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

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

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

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

5.	Integration Please carry out the following integral: $$ \int {\left((-2)x\right)}^{-6} dx$$ Correct Answer $$ \frac{-1}{320{x}^{5}} $$

6.	Integration Please carry out the following integral: $$ \int \sin\left(5x - 4\right) dx$$ Correct Answer $$ \frac{(-\cos\left(5x - 4\right))}{5} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{11} -3\left(j + 4\right) $$ What does the sum evaluate to? Correct Answer $$ -342$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 5 x -4 y &=& 3 \\ 4 x -4 y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=0, y=\frac{-3}{4} $$

10.	Differentiation A Differentiate the following equation: $$\cos\left(-5x + \sin\left(x\right)\right)$$ Correct Answer $$(-\sin\left(-5x + \sin\left(x\right)\right)\left(\cos\left(x\right) - 5\right))$$