Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 26.4 : 44.0
Correct Answer
3:5
2. Ratio: $$\frac{11}{2} : \frac{5}{9}$$
Correct Answer
99:10
3. Ratio 40 : 48
Correct Answer
5:6

2. Write the following as percentages

1. Number: 0.76
Correct Answer
76 %
2. Number: $$\frac{3}{7}$$
Correct Answer
42.9 %
3. Number: 1.9
Correct Answer
190 %

3. Write the following as a fraction

$$ 14.29 \%$$
Correct Answer
$$\frac{1}{7}$$

4. Logs

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

5. Powers

1. Please simplify the following expression: $$ {x}^{2}{x}^{-4} $$
Correct Answer
$$\frac{1}{{x}^{2}} $$
2. Please simplify the following expression: $$ {x}^{\frac{-2}{4}}{x}^{\frac{4}{4}} $$
Correct Answer
$${x}^{\frac{-1}{2}}x $$
3. Please simplify the following expression: $$ {\left({x}^{6}\right)}^{-4} $$
Correct Answer
$$ {x}^{-24} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{5}\right)}^{-6}{y}^{-6}}{{y}^{3}} $$
Correct Answer
$$ \frac{1}{{x}^{30}{y}^{9}} $$

6. Express the following ratios in their simplest forms:

1. Ratio 0.200 : 0.400
Correct Answer
5:10
2. Ratio: $$\frac{12}{3} : \frac{9}{12}$$
Correct Answer
16:3
3. Ratio 25 : 30
Correct Answer
5:6

7. Write the following as percentages

1. Number: 0.36
Correct Answer
36 %
2. Number: $$\frac{5}{3}$$
Correct Answer
167 %
3. Number: 1.3
Correct Answer
130 %

8. Write the following as a fraction

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

9. Logs

Solve the following for x: $$\ln\left({\left(5x\right)}^{-2}\right) + \ln\left({\left(2x\right)}^{6}\right) = \ln\left(x\right) + -3$$
Correct Answer
$$ x = {\left(\frac{25\exp\left(-3\right)}{64}\right)}^{\frac{1}{3}} $$

10. Powers

1. Please simplify the following expression: $$ {x}^{4}{x}^{-1} $$
Correct Answer
$${x}^{3} $$
2. Please simplify the following expression: $$ \frac{{x}^{1}}{{x}^{2}} $$
Correct Answer
$$\frac{1}{x} $$
3. Please simplify the following expression: $$ {\left({x}^{4}\right)}^{4} $$
Correct Answer
$$ {x}^{16} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{6}\right)}^{4}{y}^{6}}{{y}^{2}} $$
Correct Answer
$$ {x}^{24}{y}^{4} $$


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