## 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

The gradient of a line is \(-1\) and the line passes through the points $\left( {4,2} \right)$ and $\left( {a, – 3} \right)$.

Find the value of \(a \).\(a = \)

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

Find the value of \(k \) that the straight lines \(y = 2kx + 6\) and \(y = \dfrac{x}{4} – 5\) are perpendicular.

\(k = \)

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

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

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

If the domain of \(y = {x^3}\) is \(1 < x \le 2\), state the range of \({y^{ - 1}}\).

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

Given \(f\left( x \right) = 2x – 1\), \(g\left( x \right) = x + 1\), \(\left( {f \circ f} \right)\left( 2 \right) = a\), \(\left( {g \circ f} \right)\left( 1 \right) = b\), \(\left( {f \circ g} \right)\left( c \right) = 3\) and \(\left( {g \circ g} \right)\left( d \right) = 1\) find the domain and range of \(a + b + c + d\).

\(a + b + c + d = \)

CorrectIncorrect##### Hint

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

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

Find all values of \(k\) for which \(2{x^2} + kx – k = 0\) has a repeated root.

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

{b^2} – 4ac &\gt 0 \text{ two real solutions }\\

{b^2} – 4ac &= 0 \text{ one real solution }\\

{b^2} – 4ac &\lt 0 \text{ no real solutions }

\end{align}\) - Question 7 of 10
##### 7. Question

The product of two positive integers is 60 and the larger number is 4 more than the smaller number.

Find the numbers by building a quadratic equation.smaller number =

larger number =

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

Find any values of \(x \) for \(y = {x^2} + x + 1\) if \(y = 3\).

CorrectIncorrect - 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

For the function \(f\left( x \right) = \dfrac{{ – 2x – 1}}{{x + 1}}\), find the horizontal and vertical asymptotes.

\(x = \) , \(y = \)

CorrectIncorrect