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- 10 minutes in duration
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- 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

State whether $y=x-1$ 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 \(f\left( x \right) = ax + b\), \(f\left( 1 \right) = 7\) and \(f\left( 2 \right) = 10\), find \(a \) and \(b\).

\(a = \)

\(b = \)

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

State the domain and range of \(y = \dfrac{x}{{x + 1}}\).

CorrectIncorrect - Question 4 of 10
##### 4. 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 5 of 10
##### 5. Question

Choose vector quantities.

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

Find the vector equation of the following diagram.

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

Find \(x\) and \(y\), if \(\overrightarrow {AC} = \left( {\begin{array}{*{20}{c}}

x\\

y

\end{array}} \right)\) given \(\overrightarrow {BA} = \left( {\begin{array}{*{20}{c}}

3\\

-2

\end{array}} \right)\) and \(\overrightarrow {BC} = \left( {\begin{array}{*{20}{c}}

-1\\

6

\end{array}} \right)\).\(x = \) , \(y = \)

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

Find \(k\), correcting to two significant figures, such a vector \(k\left( {\begin{array}{*{20}{c}}

2\\

{ – 3}\\

2

\end{array}} \right)\) is in the same direction as \(\left( {\begin{array}{*{20}{c}}

2\\

{ – 3}\\

2

\end{array}} \right)\) and with length 4 units.CorrectIncorrect - Question 9 of 10
##### 9. Question

Find \(k\) given \(\vec a = \left( {\begin{array}{*{20}{c}}

k\\

-2\\

5

\end{array}} \right)\) and \(\vec b = \left( {\begin{array}{*{20}{c}}

2\\

3\\

-4

\end{array}} \right)\) are perpendicular.CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\vec a \bullet \vec b}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)

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

Find the acute angle, correcting to the nearest degree, between the lines: \(2x + y = 4\) and \(3x + 2y = 7\).

degree(s)

CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\left| {\vec a \bullet \vec b} \right|}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)