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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

Correct

Incorrect

Question 2 of 10

2. Question

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

Correct

Incorrect

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

Correct

Incorrect

Hint

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

Question 4 of 10

4. Question

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

Correct

Incorrect

Question 5 of 10

5. Question

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

amplitude = , period = degree(s)

Correct

Incorrect

Question 6 of 10

6. Question

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