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

2.	Differentiation A Differentiate the following equation: $$\ln\left({x}^{-4} - \sin\left(x\right)\right)$$ Correct Answer $$\frac{\frac{-4}{{x}^{5}} - \cos\left(x\right)}{{x}^{-4} - \sin\left(x\right)}$$

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

4.	Differentiation B Differentiate the following equation: $$\left(3 - x + \cos\left(x\right)\right)\exp\left(-3x\right)$$ Correct Answer $$\left(-1 - \sin\left(x\right)\right)\exp\left(-3x\right) - 3\left(3 - x + \cos\left(x\right)\right)\exp\left(-3x\right)$$

5.	Integration Please carry out the following integral: $$ \int \frac{-6}{-4x + 2} dx$$ Correct Answer $$ null $$

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

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

8.	Consider the following series: $$ \sum_{j=0}^{18} 5\left(j - 4\right) $$ What does the sum evaluate to? Correct Answer $$ 475$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x -y &=& 2 \\ -4 x +3y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=-8, y=-10 $$

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