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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 \(f\left( x \right) = ax + b\), \(f\left( 3 \right) = 1\) and \(f\left( 2 \right) = 2\), find \(a \) and \(b\).

\(a = \)

\(b = \)

CorrectIncorrect - Question 3 of 10
##### 3. 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 4 of 10
##### 4. Question

Find \(A \), \(B \) and \(C \) if the average rate of change between \(x = 2 \) and \(x = 2 + h\) for \(y = 3{x^3} – 5x + 3\) is \(A + Bh\).

Hence, find the gradient of the tangent to \(y = 3{x^3} – 5x + 3\) at \(x = 2 \).\(A = \) , \(B = \) , Gradient is

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

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

CorrectIncorrect - Question 6 of 10
##### 6. 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 7 of 10
##### 7. Question

Find the amplitude and period of \(y = \cos \left( {x – 60^\circ } \right)\).

amplitude = , period = degree(s)

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

Choose vector quantities.

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

Find the vector equation of the following diagram.

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

To calculate the height of a tree, Sarah measures the angle of elevation to the top as \(42^\circ \). She then walks 20 m closer to the tree and measures the angle of elevation as \(61^\circ \). Find the height of the tree.

height of the tree = m

CorrectIncorrect##### Hint

\(\dfrac{a}{{\sin A}} = \dfrac{b}{{\sin C}} = \dfrac{c}{{\sin C}}\)