Core Mathematics 2024 - WASSCE

Mathematics

Question 1

The sum of the interior angles of a polygon is 1260°. Find the number of sides.

Question 2

A building is 12 m high. A football on the ground floor is 30 m away from the foot of the building. Find, correct to the nearest degree, the angle of depression of the ball from the top of the building.

Question 3

A number is chosen at random from the set {13, 14, ...., 30}. What is the probability that it is a prime number?

Question 4

Regina is 34 years old and her daughter is 5 years. In n years, Regina will be twice as old as her daughter. Find the value of n.

Question 5

If P(−7, 8) is reflected in the line x − 2 = 0, find the coordinates of the image of P.

Question 6

If the variable P is inversely proportional to Q² and P = 2.25 when Q = 6, find P when Q = 3.

Question 7

Make x the subject of the relation: y = √(p x/r − r² x)

Question 8

Seven men complete a certain work schedule in 6 days. How long will it take two of the men to complete the same work schedule if they work at the same rate?

Question 9

If cos y is negative and sin y is negative, in which quadrant would y lie?

Question 10

The volume of a cone is 264 cm³. If the base radius is 6 cm, find the height. [Take π = 22/7]

Question 11

Find the value of x for which (2x − 1)/(x² + 2x + 1) is not defined.

Question 12

The range of a sample of 10 numbers is 5 and the largest value is 50. What is the least value?

Question 13

The mean of ten numbers is 16. When another number, k, is added, the mean becomes 18. Find the value of k.

Question 14

The probability that John and James pass an examination are 3/4 and 3/5 respectively. Find the probability that both will fail.

Question 15

The diagonals of a rhombus are 12 cm and 16 cm. Find the perimeter.

Question 16

DIAGRAM WILL BE PROVIDED In the diagram PQR is a circle with centre O and ∠OQR = 42°. Find ∠QPR.

Question 17

Solve: x(3x + 4) = 4.

Question 18

If P = {−2, 0, 2, 4, 6} and Q = {−3, −1, 0, 2, 3, 5}, find the set P ∩ Q.

Question 19

An office equipment depreciates at 15% per annum. If the cost is GH₵ 1,200.00 when new, find the value after three years.

Question 20

Solve: (x − 2)/4 − (2x − 4)/3 = 5/6.

Question 21

DIAGRAM WILL BE PROVIDED Calculate the value of t in the diagram.

Question 22

Given that 6 ⊗ 7 = y (modulo 8), find the value of y.

Question 23

Express 0.0063075 correct to three significant figures.

Question 24

Given statements p and q, the statement p ∨ q is false only if

Question 25

y 1 2 3 4 x 0 2 4 6 What is the gradient of the equation of the line?

Question 26

y | 1 | 2 | 3 | 4 x | 0 | 2 | 4 | 6 The table describes the relation y = mx + c where m and c are constants. Use the information to answer the question below Find the equation of the line described in the table.

Question 27

The second term of a Geometric Progression (G.P) is 9. If the fourth term is 81, find the common ratio.

Question 28

DIAGRAM WILL BE PROVIDED In the diagram, ∆PQR is similar to ∆PWY. WY ∥ QR, QR = 15 cm, WY = 6 cm and WP = 4 cm. Find |WQ|.

Question 29

A cylindrical container closed at both ends has a radius of 3 cm and height of 4 cm. What is the total surface area of the container? [Take π = 22/7]

Question 30

The diameter of a bicycle wheel is 21 cm. If the wheel makes 8 complete revolutions, what will be the total distance covered by the wheel? [Take π = 22/7]

Question 31

DIAGRAM WILL BE PROVIDED Find the value of x in the diagram.

Question 32

The interior angles of a triangle are (y + 10)°, (2y − 40)° and (3y − 90)°. Which of the following accurately describes the triangle?

Question 33

Given that sin A = 3/5, 0° ≤ A ≤ 90°, find the value of (tan A − cos A).

Question 34

Simplify: 3 log x + log y − 2 log z.

Question 35

Simplify: a^(−1/4) × a^(1/2) ÷ a^(−1/2).

Question 36

The area of a square parcel of land is 256 m². A rectangular field of length 20 m has the same perimeter as the parcel of land. Find the area of the field.

Question 37

Mr. Abban invested USD 1,200.00 for 3 years at 5% per annum compound interest. Find the interest earned at the end of three years.

Question 38

DIAGRAM WILL BE PROVIDED In the diagram PR is tangent to the circle at Q. The centre of the circle is O and ∠QOS = 108°. Use the information to answer the question below Find ∠OSQ.

Question 39

DIAGRAM WILL BE PROVIDED In the diagram PR is tangent to the circle at Q. The centre of the circle is O and ∠QOS = 108°. Use the information to answer the question below Find ∠SQR.

Question 40

Find the value of x that satisfies the equation: 2/3 (x + 5) = 1 − (x − 7)/2.

Question 41

A closed cuboid has length 12 cm, width 7 cm and height 5 cm. Calculate the total surface area.

Question 42

Mr. Amuzu sold his car through an agent who charged 9% commission on the selling price. If Amuzu received GH₵ 236,600.00 after the sale, find the selling price of the car.

Question 43

DIAGRAM WILL BE PROVIDED The diagram shows a triangle MNP inscribed in a circle. MQ is a tangent to the circle at M. Find ∠MPN.

Question 44

In an examination taken by 120 students, 90 passed Mathematics, 40 passed Science and 5 failed both subjects. Use the information to answer the question below How many students passed Science only

Question 45

In an examination taken by 120 students, 90 passed Mathematics, 40 passed Science and 5 failed both subjects. Use the information to answer the question below Find the probability that a student selected at random passed only one subject.

Question 46

DIAGRAM WILL BE PROVIDED In the diagram, PR is a diameter of the circle PQS with centre O. Find ∠PQS.

Question 47

If P(−7, 8) is reflected in the line x − 2 = 0, find the coordinates of the image of P.

Question 48

Find the product of 124(seven) and 23(seven).

Question 49

Given that m = 5, n = 3 and r = 2, evaluate (m² − n²) + r² / (m² + (n² − r²)).

Question 50

Three boys of ages 2, 4 and 10 shared 32 oranges in the ratio of their ages. What was the least share?