Core Mathematics Mock 2014

Question 1 of 50

3(x + 4) = 3x + 12 illustrates the

Question 2 of 50

The bearing of due east is

Question 3 of 50

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

Question 4 of 50

The maximum value of y = sin x is

Question 5 of 50

The period of y = sin x is

Question 6 of 50

The range of 4, 9, 2, 11, 7 is

Question 7 of 50

Find the equation of the line with gradient 2 passing through (0, 3).

Question 8 of 50

The y-intercept of y = −4x + 7 is

Question 9 of 50

Express 0.000362 in standard form.

Question 10 of 50

Find the value of 0.36 ÷ 0.012.

Question 11 of 50

Which set contains the whole numbers but not the negative integers?

Question 12 of 50

If the bearing of B from A is 060°, the bearing of A from B is

Question 13 of 50

A man walks 3 km north then 4 km east. His distance from the start is

Question 14 of 50

The bearing of due south-west is

Question 15 of 50

The maximum value of y = 3 sin x is

Question 16 of 50

The graph of y = cos x crosses the x-axis at

Question 17 of 50

A card is drawn from a pack of 52. The probability that it is a king is

Question 18 of 50

Find the compound interest on GH¢1,000 at 10% per annum for 2 years.

Question 19 of 50

At what simple interest rate will GH¢500 earn GH¢75 in 3 years?

Question 20 of 50

GH¢2,000 is invested at 5% compound interest per annum. Its value after 2 years is

Question 21 of 50

How long will it take GH¢800 to earn GH¢240 at 6% simple interest?

Question 22 of 50

Solve −3x > 12.

Question 23 of 50

The gradient of the line 3y = 6x − 9 is

Question 24 of 50

Find the equation of the line through (1, 2) and (3, 6).

Question 25 of 50

Evaluate 2.5 × 10³ + 4.2 × 10².

Question 26 of 50

Convert 213₄ to base ten.

Question 27 of 50

Convert 47 to base two.

Question 28 of 50

Subtract 1¾ from 2⅓.

Question 29 of 50

Correct 0.0045678 to 3 significant figures.

Question 30 of 50

Find the product of the HCF and LCM of 12 and 18.

Question 31 of 50

Simplify (2⁵ × 2⁻²) ÷ 2².

Question 32 of 50

Find the value of 27^(2/3).

Question 33 of 50

Simplify √48 + √27.

Question 34 of 50

Expand (2x − 3)(x + 4).

Question 35 of 50

If y varies directly as x and y = 12 when x = 3, find y when x = 5.

Question 36 of 50

The variance of 3, 5, 7, 9, 11 is

Question 37 of 50

The time to complete a job varies inversely as the number of workers. 12 workers take 15 days. How many workers are needed to finish in 9 days?

Question 38 of 50

If y ∝ √x and y = 6 when x = 9, find x when y = 10.

Question 39 of 50

ABCD is a cyclic quadrilateral with ∠ABC = 110° and ∠BAD = 75°. Find ∠ADC.

Question 40 of 50

A chord of length 24 cm is in a circle of radius 13 cm. Its distance from the centre is

Question 41 of 50

The sum of the first n terms of a GP is 2ⁿ − 1. Find the 5th term.

Question 42 of 50

A sphere and a cube have equal volumes. If the cube has side 4 cm, the radius of the sphere is about (π = 3.14)

Question 43 of 50

Classes 0–9, 10–19, 20–29, 30–39 have frequencies 5, 12, 8, 3. Using midpoints, the estimated mean is about

Question 44 of 50

A plane flies 300 km on a bearing of 150°. How far south of its start is it? (cos 30° ≈ 0.866)

Question 45 of 50

If x − 1/x = 3, find x² + 1/x².

Question 46 of 50

Solve |2x − 3| = 7.

Question 47 of 50

If α and β are roots of x² − 5x + 3 = 0, find 1/α + 1/β.

Question 48 of 50

Two circles of radii 5 cm and 3 cm have centres 10 cm apart. The length of the direct common tangent is

Question 49 of 50

The graph of y = sin x is shifted 90° to the left. The new graph is

Question 50 of 50

The probability that a student is late on any day is 0.1. Find the probability that he is late on exactly one of two days.