## 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!

#### Quiz Summary

0 of 10 Questions completed

Questions:

#### Information

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading…

You must sign in or sign up to start the quiz.

You must first complete the following:

#### Results

#### Results

0 of 10 Questions answered correctly

Your time:

Time has elapsed

You have reached 0 of 0 point(s), (0)

Earned Point(s): 0 of 0, (0)

0 Essay(s) Pending (Possible Point(s): 0)

#### Categories

- Not categorized 0%

### The result is not promising.

### You will need to push yourself a bit further.

### You are almost getting there.

### Stay focused to obtain better results!

### Excellent!

### We are so impressed with your result!

### Fantastic Result!

### We hope you’ll keep continued this serial of good marks.

- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10

- Current
- Review
- Answered
- Correct
- Incorrect

- 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