Section A
Answer all the questions. Answers must be written
within the answer boxes provided.
Working may be continued below the lines, if necessary.
1. [Maximum
mark: 5]
If 
is the arithmetic mean between a
and b then find the value of n
2. [Maximum mark : 6]
Find the exact value of x satisfying the
equation 23x-2. 32x-3 = 36x-1 giving your
answer in the simplified form 
where p
and q are integers
3. [Maximum mark:6]
\;find\;the\;common\;ratio\;r\\&space;(b)\;find\;the\;set\;of\;values\;of\;x\;for\;which\;the\;geometric\;series\;\\&space;sinx\;+\;sin2x\;+\;4sinxcos^{2}x\;+....\;converges\\&space;Consider\;x\:=\:arccos(\frac{1}{4}),\;x>0\\&space;(c)\;Show\;that\;the\;sum\;to\;infinity\;of\;this\;series\;is\;\frac{\sqrt(15)}{2}\\ "(a)\;find\;the\;common\;ratio\;r\\ (b)\;find\;the\;set\;of\;values\;of\;x\;for\;which\;the\;geometric\;series\;\\ sinx\;+\;sin2x\;+\;4sinxcos^{2}x\;+....\;converges\\ Consider\;x\:=\:arccos(\frac{1}{4}),\;x>0\\ (c)\;Show\;that\;the\;sum\;to\;infinity\;of\;this\;series\;is\;\frac{\sqrt(15)}{2}\\")
8. [Maximum mark: 8]
3. [Maximum mark:6]
The roots of a quadratic equation are a
and b x2-2x-4. Without solving the equation,
(a) Find
the value of a2+b2 [4]
(b) Find
a quadratic equation whose roots are a2 and b2 [2]
4. [Maximum
mark: 7]
Consider the complex numbers u=2+3i and v=3+2i
(a) Given
that 
Express w in the form of a+bi where a
and b are real numbers [4]
(b) Find w* and express it in the form reiθ [3]
5. [Maximum mark:6]
=\;\left\{\begin{matrix}&space;1-2x\;,x\leq&space;2&space;&&space;\\&space;\frac{3(x-2)^2}{4}-3\;,x>2&&space;\end{matrix}\right. "f(x)=\;\left\{\begin{matrix} 1-2x\;,x\leq 2 & \\ \frac{3(x-2)^2}{4}-3\;,x>2& \end{matrix}\right.")
(b) Find w* and express it in the form reiθ [3]
5. [Maximum mark:6]
The function f is
defined by
(a). Determine whether or
not f is continuous [2]
The graph of the
function g is obtained by applying the following transformations to the graph
of f:
A reflection in the
y-axis followed by a translation by the vector 
(b). Find g(x) [4]
6. [Maximum mark:9]
Showing clearly any asymptotes and stating the coordinates of any points of intersection with the axes [4]
6. [Maximum mark:9]
Sketch the graph of
Showing clearly any asymptotes and stating the coordinates of any points of intersection with the axes [4]
Hence of otherwise solve the inequality
[5]
7. [Maximum mark: 7]
7. [Maximum mark: 7]
8. [Maximum mark: 8]
9. [Maximum mark: 7]
10. [Maximum mark:8]
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