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- 10 diagnosis quiz questions
- 10 minutes in duration
- Required to attempt all questions
- A mixture of short answer and multiple-choice questions
- Instant feedback straight after the test

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- Question 1 of 10
##### 1. Question

Expand and simplify \(\left( {{x^{\frac{1}{2}}} + {x^{ – \frac{1}{2}}}} \right)\left( {{x^{\frac{1}{2}}} – {x^{ – \frac{1}{2}}}} \right)\).

CorrectIncorrect - Question 2 of 10
##### 2. Question

Solve \({4^x} – 6 \times {2^x} + 8 = 0\). There could be more than one answer.

CorrectIncorrect - Question 3 of 10
##### 3. Question

Solve \({\log _{10}}x = \dfrac{1}{2}\) .

CorrectIncorrect##### Hint

\(a = {b^x} \Leftrightarrow x = {\log _b}a\)

- Question 4 of 10
##### 4. Question

Find \(k\) if \(\dfrac{1}{3}{\log _e}64 – \dfrac{1}{2}{\log _e}4 = {\log _e}k\).

\( k = \)

CorrectIncorrect##### Hint

\({\log _e}x – {\log _e}y = {\log _e}\left( {x \div y} \right)\)

- Question 5 of 10
##### 5. Question

Solve \({\log _3}27 + {\log _3}\frac{1}{3} = {\log _3}x\).

\(x = \)

CorrectIncorrect - Question 6 of 10
##### 6. Question

Solve \({e^{2x}} = 2{e^x}\).

CorrectIncorrect##### Hint

- Question 7 of 10
##### 7. Question

Solve \({2^x} – 2 \times {4^x} = 0\).

\(x = \)

CorrectIncorrect##### Hint

\({a^x} = y \Leftrightarrow x = {\log _a}y\)

- Question 8 of 10
##### 8. Question

Find the equation of the graph in red, where the graph of $y=2^x$ is given in blue.

CorrectIncorrect##### Hint

$y=a^x$ is shifted to the right by $b$ units, $y=a^{x-b}$.

$y=a^x$ is shifted to the left by $b$ units, $y=a^{x+b}$.

$y=a^x$ is shifted up by $c$ units, $y=a^x + c$.

$y=a^x$ is shifted down by $c$ units, $y=a^x – c$. - Question 9 of 10
##### 9. Question

Find the equation of the graph in red, where the graph of $y=e^x$ is given in blue.

CorrectIncorrect##### Hint

$y=a^x$ is shifted to the right by $b$ units, $y=a^{x-b}$.

$y=a^x$ is shifted to the left by $b$ units, $y=a^{x+b}$.

$y=a^x$ is shifted up by $c$ units, $y=a^x + c$.

$y=a^x$ is shifted down by $c$ units, $y=a^x – c$. - Question 10 of 10
##### 10. Question

The mass of radioactive \(t \) hours after establishment is \({R_t} = 800 \times {0.8^{0.5t}}\) grams. Find the time for the mass to reach 300 grams. Answer correct to the nearest minute.

hour(s) minute(s)

CorrectIncorrect##### Hint

\({a^x} = y \Rightarrow x = {\log _a}y\)