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- 10 minutes in duration
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- 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

Find \(a \) and \(b \), if \(a \), \(1 \), \(a+b \) forms a geometric sequence, and \(b \), \(0.5 \), \(a-b \) forms an arithmetic sequence.

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

CorrectIncorrect##### Hint

\(Ge{o_n} = {u_1}{r^{n – 1}}\) and \(Ar{i_n} = {u_1} + \left( {n – 1} \right)d\)

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

Solve \({\log _{10}}x = – 5\), correcting to one significant figures.

$x=$

CorrectIncorrect##### Hint

\(a = {b^x} \Leftrightarrow x = {\log _b}a\)

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

State the domain and range of \(y = {x^2} – 2x\).

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

The perimeter of a rectangular playing field is 170 m and the length of the diagonals of the field is 65 m. Calculate the dimensions of the field.

shorter side =

longer side =

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

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

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

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

If \(\cos \theta = 0.4\) and \(\theta \) is obtuse, find the value of \(\cos \dfrac{\theta }{2}\), correcting to two decimal places.

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

\cos 2\theta &= {\cos ^2}\theta – {\sin ^2}\theta \\

&= 2{\cos ^2}\theta – 1\\

&= 1 – 2{\sin ^2}\theta

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

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

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

Find the probability that a randomly chosen student plays rugby given that he plays soccer.

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

Find \(\int {\left( {\sin x + \cos 4x} \right)dx} \).

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\)