Maths Exam

1. Express the following ratios in their simplest forms:

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

2. Write the following as percentages

1. Number: 0.88
Correct Answer
88 %
2. Number: $$\frac{3}{2}$$
Correct Answer
150 %
3. Number: 1.7
Correct 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 : 0.300
Correct Answer
5:10
2. Ratio: $$\frac{2}{11} : \frac{9}{1}$$
Correct Answer
2:99
3. Ratio 0.0600 : 0.120
Correct Answer
1:2

7. Write the following as percentages

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