1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x -2 y &=& 4 \\ -5 x +6y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=4, y=4 $$

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

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

4.

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

5.	Integration Please carry out the following integral: $$ \int {\left(x + 2\right)}^{-5} dx$$ Correct Answer $$ \frac{-1}{4{\left(x + 2\right)}^{4}} $$

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

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 $$ A\exp\left(x\right) + B\exp\left(\frac{(-x)}{5}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{11} 4\left(j - 5\right) $$ What does the sum evaluate to? Correct Answer $$ 24$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x -3 y &=& 4 \\ x -3 y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{3}{2}, y=\frac{1}{6} $$

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