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- 10 minutes in duration
- Required to attempt all questions
- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

State whether $x=2$ is a function or not.

CorrectIncorrect##### Hint

The relation is a function if each vertical line cuts the graph no more than once.

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

Given \(f\left( 1 \right) = 2\), \(g\left( 4 \right) = 5\), \(\left( {g \circ f} \right)\left( 1 \right) = 3\) and \(\left( {g \circ f} \right)\left( 2 \right) = 5\), find \(f\left( 2 \right) + g\left( 2 \right)\).

\(f\left( 2 \right) + g\left( 2 \right) = \)

CorrectIncorrect##### Hint

\(\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right)\)

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

Determine whether \(f\left( x \right) = \dfrac{1}{{1 – 2{x^2}}}\) is odd, even or neither.

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

Find the vertical and horizontal asymptotes of \(y = \dfrac{{x – 2}}{{x – 1}}\).

\( vertical \ asymptote: \ x = \)

\( horizontal \ asymptote: \ y = \)

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

If the domain of \(y = 2x – 1\) is \(1 \le x < 2\), state the range of \({y^{ - 1}}\).

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

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} + 4x + 3}}\).

CorrectIncorrect - Question 7 of 10
##### 7. 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 8 of 10
##### 8. Question

Express \({\log _b}108\) in terms of \(x,y\) or \(z\) , given \(x = {\log _b}2,y = {\log _b}3,z = {\log _b}5\).

CorrectIncorrect##### Hint

\({\log _b}xy = {\log _b}x + {\log _b}y\)

- Question 9 of 10
##### 9. Question

Solve \({\log _5}x = {\log _5}8 – {\log _5}\left( {6 – x} \right)\).

CorrectIncorrect - 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

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