﻿ Maths Exam

### Maths Exam

1. Express the following ratios in their simplest forms:

 1 Ratio 19.8 : 33.0Correct Answer 3:5 2 Ratio: $$\frac{3}{4} : \frac{11}{1}$$Correct Answer 3:44 3 Ratio 2.20 : 4.40Correct Answer 1:2

2. Write the following as percentages

 1 Number: 0.44Correct Answer 44 % 2 Number: $$\frac{7}{3}$$Correct Answer 233 % 3 Number: 1.8Correct Answer 180 %

3. Write the following as a fraction

 $$50.00 \%$$Correct Answer $$\frac{1}{2}$$

4. Logs

 Solve the following for x: $$\ln\left({\left(3x\right)}^{-1}\right) + \ln\left({\left(4x\right)}^{-4}\right) = \ln\left(x\right) + 4$$Correct Answer $$x = {\left(768\exp\left(4\right)\right)}^{\frac{-1}{6}}$$

5. Powers

 1 Please simplify the following expression: $${x}^{4}{x}^{-1}$$Correct Answer $${x}^{3}$$ 2 Please simplify the following expression: $$\frac{{x}^{-3}}{{x}^{3}}$$Correct Answer $$\frac{1}{{x}^{6}}$$ 3 Please simplify the following expression: $${\left({x}^{-5}\right)}^{6}$$Correct Answer $${x}^{-30}$$ 4 Please simplify the following expression: $$\frac{{\left({x}^{5}\right)}^{-5}{y}^{-1}}{{y}^{6}}$$Correct Answer $$\frac{1}{{x}^{25}{y}^{7}}$$

6. Express the following ratios in their simplest forms:

 1 Ratio 4.40 : 15.4Correct Answer 2:7 2 Ratio: $$\frac{4}{4} : \frac{1}{5}$$Correct Answer 5:1 3 Ratio 6 : 42Correct Answer 1:7

7. Write the following as percentages

 1 Number: 0.48Correct Answer 48 % 2 Number: $$\frac{2}{3}$$Correct Answer 66.7 % 3 Number: 1.4Correct Answer 140 %

8. Write the following as a fraction

 $$33.33 \%$$Correct Answer $$\frac{1}{3}$$

9. Logs

 Solve the following for x: $$\ln\left({\left(5x\right)}^{2}\right) + -4\ln\left(x\right) = \ln\left(x\right) + 3$$Correct Answer $$x = {\left(\frac{\exp\left(3\right)}{25}\right)}^{\frac{-1}{3}}$$

10. Powers

 1 Please simplify the following expression: $${x}^{1}{x}^{1}$$Correct Answer $${x}^{2}$$ 2 Please simplify the following expression: $$\frac{{x}^{1}}{{x}^{6}}$$Correct Answer $$\frac{1}{{x}^{5}}$$ 3 Please simplify the following expression: $${\left({x}^{-1}\right)}^{6}$$Correct Answer $${x}^{-6}$$ 4 Please simplify the following expression: $$\frac{{\left({x}^{5}\right)}^{-5}{y}^{-1}}{{y}^{4}}$$Correct Answer $$\frac{1}{{x}^{25}{y}^{5}}$$

## Atomistic Simulation of Metals

This presents an interactive simulation of atoms making up a nanoscopic particle of metal.

## 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.