GCE Mathematics 2019
Past Questions

If $\log_x 64 = 3$, find the value of $x$.

If $\log_x 64 = 3$, find the value of $x$.

Factorize completely: $2x^2 - 8x$

Find the sum of the roots of the equation 3x² - 7x + 2 = 0.

z varies jointly as x and the square root of y. If z = 24 when x = 4 and y = 9, find z when x = 3 and y = 16.

In triangle XYZ, XY = 8 cm, YZ = 6 cm and angle XYZ = 90°. A point W lies on XZ such that YW is perpendicular to XZ. Find the length of YW.

If sin θ = 3/5, find cos θ, given that θ is acute.

The angle of elevation of the top of a tower from a point 50 m away on level ground is 30°. Find the height of the tower, correct to the nearest metre. [Take √3 = 1.732]

The table shows the frequency distribution of the heights (in cm) of 40 students. Height (cm): 150–154, 155–159, 160–164, 165–169 Frequency: 8, 14, 12, 6 Calculate the mean height of the students.

A box contains 6 defective and 14 non-defective bulbs. Two bulbs are drawn one after the other without replacement. What is the probability that both bulbs are defective?

Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 4, 6, 8, 10} and B = {1, 2, 3, 4, 5}, find (A ∪ B)'.

Consider the statements: p = 'It is raining' and q = 'The road is wet.' Which of the following represents the contrapositive of the statement 'If it is raining, then the road is wet'?

What is the gradient of the line passing through the points (2, −3) and (5, 6)?

(a) Solve for x in the equation: 3^(2x+1) - 26(3^x) - 9 = 0. [6 marks] (b) Given that log(base 2)(y + 3) + log(base 2)(y - 3) = log(base 2)(7y - 3), find the value of y. [5 marks] (c) Simplify: (sqrt(…

Given that α and β are the roots of the quadratic equation 3x² - 5x + 1 = 0: (a) Write down the values of (α + β) and αβ. [2 marks] (b) Find the value of: (i) α² + β² [3 marks] (ii) α³ + β³ …

a) (i) Prove the trigonometric identity: (sin x + cos x)² + (sin x - cos x)² = 2 (ii) Hence, or otherwise, show that: (sin x + cos x)² = 1 + sin 2x b) In triangle ABC, AB = 7 cm, BC…

The ages, in years, of 8 teachers in a school are: 32, 45, 28, 50, 36, 41, 29, 39 (a) Find the mean age of the teachers. (b) Calculate the median age. (c) Find the interquartile range of the distribu…