1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x +2y &=& 2 \\ 3 x +2y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=0, y=1 $$

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

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

4.	Differentiation B Differentiate the following equation: $$\left(\sqrt{x} + \sin\left(x\right)\right)\cos\left(5 - x\right)$$ Correct Answer $$\left(\frac{1}{2\sqrt{x}} + \cos\left(x\right)\right)\cos\left(5 - x\right) + \left(\sqrt{x} + \sin\left(x\right)\right)\sin\left(5 - x\right)$$

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

6.	Integration Please carry out the following integral: $$ \int \sqrt{-2x + 1} dx$$ Correct Answer $$ \frac{(-{\left(-2x + 1\right)}^{\frac{3}{2}})}{3} $$

7.	Consider the following differential equation: $$ 4\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + y = 0 $$ 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: $$ \sum_{j=0}^{13} j + 5 $$ What does the sum evaluate to? Correct Answer $$ 161$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 2 x +2y &=& 2 \\ -6 x -3 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-5}{3}, y=\frac{8}{3} $$

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