Core Mathematics 2023 - WASSCE

WASSCE CORE MATHEMATICS

Question 1

A point on the ground is 5 m away from the foot of a vertical wall 12 m high. Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall.

Question 2

The gradient of the line passing through the points (3, 6) and (x, 4) is (-\frac{2}{5}). Find the value of x.

Question 3

A woman pours 85 litres of kerosene into a cylindrical container with radius 7 cm. Calculate, correct to the nearest cm, the depth of the kerosene in the container. [\text{Take } \pi = \frac{22}{7}]

Question 4

Given that (x^2 - 11x + m) is a perfect square, find the value of m.

Question 5

The sides of a scalene triangle are 4 cm, 9 cm and 11 cm. Calculate, correct to the nearest whole number, the area of the triangle.

Question 6

In a hall, there are 175 persons. 12% are children, 56 are men and the rest are women. If one person is selected at random from the hall, find the probability that a woman is selected.

Question 7

A student measured the length of a classroom and obtained 3.99 m which is less than the actual length. If the percentage error was 5%, what was the actual length?

Question 8

A car covers the first 80 km of a journey in 2 hours and completes the journey by travelling further 2.5 hours at 50 km/h. What is the average speed of the entire journey?

Question 9

If (\log x = 2 - 3\log 2), find the value of x.

Question 10

The graph of (y = x^2 - 5x + k) passes through the point (3, 1). Find the value of k.

Question 11

Diagram will be provided Find the value of x in the diagram.

Question 12

Diagram will be provided In the diagram, (p + q = 250^\circ). Find the angle marked s.

Question 13

If (x : y : z = 2 : 3 : 4), evaluate (\dfrac{9x + 3y}{6z - 2y}).

Question 14

Find the mean of ((x + y)), ((2x + 3y)), ((2x - 2y)) and ((3x - 2y)).

Question 15

A box contains 2 red, 6 white and 5 black balls, all of the same size. If a ball is selected at random, what is the probability that it is black?

Question 16

Diagram will be provided In the diagram, MNPQ is a circle, centre O. (\angle MQN = 43^\circ) and (\angle QNP = 57^\circ). Find the value of y.

Question 17

Diagram will be provided Describe the locus, l in the diagram.

Question 18

The base radius and slant height of a solid cone are 8 cm and 14 cm respectively. Calculate, correct to two decimal places, its volume. [\text{Take } \pi = \frac{22}{7}]

Question 19

Abudu can do a piece of work in 6 days and Efah can do the same work in 3 days. What fraction of the work can both do together in a day?

Question 20

If (P = {x: 1 \le x \le 6}) and (Q = {x: 2 < x < 9}) where (x \in R), find (P \cap Q).

Question 21

Given that (p^2 + q^2 + r^2 = 50), (p = 5) and (\sqrt{q} = 2), find the positive value of r.

Question 22

If (\frac{1}{2}) and -3 are the roots of (px^2 + qx + r = 0), find the values of p, q and r.

Question 23

A cylindrical container closed at both ends has radius 5 cm and height 10 cm. Calculate to two decimal places, the total surface area. [\text{Take } \pi = \frac{22}{7}]

Question 24

Badu is four times as old as Juliet. In 10 years Badu will be twice as old as Juliet. Find Juliet's age.

Question 25

When the point (4, 5) is rotated through an angle in the anticlockwise direction about the origin, its image is (-5, 4). What is the angle of rotation?

Question 26

Diagram will be provided Find the value of x in the diagram.

Question 27

A woman bought a washing machine for USD 18,000.00. If the exchange rate is USD 0.045 to ₦1.00, find in ₦, the cost of the machine.

Question 28

Determine the least value of x such that (7 + x \equiv 3 \pmod{8}).

Question 29

If (\dfrac{4m + 3n}{4m - 3n} = \frac{5}{2}), find the ratio of m : n.

Question 30

Yakubu received (12\frac{1}{2}%) of the sales made in a certain mouth. If the amount he received was USD 35,000.00, what was the total sales made?

Question 31

The angle of elevation of the top of a vertical pole from a point, P on a level ground is 60°. The distance from P to the foot of the pole is 55 m. Find the height of the pole.

Question 32

The ratio of girls to boys in a certain committee is 5 : 2. If there are 35 members in the committee, how many more boys must be added to the committee to have the ratio of girls to boys as 5 : 4?

Question 33

Find the values of x for which (\dfrac{x + 1}{3x^2 - 12}) is not defined.

Question 34

Given that (\tan x = \frac{12}{5}), find the value of ((\sin x \cos x))

Question 35

Consider these two statements: P: N is an odd number Q: N is a prime number greater than 2. Express "If N is not an odd number then N is not a prime number greater than 2" in symbolic form.

Question 36

A sector which subtends an angle 150° is cut from a circular plate of radius 14 cm. Find, correct to one decimal place, the perimeter of the remaining plate. [\text{Take } \pi = \frac{22}{7}]

Question 37

One side of a gutter is 15 cm lower than the other side. A plank of wood, which is laid across the gutter to form a bridge, slopes at an angle of 35° to the horizontal. How wide is the gutter?

Question 38

Diagram will be provided In the diagram, MOP is the diameter of the circle MNP centre O. (\angle NMP = (2x)^\circ) and (\angle EPM = (5x + 18)^\circ). Find the value of x.

Question 39

The height of a square base pyramid is thrice the length of a side of its base. If the base area is 324 cm², find the volume of the pyramid.

Question 40

If (4^x = \frac{1}{1024}), find the value of x

Question 41

"Diagram will be provided" In the diagram, O is the centre of the circle WXY. (|WX| = |XZ|) and (\angle ZXY = 26^\circ). Find (\angle XYZ).

Question 42

Evaluate (141_6 + 233_6 - 102_6)

Question 43

In the first year, Mr. Kwakye's annual salary was USD 1,560.00. His salary was increased each year by a constant value, y until it was USD 13,980.00 in the 13th year. Calculate the value of y.

Question 44

Given that (\frac{16}{9}, x, 1, y) is a Geometric Progression (G.P), find the value of xy.

Question 45

A chord of a circle, 12 cm long subtends an angle of 150° at the centre of the circle. Find the radius of the circle.

Question 46

The lines (3x + 2y = 4) and (y = 2x - 5) intersect at a point P(x, y). Find the coordinates of P.

Question 47

Make u the subject of the relation (\dfrac{t}{s+u} = \dfrac{s}{t-u}).

Question 48

"Table will be provided"The table shows the number of subjects registered by a class of students for an examination. Use the information to answer the question below Calculate the mean of the distribution.

Question 49

"Table will be provided" The table shows the number of subjects registered by a class of students for an examination. Use the information to answer the question below Find the median.

Question 50

A rectangular tank of sides 4 m by 8 m by 11 m has the same volume as a cylindrical tank of height 7 m. Calculate the base radius of the cylindrical tank. [\text{Take } \pi = \frac{22}{7}]