$$\begin{gathered} What is 0.00367254 written in scientific notation, correct to 4 significant figures \\ \left(A\right) 3.672\times {10}^{-2} \\ \left(B\right)3.671\times {10}^{-2} \\ \left(C\right)3.673\times {10}^{-3} \\ \left(D\right)3.7\times {10}^{-3} \end{gathered}$$

$$\begin{gathered} In an arithmetic sequence, the sixth term is 13 and the tenth term is 1: \\ \left(i\right) Find the first term and the common difference. \\ \left(ii\right) Find the sum of the first twenty terms. \end{gathered}$$

$Solve \frac{2\mathcal{x}}{3}-1=\frac{\mathcal{x}}{2}$

$Evaluate li{m}_{m\to 4}\left(\frac{2m^2-9m+4}{m^2-16}\right)$

$$\begin{gathered} If {(2\sqrt{2}-\sqrt{6})}^2=a-b\sqrt{3} \\ find the value of a and b. \end{gathered}$$

$Solve the inequality \left|2\mathcal{x}-3\right|\le 3.$

$$\begin{gathered} Which of the following is the solution to 3^{\mathcal{x}}=50? \\ \left(A\right) \mathcal{x}=1.70 \\ \left(B\right) \mathcal{x}=3.56 \\ \left(C\right) \mathcal{x}=3.60 \\ \left(D\right) \mathcal{x}=3.91 \end{gathered}$$

$$\begin{gathered} Differentiate {\cos }^{2}3\mathcal{x} with respect to \mathcal{x} \\ Hence Evaluate {\int }_{\frac{\mathrm{\pi }}{6}}^{\mathrm{\pi }} \cos 3\mathcal{x} \sin 3\mathcal{x}d\mathcal{x}. \end{gathered}$$

$Solve 8{\sin }^2\mathcal{x}=\cos ec\mathcal{x} for 0\le \mathcal{x}\le 2\mathrm{\pi }$

$$\begin{gathered} Simplify \frac{6a^2-9a}{3-2a} \\ Find the value of \frac{mn}{m-n} when m=6.92\times {10}^5 and 7.9\times {10}^4 \\ correct to 3 significant figures. \\ Solve |3\mathcal{y}-2| <7 \\ Solve (\mathcal{x}+3)(\mathcal{x}-1)=32 \end{gathered}$$