1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x +5y &=& 2 \\ 3 x +3y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{-14}{3}, y=6 $$

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

3.	Differentiation A Differentiate the following equation: $$\exp\left(\cos\left({x}^{-5}\right)\right)$$ Correct Answer $$\frac{5\exp\left(\cos\left({x}^{-5}\right)\right)\sin\left({x}^{-5}\right)}{{x}^{6}}$$

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Differentiation B Differentiate the following equation: $$\frac{6x\exp\left(-2 - x\right)}{\cos\left(x\right)}$$ Correct Answer $$\frac{6\left(\exp\left(-2 - x\right) - x\exp\left(-2 - x\right)\right)}{\cos\left(x\right)} - \frac{-6x\exp\left(-2 - x\right)\sin\left(x\right)}{{\cos\left(x\right)}^{2}}$$

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

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

7.	Consider the following differential equation: $$ -2\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 6y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left((-x)\right) + B\exp\left(3x\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{15} -3\left(j + 2\right) $$ What does the sum evaluate to? Correct Answer $$ -456$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x -5 y &=& 2 \\ -3 x +3y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{-13}{3}, y=-3 $$

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