1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -x +6y &=& 4 \\ -x +y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{-14}{5}, y=\frac{1}{5} $$

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

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

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

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

6.	Integration Please carry out the following integral: $$ \int \sqrt{4x + 5} dx$$ Correct Answer $$ \frac{{\left(4x + 5\right)}^{\frac{3}{2}}}{6} $$

7.	Consider the following differential equation: $$ (-\frac{d^2y}{dx^2}) + 2\frac{dy}{dx} - y = 0 $$ 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: $$ \sum_{j=0}^{14} 3\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ 180$$

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

10.	Differentiation A Differentiate the following equation: $$\left(3 + x\right)\cos\left(x\right) - \ln\left(x - 4\right)$$ Correct Answer $$\cos\left(x\right) - \left(3 + x\right)\sin\left(x\right) - \frac{1}{x - 4}$$