1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -5 x +5y &=& 1 \\ -4 x +3y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-7}{5}, y=\frac{-6}{5} $$

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

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

4.	Differentiation B Differentiate the following equation: $$\frac{5x\cos\left(x - 2\right)}{\exp\left(x\right)}$$ Correct Answer $$\frac{5\left(\cos\left(x - 2\right) - x\sin\left(x - 2\right)\right)}{\exp\left(x\right)} - \frac{5x\cos\left(x - 2\right)}{\exp\left(x\right)}$$

5.	Integration Please carry out the following integral: $$ \int \sqrt{-3x} dx$$ Correct Answer $$ \frac{-2{\left((-3)x\right)}^{\frac{3}{2}}}{9} $$

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

7.	Consider the following differential equation: $$ 2\frac{d^2y}{dx^2} + 3\frac{dy}{dx} - 5y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(x\right) + B\exp\left(\frac{-5x}{2}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{10} 5\left(j + 1\right) $$ What does the sum evaluate to? Correct Answer $$ 330$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x +4y &=& 3 \\ x -4 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{5}{2}, y=\frac{1}{8} $$

10.	Differentiation A Differentiate the following equation: $$\cos\left(\sqrt{2x}\right)$$ Correct Answer $$\frac{-2\sin\left(\sqrt{2x}\right)}{2.8284271247461903\sqrt{x}}$$