(a) Given that \(\sin x = \frac{5}{13}, 0° \leq x \leq 90°\), find \(\frac{\cos x - 2 \sin x }{2\tan x}\).

(b)

The diagram represents the vertical cross-section of a mountain with height NQ standing on a horizontal ground PRN. If the angles of elevation of the top of the mountain from P and R are 30° and 70° respectively and PR = 500m, calculate, correct to 3 significant figures :

(i) |QP| ; (ii) the height of the mountain.

In the diagram, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate the perimeter of the rhombus

• A. 34cm
• B. 52cm
• C. 56cm
• D. 96cm

If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?

• A. 90°
• B. 63°
• C. 60°
• D. 26°

Solve for y in the equation 10^1 x 5(2y - 2) x 4(y - 1) = 1

• A. 3/4
• B. 5/4
• C. 2/3
• D. 5

The salary of a man was increased in the ratio 40:47. calculate the percentage increase in the salary

• A. 85.1%
• B. 58.5%
• C. 17.5%
• D. 14.9%

In the diagram below, forces P, Q and 50N are acting on a body at M. If the system is in equilibrium, calculate, in terms of \(\theta\), the magnitude of P.

• A. \(\frac{50 \cos \theta}{\sin (\theta + 45)°}\)
• B. \(\frac{50 \cos \theta}{\cos (\theta + 45)°}\)
• C. \(\frac{50 \sin \theta}{\cos (\theta + 45)°}\)
• D. \(\frac{50 \sin \theta}{\sin (\theta + 45)°}\)

A number consists of 2 digits whose sum is 8, if 8 is subtracted from the number, the digits interchanges their place. The number is

• (a) 44
• (b) 35
• (c) 62
• (d) 33

Subtract ninety nine from nine hundred and ninety and then, add it to eight hundred and sixty five. What will be the final answer?

• (a) 1756
• (b) 1855
• (c) 1954
• (d) 1180

For what of n isⁿ⁺¹C₃ = 4(ⁿC₃)?

• A. 6
• B. 5
• C. 4
• D. 3

Three of the angles of a hexagon are each X^o. The others are each 3X^o. Find X

• A. 30^o
• B. 40^o
• C. 60^o
• D. 80^o