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### Maths Exam

1. Express the following ratios in their simplest forms:

 1 Ratio 5.50 : 11.0Correct Answer 1:2 2 Ratio: $$\frac{12}{10} : \frac{12}{11}$$Correct Answer 11:10 3 Ratio 0.0900 : 0.0600Correct Answer 3:2

2. Write the following as percentages

 1 Number: 0.37Correct Answer 37 % 2 Number: $$\frac{5}{7}$$Correct Answer 71.4 % 3 Number: 1.5Correct Answer 150 %

3. Write the following as a fraction

 $$20.00 \%$$Correct Answer $$\frac{1}{5}$$

4. Logs

 Solve the following for x: $$\ln\left({\left((-2)x\right)}^{-3}\right) + \ln\left({\left((-4)x\right)}^{-1}\right) = \ln\left(x\right) + 2$$Correct Answer $$x = {\left(32\exp\left(2\right)\right)}^{\frac{-1}{5}}$$

5. Powers

 1 Please simplify the following expression: $${x}^{5}{x}^{5}$$Correct Answer $${x}^{10}$$ 2 Please simplify the following expression: $${x}^{\frac{1}{3}}{x}^{\frac{-2}{3}}$$Correct Answer $${x}^{\frac{1}{3}}{x}^{\frac{-2}{3}}$$ 3 Please simplify the following expression: $${\left({x}^{2}\right)}^{5}$$Correct Answer $${x}^{10}$$ 4 Please simplify the following expression: $$\frac{{\left({x}^{3}\right)}^{1}{y}^{-6}}{{y}^{-1}}$$Correct Answer $$\frac{{x}^{3}}{{y}^{5}}$$

6. Express the following ratios in their simplest forms:

 1 Ratio 0.240 : 0.560Correct Answer 3:7 2 Ratio: $$\frac{11}{3} : \frac{3}{4}$$Correct Answer 44:9 3 Ratio 11.0 : 27.5Correct Answer 2:5

7. Write the following as percentages

 1 Number: 0.28Correct Answer 28 % 2 Number: $$\frac{3}{2}$$Correct Answer 150 % 3 Number: 1.6Correct Answer 160 %

8. Write the following as a fraction

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

9. Logs

 Solve the following for x: $$\ln\left(-5x\right) + \ln\left({\left((-4)x\right)}^{-5}\right) = \ln\left(x\right) + 1$$Correct Answer $$x = {\left(\frac{1024\exp\left(1\right)}{5}\right)}^{\frac{-1}{5}}$$

10. Powers

 1 Please simplify the following expression: $${x}^{-5}{x}^{6}$$Correct Answer $$x$$ 2 Please simplify the following expression: $${x}^{\frac{-1}{-2}}{x}^{\frac{-4}{-2}}$$Correct Answer $${x}^{\frac{1}{2}}{x}^{2}$$ 3 Please simplify the following expression: $${\left({x}^{-2}\right)}^{-5}$$Correct Answer $${x}^{10}$$ 4 Please simplify the following expression: $$\frac{{\left({x}^{-2}\right)}^{-5}{y}^{5}}{{y}^{-1}}$$Correct Answer $${x}^{10}{y}^{6}$$

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