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
|
Community |
Timber Production (tonnes) |
|
Bibiani Amenfi Oda Wiawso Sankore |
600 900 1800 1500 2400 |
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 \(\frac{1 - x}{x} + \frac{x}{1 - x} = \frac{5}{2}\)
The sum of the first ten terms of an Arithmetic Progression (A.P.) is 130. If the fifth term is 3 times the first term, find the:
(a) In a right-angled triangle, sin X = \(\frac{3}{5}\). Evaluate, leaving the answer as a fraction, 5 (cosX)\(^2\) – 3.
(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\(\frac{22}{7}\)]
