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

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

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

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

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

6.	Integration Please carry out the following integral: $$ \int {\left(x + 4\right)}^{-2} dx$$ Correct Answer $$ \frac{-1}{x + 4} $$

7.	Consider the following differential equation: $$ -5\frac{d^2y}{dx^2} - 6\frac{dy}{dx} - 5y = 0 $$ Find the general solution to the above equation. Correct Answer $$ \exp\left(\frac{-3x}{5}\right)\left(A\sin\left(\frac{-4x}{5}\right) + B\cos\left(\frac{-4x}{5}\right)\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{11} (-\left(j + 1\right)) $$ What does the sum evaluate to? Correct Answer $$ -78$$

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

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