## 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

Find \(a\) and \(b\), if \(\dfrac{{{{\left( {{x^2} + 1} \right)}^3}}}{{{x^2} – 2}} = \dfrac{{ax{{\left( {{x^2} + 1} \right)}^2}\left( {2{x^2} + b} \right)}}{{{{\left( {{x^2} – 2} \right)}^2}}}\).

\(a = \) , \(b = \)

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}\dfrac{u}{v} = \dfrac{{u’v – uv’}}{{{v^2}}}\)

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

Express \({\log _b}108\) in terms of \(x,y\) or \(z\) , given \(x = {\log _b}2,y = {\log _b}3,z = {\log _b}5\).

CorrectIncorrect##### Hint

\({\log _b}xy = {\log _b}x + {\log _b}y\)

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

The mass of bacteria \(t\) hours after establishment is \({A_t} = 500 \times {1.6^{1.1t}}\) grams. Find the time for the mass to reach 600 grams. Answer correct to the nearest minute.

minute(s)

CorrectIncorrect##### Hint

\({a^x} = y \Rightarrow x = {\log _a}y\)

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

Find \(a \) and \(b \) , if $\dfrac{{\sqrt 7 + \sqrt 8 }}{{3\sqrt 7 – 3\sqrt 8 }} + \dfrac{{2\sqrt 8 – 2\sqrt 7 }}{{3\sqrt 8 + 3\sqrt 7 }} = a + b\sqrt {14} $.

\(a = \) , \(b = \)

CorrectIncorrect##### Hint

\(\dfrac{1}{{\sqrt a + \sqrt b }} = \dfrac{1}{{\sqrt a + \sqrt b }} \times \dfrac{{\sqrt a – \sqrt b }}{{\sqrt a – \sqrt b }} = \dfrac{{\sqrt a – \sqrt b }}{{a – b}}\)

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

Given \(f\left( x \right) = ax + b\left( {a \ne 0} \right)\), \(\left( {f \circ f} \right)\left( x \right) = x\) and \(f\left( 5 \right) = – 4\), find \(f\left( 1 \right)\).

\(f\left( 1 \right) = \)

CorrectIncorrect##### Hint

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

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

Two numbers differ by 3 such that three times the larger number plus twice the smaller number is equal to 54. Find the numbers.

smaller number = , larger number =

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

Given \(P\left( A \right) = \dfrac{1}{2}\) and \(P\left( B \right) = \dfrac{1}{3}\), find \(P\left( {B’} \right)\), correcting to one decimal place.

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

Find the smallest angle in the triangle, correcting to the nearest degree.

degree(s)

CorrectIncorrect##### Hint

\(\cos A = \dfrac{{{b^2} + {c^2} – {a^2}}}{{2bc}}\)

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

Find the positive angle of inclination, in radian correcting to three significant figures, of a line having a gradient of -2.

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

Solve \(\tan x = \dfrac{1}{{\sqrt 3 }}\) for \(- 360^\circ \le x \le 360^\circ \). Write four answers in ascending order.

\(x = \) \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\)

CorrectIncorrect