FINISHED! EVERY YEAR 11 RESOURCE IS NOW AVAILABLE.
VCE Maths Methods Integral Calculus Mini Test 6
Adapted for Year 11. Unit 1 & 2.
Number of marks: 4
Reading time: 1 minute
Writing time: 6 minutes
Section A – Calculator Allowed
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Let \(a \in (0, \infty)\) and \(b \in R\).
Consider the function \(h: [-a, 0) \cup (0, a] \to R, h(x) = \frac{a}{x} + b\).
The range of \(h\) is
- A. \([b-1, b+1]\)
- B. \((b-1, b+1)\)
- C. \((-\infty, b-1) \cup (b+1, \infty)\)
- D. \((-\infty, b-1] \cup [b+1, \infty)\)
- E. \([b-1, \infty)\)
Which one of the following statements is true for \(f: R \to R, f(x) = x + \sin(x)\)?
- A. The graph of \(f\) has a horizontal asymptote
- B. There are infinitely many solutions to \(f(x) = 4\)
- C. \(f\) has a period of \(2\pi\)
- D. \(f'(x) \ge 0\) for \(x \in R\)
- E. \(f'(x) = \cos(x)\)
End of Section A
Section B – No Calculator
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In questions where a numerical answer is required, an exact value must be given unless otherwise specified.
• In questions where more than one mark is available, appropriate working must be shown.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Let \( f'(x) = x^3 + x \).
Find \( f(x) \) given that \( f(1) = 2 \). 2 marks
End of examination questions
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
