Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 11.0 : 13.2
Correct Answer
5:6
2. Ratio: $$\frac{6}{1} : \frac{1}{7}$$
Correct Answer
42:1
3. Ratio 33.0 : 92.4
Correct Answer
5:14

2. Write the following as percentages

1. Number: 0.47
Correct Answer
47 %
2. Number: $$\frac{7}{2}$$
Correct Answer
350 %
3. Number: 2.0
Correct Answer
200 %

3. Write the following as a fraction

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

4. Logs

Solve the following for x: $$4\ln\left(-4x\right) + 4\ln\left(4x\right) = \ln\left(x\right) + -6$$
Correct Answer
$$ x = {\left(\frac{\exp\left(-6\right)}{{4}^{8}}\right)}^{\frac{1}{7}} $$

5. Powers

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

6. Express the following ratios in their simplest forms:

1. Ratio 24 : 16
Correct Answer
3:2
2. Ratio: $$\frac{5}{1} : \frac{10}{5}$$
Correct Answer
5:2
3. Ratio 8.80 : 26.4
Correct Answer
1:3

7. Write the following as percentages

1. Number: 0.32
Correct Answer
32 %
2. Number: $$\frac{2}{3}$$
Correct Answer
66.7 %
3. Number: 1.2
Correct Answer
120 %

8. Write the following as a fraction

$$ 28.57 \%$$
Correct Answer
$$\frac{2}{7}$$

9. Logs

Solve the following for x: $$-6\ln\left(-4x\right) + \ln\left({\left(6x\right)}^{5}\right) = \ln\left(x\right) + -4$$
Correct Answer
$$ x = {\left(\frac{128\exp\left(-4\right)}{243}\right)}^{\frac{-1}{2}} $$

10. Powers

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


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