1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -3 x +5y &=& 1 \\ -3 x +y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{-1}{3}, y=0 $$

2.	Differentiation A Differentiate the following equation: $$\exp\left(2x\ln\left(x\right)\right)$$ Correct Answer $$2\exp\left(2x\ln\left(x\right)\right)\left(\ln\left(x\right) + 1\right)$$

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

4.	Differentiation B Differentiate the following equation: $${5}^{\frac{(-x) + 5{6}^{x}}{5}}$$ Correct Answer $$\frac{{5}^{\frac{(-x) + 5{6}^{x}}{5}}\ln\left(5\right)\left(5{6}^{x}\ln\left(6\right) - 1\right)}{5}$$

5.	Integration Please carry out the following integral: $$ \int {\left(3x - 5\right)}^{1} dx$$ Correct Answer $$ \frac{{\left(3x - 5\right)}^{2}}{6} $$

6.	Integration Please carry out the following integral: $$ \int \sqrt{x} dx$$ Correct Answer $$ \frac{2{x}^{\frac{3}{2}}}{3} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{17} j + 3 $$ What does the sum evaluate to? Correct Answer $$ 207$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -x +y &=& 3 \\ x +5y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-13}{6}, y=\frac{5}{6} $$

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