QCAA Maths Methods Paper 2 Integral Calculus Mini Test 4
External Assessment Paper 2 — Technology-active
Number of marks: 10
Perusal time: 1 minute
Writing time: 15 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
The limit of \(\frac{12^h - 1}{h}\) as \(h\) approaches 0 is closest to
- (A) 0.0
- (B) 1.0
- (C) 2.5
- (D) 3.0
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]
A snail is travelling along a straight path from point \(A\). The snail's velocity (cm min\(^{-1}\)) is modelled by \(v(t) = 1.4 \ln(1 + t^2)\), where \(t\) is time (in minutes) for \(0 \le t \le 15\).
An ant passes point \(A\) 12 minutes after the snail and follows the snail's path. The ant moves with a constant acceleration of 2 cm min\(^{-2}\) and passes the snail at \(t = 15\) minutes.
Determine the ant's velocity at point \(A\).
END OF PAPER
