(a) Make m the subject of the relations \(h = \frac{mt}{d(m + p)}\).

(b)  

In the diagram, WY and WZ are straight lines, O is the centre of circle WXM and < XWM = 48°. Calculate the value of < WYZ.

(c) An operation \(\star\) is defind on the set X = {1, 3, 5, 6} by \(m \star n = m + n + 2 (mod 7)\) where \(m, n \in X\).

(i) Draw a table for the operation.

(ii) Using the table, find the truth set of : (I) \(3 \star n = 3\) ; (II) \(n \star n = 3\).

A water reservoir in the form of a cone mounted on a hemisphere is built such that the plane face of the hemisphere fits exactly to the base of the cone and the height of the cone is 6 times thr radius of its base.

(a) Illustrate this information in a diagram.

(b) If the volume of the reservoir is \(333\frac{1}{3}\pi m^{3}\), calculate, correct to the nearest whole number, the :

(I) volume of the hemisphere ; (II) Total surface area of the reservoir. [Take \(\pi = \frac{22}{7}\)].

The table shows the marks scored by some candidates in an examination.

(a) Construct a cumulative frequency table for the distribution and draw a cumulative frequency curve.

(b) Use the curve to estimate, correct to one decimal place, the :

(i) Lowest mark for distinction if 5% of the candidates passed with distinction ; (ii) probability of selecting a candidate who scored at most 45%.

(a) Without using tables or calculator, simplify : \(\frac{0.6 \times 32 \times 0.004}{1.2 \times 0.008 \times 0.16}\), leaving the answer in standard form (scientific notation).

(b) 

In the diagram, \(\overline{EF}\) is parallel to \(\overline{GH}\). If \(< AEF = 3x°, < ABC = 120°\) and \(< CHG = 7x°\), find the value of \(< GHB\).

(a) Simplify : \(3\sqrt{75} - \sqrt{12} + \sqrt{108}\), leaving the answer in surd form (radicals).

(b) If \(124_{n} = 232_{five}\), find n.