$$\begin{gathered} Consider the Argand diagram below. \\ Which inequality could define the shaded area? \end{gathered}$$

$$\begin{gathered} Consider the hyperbola with the equation \frac{{\mathcal{x}}^2}{9}-\frac{{\mathcal{Y}}^2}{5}=1 \\ What are the coordinates of the vertex of the hyperbola? \end{gathered}$$

$What is the value of \int sec\mathcal{x}d\mathcal{x} Use the substitution t=\tan \frac{\mathcal{x}}{2} .$

$$\begin{gathered} Let I_n={\int }_0^{\mathrm{\pi }}{\sin }^{n}tdt , where 0\le \mathcal{x}\le \frac{\mathcal{x}}{2}. \\ Which of the following is the correct expression for I_n? \end{gathered}$$

$$\begin{gathered} The polynomial equation {\mathcal{x}}^3+4{\mathcal{x}}^2-2\mathcal{x}-5=0 has roots , \alpha , \beta and \gamma . Which of the \\ following polynomial equations have roots {\alpha }^{2 }, {\beta }^2 and {\gamma }^2? \end{gathered}$$

$Which pair of coordinates gives the foci of 4{\mathcal{x}}^2-25{\mathcal{y}}^2=100?$

$$\begin{gathered} What are the values of a and b for which the following identity is true? \\ \frac{3{\mathcal{x}}^2+7}{({\mathcal{x}}^2+9)({\mathcal{x}}^2+4)}=\frac{a}{{\mathcal{x}}^2+9}+\frac{b}{{\mathcal{x}}^2+4} \end{gathered}$$

$Which expression is equal to \int \frac{d\mathcal{x}}{\sqrt{4\mathcal{x}-{\mathcal{x}}^2}}?$

$$\begin{gathered} The polynomial 4{\mathcal{x}}^3+{\mathcal{x}}^2-3\mathcal{x}+5=0 has roots \alpha \beta , and \gamma . \\ Which polynomial equation has roots \frac{\alpha }{2},\frac{\beta }{2}, and \frac{\gamma }{2}. \end{gathered}$$

$$\begin{gathered} Given that z=\sqrt{3}+\frac{1+\mathcal{i}}{1-\mathcal{i}}, find \\ lm\left(z\right) \\ \overline{z} \\ z in modulus argument form \end{gathered}$$