1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x +4y &=& 4 \\ -6 x -6 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-16}{3}, y=5 $$

2.	Differentiation A Differentiate the following equation: $$-4x - \ln\left(x\right) + \frac{2}{x}$$ Correct Answer $$-4 - \frac{1}{x} + \frac{-2}{{x}^{2}}$$

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

4.	Differentiation B Differentiate the following equation: $$\left(6 - x + \ln\left(x\right)\right)\ln\left(\frac{-4}{x}\right)$$ Correct Answer $$\left(\frac{1}{x} - 1\right)\ln\left(\frac{-4}{x}\right) + \frac{(-\left(6 - x + \ln\left(x\right)\right))}{x}$$

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

6.	Integration Please carry out the following integral: $$ \int {\left((-5)x\right)}^{-4} dx$$ Correct Answer $$ \frac{-1}{1875{x}^{3}} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{16} -6\left(j + 4\right) $$ What does the sum evaluate to? Correct Answer $$ -1224$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x +2y &=& 4 \\ -3 x +6y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{11}{6}, y=\frac{13}{12} $$

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