If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)
- A. \(\frac{8}{3}\)
- B. \(\frac{3}{2}\)
- C. \(\frac{4}{3}\)
- D. \(\frac{2}{3}\)
The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8m above the ground. How long is the ladder?
- A. 14m
- B. 12m
- C. 10m
- D. 7m
Find the equation of a straight line passing through the point (1, -5) and having gradient of \(\frac{3}{4}\)
- A. 3x + 4y - 23 = 0
- B. 3x + 4y +23 = 0
- C. 3x - 4y +23 = 0
- D. 3x - 4y - 23 = 0
A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?
- A. \(\frac{2}{3}\)
- B. \(\frac{3}{5}\)
- C. \(\frac{7}{20}\)
- D. \(\frac{12}{25}\)
The interior angles of a polygon are 3x\(^o\), 2x\(^o\), 4x\(^o\), 3x\(^o\) and 6x\(^o\). Find the size of the smallest angle of the polygon.
- A. 80\(^o\)
- B. 60\(^o\)
- C. 40\(^o\)
- D. 30\(^o\)
Factorize completely; (2x + 2y)(x – y) + (2x – 2y)(x + y)
- A. 4(x - y)(x + y)
- B. (4(x - y)
- C. 2(x - y)(x + y)
- D. 2(x - y)
In the diagram, POS and ROT are straight lines. OPQR is a parallelogram, |OS| = |OT| and ∠OST = 50°. Calculate the value of ∠OPQ.
- A. 100\(^o\)
- B. 120\(^o\)
- C. 140\(^o\)
- D. 160\(^o\)
A rectangular board has a length of 15cm and width x cm. If its sides are doubled, find its new area.
- A. 60x cm\(^2\)
- B. 45x cm\(^2\)
- C. 30x cm\(^2\)
- D. 15x cm\(^2\)
Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm. [Take \(\pi = \frac{22}{7}\)]
- A. 70\(^o\)
- B. 84\(^o\)
- C. 96\(^o\)
- D. 156\(^o\)
Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?
- A. $130,000.00
- B. $128,000.00
- C. $125,000.00
- D. $120,000.00
Make b the subject of the relation lb = \(\frac{1}{2}\) (a + b)h
- A. \(\frac{ah}{2l - h}\)
- B. \(\frac{2l - h}{al}\)
- C. \(\frac{al}{2l - h}\)
- D. \(\frac{al}{2 - h}\)
An arc subtends an angle of 72\(^o\) at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take \(\pi = \frac{22}{7}\)]
- A. 6.6 cm
- B. 8.8 cm
- C. 4.4 cm
- D. 2.2 cm
If log\(_x\) 2 = 0.3, evaluate log\(_x\) 8.
- A. 2.4
- B. 1.2
- C. 0.9
- D. 0.6
In XYZ, |YZ| = 32cm, < YXZ 53\(^o\) and XZY = 90\(^o\). Find, correct to the nearest centimetre, |XZ|
- A. 31 cm
- B. 25 cm
- C. 20 cm
- D. 13 cm
If 2\(^{a}\) = \(\sqrt{64}\) and \(\frac{b}{a}\) = 3, evaluate a\(^2 + b^{2}\)
- A. 250
- B. 160
- C. 90
- D. 48
The total surface area of a solid cylinder 165cm\(^2\). Of the base diameter is 7cm, calculate its height. [Take \(\pi = \frac{22}{7}\)]
- A. 7.5 cm
- B. 4.5 cm
- C. 4.0 cm
- D. 2.0 cm
Which of these values would make \(\frac{3p – 1}{p^{2} – p}\) undefined?
- A. 1
- B. \(\frac{1}{3}\)
- C. -\(\frac{1}{3}\)
- D. -1
Simplify: \(\frac{x^2 – 5x – 14}{x^2 – 9x + 14}\)
- A. \(\frac{x - 7}{x + 7}\)
- B. \(\frac{x + 7}{x - 7}\)
- C. \(\frac{x - 2}{x + 4}\)
- D. \(\frac{x + 2}{x - 2}\)
There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
- A. \(\frac{1}{6}\)
- B. \(\frac{1}{4}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{1}{2}\)
If (0.25)\(^y\) = 32, find the value of y.
- A. y = - \(\frac{5}{2}\)
- B. y = -\(\frac{3}{2}\)
- C. y = \(\frac{3}{2}\)
- D. y = \(\frac{5}{2}\)
If 3p = 4q and 9p = 8q – 12, find the value of pq.
- A. 12
- B. 7
- C. -7
- D. -12