1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -2 x +y &=& 3 \\ 3 x -6 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-20}{9}, y=\frac{-13}{9} $$

2.	Differentiation A Differentiate the following equation: $$\sqrt{\ln\left({x}^{2}\right)}$$ Correct Answer $$\frac{1}{x\sqrt{\ln\left({x}^{2}\right)}}$$

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

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

5.	Integration Please carry out the following integral: $$ \int \sqrt{x - 4} dx$$ Correct Answer $$ \frac{2{\left(x - 4\right)}^{\frac{3}{2}}}{3} $$

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

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

8.	Consider the following series: $$ \sum_{j=0}^{11} (-\left(j - 6\right)) $$ What does the sum evaluate to? Correct Answer $$ 6$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x -5 y &=& 1 \\ 3 x -3 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{-17}{3}, y=-7 $$

10.	Differentiation A Differentiate the following equation: $$\sqrt{\cos\left(x\right)} + \sqrt{5x}$$ Correct Answer $$\frac{(-\sin\left(x\right))}{2\sqrt{\cos\left(x\right)}} + \frac{\sqrt{5}}{2\sqrt{x}}$$