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2017 VCE Maths Methods Mini Test 3
Adapted for Year 11. Unit 1 & 2.
Number of marks: 7
Reading time: 1 minute
Writing time: 11 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.
A box contains five red marbles and three yellow marbles. Two marbles are drawn at random from the box without replacement.
The probability that the marbles are of different colours is
- A. \(\frac{5}{8}\)
- B. \(\frac{3}{5}\)
- C. \(\frac{15}{28}\)
- D. \(\frac{15}{56}\)
- E. \(\frac{30}{28}\)
Let \(f\) and \(g\) be functions such that \(f(2) = 5\), \(f(3) = 4\), \(g(2) = 5\), \(g(3) = 2\) and \(g(4) = 1\).
The value of \(f(g(3))\) is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
Part of the graph of the function \(f\) is shown below. The same scale has been used on both axes.
The corresponding part of the graph of the inverse function \(f^{-1}\) is best represented by
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 \(f: [-3, 0] \to R, f(x) = (x+2)^2(x-1)\).
a. Show that \((x+2)^2(x-1) = x^3 + 3x^2 - 4\). 1 mark
b. Sketch the graph of \(f\) on the axes below. Label the axis intercepts and any stationary points with their coordinates. 3 marks
End of examination questions
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