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VCE Maths Methods Functions Mini Test 1
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.
Consider the function \( f(x) = \frac{2x+1}{3-x} \), with domain \( x \in \mathbb{R} \setminus \{3\} \).
The inverse of \( f \) is
- A. \( f^{-1}(x) = \frac{3x - 1}{x + 2} \) with domain \( x \in \mathbb{R} \setminus \{3\} \)
- B. \( f^{-1}(x) = 3 - \frac{7}{x + 2} \) with domain \( x \in \mathbb{R} \setminus \{-2\} \)
- C. \( f^{-1}(x) = 3 + \frac{5}{x + 2} \) with domain \( x \in \mathbb{R} \setminus \{-2\} \)
- D. \( f^{-1}(x) = \frac{1 - 3x}{x + 2} \) with domain \( x \in \mathbb{R} \setminus \{-2\} \)
The graph of \( y = f(x) \) is shown below
Which of the following options best represents the graph of \( y = f(2x + 1) \)?
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.
The function \( h : [0, \infty) \rightarrow \mathbb{R},\ h(t) = \frac{3000}{t + 1} \) models the population of a town after \( t \) years.
a. Use the model \( h(t) \) to predict the population of the town after four years. 1 mark
Let \(f: [0, 2] \to \mathbb{R}\), where \(f(x) = \frac{1}{\sqrt{2}}\sqrt{x}\).
a. Find the domain and the rule for \(f^{-1}\), the inverse function of \(f\). 2 marks
The graph of \(y = f(x)\), where \(x \in [0, 2]\), is shown on the axes below.
b. On the axes above, sketch the graph of \(f^{-1}\) over its domain. Label the endpoints and point(s) of intersection with the function \(f\), giving their coordinates. 2 marks
End of examination questions
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