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

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

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

4.

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

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

6.	Integration Please carry out the following integral: $$ \int {\left(6x - 5\right)}^{-5} dx$$ Correct Answer $$ \frac{-1}{24{\left(6x - 5\right)}^{4}} $$

7.	Consider the following differential equation: $$ 2\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 3y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left((-x)\right) + B\exp\left(\frac{-3x}{2}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{11} -6\left(j + 6\right) $$ What does the sum evaluate to? Correct Answer $$ -828$$

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

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