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

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

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

4.

Differentiation B Differentiate the following equation: $$\frac{-5x\left((-x) - \exp\left(x\right)\right)}{\exp\left(x\right)}$$ Correct Answer $$\frac{-5\left((-x) - \exp\left(x\right) + x\left(-1 - \exp\left(x\right)\right)\right)}{\exp\left(x\right)} - \frac{-5x\left((-x) - \exp\left(x\right)\right)}{\exp\left(x\right)}$$

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

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

7.	Consider the following differential equation: $$ -4\frac{d^2y}{dx^2} - 6\frac{dy}{dx} - 2y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left((-x)\right) + B\exp\left(\frac{(-x)}{2}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{10} j - 3 $$ What does the sum evaluate to? Correct Answer $$ 22$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -x +3y &=& 2 \\ -5 x +6y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{2}{3}, y=\frac{8}{9} $$

10.	Differentiation A Differentiate the following equation: $$\ln\left(\frac{-5x}{\exp\left(x\right)}\right)$$ Correct Answer $$\frac{(-\exp\left(x\right)\left(\frac{-5}{\exp\left(x\right)} - \frac{-5x}{\exp\left(x\right)}\right))}{5x}$$