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

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

3.	Differentiation A Differentiate the following equation: $$\sqrt{\frac{x\sin\left(x\right)}{2}}$$ Correct Answer $$\frac{\sin\left(x\right) + x\cos\left(x\right)}{2.8284271247461903\sqrt{x}\sqrt{\sin\left(x\right)}}$$

4.	Differentiation B Differentiate the following equation: $$\left(-6x - \sqrt{x}\right)\sin\left(2x\right)$$ Correct Answer $$\left(-6 - \frac{1}{2\sqrt{x}}\right)\sin\left(2x\right) + 2\left(-6x - \sqrt{x}\right)\cos\left(2x\right)$$

5.	Integration Please carry out the following integral: $$ \int \sqrt{-3x - 6} dx$$ Correct Answer $$ \frac{-2{\left(-3x - 6\right)}^{\frac{3}{2}}}{9} $$

6.	Integration Please carry out the following integral: $$ \int {\left(-5x - 2\right)}^{4} dx$$ Correct Answer $$ \frac{(-{\left(-5x - 2\right)}^{5})}{25} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{10} j + 3 $$ What does the sum evaluate to? Correct Answer $$ 88$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -2 y &=& 2 \\ -5 x +4y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{7}{3}, y=\frac{11}{3} $$

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