WAEC 2021 Mathematics | Essay

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Question 1
Mr Sarfo borrowed $ 25,000.00 from AFIAK Financial Services at 21 % simple interest per annum for 3 years. If he was able to pay back the loan in 2 years at equal yearly instalments, how much did he pay each year?
Question Parts
(a)
Two consecutive numbers are such that the sum of thrice the smaller and twice the larger is 17. Find, correct to three significant figures, the smaller number as a percentage of the sum of the two numbers.
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Question 2
A man left town M at 10:00 a.m. and travelled by car to town N at an average speed of 72 km/h. He spent 2 hours for a meeting and returned to town M by bus at an average speed of 40 km/h. If the distance covered by the bus was 2 km longer than that of the car and he arrived at town M at 1:55 p.m., calculate the distance from M to N.
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Question 3
The points X, Y and Z are located such that Y is 15 km south of X, Z is 20 km from X on a bearing of 270°. Calculate, correct to:
Question Parts
(a)
|Y Z|;
(b)
the nearest degree, the bearing of Y from Z.
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Question 4
In the diagram, AD is a diameter of a circle with centre Q. If ABD is a triangle in a semi-circle and ∠OAB= 34°, find:
Question Parts
(a)
∠OBD;
(b)
∠OCB.
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Question 5
A man shared his property among his children as follows: Represent the information on a pie chart.
Question Parts
(a)
A box contains 5 red, 3 green and 4 blue identical beads. Calculate the probability that a girl takes away two red beads, one after the other, from the box.
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Question 6
In a class of 80 students, \( \frac{3}{4} \) study Biology and \( \frac{3}{5} \) study Physics. If each student studies at least one of the subjects:
Question Parts
(i)
draw a Venn diagram to represent this information;
(ii)
how many students study both subjects;
(iii)
find the fraction of the class that study Biology but not Physics.
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Question 7
Johnson and Jocatol Ltd. owned a business office with floor measuring 15 m by 8 m which was to be carpeted. The cost of carpeting was GH¢ 890.00 per square metre. If a total of GH¢ 216,120.00 was spent on painting and carpeting, how much was the cost of painting?
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Question 8
Copy and complete the table of values for the relation \( y=2x^{2}-x-2 \) for \( -4 \leq x \leq 4 \).
Question Parts
(a)
Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of \( y=2x^{2}-x-2 \) for \( -4 \leq x \leq 4 \).
(b)
On the same axes, draw the graph of \( y=2x+3 \).
(c)
Use the graph to find the:
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Question 9
In \( \triangle PQR, \angle PQR=90^{ extcirc} \). If the area is \( 216 \mathrm{~cm}^{2} \) and \( |\overline{PQ}|:|\overline{PR}| \) is 3:4, find \( |\overline{PR}| \).
Question Parts
(a)
The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?
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Question 10
In the diagram, PORS is a trapezium with \( \overline{QR} // \overline{PS} \). U and T are points on \( \overline{PS} \) such that \( |\overline{PU}|=5 \mathrm{~cm},|\overline{QU}|= 12 \mathrm{~cm} \) and \( \angle PUQ=\angle STR=90^{ extcirc} \). If the area of \( \triangle PQR=20 \mathrm{~cm}^{2} \), calculate, correct to the nearest whole number, the: (a) perimeter; (b) area; of the trapezium.
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Question 11
A cottage is on a bearing of 200° and 110° from Dogbe's and Manu's farms respectively. If Dogbe walked 5 km and Manu 3 km from the cottage to their farms, find, correct to:
Question Parts
(i)
two significant figures, the distance between the two farms;
(ii)
the nearest degree, the bearing of Manu's farm from Dogbe's.
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Question 12
The table shows the distribution of the number of hours per day spent in studying by 50 students. Calculate, correct to two decimal places, the: (a) mean, (b) standard deviation.
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Question 13
In the diagram, PORS is a circle. \( |\overline{PQ}|=|\overline{PQ}|, \angle SPR=26^{ extcirc} \) and the interior angles of \( \triangle PQS \) are in the ratio 2:3:3. Calculate:
Question Parts
(i)
∠POR;
(ii)
∠RPQ;
(iii)
∠PQR.
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