2020 QCAA Maths Methods Paper 2 Mini Test 3
External Assessment Paper 2 — Technology-active
Number of marks: 10
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 2pi )
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) = cosleft(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]
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