Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 0.400 : 0.120
Correct Answer
10:3
2. Ratio: $$\frac{9}{6} : \frac{1}{8}$$
Correct Answer
12:1
3. Ratio 26.4 : 17.6
Correct Answer
3:2

2. Write the following as percentages

1. Number: 0.51
Correct Answer
51 %
2. Number: $$\frac{7}{3}$$
Correct Answer
233 %
3. Number: 1.2
Correct Answer
120 %

3. Write the following as a fraction

$$ 66.67 \%$$
Correct Answer
$$\frac{2}{3}$$

4. Logs

Solve the following for x: $$-4\ln\left(2x\right) + \ln\left({\left(4x\right)}^{-4}\right) = \ln\left(x\right) + 3$$
Correct Answer
$$ x = {\left(4096\exp\left(3\right)\right)}^{\frac{-1}{9}} $$

5. Powers

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

6. Express the following ratios in their simplest forms:

1. Ratio 0.0400 : 0.0800
Correct Answer
1:2
2. Ratio: $$\frac{7}{10} : \frac{7}{4}$$
Correct Answer
2:5
3. Ratio 6.60 : 4.40
Correct Answer
3:2

7. Write the following as percentages

1. Number: 0.42
Correct Answer
42 %
2. Number: $$\frac{7}{2}$$
Correct Answer
350 %
3. Number: 1.7
Correct Answer
170 %

8. Write the following as a fraction

$$ 40.00 \%$$
Correct Answer
$$\frac{2}{5}$$

9. Logs

Solve the following for x: $$\ln\left({\left(5x\right)}^{-4}\right) + 6\ln\left(x\right) = \ln\left(x\right) + -4$$
Correct Answer
$$ x = 625\exp\left(-4\right) $$

10. Powers

1. Please simplify the following expression: $$ {x}^{1}{x}^{-1} $$
Correct Answer
$$1 $$
2. Please simplify the following expression: $$ \frac{{x}^{1}}{{x}^{-1}} $$
Correct Answer
$${x}^{2} $$
3. Please simplify the following expression: $$ {\left({x}^{-3}\right)}^{3} $$
Correct Answer
$$ {x}^{-9} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{6}\right)}^{6}{y}^{-5}}{{y}^{1}} $$
Correct Answer
$$ \frac{{x}^{36}}{{y}^{6}} $$


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