1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -3 y &=& 2 \\ 2 x +y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{11}{10}, y=\frac{4}{5} $$

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

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

4.

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

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

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

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

8.	Consider the following series: $$ \sum_{j=0}^{19} -4\left(j + 3\right) $$ What does the sum evaluate to? Correct Answer $$ -1000$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x -2 y &=& 4 \\ 2 x +6y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{13}{5}, y=\frac{-7}{10} $$

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