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

Sean is biking with a constant speed towards town B from town A. With the aid of wind, which has a speed of 2.5 km it takes him only one hour to reach the destination. However, on the way back to town A he has to bike against the wind, and it takes him three hours to reach town A. Find Sean’s speed.

km/h

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

Solve \({9^x} = {3^x} + 6\).

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

Consider the sequence $7,14,28, \cdots $. Find the number of terms that are less than $1{\rm{ }}000{\rm{ }}000$.

Number of terms is

CorrectIncorrect##### Hint

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

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

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} + 1}}\).

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

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

amplitude = , period = degree(s)

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

Find the acute angle, correcting to the nearest degree, between the lines: \(x + 2y = 4\) and \(5x – 2y = 3\).

degree(s)

CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\left| {\vec a \bullet \vec b} \right|}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)

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

Find \(\theta \), correcting to the nearest degree, if the area of the triangle is 12 cm

^{2}.\(\theta = \) degree(s)

CorrectIncorrect##### Hint

\(Area = \dfrac{1}{2}ab\sin C\)

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

Find the value of \(k \) that the straight lines \(y = 2kx + 6\) and \(y = \dfrac{x}{4} – 5\) are perpendicular.

\(k = \)

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

Find the financial expectation of a ticket in a raffle. The raffle has 500 tickets and there is one prize worth 200 dollars.

dollar(s)

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

Find the interquartile range of the data represented in box-and-whisker plot.

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

1 & 4 & 7 & 9 &&& \\

2 & 1 & 3 & 7 & 8 & 9 & \\

3 & 0 & 0 & 3 & 4 && \\

4 & 1 & 7 &&&& \\

\end{array} \)List the scores in ascending order.

The upper quartile is .

The lower quartile is .

The interquartile range is .

CorrectIncorrect##### Hint

Interquartile Range = Upper Quartile – Lower Quartile