Exam Body

Year

Subject

Paper Type

WAEC 2021 Mathematics | Essay

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Question 1 View Details

Question Parts

(a)

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?

(b)

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 View Details

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 View Details

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)

two significant figures |Y Z|;

(b)

the nearest degree, the bearing of Y from Z.

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Question 4 View Details

In the diagram, AD is a diameter of a circle with centre O. 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 View Details

Question Parts

(a)

A man shared his property among his children as follows: $ \begin{array}{|l|c|c|c|c|c|} \hline \text{Child's name} & \text{Ann} & \text{Afia} & \text{Kojo} & \text{Nuno} & \text{Akosua} \\ \hline \text{Percentage share} & 5 & 15 & 10 & 45 & 25 \\ \hline \end{array} $ Represent the information on a pie chart.

(b)

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 View Details

(a) 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.

(b)

Johnson and Jocatol Ltd. owned a business office with floor measuring $15\text{ m} $ by $8\text{ m}$ which was to be carpeted. The cost of carpeting was $\text{GH¢}\ 890.00$ per square metre. If a total of $\text{GH¢}\ 216,120.00$ was spent on painting and carpeting, how much was the cost of painting?

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Question 7 View Details

Question Parts

(a)

Copy and complete the table of values for the relation $ y=2 x^{2}-x-2 $ for $ -4 \leq x \leq 4 $.$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & & 19 & & & -2 & & & & 26 \\ \hline\end{array}$

(b)

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=2 x^{2}-x-2 $ for $ -4 \leq x \leq 4 $.

(c)

On the same axes, draw the graph of $ y=2 x+3 $.

(d)

Use the graph to find the: (i) roots of the equation $ 2 x^{2}-3 x-5=0 $

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Question 8 View Details

Question Parts

(a)

In $ \triangle PQR, \angle PQR=90^{\circ} $. If the area is $ 216 \mathrm{~cm}^{2} $ and $ |\overline{PQ}|:|\overline{PR}| $ is 3:4, find $ |\overline{PR}| $.

(b)

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 9 View Details

In the diagram, PQRS 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^{\circ} $. If the area of $ \triangle PQR=20 \mathrm{~cm}^{2} $, calculate, correct to the nearest whole number, the:

Question Parts

(a)

perimeter;

(b)

area; of the trapezium.

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Question 10 View Details

(a) 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.

(b)

A ladder $ 10 m $ long leaned against a vertical wall $ x m $ high. The distance between the wall and the foot of the ladder is 2 m longer than the height of the wall. Calculate the value of $ x $.

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Question 11 View Details

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:

Question Parts

(a)

mean

(b)

standard deviation.

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Question 12 View Details

In the diagram, PQRS is a circle. $ |\overline{PQ}|=|\overline{QS}|, \angle SPR=26^{\circ} $ and the interior angles of $ \triangle PQS $ are in the ratio 2:3:3. Calculate:

Question Parts

(i)

∠PQR;

(ii)

∠RPQ;

(iii)

∠PRQ.

(b)

The coordinates of two points P and Q in a plane are (7,3) and (5,x) respectively, where x is a real number. If |PQ|=√29 units, find the value of x.

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Question 13 View Details

Question Parts

(a)

On Sam's first birthday celebration, his grandfather deposited an amount of $ \$ 1,000.00 $ in a bank compounded at $ 4 \% $ interest annually. Find how much is in the account if Sam is 4 years old.

(b)

In the diagram, $ A B C D $ are points on the circle centre O. If $ |\overline{A B}|=|\overline{B C}| $ and $ \angle A D C=50^{\circ} $, find $ \angle B A D $.

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