﻿ Maths Exam

### Maths Exam

1. Express the following ratios in their simplest forms:

 1 Ratio 22.0 : 44.0Correct Answer 5:10 2 Ratio: $$\frac{7}{12} : \frac{6}{5}$$Correct Answer 35:72 3 Ratio 0.200 : 0.240Correct Answer 5:6

2. Write the following as percentages

 1 Number: 0.88Correct Answer 88 % 2 Number: $$\frac{3}{2}$$Correct Answer 150 % 3 Number: 1.7Correct Answer 170 %

3. Write the following as a fraction

 $$80.00 \%$$Correct Answer $$\frac{4}{5}$$

4. Logs

 Solve the following for x: $$3\ln\left(3x\right) + 5\ln\left(3x\right) = \ln\left(x\right) + 3$$Correct Answer $$x = {\left(\frac{\exp\left(3\right)}{{3}^{8}}\right)}^{\frac{1}{7}}$$

5. Powers

 1 Please simplify the following expression: $${x}^{3}{x}^{2}$$Correct Answer $${x}^{5}$$ 2 Please simplify the following expression: $${x}^{\frac{1}{6}}{x}^{\frac{5}{6}}$$Correct Answer $${x}^{\frac{1}{6}}{x}^{\frac{5}{6}}$$ 3 Please simplify the following expression: $${\left({x}^{-4}\right)}^{-2}$$Correct Answer $${x}^{8}$$ 4 Please simplify the following expression: $$\frac{{\left({x}^{-2}\right)}^{-3}{y}^{3}}{{y}^{-6}}$$Correct Answer $${x}^{6}{y}^{9}$$

6. Express the following ratios in their simplest forms:

 1 Ratio 0.150 : 0.300Correct Answer 5:10 2 Ratio: $$\frac{2}{11} : \frac{9}{1}$$Correct Answer 2:99 3 Ratio 0.0600 : 0.120Correct Answer 1:2

7. Write the following as percentages

 1 Number: 0.16Correct Answer 16 % 2 Number: $$\frac{5}{6}$$Correct Answer 83.3 % 3 Number: 1.2Correct Answer 120 %

8. Write the following as a fraction

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

9. Logs

 Solve the following for x: $$3\ln\left(-4x\right) + 3\ln\left(-2x\right) = \ln\left(x\right) + 5$$Correct Answer $$x = {\left(\frac{\exp\left(5\right)}{512}\right)}^{\frac{1}{5}}$$

10. Powers

 1 Please simplify the following expression: $${x}^{-1}{x}^{-2}$$Correct Answer $$\frac{1}{{x}^{3}}$$ 2 Please simplify the following expression: $$\frac{{x}^{-3}}{{x}^{-2}}$$Correct Answer $$\frac{1}{x}$$ 3 Please simplify the following expression: $${\left({x}^{6}\right)}^{6}$$Correct Answer $${x}^{36}$$ 4 Please simplify the following expression: $$\frac{{\left({x}^{2}\right)}^{5}{y}^{-6}}{{y}^{-3}}$$Correct Answer $$\frac{{x}^{10}}{{y}^{3}}$$

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