1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -4 x +6y &=& 1 \\ 3 x -3 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{5}{2}, y=\frac{11}{6} $$

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

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

4.	Differentiation B Differentiate the following equation: $$\frac{\frac{6\ln\left(x\right)}{x} - x\left(x + 6\right)}{3}$$ Correct Answer $$\frac{\frac{6}{{x}^{2}} - \frac{6\ln\left(x\right)}{{x}^{2}} - \left(2x + 6\right)}{3}$$

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

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

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: $$ \sum_{j=0}^{14} 3\left(j - 5\right) $$ What does the sum evaluate to? Correct Answer $$ 90$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x +5y &=& 2 \\ -5 x -4 y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=-13, y=16 $$

10.	Differentiation A Differentiate the following equation: $$\cos\left(-2x - {x}^{-6}\right)$$ Correct Answer $$(-\sin\left(-2x - {x}^{-6}\right)\left(-2 - \frac{-6}{{x}^{7}}\right))$$