QCAA Maths Methods Differential Calculus Mini Test 5

 External Assessment Paper 1 — Technology-free 

Number of marks: 12

Perusal time: 1 minute

Writing time: 18 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.



QUESTION 1 [2022 Paper 1 Q1]

Consider the graph of \(f'(x)\) for \(a \le x \le b\).

Graph of the derivative function f'(x) on the interval [a, b]. The graph is a parabola opening upwards, with x-intercepts at some negative value and at x=0. The interval shown is from a (a negative value) to b (a positive value).

Which statement describes all the local maxima and minima of the graph of \(f(x)\) over \(a \le x \le b\)?

  • (A) one local minimum and one local maximum
  • (B) one local minimum and two local maxima
  • (C) one local minimum only
  • (D) one local maximum only
Correct Answer: A
Click here for full solution

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.



QUESTION 2 (4 marks) [2022 Paper 1 Q15]

The derivative of a function is given by \(f'(x) = e^x(x-4)\).

Determine the interval on which the graph of \(f(x)\) is both decreasing and concave up.

QUESTION 3 (7 marks) [2021 Paper 1 Q20]

The population of rabbits (\(P\)) on an island, in hundreds, is given by \(P(t) = t^2 \ln(3t) + 6\), \(t > 0\), where \(t\) is time in years.

Determine the intervals of time when the population is increasing and the intervals when it is decreasing.

END OF PAPER

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