1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -5 x -6 y &=& 3 \\ 4 x +3y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{7}{3}, y=\frac{-22}{9} $$

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

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

4.	Differentiation B Differentiate the following equation: $$\left(x - 5 + \sin\left(x\right)\right)\sin\left(-6 - x\right)$$ Correct Answer $$\left(1 + \cos\left(x\right)\right)\sin\left(-6 - x\right) - \left(x - 5 + \sin\left(x\right)\right)\cos\left(-6 - x\right)$$

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

6.	Integration Please carry out the following integral: $$ \int {\left((-6)x\right)}^{3} dx$$ Correct Answer $$ -54{x}^{4} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{16} 2\left(j + 4\right) $$ What does the sum evaluate to? Correct Answer $$ 408$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x +6y &=& 1 \\ -6 x -6 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-3}{2}, y=\frac{7}{6} $$

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