Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 4 : 28
Correct Answer
1:7
2. Ratio: $$\frac{3}{8} : \frac{2}{4}$$
Correct Answer
3:4
3. Ratio 0.140 : 0.490
Correct Answer
2:7

2. Write the following as percentages

1. Number: 0.39
Correct Answer
39 %
2. Number: $$\frac{5}{6}$$
Correct Answer
83.3 %
3. Number: 1.2
Correct Answer
120 %

3. Write the following as a fraction

$$ 40.00 \%$$
Correct Answer
$$\frac{2}{5}$$

4. Logs

Solve the following for x: $$\ln\left(-6x\right) + 5\ln\left(-4x\right) = \ln\left(x\right) + -3$$
Correct Answer
$$ x = {\left(\frac{\exp\left(-3\right)}{6144}\right)}^{\frac{1}{5}} $$

5. Powers

1. Please simplify the following expression: $$ {x}^{4}{x}^{5} $$
Correct Answer
$${x}^{9} $$
2. Please simplify the following expression: $$ {x}^{\frac{-4}{6}}{x}^{\frac{5}{6}} $$
Correct Answer
$${x}^{\frac{-2}{3}}{x}^{\frac{5}{6}} $$
3. Please simplify the following expression: $$ {\left({x}^{-3}\right)}^{6} $$
Correct Answer
$$ {x}^{-18} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{1}\right)}^{-4}{y}^{-2}}{{y}^{1}} $$
Correct Answer
$$ \frac{1}{{x}^{4}{y}^{3}} $$

6. Express the following ratios in their simplest forms:

1. Ratio 0.210 : 0.140
Correct Answer
3:2
2. Ratio: $$\frac{9}{2} : \frac{3}{11}$$
Correct Answer
33:2
3. Ratio 0.0700 : 0.350
Correct Answer
1:5

7. Write the following as percentages

1. Number: 0.65
Correct Answer
65 %
2. Number: $$\frac{7}{3}$$
Correct Answer
233 %
3. Number: 2.0
Correct Answer
200 %

8. Write the following as a fraction

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

9. Logs

Solve the following for x: $$\ln\left({\left(3x\right)}^{-6}\right) + \ln\left({\left(4x\right)}^{4}\right) = \ln\left(x\right) + -2$$
Correct Answer
$$ x = {\left(\frac{729\exp\left(-2\right)}{256}\right)}^{\frac{-1}{3}} $$

10. Powers

1. Please simplify the following expression: $$ {x}^{3}{x}^{5} $$
Correct Answer
$${x}^{8} $$
2. Please simplify the following expression: $$ \frac{{x}^{-5}}{{x}^{-5}} $$
Correct Answer
$$1 $$
3. Please simplify the following expression: $$ {\left({x}^{6}\right)}^{4} $$
Correct Answer
$$ {x}^{24} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{-1}\right)}^{-5}{y}^{2}}{{y}^{-4}} $$
Correct Answer
$$ {x}^{5}{y}^{6} $$


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