(a) Using ruler a pair of compasses only, construct:

(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\(^o\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;

(ii) locus \(l_1\) of points equidistant from P and R;

(iii) locus \(l_2\) of points equidistant from Q and R

 (b) Measure: (i) |QR|;

ii. < PSR

ii. < PSR

iii. |QY|, where Y is the point of intersection h and h. 

1. A donkey is tied with a rope to a post which is 15 m from a fence. If the length of the rope between the donkey and the post is 17m, calculate the length of the fence within the reach of the donkey.

2. The base of a right pyramid with vertex, V, is a square, PQRS, of side 15 cm. If the slant height is 32 cm long:

3. represent the information in a diagram;

4. calculate its:

5. height, correct to one decimal place;

6. volume, correct to the nearest \(cm^3\)

a) Copy and complete the following table of values for y = 2 cos x – sin x ,\(0^o \leq x \leq 300^o\)

\[\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\ \hline Y & 2.00 & & 0.13 &  & -1.87 & & -2.00 &  & -0.13 & &  \end{array}\]

(b) Using scales of 2 cm to 30\(^o\) on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 2 cos x – sin x for \(0^o \leq x \leq 300^o\)

(c) Use the graph to find the value(s) of x for which:

(i) 2 cos x – sin x = 1;

(ii) tan x = 2.

If log\(_a\)(y + 2) = 1 + log\(_a\) x, find x in terms of y.

2. The table shows the distribution of timber production in five communities in a certain year

1. Draw a pie chart to represent the information.

2. What percentage of timber produced that year was from Amenfi?

3. If a tonne of timber is sold at $560.00, how much more revenue would Oda community receive than Bibiani?

(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?

(b) Using the method of completing the square, solve \(\frac{1 - x}{x} + \frac{x}{1 - x} = \frac{5}{2}\)