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

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

3.	Differentiation A Differentiate the following equation: $$\cos\left(x\right)\sqrt{x} - \exp\left(x - 5\right)$$ Correct Answer $$(-\sin\left(x\right)\sqrt{x}) + \frac{\cos\left(x\right)}{2\sqrt{x}} - \exp\left(x - 5\right)$$

4.

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

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: $$ \int {\left(x - 1\right)}^{-3} dx$$ Correct Answer $$ \frac{-1}{2{\left(x - 1\right)}^{2}} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{19} -2\left(j - 4\right) $$ What does the sum evaluate to? Correct Answer $$ -220$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x +3y &=& 4 \\ 2 x +5y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=-17, y=7 $$

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