2016 VCE Maths Methods Mini Test 3
Number of marks: 11
Reading time: 2 minutes
Writing time: 16 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.
The average rate of change of the function \(f\) with rule \(f(x) = 3x^2 - 2\sqrt{x+1}\), between \(x=0\) and \(x=3\), is
- A. 8
- B. 25
- C. \(\frac{53}{9}\)
- D. \(\frac{25}{3}\)
- E. \(\frac{13}{9}\)
Which one of the following is the inverse function of \(g: [3, \infty) \to R, g(x) = \sqrt{2x-6}\)?
- A. \(g^{-1}: [3, \infty) \to R, g^{-1}(x) = \frac{x^2+6}{2}\)
- B. \(g^{-1}: [0, \infty) \to R, g^{-1}(x) = (2x-6)^2\)
- C. \(g^{-1}: [0, \infty) \to R, g^{-1}(x) = \sqrt{\frac{x}{2}+6}\)
- D. \(g^{-1}: [0, \infty) \to R, g^{-1}(x) = \frac{x^2+6}{2}\)
- E. \(g^{-1}: R \to R, g^{-1}(x) = \frac{x^2+6}{2}\)
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 \(f: R \setminus \{1\} \to R\), where \(f(x) = 2 + \frac{3}{x-1}\).
a. Sketch the graph of \(f\). Label the axis intercepts with their coordinates and label any asymptotes with the appropriate equation. 3 marks
b. Find the area enclosed by the graph of \(f\), the lines \(x=2\) and \(x=4\), and the x-axis. 2 marks
A paddock contains 10 tagged sheep and 20 untagged sheep. Four times each day, one sheep is selected at random from the paddock, placed in an observation area and studied, and then returned to the paddock.
a. What is the probability that the number of tagged sheep selected on a given day is zero? 1 mark
b. What is the probability that at least one tagged sheep is selected on a given day? 1 mark
c. What is the probability that no tagged sheep are selected on each of six consecutive days? Express your answer in the form \(\left(\frac{a}{b}\right)^c\), where \(a\), \(b\) and \(c\) are positive integers. 1 mark
End of examination questions
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