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

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

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

4.	Differentiation B Differentiate the following equation: $$\frac{\sqrt{x} + \sin\left(x\right)}{\sqrt{x + 1}}$$ Correct Answer $$\frac{\frac{1}{2\sqrt{x}} + \cos\left(x\right)}{\sqrt{x + 1}} - \frac{\sqrt{x} + \sin\left(x\right)}{2{\left(x + 1\right)}^{1.5}}$$

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

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

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

8.	Consider the following series: $$ \sum_{j=0}^{15} 2\left(j - 5\right) $$ What does the sum evaluate to? Correct Answer $$ 80$$

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

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