Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 16.5 : 11.0
Correct Answer
3:2
2. Ratio: $$\frac{5}{1} : \frac{7}{10}$$
Correct Answer
50:7
3. Ratio 0.250 : 0.150
Correct Answer
5:3

2. Write the following as percentages

1. Number: 0.25
Correct Answer
25 %
2. Number: $$\frac{7}{3}$$
Correct Answer
233 %
3. Number: 1.8
Correct Answer
180 %

3. Write the following as a fraction

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

4. Logs

Solve the following for x: $$-5\ln\left(x\right) + -6\ln\left((-x)\right) = \ln\left(x\right) + -5$$
Correct Answer
$$ x = {\exp\left(-5\right)}^{\frac{-1}{12}} $$

5. Powers

1. Please simplify the following expression: $$ {x}^{3}{x}^{2} $$
Correct Answer
$${x}^{5} $$
2. Please simplify the following expression: $$ {x}^{\frac{-2}{-5}}{x}^{\frac{3}{-5}} $$
Correct Answer
$${x}^{\frac{2}{5}}{x}^{\frac{-3}{5}} $$
3. Please simplify the following expression: $$ {\left({x}^{-4}\right)}^{-2} $$
Correct Answer
$$ {x}^{8} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{-4}\right)}^{-2}{y}^{-5}}{{y}^{5}} $$
Correct Answer
$$ \frac{{x}^{8}}{{y}^{10}} $$

6. Express the following ratios in their simplest forms:

1. Ratio 0.240 : 0.800
Correct Answer
3:10
2. Ratio: $$\frac{9}{9} : \frac{5}{10}$$
Correct Answer
2:1
3. Ratio 0.150 : 0.210
Correct Answer
5:7

7. Write the following as percentages

1. Number: 0.11
Correct Answer
11 %
2. Number: $$\frac{3}{7}$$
Correct Answer
42.9 %
3. Number: 1.5
Correct Answer
150 %

8. Write the following as a fraction

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

9. Logs

Solve the following for x: $$\ln\left({\left(5x\right)}^{6}\right) + \ln\left({\left(3x\right)}^{-2}\right) = \ln\left(x\right) + 5$$
Correct Answer
$$ x = {\left(\frac{9\exp\left(5\right)}{15625}\right)}^{\frac{1}{3}} $$

10. Powers

1. Please simplify the following expression: $$ {x}^{5}{x}^{-2} $$
Correct Answer
$${x}^{3} $$
2. Please simplify the following expression: $$ {x}^{\frac{4}{3}}{x}^{\frac{-6}{3}} $$
Correct Answer
$$\frac{{x}^{\frac{4}{3}}}{{x}^{2}} $$
3. Please simplify the following expression: $$ {\left({x}^{4}\right)}^{4} $$
Correct Answer
$$ {x}^{16} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{2}\right)}^{-6}{y}^{-2}}{{y}^{2}} $$
Correct Answer
$$ \frac{1}{{x}^{12}{y}^{4}} $$


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