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Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 5.50 : 11.0
Correct Answer
1:2
2. Ratio: $$\frac{12}{10} : \frac{12}{11}$$
Correct Answer
11:10
3. Ratio 0.0900 : 0.0600
Correct Answer
3:2

2. Write the following as percentages

1. Number: 0.37
Correct Answer
37 %
2. Number: $$\frac{5}{7}$$
Correct Answer
71.4 %
3. Number: 1.5
Correct Answer
150 %

3. Write the following as a fraction

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

4. Logs

Solve the following for x: $$\ln\left({\left((-2)x\right)}^{-3}\right) + \ln\left({\left((-4)x\right)}^{-1}\right) = \ln\left(x\right) + 2$$
Correct Answer
$$ x = {\left(32\exp\left(2\right)\right)}^{\frac{-1}{5}} $$

5. Powers

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

6. Express the following ratios in their simplest forms:

1. Ratio 0.240 : 0.560
Correct Answer
3:7
2. Ratio: $$\frac{11}{3} : \frac{3}{4}$$
Correct Answer
44:9
3. Ratio 11.0 : 27.5
Correct Answer
2:5

7. Write the following as percentages

1. Number: 0.28
Correct Answer
28 %
2. Number: $$\frac{3}{2}$$
Correct Answer
150 %
3. Number: 1.6
Correct Answer
160 %

8. Write the following as a fraction

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

9. Logs

Solve the following for x: $$\ln\left(-5x\right) + \ln\left({\left((-4)x\right)}^{-5}\right) = \ln\left(x\right) + 1$$
Correct Answer
$$ x = {\left(\frac{1024\exp\left(1\right)}{5}\right)}^{\frac{-1}{5}} $$

10. Powers

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


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