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

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

3.	Differentiation A Differentiate the following equation: $$\ln\left(x + 5 + \ln\left(x\right)\right)$$ Correct Answer $$\frac{1 + \frac{1}{x}}{x + 5 + \ln\left(x\right)}$$

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Differentiation B Differentiate the following equation: $$\left(x + 1 - \sin\left(x\right)\right)\ln\left(\sin\left(x\right)\right)$$ Correct Answer $$\left(1 - \cos\left(x\right)\right)\ln\left(\sin\left(x\right)\right) + \frac{\left(x + 1 - \sin\left(x\right)\right)\cos\left(x\right)}{\sin\left(x\right)}$$

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

6.	Integration Please carry out the following integral: $$ \int \ln\left(x + 4\right) dx$$ Correct Answer $$ \left(x + 4\right)\ln\left(x + 4\right) - \left(x + 4\right) $$

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

8.	Consider the following series: $$ \sum_{j=0}^{18} 6\left(j + 2\right) $$ What does the sum evaluate to? Correct Answer $$ 1254$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x +6y &=& 2 \\ -2 x -2 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-8}{3}, y=\frac{5}{3} $$

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