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- 10 minutes in duration
- Required to attempt all questions
- A mixture of short answer and multiple-choice questions
- Instant feedback straight after the test

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- Question 1 of 10
##### 1. Question

Solve \( 3x^2 – 10x + 4 \lt 2x^2 – 5x – 2 \).

\( \lt x \lt \)

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

Find the amplitude and period of \(y = 2 \cos x\).

amplitude = , period = degree(s)

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

Solve \(\sin \left( {x – 45^\circ } \right) = \dfrac{1}{{\sqrt 2 }}\) for \( 0^\circ \le x \le 540^\circ \). Write four answers in ascending order.

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

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

Solve \(\sin 4x = \sin 2x\) for \(0^\circ \le x \le 360^\circ \). Write answers in ascending order.

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

CorrectIncorrect##### Hint

\(\sin 2x = 2\sin x\cos x\)

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

Find \(\dfrac{d}{{dx}}{\log _e}{e^x}{\left( {{e^{2x}} – 1} \right)^3}\).

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}{\log _e}f\left( x \right) = \dfrac{1}{{f\left( x \right)}} \times f’\left( x \right)\)

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

Find \(\int {\left( {\sin x + \cos x} \right)dx} \).

CorrectIncorrect##### Hint

\(\int {\sin \left( {ax + b} \right)dx} = – \dfrac{1}{a}\cos \left( {ax + b} \right) + C\\

\int {\cos \left( {ax + b} \right)dx} = \dfrac{1}{a}\sin \left( {ax + b} \right) + C\) - Question 7 of 10
##### 7. Question

A particle has velocity function \(v\left( t \right) = \sin 2t\) cm/s as it moves in a straight line. The particle is initially 0.5 cm to the right of the origin. Find the displacement of the particle at the end of \(\pi \) seconds.

cm

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

The initial population of horses is 500 and it is decreasing by \(r\% \) each month. Find \(r \) for which the population after 10 months reaches 200. Answer correct to two decimal places.

\(r \)

CorrectIncorrect##### Hint

\({T_n} = {u_1}{r^{n – 1}}\)

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

Select the corresponding frequency table for the cumulative frequency graph shown.

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

In which of the following subjects did John achieve his best result?

\( \begin {array} {|c|c|c|} \hline

subject & mean & standard \ deviation & John’s \ mark \\ \hline

chemist & 75 & 7 & 73 \\ \hline

economy & 70 & 6 & 73 \\ \hline

finance & 65 & 5 & 73 \\ \hline

geography & 80 & 8 & 73 \\ \hline

\end{array} \)\(z\)-score on chemistry:

\(z\)-score on economy:

\(z\)-score on finance:

\(z\)-score on geography:

Which is the best result? (chemistry/economy/finance/geography)

CorrectIncorrect