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### Maths Exam

1. Solution of linear equations

 We have the following equations: $$\begin{eqnarray} -2 x -y &=& 4 \\ -5 x -y &=& 4 \end{eqnarray}$$ Correct Answer $$x=0, y=-4$$

2. Differentiation A

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

3. Differentiation A

 Differentiate the following equation: $${\cos\left(2x\right)}^{2}$$Correct Answer $$-4\cos\left(2x\right)\sin\left(2x\right)$$

4. Differentiation B

 Differentiate the following equation: $$\frac{\sqrt{6}\sqrt{x}}{\ln\left(-3 - x\right)}$$Correct Answer $$\frac{\sqrt{6}}{2\sqrt{x}\ln\left(-3 - x\right)} - \frac{(-\sqrt{6}\sqrt{x})}{{\ln\left(-3 - x\right)}^{2}\left(-3 - x\right)}$$

5. Integration

 Please carry out the following integral: $$\int \ln\left(-4x\right) dx$$Correct Answer $$\frac{(-\left(-4x\ln\left(-4x\right) + 4x\right))}{4}$$

6. Integration

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

7. Consider the following differential equation: $$-4\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 0$$

 Find the general solution to the above equation.Correct Answer $$A\exp\left(\frac{-3x}{4}\right) + B\exp\left(2x\right)$$

8. Consider the following series: $$\sum_{j=0}^{11} 6\left(j - 2\right)$$

 What does the sum evaluate to?Correct Answer $$252$$

9. Solution of linear equations

 We have the following equations: $$\begin{eqnarray} 6 x +6y &=& 1 \\ -3 x -2 y &=& 2 \end{eqnarray}$$ Correct Answer $$x=\frac{-7}{3}, y=\frac{5}{2}$$

10. Differentiation A

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

## Maths Exam Generator

Auto-generated maths exams, with and without answers. Set at A-level / end of high school / beginning of university.

## Benzene QMC Gallery

A gallery of images from an attempt to model the benzene ground state using a variational and diffusion monte carlo method.

## Simulation of flooding in new orleans

A not-very-accurate simulation of the flooding in new orleans.

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