## 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

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