Calculate the variance of 2, 4, 7, 8 and 9
- A. 7.2
- B. 6.8
- C. 3.5
- D. 2.6
In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Calculate the value of x.
- A. 70\(^o\)
- B. 58\(^o\)
- C. 55\(^o\)
- D. 48\(^o\)
In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Find the value of y.
- A. 70\(^o\)
- B. 60\(^o\)
- C. 52\(^o\)
- D. 18\(^o\)
In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70\(^o\), calculate the length of arc ZY. [Take \(\pi = \frac{22}{7}\)]
- A. 11cm
- B. 22 cm
- C. 44 cm
- D. 80 cm
From the top of a vertical cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
- A. 56\(^o\)
- B. 75\(^o\)
- C. 16\(^o\)
- D. 15\(^o\)
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