively. Find the equation of the line.
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