2018 VCE Maths Methods Mini Test 5
Number of marks: 9
Reading time: 2 minutes
Writing time: 13 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.
If \(\int_1^{12} g(x)dx = 5\) and \(\int_{12}^{5} g(x)dx = -6\), then \(\int_1^{5} g(x)dx\) is equal to
- A. \(-11\)
- B. \(-1\)
- C. \(1\)
- D. \(3\)
- E. \(11\)
A tangent to the graph of \(y = \log_e(2x)\) has a gradient of 2.
This tangent will cross the y-axis at
- A. \(0\)
- B. \(-0.5\)
- C. \(-1\)
- D. \(-1 - \log_e(2)\)
- E. \(-2\log_e(2)\)
The function \(f\) has the property \(f(x + f(x)) = f(2x)\) for all non-zero real numbers \(x\).
Which one of the following is a possible rule for the function?
- A. \(f(x) = 1-x\)
- B. \(f(x) = x-1\)
- C. \(f(x) = x\)
- D. \(f(x) = \frac{x}{2}\)
- E. \(f(x) = \frac{1-x}{2}\)
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 \( f: (2, \infty) \rightarrow \mathbb{R} \), where \( f(x) = \frac{1}{(x-2)^2} \).
State the rule and domain of \( f^{-1} \). 3 marks
Two boxes each contain four stones that differ only in colour.
Box 1 contains four black stones.
Box 2 contains two black stones and two white stones.
A box is chosen randomly and one stone is drawn randomly from it.
Each box is equally likely to be chosen, as is each stone.
a. What is the probability that the randomly drawn stone is black? 2 marks
b. It is not known from which box the stone has been drawn.
Given that the stone that is drawn is black, what is the probability that it was drawn from Box 1? 2 marks
End of examination questions
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