Maths Exam

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

2.	Differentiation A Differentiate the following equation: $$1 - \exp\left(x\right)\cos\left(x\right)$$

3.	Differentiation A Differentiate the following equation: $$\sqrt{\left(x - 5\right)\ln\left(x\right)}$$

4.	Differentiation B Differentiate the following equation: $$\left(\frac{-2}{x} - 5x\right)\sin\left(\frac{(-x)}{3}\right)$$

5.	Integration Please carry out the following integral: $$ \int \frac{-6}{2x - 5} dx$$

6.	Integration Please carry out the following integral: $$ \int \frac{-3}{-6x} dx$$

7.	Consider the following differential equation: $$ -5\frac{d^2y}{dx^2} - \frac{dy}{dx} + 4y = 0 $$ Find the general solution to the above equation.

8.	Consider the following series: $$ \sum_{j=0}^{10} j + 4 $$ What does the sum evaluate to?

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

10.	Differentiation A Differentiate the following equation: $$2{x}^{1.5} + \exp\left(\cos\left(x\right)\right)$$