Find the value of x in the diagram

• A. 10°
• B. 28°
• C. 36°
• D. 44°

The weight W kg of a metal bar varies jointly as its length L meters and the square of its diameter d meters. If w = 140 when d = 4²/₃ and L = 54, find d in terms of W and L.

• A. \(\sqrt{\frac{42W}{5L}}\)
• B. \(\sqrt{\frac{6L}{42W}}\)
• C. \(\frac{42W}{5L}\)
• C. \(\frac{5L}{42W}\)

If 8^{\(\frac{x}{2}\)} = (2^{\(\frac{3}{8}\)})(4\(\frac{3}{4}\)), find x

• A. \(\frac{3}{8}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{4}{5}\)
• D. \(\frac{5}{4}\)

From a point Z, 60 m north of X, a man walks 60√3m eastwards to another point Y. Find the bearing of Y from X.

• A. 0.30^o
• B. 045^o
• C. 060^o
• D. 090^o

If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.

• A. \(a = b^{3} - 3\)
• B. \(a = b^{3} - 9\)
• C. \(a = 9b^{3}\)
• D. \(a = \frac{b^{3}}{9}\)

Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4, 2).

• A. 5y - 2x -18 = 0
• B. 5y + 2x - 18 = 0
• C. 5y - 2x + 18 = 0
• D. 5y + 2x - 2 = 0

A cylindrical tank has a capacity of 3080 m³. What is the depth of the tank if the diameter of its base is 14 m?

(Take pi = 22/7)

• A. 23 m
• B. 25 m
• C. 20 m
• D. 22 m

Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o - q}{1 - tan 30^o}\)

• A. \(\sqrt{3 - 2}\)
• B. 2 - \(\sqrt{3}\)
• C. \(\sqrt{3}\)
• D. -2

(a) A boy had M Dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to \(\frac{1}{3}\) of M, find the value of M.

(b) A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, \(\frac{13}{30}\) by air and \(\frac{4}{15}\) by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?

In the diagram, O is the centre of the circle. OM||XZ and ∠ZOM = 25°. Calculate ∠XYZ

• A. 50°
• B. 55°
• C. 60°
• D. 65°