Core Mathematics Mock 2021

Question 1 of 50

The point (2, 7) is translated by the vector (−4, 3). What is its image?

Question 2 of 50

Which transformation does NOT keep the size of a shape the same?

Question 3 of 50

If GH¢15 = US$1, how many US dollars do you get for GH¢1,200?

Question 4 of 50

What is the total surface area of a cube with sides of 5 cm?

Question 5 of 50

Find the mean of 3, 7, 7, 9 and 14.

Question 6 of 50

What is the mode of 2, 4, 4, 5, 5, 5, 6?

Question 7 of 50

6 workers take 10 days to build a wall. How long would 4 workers take, working at the same rate?

Question 8 of 50

A map has a scale of 1 : 50,000. What real distance does 4 cm on the map represent?

Question 9 of 50

GH¢900 is shared in the ratio 2 : 3 : 4. What is the largest share?

Question 10 of 50

A car uses 8 litres of fuel for every 100 km. How much fuel does it need for 350 km?

Question 11 of 50

What is the 10th term of the arithmetic sequence 3, 7, 11, …?

Question 12 of 50

What is the common ratio of the geometric sequence 81, 27, 9, …?

Question 13 of 50

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

Question 14 of 50

What is the volume of a sphere of radius 3 cm, in terms of π?

Question 15 of 50

Find the median of 12, 5, 9, 15, 7 and 10.

Question 16 of 50

Simplify (x² − 9)/(x² + x − 6).

Question 17 of 50

A cone has a base radius of 6 cm and slant height 10 cm. Find its height.

Question 18 of 50

In a cyclic quadrilateral PQRS, ∠P = 3x and ∠R = 2x + 20°. Find x.

Question 19 of 50

O is the centre of a circle. ∠AOB = 2y and ∠ACB = 50° where C is on the major arc. Find y.

Question 20 of 50

The points (1, 2), (3, k) and (5, 10) are collinear. Find k.

Question 21 of 50

Find the area of the triangle with vertices (0, 0), (4, 0) and (4, 6).

Question 22 of 50

The line 3x + ky = 6 has gradient −3/2. Find k.

Question 23 of 50

A cuboid has a square base of side x cm and height 10 cm. Its volume is 250 cm³. Find x.

Question 24 of 50

In a pie chart of a family budget of GH¢3,600, food takes 120°. How much is spent on food?

Question 25 of 50

Ama passes with probability 0.8 and Kofi with 0.7, independently. P(neither passes) is

Question 26 of 50

Find the value of x if 124₅ = x₁₀.

Question 27 of 50

The marks of 5 students have mean 60. Four of the marks are 50, 55, 65 and 70. The fifth mark is

Question 28 of 50

If n(A ∪ B) = 40, n(A) = 25 and n(A ∩ B) = 7, find n(B).

Question 29 of 50

Of 100 traders, 60 sell rice, 45 sell beans and 20 sell both. How many sell beans only?

Question 30 of 50

The number 3,456.789 rounded to 3 significant figures is

Question 31 of 50

In triangle PQR, PQ = PR and ∠QPR = 40°. Find ∠PQR.

Question 32 of 50

Simplify (sin 30° + cos 60°) ÷ tan 45°.

Question 33 of 50

In a class, the ratio of boys to girls is 3 : 2. A student is chosen at random. P(girl) is

Question 34 of 50

A regular polygon has 20 sides. Each exterior angle is

Question 35 of 50

In a circle, an inscribed angle subtending a semicircle is

Question 36 of 50

The median of a cumulative frequency curve for 40 values is read at the

Question 37 of 50

The lower quartile for 40 values is read at the

Question 38 of 50

If p = 2i + 3j and q = −i + 4j, find |2p − q|.

Question 39 of 50

Town B is 10 km from A on a bearing of 030°. How far north of A is B? (cos 30° ≈ 0.866)

Question 40 of 50

The cost of a building job varies jointly as the number of workers and the number of days. 6 workers for 10 days cost GH¢9,000. Find the cost for 4 workers for 15 days.

Question 41 of 50

Which statement is the contrapositive of "If a number is even, it is divisible by 2"?

Question 42 of 50

y varies inversely as the square of x. When x = 2, y = 9. Find y when x = 3.

Question 43 of 50

Given "All prefects are disciplined" and "Kofi is a prefect", the valid conclusion is

Question 44 of 50

Two tangents from an external point T touch a circle with centre O at A and B. If ∠ATB = 50°, find ∠AOB.

Question 45 of 50

A tangent from a point 13 cm from the centre of a circle of radius 5 cm has length

Question 46 of 50

A man walks 5 km on bearing 090° and then 12 km on bearing 180°. Find the bearing of his final position from the start (tan⁻¹ 2.4 ≈ 67.4°).

Question 47 of 50

P is 6 km east and 8 km north of Q. The bearing of Q from P is about (tan⁻¹ 0.75 ≈ 36.9°)

Question 48 of 50

If 4^(x) × 2^(x + 1) = 32, find x.

Question 49 of 50

The sum of a number and its reciprocal is 10/3. Find the number.

Question 50 of 50

In a circle, chords AB and CD intersect at X inside the circle. AX = 4, XB = 6, CX = 3. Find XD.