Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 0.210 : 0.0600
Correct Answer
7:2
2. Ratio: $$\frac{9}{2} : \frac{7}{10}$$
Correct Answer
45:7
3. Ratio 35 : 15
Correct Answer
7:3

2. Write the following as percentages

1. Number: 0.70
Correct Answer
70 %
2. Number: $$\frac{5}{3}$$
Correct Answer
167 %
3. Number: 2.0
Correct Answer
200 %

3. Write the following as a fraction

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

4. Logs

Solve the following for x: $$\ln\left({\left(2x\right)}^{-6}\right) + -2\ln\left(x\right) = \ln\left(x\right) + -3$$
Correct Answer
$$ x = {\left(64\exp\left(-3\right)\right)}^{\frac{-1}{9}} $$

5. Powers

1. Please simplify the following expression: $$ {x}^{-1}{x}^{-5} $$
Correct Answer
$$\frac{1}{{x}^{6}} $$
2. Please simplify the following expression: $$ \frac{{x}^{3}}{{x}^{2}} $$
Correct Answer
$$x $$
3. Please simplify the following expression: $$ {\left({x}^{4}\right)}^{1} $$
Correct Answer
$$ {x}^{4} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{6}\right)}^{3}{y}^{-2}}{{y}^{5}} $$
Correct Answer
$$ \frac{{x}^{18}}{{y}^{7}} $$

6. Express the following ratios in their simplest forms:

1. Ratio 0.210 : 0.300
Correct Answer
7:10
2. Ratio: $$\frac{3}{7} : \frac{2}{1}$$
Correct Answer
3:14
3. Ratio 16.5 : 11.0
Correct Answer
3:2

7. Write the following as percentages

1. Number: 0.086
Correct Answer
8.6 %
2. Number: $$\frac{3}{4}$$
Correct Answer
75.0 %
3. Number: 1.7
Correct Answer
170 %

8. Write the following as a fraction

$$ 85.71 \%$$
Correct Answer
$$\frac{6}{7}$$

9. Logs

Solve the following for x: $$-4\ln\left(-4x\right) + \ln\left({\left(5x\right)}^{6}\right) = \ln\left(x\right) + -1$$
Correct Answer
$$ x = \frac{256\exp\left(-1\right)}{15625} $$

10. Powers

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


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