Core Mathematics Mock 2013

Question 1 of 50

Solve 3(x − 2) = 2(x + 1).

Question 2 of 50

Find the area of a circle of diameter 14 cm (π = 22/7).

Question 3 of 50

Find the total surface area of a cube of side 5 cm.

Question 4 of 50

Find the area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm.

Question 5 of 50

Each exterior angle of a regular polygon is 40°. How many sides has it?

Question 6 of 50

The sum of the interior angles of a hexagon is

Question 7 of 50

In a right-angled triangle, the two shorter sides are 6 cm and 8 cm. The hypotenuse is

Question 8 of 50

Two angles of a triangle are 45° and 75°. The third angle is

Question 9 of 50

Alternate angles formed by a transversal and parallel lines are

Question 10 of 50

Find the midpoint of (−2, 4) and (6, 0).

Question 11 of 50

Find the value of cos 60°.

Question 12 of 50

If sin x = 0.5 and x is acute, find x.

Question 13 of 50

In a pie chart, a sector of 72° represents what fraction of the total?

Question 14 of 50

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

Question 15 of 50

Solve (x + 1)/3 = (x − 1)/2.

Question 16 of 50

Find the sum of the roots of 2x² − 8x + 3 = 0.

Question 17 of 50

Simplify 1/x + 1/(2x).

Question 18 of 50

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

Question 19 of 50

Find the length of an arc that subtends 90° at the centre of a circle of radius 14 cm (π = 22/7).

Question 20 of 50

Find the area of a sector of angle 60° in a circle of radius 6 cm (π = 3.14).

Question 21 of 50

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

Question 22 of 50

A rectangular tank 2 m by 1.5 m by 1 m is full of water. How many litres does it hold?

Question 23 of 50

Find the volume of a sphere of radius 3 cm (π = 3.14).

Question 24 of 50

The angle subtended by a diameter at the circumference is

Question 25 of 50

Opposite angles of a cyclic quadrilateral add up to

Question 26 of 50

Find the gradient of the line 4x − 2y + 6 = 0.

Question 27 of 50

The line y = 3x − 6 meets the x-axis at

Question 28 of 50

Find the distance between (−1, 3) and (5, −5).

Question 29 of 50

Find the equation of the line through (2, 5) with gradient −1.

Question 30 of 50

If tan θ = 3/4 and θ is acute, find sin θ.

Question 31 of 50

A ladder 10 m long leans against a wall making 60° with the ground. How high up the wall does it reach? (sin 60° ≈ 0.866)

Question 32 of 50

From a point 20 m from the foot of a tree, the angle of elevation of the top is 45°. The height of the tree is

Question 33 of 50

The mean of 5 numbers is 12. If one number is removed, the mean of the rest is 11. The removed number is

Question 34 of 50

Find the median of 7, 2, 9, 4, 6, 3.

Question 35 of 50

A letter is chosen at random from the word MATHEMATICS. The probability that it is M is

Question 36 of 50

The mean of x and y is 8 and the mean of x, y and z is 10. Find z.

Question 37 of 50

In a survey, 45 people read Daily Graphic, 30 read Times and 12 read both. If 10 read neither, how many were surveyed?

Question 38 of 50

Given A = {x : 2 < x ≤ 7, x an integer}, n(A) is

Question 39 of 50

Of 80 students, 50 study Twi, 40 study French and x study both, with 5 studying neither. Find x.

Question 40 of 50

Kofi borrows GH¢4,000 at 12% simple interest per annum and repays GH¢5,440. How long did he borrow?

Question 41 of 50

Express 0.0004572 correct to 2 significant figures in standard form.

Question 42 of 50

Convert 213 (base 4) to base 10.

Question 43 of 50

If 23ₓ = 17 (base 10), find x.

Question 44 of 50

Simplify (√12 + √27) / √3.

Question 45 of 50

Find the LCM of 24, 36 and 40.

Question 46 of 50

Evaluate log₂ 32 − log₃ 27.

Question 47 of 50

The probability that Ama passes a test is 3/5. If she takes two independent tests, P(passes at least one) is

Question 48 of 50

If n(U) = 60, n(A) = 35, n(B) = 30 and n(A′ ∩ B′) = 5, find n(A ∩ B).

Question 49 of 50

A sum of money doubles in 8 years at simple interest. The rate per annum is

Question 50 of 50

A machine bought for GH¢12,000 depreciates at 15% per annum (reducing balance). Its value after 2 years is