Core Mathematics Mock 2025

Question 1 of 50

What is the size of an angle in a semicircle?

Question 2 of 50

Find the midpoint of the line joining (2, 4) and (6, 10).

Question 3 of 50

In a class, n(A) = 12, n(B) = 9 and n(A ∩ B) = 4. Find n(A ∪ B).

Question 4 of 50

Solve x² − 5x + 6 = 0.

Question 5 of 50

Simplify (x² − 4)/(x + 2).

Question 6 of 50

Solve the simultaneous equations x + y = 7 and x − y = 1.

Question 7 of 50

Solve the inequality 2(x − 3) ≥ x + 1.

Question 8 of 50

y varies directly as x, and y = 12 when x = 3. Find y when x = 5.

Question 9 of 50

Find the volume of a cylinder of radius 7 cm and height 10 cm. (Take π = 22/7)

Question 10 of 50

Find the total surface area of a cube of side 4 cm.

Question 11 of 50

An arc subtends an angle of 100° at the centre of a circle. What angle does it subtend at the circumference?

Question 12 of 50

One angle of a cyclic quadrilateral is 70°. Find the angle opposite it.

Question 13 of 50

Find the distance between the points (1, 2) and (4, 6).

Question 14 of 50

Find the equation of the line with gradient 2 that passes through (0, −3).

Question 15 of 50

If sin θ = 3/5 and θ is acute, find cos θ.

Question 16 of 50

The point (4, 1) is rotated 90° anticlockwise about the origin. What is its image?

Question 17 of 50

A triangle of area 5 cm² is enlarged by a scale factor of 3. What is the area of its image?

Question 18 of 50

Find the sum of the first 20 terms of the arithmetic sequence 2, 5, 8, …

Question 19 of 50

What is the 6th term of the geometric sequence 2, 6, 18, …?

Question 20 of 50

Find the sum to infinity of the geometric series 12 + 6 + 3 + …

Question 21 of 50

Find the volume of a cone with a radius of 3 cm and a height of 7 cm. (Take π = 22/7.)

Question 22 of 50

Find the curved surface area of a cylinder with a radius of 3.5 cm and a height of 10 cm. (Take π = 22/7.)

Question 23 of 50

p varies directly as the square of q, and p = 18 when q = 3. Find p when q = 5.

Question 24 of 50

x varies jointly as y and z. x = 24 when y = 2 and z = 3. Find x when y = 5 and z = 4.

Question 25 of 50

What is the negation of the statement "All the students passed"?

Question 26 of 50

What is the contrapositive of "If it rains, the ground is wet"?

Question 27 of 50

Solve 2x² + x − 6 = 0.

Question 28 of 50

What is the sum of the roots of x² − 9x + 14 = 0?

Question 29 of 50

The discriminant of x² + 4x + 7 = 0 shows that the equation has

Question 30 of 50

If f(x) = x² + 1 and g(x) = 2x, find f(g(3)).

Question 31 of 50

Find the inverse of f(x) = 3x − 2.

Question 32 of 50

For 0° ≤ x ≤ 360°, sin x = 0.5 when x =

Question 33 of 50

A bag holds 4 red and 6 blue balls. Two are drawn without replacement. What is the probability that both are red?

Question 34 of 50

In how many ways can 2 prefects be chosen from 5 candidates?

Question 35 of 50

Kofi is 3 times as old as his son. In 10 years he will be twice as old. How old is the son now?

Question 36 of 50

A chord 16 cm long is 6 cm from the centre of a circle. Find the area of the circle in terms of π.

Question 37 of 50

The angle between a tangent and a chord at the point of contact is 64°. Find the angle in the alternate segment.

Question 38 of 50

The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides does it have?

Question 39 of 50

Two similar triangles have corresponding sides 4 cm and 6 cm. If the smaller has area 32 cm², find the area of the larger.

Question 40 of 50

Find the equation of the perpendicular bisector of the line joining (2, 4) and (6, 8).

Question 41 of 50

If sin θ = 5/13 and θ is obtuse, find cos θ.

Question 42 of 50

A boat sails 8 km on a bearing of 060° from P to Q. How far east of P is Q? (sin 60° ≈ 0.866)

Question 43 of 50

Find the area of triangle PQR with PQ = 10 cm, QR = 12 cm and ∠PQR = 150°.

Question 44 of 50

The mean of 5, x, 8, 2x and 10 is 10. Find x.

Question 45 of 50

A bag contains 4 red, 5 blue and 3 green balls. Two balls are drawn without replacement. Find the probability that both are blue.

Question 46 of 50

The probability that A hits a target is 2/3 and B is 3/4. Both fire once independently. Find the probability that the target is hit at least once.

Question 47 of 50

Find the standard deviation of 2, 4, 6, 8, 10.

Question 48 of 50

From the top of a 30 m tower, the angles of depression of two cars in line due east are 30° and 60°. Find the distance between the cars. (√3 ≈ 1.732)

Question 49 of 50

In triangle ABC, a = 7 cm, b = 8 cm and c = 13 cm. Find angle C.

Question 50 of 50

Solve 2cos²x − cos x − 1 = 0 for 0° ≤ x ≤ 360°.