Core Mathematics Mock 2020

Question 1 of 50

What is the range of 18, 25, 11, 30 and 22?

Question 2 of 50

The angle in a semicircle is

Question 3 of 50

A tangent to a circle meets the radius at the point of contact at

Question 4 of 50

What is the period of y = sin x, in degrees?

Question 5 of 50

On the graph of y = cos x, the value 1 is reached at x =

Question 6 of 50

Simplify 2³ × 2⁴.

Question 7 of 50

A die is thrown 60 times and shows a 6 on 13 of them. What is the relative frequency of a 6?

Question 8 of 50

In a pie chart of 180 pupils, what angle does a group of 45 pupils get?

Question 9 of 50

The bearing of B from A is 060°. What is the bearing of A from B?

Question 10 of 50

If a = (2, 3) and b = (−1, 4), find a + 2b.

Question 11 of 50

For any angle θ, sin²θ + cos²θ equals

Question 12 of 50

y varies directly as x, and y = 12 when x = 4. Find y when x = 7.

Question 13 of 50

y varies inversely as x, and y = 6 when x = 4. Find y when x = 3.

Question 14 of 50

If p is true and q is false, the statement "p and q" (p ∧ q) is

Question 15 of 50

Evaluate log₂ 32.

Question 16 of 50

An arc subtends an angle of 140° at the centre of a circle. What angle does it subtend at the circumference?

Question 17 of 50

The opposite angles of a cyclic quadrilateral add up to

Question 18 of 50

Angles in the same segment of a circle are

Question 19 of 50

To construct an angle of 60° with a ruler and compasses, you construct

Question 20 of 50

What is the maximum value of y = 3 sin x?

Question 21 of 50

The graph of y = tan x has an asymptote (is undefined) at x =

Question 22 of 50

A and B are mutually exclusive, with P(A) = 0.5 and P(B) = 0.4. Find P(A or B).

Question 23 of 50

In how many ways can 4 different books be arranged on a shelf?

Question 24 of 50

The standard deviation of a set of data measures

Question 25 of 50

On a cumulative frequency curve, the median is read off at

Question 26 of 50

Evaluate 27^(2/3).

Question 27 of 50

Evaluate log₁₀ 0.001.

Question 28 of 50

Evaluate log 2 + log 5 (base 10).

Question 29 of 50

Convert 213 (base four) to base ten.

Question 30 of 50

Two ships leave a port at the same time; one sails 12 km north, the other 5 km east. How far apart are they?

Question 31 of 50

The cost C of hiring a bus is GH¢200 plus GH¢5 per km. How far can be travelled for GH¢450?

Question 32 of 50

A recipe uses flour and sugar in the ratio 5 : 2. How much flour is needed with 300 g of sugar?

Question 33 of 50

The modal class of the distribution 0–9 (5), 10–19 (12), 20–29 (8), 30–39 (3) is

Question 34 of 50

The angle between a tangent and a radius at the point of contact is

Question 35 of 50

The graph of y = 2 + sin x has a maximum value of

Question 36 of 50

For 0° ≤ x ≤ 360°, how many solutions does sin x = 0.4 have?

Question 37 of 50

In a class of 50, 30 offer Physics, 25 Chemistry and 8 neither. How many offer both?

Question 38 of 50

Find the compound interest on GH¢8,000 for 3 years at 5% per annum, compounded yearly.

Question 39 of 50

Evaluate (2.4 × 10⁵) ÷ (8 × 10⁻²), leaving your answer in standard form.

Question 40 of 50

If log₁₀ x = 2.4771, find x given log₁₀ 3 = 0.4771.

Question 41 of 50

Find the least number which when divided by 6, 8 and 12 leaves a remainder of 5.

Question 42 of 50

The sum of two numbers is 15 and the sum of their squares is 113. Find the numbers.

Question 43 of 50

The graph of y = 3sin 2x has amplitude and period

Question 44 of 50

From a group of 5 boys and 3 girls, 2 are chosen at random. P(one boy and one girl) is

Question 45 of 50

At what rate per annum will GH¢2,500 amount to GH¢3,025 in 2 years at compound interest?

Question 46 of 50

Find the value of n if 2ⁿ × 4ⁿ⁺¹ = 128.

Question 47 of 50

Simplify 3/(√5 − √2) − 3/(√5 + √2).

Question 48 of 50

Convert 0.375 to base two.

Question 49 of 50

If (x + 2) is a factor of x³ + px² − x − 2, find p.

Question 50 of 50

Solve the equation 2^(2x) − 3(2^(x + 1)) + 8 = 0.