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

2.	Differentiation A Differentiate the following equation: $$\sin\left(\cos\left(6 - x\right)\right)$$ Correct Answer $$\cos\left(\cos\left(6 - x\right)\right)\sin\left(6 - x\right)$$

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

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

5.	Integration Please carry out the following integral: $$ \int \ln\left(x - 1\right) dx$$ Correct Answer $$ \left(x - 1\right)\ln\left(x - 1\right) - \left(x - 1\right) $$

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

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

8.	Consider the following series: $$ \sum_{j=0}^{14} 6\left(j - 5\right) $$ What does the sum evaluate to? Correct Answer $$ 180$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x -y &=& 1 \\ -3 x -3 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{1}{12}, y=\frac{-3}{4} $$

10.	Differentiation A Differentiate the following equation: $$\sqrt{\left(x - 6\right)\left(x - 1\right)}$$ Correct Answer $$\frac{2x - 7}{2\sqrt{x - 6}\sqrt{x - 1}}$$