1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -4 x +6y &=& 2 \\ -x +y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=-5, y=-3 $$

2.	Differentiation A Differentiate the following equation: $$\cos\left(\exp\left(2 + x\right)\right)$$ Correct Answer $$(-\sin\left(\exp\left(2 + x\right)\right)\exp\left(2 + x\right))$$

3.	Differentiation A Differentiate the following equation: $$\cos\left(\ln\left({x}^{2}\right)\right)$$ Correct Answer $$\frac{-2\sin\left(\ln\left({x}^{2}\right)\right)}{x}$$

4.	Differentiation B Differentiate the following equation: $$\frac{\sqrt{2}\cos\left(-3x\right)}{\sqrt{x}}$$ Correct Answer $$\frac{3\sqrt{2}\sin\left(-3x\right)}{\sqrt{x}} - \frac{\cos\left(-3x\right)}{\sqrt{2}{x}^{1.5}}$$

5.	Integration Please carry out the following integral: $$ \int \sin\left(3x - 1\right) dx$$ Correct Answer $$ \frac{(-\cos\left(3x - 1\right))}{3} $$

6.	Integration Please carry out the following integral: $$ \int \sin\left(2x\right) dx$$ Correct Answer $$ \frac{(-\cos\left(2x\right))}{2} $$

7.	Consider the following differential equation: $$ -6\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{-2x}{3}\right) + B\exp\left(\frac{3x}{2}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{16} 6\left(j + 3\right) $$ What does the sum evaluate to? Correct Answer $$ 1122$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -5 x +5y &=& 1 \\ -5 x +4y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{-16}{5}, y=-3 $$

10.	Differentiation A Differentiate the following equation: $$\sin\left(\frac{1}{{x}^{3}}\right)$$ Correct Answer $$\frac{-3\cos\left(\frac{1}{{x}^{3}}\right)}{{x}^{4}}$$