Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 55.0 : 38.5
Correct Answer
10:7
2. Ratio: $$\frac{4}{1} : \frac{7}{9}$$
Correct Answer
36:7
3. Ratio 0.180 : 0.600
Correct Answer
3:10

2. Write the following as percentages

1. Number: 0.40
Correct Answer
40 %
2. Number: $$\frac{7}{8}$$
Correct Answer
87.5 %
3. Number: 1.3
Correct Answer
130 %

3. Write the following as a fraction

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

4. Logs

Solve the following for x: $$5\ln\left(-5x\right) + 5\ln\left(-5x\right) = \ln\left(x\right) + 4$$
Correct Answer
$$ x = {\left(\frac{\exp\left(4\right)}{{5}^{10}}\right)}^{\frac{1}{9}} $$

5. Powers

1. Please simplify the following expression: $$ {x}^{5}{x}^{3} $$
Correct Answer
$${x}^{8} $$
2. Please simplify the following expression: $$ \frac{{x}^{2}}{{x}^{5}} $$
Correct Answer
$$\frac{1}{{x}^{3}} $$
3. Please simplify the following expression: $$ {\left({x}^{4}\right)}^{1} $$
Correct Answer
$$ {x}^{4} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{-4}\right)}^{4}{y}^{2}}{{y}^{6}} $$
Correct Answer
$$ \frac{1}{{y}^{4}{x}^{16}} $$

6. Express the following ratios in their simplest forms:

1. Ratio 7.70 : 38.5
Correct Answer
1:5
2. Ratio: $$\frac{8}{2} : \frac{8}{6}$$
Correct Answer
3:1
3. Ratio 61.6 : 44.0
Correct Answer
7:5

7. Write the following as percentages

1. Number: 0.90
Correct Answer
90 %
2. Number: $$\frac{2}{3}$$
Correct Answer
66.7 %
3. Number: 1.9
Correct Answer
190 %

8. Write the following as a fraction

$$ 42.86 \%$$
Correct Answer
$$\frac{3}{7}$$

9. Logs

Solve the following for x: $$\ln\left({\left(3x\right)}^{-6}\right) + \ln\left({\left(5x\right)}^{6}\right) = \ln\left(x\right) + 6$$
Correct Answer
$$ x = {\left(\frac{729\exp\left(6\right)}{15625}\right)}^{-1} $$

10. Powers

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