Core Mathematics Mock 2026

Question 1 of 50

Solve for x: 3x − 7 = 2x + 5.

Question 2 of 50

Find the mean of 4, 7, 9, 10 and 15.

Question 3 of 50

Find the value of 17 (mod 5).

Question 4 of 50

Simplify 2⅓ − 1¾.

Question 5 of 50

Find the value of log₂ 32.

Question 6 of 50

A trader bought an item for GH₵ 80.00 and sold it for GH₵ 100.00. Find the percentage profit.

Question 7 of 50

The angles of a triangle are x°, 2x° and 3x°. Find the largest angle.

Question 8 of 50

Factorise completely: x² − 9.

Question 9 of 50

Express 0.000452 in standard form.

Question 10 of 50

Convert 214₅ to a number in base ten.

Question 11 of 50

Simplify (2√3)².

Question 12 of 50

Rationalise 6/√3.

Question 13 of 50

Evaluate log₁₀ 1000 − log₁₀ 10.

Question 14 of 50

If 2^(x + 1) = 16, find x.

Question 15 of 50

Express the recurring decimal 0.333… as a fraction.

Question 16 of 50

Evaluate 27^(−2/3).

Question 17 of 50

Find the amount when GH₵ 1,000 is invested for 2 years at 10% compound interest per annum.

Question 18 of 50

Make r the subject of the formula V = πr²h.

Question 19 of 50

y varies inversely as x, and y = 4 when x = 6. Find y when x = 8.

Question 20 of 50

Find the 20th term of the arithmetic progression 3, 7, 11, …

Question 21 of 50

Find the sum of the first 10 terms of the AP 2, 5, 8, …

Question 22 of 50

Find the 5th term of the geometric progression 2, 6, 18, …

Question 23 of 50

Find the area of a sector of a circle of radius 7 cm that subtends an angle of 90° at the centre. (Take π = 22/7)

Question 24 of 50

A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. How high up the wall does it reach?

Question 25 of 50

Factorise 2x² − 18 completely.

Question 26 of 50

Simplify 2/x + 3/(2x).

Question 27 of 50

Three consecutive odd numbers add up to 57. What is the largest of them?

Question 28 of 50

Which of these relations is NOT a function?

Question 29 of 50

An angle is 20° more than its complement. Find the angle.

Question 30 of 50

Each interior angle of a regular polygon is 150°. How many sides does it have?

Question 31 of 50

The probability of rain on any day is 0.3, independently of other days. What is the probability of no rain on two days running?

Question 32 of 50

Two fair dice are thrown. What is the probability that the total is 11?

Question 33 of 50

Simplify √50 − √18.

Question 34 of 50

Rationalise the denominator of 6/√3.

Question 35 of 50

Solve −2x + 3 ≤ 11.

Question 36 of 50

Solve log₁₀(x + 3) + log₁₀(x − 3) = log₁₀ 16.

Question 37 of 50

Express 0.4̇5̇ (0.454545...) as a fraction in its lowest terms.

Question 38 of 50

Evaluate (1/27)^(−2/3) × 16^(−3/4).

Question 39 of 50

If α and β are roots of 2x² − 5x + 1 = 0, find α² + β².

Question 40 of 50

Solve the simultaneous equations x + y = 5 and x² + y² = 13.

Question 41 of 50

Make r the subject of A = P(1 + r/100)ⁿ.

Question 42 of 50

If y varies directly as x² and inversely as z, and y = 12 when x = 2 and z = 3, find y when x = 3 and z = 9.

Question 43 of 50

Find the range of values of x for which x² − x − 6 < 0.

Question 44 of 50

Find k if x² + kx + 9 = 0 has equal roots and k > 0.

Question 45 of 50

Solve 1/(x − 1) + 2/(x + 1) = 1.

Question 46 of 50

A sector of a circle of radius 14 cm subtends 135° at the centre. Find its perimeter (π = 22/7).

Question 47 of 50

Find the total surface area of a closed cylinder of radius 7 cm and height 10 cm (π = 22/7).

Question 48 of 50

A rectangular tank 3 m by 2 m is filled to a depth of 1.5 m. Water flows out at 50 litres per minute. How long will it take to empty?

Question 49 of 50

The volume of a sphere is 288π cm³. Find its radius.

Question 50 of 50

A sector of angle 216° from a circle of radius 10 cm is folded into a cone. Find the base radius of the cone.