Core Mathematics Mock 2011

Question 1 of 50

If a ∗ b = a² − b, evaluate 3 ∗ 4.

Question 2 of 50

A tangent to a circle is perpendicular to the

Question 3 of 50

If U = {1, ..., 10} and A = {2, 4, 6, 8, 10}, find n(A′).

Question 4 of 50

Which of these numbers is rational?

Question 5 of 50

The additive inverse of −8 is

Question 6 of 50

Express 7/20 as a decimal.

Question 7 of 50

Find 2/5 of GH¢350.

Question 8 of 50

If f(x) = 4x − 7, find f(3).

Question 9 of 50

Solve 7 − 2x = 1.

Question 10 of 50

Solve x/4 + 3 = 5.

Question 11 of 50

Complementary angles add up to

Question 12 of 50

The magnitude of the vector (5, 12) is

Question 13 of 50

Simplify √12 × √3.

Question 14 of 50

The angle at the centre of a circle is 110°. The angle at the circumference on the same arc is

Question 15 of 50

In a class of 40, 25 take French, 20 take Twi and 8 take both. How many take neither?

Question 16 of 50

Find the amount when GH¢5,000 is invested at 8% simple interest for 3 years.

Question 17 of 50

A car worth GH¢40,000 depreciates by 10% each year. Its value after 2 years is

Question 18 of 50

Is the set of whole numbers closed under subtraction?

Question 19 of 50

(2 × 3) × 4 = 2 × (3 × 4) illustrates the

Question 20 of 50

A price rose from GH¢80 to GH¢92. The percentage increase is

Question 21 of 50

Factorise 9y² − 25.

Question 22 of 50

Expand (x − 5)².

Question 23 of 50

Which relation is a function?

Question 24 of 50

A regular polygon has interior angles of 150°. How many sides has it?

Question 25 of 50

The hypotenuse of a right triangle is 13 cm and one side is 5 cm. The other side is

Question 26 of 50

In a right triangle, the side opposite 30° is 4 cm. The hypotenuse is

Question 27 of 50

If cos θ = 0.6 and θ is acute, sin θ =

Question 28 of 50

A circular garden has a radius of 3.5 m. Its circumference is (π = 22/7)

Question 29 of 50

A triangle has base 12 cm and area 48 cm². Its height is

Question 30 of 50

A water tank is a cube of side 2 m. Its capacity in litres is

Question 31 of 50

In a survey of 60 students, 15 prefer football. The sector angle for football on a pie chart is

Question 32 of 50

Data such as the colours of cars is

Question 33 of 50

The heights of students is an example of

Question 34 of 50

A coin is tossed and a die is thrown. P(head and a 6) is

Question 35 of 50

The probability that Ama passes is 0.8 and Kofi passes is 0.7, independently. P(both pass) is

Question 36 of 50

Solve simultaneously x + y = 7 and x − y = 1. Find xy.

Question 37 of 50

Find the value of k if x² + kx + 9 is a perfect square (k > 0).

Question 38 of 50

Solve x² − 4x − 12 = 0.

Question 39 of 50

If 2ˣ = 8 and 3ʸ = 81, find x + y.

Question 40 of 50

The nth term of the sequence 5, 9, 13, 17, … is

Question 41 of 50

Solve 4^(2x − 1) = 64.

Question 42 of 50

The roots of x² − 5x + 6 = 0 are α and β. Find α² + β².

Question 43 of 50

Simplify (x² − 9)/(x² + 2x − 3).

Question 44 of 50

The sum of the first 10 terms of 3 + 7 + 11 + … is

Question 45 of 50

Find the 6th term of the GP 2, 6, 18, …

Question 46 of 50

If f(x) = 3x − 2, find f⁻¹(7).

Question 47 of 50

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

Question 48 of 50

Simplify 1/(x − 1) − 1/(x + 1).

Question 49 of 50

If x + 1/x = 3, find x² + 1/x².

Question 50 of 50

The sum of an infinite GP with first term 8 and ratio 1/2 is