1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -x +y &=& 4 \\ 3 x -2 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=12, y=16 $$

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

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

4.

Differentiation B Differentiate the following equation: $$\frac{\left(x + 5\right)\exp\left(\sqrt{x}\right)}{6 + x}$$ Correct Answer $$\frac{\exp\left(\sqrt{x}\right) + \frac{\left(x + 5\right)\exp\left(\sqrt{x}\right)}{2\sqrt{x}}}{6 + x} - \frac{\left(x + 5\right)\exp\left(\sqrt{x}\right)}{{\left(6 + x\right)}^{2}}$$

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

6.	Integration Please carry out the following integral: $$ \int \frac{3}{(-x)} dx$$ Correct Answer $$ null $$

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

8.	Consider the following series: $$ \sum_{j=0}^{19} 6\left(j + 6\right) $$ What does the sum evaluate to? Correct Answer $$ 1860$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 2 x -y &=& 2 \\ 2 x -6 y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{9}{10}, y=\frac{-1}{5} $$

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