2021 QCE Maths Methods Paper 2 Mini Test 3
External Assessment Paper 2 — Technology-active
Number of marks: 9
Perusal time: 1 minute
Writing time: 15 minutes
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
Consider the function \( f(x) = e^x \sin(x) \), \( 0 \le x \le 2\pi \)
a) State the exact values of the x-intercepts of the graph of \( f(x) \). [2 marks]
b) Write an expression for the area enclosed between the graph of \( f(x) \) and the x-axis. [2 marks]
c) Determine the area enclosed between the graph of \( f(x) \) and the x-axis to the nearest square unit. [1 mark]
The velocity function of an object in m s\(^{-1}\) is given by \( v(t) = \cos\left(6t+\frac{\pi}{2}\right) + 2 \), \( 0 \le t \le 5 \). Initially, the object is at the origin.
a) Determine the displacement function. [2 marks]
b) What is the displacement of the object from the origin, in metres (m), after three seconds? [2 marks]
END OF PAPER
