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

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

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

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

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

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

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

8.	Consider the following series: $$ \sum_{j=0}^{15} 5\left(j + 4\right) $$ What does the sum evaluate to? Correct Answer $$ 920$$

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

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