Are you ready to take your first step toward achieving your goal?
- 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
OK, let’s get started now!
Are you ready to take your first step toward achieving your goal?
- Ten diagnosis quiz questions
- Ten minutes in duration
- Required to attempt all questions
- A mixture of short-answer and multiple-choice questions
- Instant feedback straight after the quiz
OK, let’s get started now!
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- Question 1 of 10
1. Question
State whether $x=2$ is a function or not.
CorrectIncorrectHint
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 \(f\left( 2 \right) + g\left( 2 \right)\).
\(f\left( 2 \right) + g\left( 2 \right) = \)
CorrectIncorrectHint
\(\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right)\)
- 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.
CorrectIncorrectHint
$y=a^x$ 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
CorrectIncorrectHint
\(\dfrac{a}{{\sin A}} = \dfrac{b}{{\sin C}} = \dfrac{c}{{\sin C}}\)