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

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

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

4.

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

5.	Integration Please carry out the following integral: $$ \int \frac{5}{-4x} dx$$ Correct Answer $$ null $$

6.	Integration Please carry out the following integral: $$ \int {\left(-5x - 1\right)}^{-4} dx$$ Correct Answer $$ \frac{1}{15{\left(-5x - 1\right)}^{3}} $$

7.	Consider the following differential equation: $$ 5\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0 $$ Find the general solution to the above equation. Correct Answer $$ \exp\left(\frac{-2x}{5}\right)\left(A\sin\left(\frac{4x}{5}\right) + B\cos\left(\frac{4x}{5}\right)\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{19} -5\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ -650$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 2 x +2y &=& 1 \\ 3 x +6y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=0, y=\frac{1}{2} $$

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