1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -5 x +2y &=& 3 \\ 2 x +y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{1}{9}, y=\frac{16}{9} $$

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

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

4.	Differentiation B Differentiate the following equation: $${4}^{2x}{3}^{\ln\left(x\right)}$$ Correct Answer $$2{4}^{2x}\ln\left(4\right){3}^{\ln\left(x\right)} + \frac{{4}^{2x}{3}^{\ln\left(x\right)}\ln\left(3\right)}{x}$$

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

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

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: $$ \sum_{j=0}^{15} -6\left(j - 6\right) $$ What does the sum evaluate to? Correct Answer $$ -144$$

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

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