Maths Exam

1. Express the following ratios in their simplest forms:

1. Ratio 4 : 8
Correct Answer
1:2
2. Ratio: $$\frac{12}{3} : \frac{2}{11}$$
Correct Answer
22:1
3. Ratio 0.0500 : 0.250
Correct Answer
1:5

2. Write the following as percentages

1. Number: 0.70
Correct Answer
70 %
2. Number: $$\frac{3}{7}$$
Correct Answer
42.9 %
3. Number: 1.3
Correct Answer
130 %

3. Write the following as a fraction

$$ 80.00 \%$$
Correct Answer
$$\frac{4}{5}$$

4. Logs

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

5. Powers

1. Please simplify the following expression: $$ {x}^{-3}{x}^{1} $$
Correct Answer
$$\frac{1}{{x}^{2}} $$
2. Please simplify the following expression: $$ \frac{{x}^{-6}}{{x}^{4}} $$
Correct Answer
$$\frac{1}{{x}^{10}} $$
3. Please simplify the following expression: $$ {\left({x}^{3}\right)}^{-4} $$
Correct Answer
$$ {x}^{-12} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{5}\right)}^{-6}{y}^{3}}{{y}^{-6}} $$
Correct Answer
$$ \frac{{y}^{9}}{{x}^{30}} $$

6. Express the following ratios in their simplest forms:

1. Ratio 42 : 12
Correct Answer
7:2
2. Ratio: $$\frac{10}{8} : \frac{5}{11}$$
Correct Answer
11:4
3. Ratio 38.5 : 11.0
Correct Answer
7:2

7. Write the following as percentages

1. Number: 0.19
Correct Answer
19 %
2. Number: $$\frac{7}{8}$$
Correct Answer
87.5 %
3. Number: 1.5
Correct Answer
150 %

8. Write the following as a fraction

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

9. Logs

Solve the following for x: $$\ln\left({\left(6x\right)}^{3}\right) + -6\ln\left(2x\right) = \ln\left(x\right) + -2$$
Correct Answer
$$ x = {\left(\frac{8\exp\left(-2\right)}{27}\right)}^{\frac{-1}{4}} $$

10. Powers

1. Please simplify the following expression: $$ {x}^{3}{x}^{-6} $$
Correct Answer
$$\frac{1}{{x}^{3}} $$
2. Please simplify the following expression: $$ \frac{{x}^{2}}{{x}^{-5}} $$
Correct Answer
$${x}^{7} $$
3. Please simplify the following expression: $$ {\left({x}^{6}\right)}^{2} $$
Correct Answer
$$ {x}^{12} $$
4. Please simplify the following expression: $$ \frac{{\left({x}^{2}\right)}^{-2}{y}^{-3}}{{y}^{3}} $$
Correct Answer
$$ \frac{1}{{x}^{4}{y}^{6}} $$


Other Articles:

Quantum Mechanics

A no-nonsense description of quantum mechanics with no maths or philosophy. The concepts are explained with animations, which are mainly computer simulations of electrons.

Saturn's rings

A simulation of Saturn's rings --- a few thousand particles are simulated, in a repeating tiled region. You use the mouse and keys to fly in it.

Chernobyl Simulation

An attempt to simulate the normal running, and then accident of the Chernobyl nuclear reactor.




© Hugo2015. Session @sessionNumber