Core Mathematics Mock 2022

Question 1 of 50

Which of these is primary data?

Question 2 of 50

Which chart best shows how a student's height changed over several years?

Question 3 of 50

What is the image of the point (3, −5) after a reflection in the x-axis?

Question 4 of 50

A rhombus has diagonals of 16 m and 10 m. What is its area?

Question 5 of 50

A prism has a volume of 480 cm³ and a height of 12 cm. What is its base area?

Question 6 of 50

A parallelogram has a base of 9 m, a perpendicular height of 4 m and a slanting side of 5 m. What is its area?

Question 7 of 50

What is the class width of the class 20–29 (whole-number data)?

Question 8 of 50

A fair coin and a fair die are tossed together. How many outcomes are in the sample space?

Question 9 of 50

Which pair of events is independent?

Question 10 of 50

Convert 1101 (base two) to base ten.

Question 11 of 50

Convert 25 (base ten) to base five.

Question 12 of 50

Write 0.000 47 in standard form.

Question 13 of 50

Solve the simultaneous equations x + y = 10 and x − y = 4.

Question 14 of 50

Solve x² − 7x + 10 = 0.

Question 15 of 50

A taxi charges GH¢5 plus GH¢3 per kilometre. A trip cost GH¢41. How long was it?

Question 16 of 50

An angle and its complement differ by 30°. Find the smaller angle.

Question 17 of 50

How many diagonals does a hexagon have?

Question 18 of 50

Two dice are thrown. The probability that the total is 7 is

Question 19 of 50

Solve 3 ≤ 2x + 1 < 9.

Question 20 of 50

Factorise 6x² − x − 2.

Question 21 of 50

The angle of depression of a boat from a cliff 50 m high is 30°. How far is the boat from the foot of the cliff? (tan 30° ≈ 0.577)

Question 22 of 50

Arrange 0.6, 5/8, 3/5 from smallest to largest.

Question 23 of 50

Using the same figures (Ama 0.8, Kofi 0.7), P(neither passes) is

Question 24 of 50

P varies jointly as Q and R. If P = 24 when Q = 2 and R = 3, find P when Q = 4 and R = 5.

Question 25 of 50

A chord is 6 cm from the centre of a circle of radius 10 cm. Its length is

Question 26 of 50

Two cards are drawn without replacement from 3 red and 2 blue cards. P(both red) is

Question 27 of 50

Simplify (0.0036 × 0.5) ÷ 0.0012, giving the answer in standard form.

Question 28 of 50

Find the value of x if 2x₅ = 13 in base ten (2x₅ means 2 followed by digit x in base five).

Question 29 of 50

If 3^(x − 1) = 27^(x + 1), find x.

Question 30 of 50

Simplify (√5 + 2)² − (√5 − 2)².

Question 31 of 50

Rationalise 2/(√3 − 1).

Question 32 of 50

If log 2 = 0.3010 and log 3 = 0.4771, find log 18.

Question 33 of 50

The product of two consecutive positive even numbers is 168. Find the smaller number.

Question 34 of 50

Find the values of x for which (x + 2)/(x² − 4) is undefined.

Question 35 of 50

Find the quadratic equation whose roots are −2 and 5.

Question 36 of 50

Solve the simultaneous equations 3x − 2y = 4 and 2x + 3y = 7.

Question 37 of 50

Find the range of x satisfying 2 ≤ 3x − 4 < 11.

Question 38 of 50

Solve 3x² − 5x − 2 = 0.

Question 39 of 50

A rotation of 90° anticlockwise about the origin maps (4, 1) to

Question 40 of 50

The 2nd and 5th terms of a GP are 6 and 162. Find the common ratio.

Question 41 of 50

A cone of height 12 cm and base radius 5 cm has a curved surface area of

Question 42 of 50

Solve √(x + 6) = x.

Question 43 of 50

The point (3, −2) is reflected in the line y = −x. Its image is

Question 44 of 50

A triangle with area 6 cm² is enlarged by scale factor −2. The area of the image is

Question 45 of 50

If x : y = 3 : 4 and y : z = 6 : 5, find x : z.

Question 46 of 50

A car covers 240 km at 60 km/h and returns at 40 km/h. Its average speed for the whole journey is

Question 47 of 50

10 men can do a job in 12 days. After 4 days, 2 men leave. How many more days are needed to finish?

Question 48 of 50

The sum of the first n terms of an AP is n² + 2n. Find the 10th term.

Question 49 of 50

How many terms of the AP 2, 5, 8, ... give a sum of 155?

Question 50 of 50

A hemispherical bowl of radius 9 cm holds how much water? (π = 22/7)