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

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

3.	Differentiation A Differentiate the following equation: $$\sin\left(\left(1 - x\right)\exp\left(x\right)\right)$$ Correct Answer $$\cos\left(\left(1 - x\right)\exp\left(x\right)\right)\left((-\exp\left(x\right)) + \left(1 - x\right)\exp\left(x\right)\right)$$

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

5.	Integration Please carry out the following integral: $$ \int {\left(5x + 1\right)}^{2} dx$$ Correct Answer $$ \frac{{\left(5x + 1\right)}^{3}}{15} $$

6.	Integration Please carry out the following integral: $$ \int \frac{5}{2x} dx$$ Correct Answer $$ null $$

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

8.	Consider the following series: $$ \sum_{j=0}^{13} (-\left(j + 2\right)) $$ What does the sum evaluate to? Correct Answer $$ -119$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -y &=& 1 \\ 2 x -2 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=0, y=-1 $$

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