C
Find the equation of the normal to the curve $y=(x^2+x+1)(x-3)$ at the point where it cuts the $x-axis$

C
Find the equation of the tangents to the curve $y=x^3$ at points $(2,8)$.

C
Given $|z|=10$ and $arg z=120^o$, write down $z$

C
Solve $x^2-6x+13=0$, where $x\epsilon \mathbb{c}$

C
Find, by completing the square, the greatest value of the function $f(x)=1-6x-x^2$

C
Express the function $f(x)=2x^2-12x+23$ in the form $a(x-p)^2+q$.

C
Solve the following equation $2x^2-6x-3=0$

C
Solve the following equation $5x^2-6x-2=0$

C
Solve the equation $2x^2+7x-15=0$

C
Find the remainder when $4x^3-6x+5$ is divided by $2x+1$.

C
The roots of the equation $2x^2-7x+4=0$ are $\alpha$, $\beta$. Find an equation with integral coefficients whose roots are $\frac{\alpha}{\beta}$, $\frac{\beta}{\alpha}$.

C
The roots of the equation $3x^2+4x-5=0$ are $\alpha$ and $\beta$. Find the values of (a) $\frac{1}{\alpha}+\frac{1}{\beta}$ (b) $\alpha^2+\beta^2$

C
Simplify $\frac{\log 125}{\log 25}$

C
Simplify $\frac{(1+x)^{\frac{1}{2}}-\frac{1}{2}x(1+x)^{-\frac{1}{2}}}{1+x}$

C
Find the value of $(\frac{27}{8})^{-\frac{2}{3}}.$

C
Rationalize the denominators of (a) $\frac{1}{\sqrt{2}}$ (b) $\frac{1}{3-\sqrt2}$

C
Simplify $\sqrt{50}+\sqrt{2}-2\sqrt{18}+\sqrt{8}$

C
Express $6\sqrt{5}$ as a simple square root.

C
Write $\sqrt{63}$ as the simplest possible surd.
You invest $\$3,000$in a two year investment that pays you$12\%\$ per annum. Calculate the future value of the investment.