$$\begin{gathered} Find and simplify the derivative of each of the following \\ \left(i\right) {\mathcal{x}}^3-3{\mathcal{x}}^2+\mathcal{x}-2 \\ \left(ii\right) \sqrt{1-\mathcal{x}} \\ \left(iii\right) \mathcal{x}\sqrt{1-{\mathcal{x}}^2} \\ \left(iv\right) \frac{\mathcal{x}+2}{1-\mathcal{x}} \end{gathered}$$

Differentiate $\frac{\mathcal{x}}{\cos \mathcal{x}+1}$ with respect to $\mathcal{x}$

$$\begin{gathered} Differentiate \\ {\left(1+\cos 2\mathcal{x}\right)}^3 \\ {\mathcal{x}}^2{e}^{\mathcal{x}+2} \end{gathered}$$

$$\begin{gathered} Find: \\ \int \frac{\cos }{\sin }d\mathcal{x} \\ {\int }_{\frac{1}{2}}^2\left(1-\frac{1}{{\mathcal{x}}^2}\right)d\mathcal{x} \end{gathered}$$

i) $3{\mathcal{x}}^2-5\mathcal{x}+7$

ii) $\frac{3}{{\mathcal{x}}^4}$

iii) ${({\mathcal{x}}^2-1)}^5$

iv) ${\mathcal{x}}^2{(1-\mathcal{x})}^4$

Solve |$\mathcal{X}$-2|<3 and graph your answer on a number line.

Rationalise the denominator and simplify

 $\frac{3+2\sqrt{5}}{2\sqrt{5}-1}$

Differentiate and simplify

(i) $\frac{{\mathcal{X}}^2}{2}-\sqrt{3\mathcal{X}}$

(ii)$\frac{6\mathcal{X}+5}{1-3\mathcal{X}}$

(iii)$\sqrt{2\mathcal{X}+8}$

$$\begin{gathered} Differentiate with respect to \mathcal{x}: \\ {\left({\mathcal{x}}^2+4\right)}^5 \\ {e}^{\mathcal{x}}{\log }_e\mathcal{x} \\ \frac{\sin \mathcal{x}}{\mathcal{x}-1} \end{gathered}$$

i) Find $\int \left(3{\mathcal{x}}^2+4\mathcal{x}-7\right)d\mathcal{x}$

ii) Evaluate ${\int }_0^3\left(2{\mathcal{x}}^2+\mathcal{x}\right)d\mathcal{x}$

iii) Find $\int \frac{1-{\mathcal{x}}^3}{{\mathcal{x}}^2}d\mathcal{x}$

$Use Simpson\text{'}s rule with five function values to approximate the volume generate by y=\sin x rotated around x-axis between x=0 and x=\frac{\mathrm{\pi }}{2}$

$Find \int 5 \cos x^{0}dx$

$$\begin{gathered} Evaluate \\ \sum _{x=2}^{10} (3x-5) \end{gathered}$$