2025 VCE Maths Methods Mini Test 1
Number of marks: 10
Reading time: 2 minutes
Writing time: 15 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 function that has a range of \([6, 12]\) is
- A. \(f:\mathbb{R}\rightarrow \mathbb{R}\), \(f(x)=6+3\cos(9x)\)
- B. \(f:\mathbb{R}\rightarrow \mathbb{R}\), \(f(x)=6+6\cos(3x)\)
- C. \(f:\mathbb{R}\rightarrow \mathbb{R}\), \(f(x)=9-3\cos(6x)\)
- D. \(f:\mathbb{R}\rightarrow \mathbb{R}\), \(f(x)=9-6\cos(3x)\)
All asymptotes of the graph of \(y=2\tan\left(\pi\left(x+\frac{1}{2}\right)\right)\) are given by
- A. \(x=k\), \(k\in \mathbb{Z}\)
- B. \(x=2k\), \(k\in \mathbb{Z}\)
- C. \(x=2k+1\), \(k\in \mathbb{Z}\)
- D. \(x=\frac{4k+1}{2}\), \(k\in \mathbb{Z}\)
The graph of \(y=f(x)\) is shown below.
Which one of the following options best represents the graph of \(y=f(-x)+2\)?
Consider the system of equations below containing the parameter \(k\), where \(k\in \mathbb{R}\)
\(kx+3y=k^{2}\)
\(2x+(2k+1)y=6-2k\)
Find the value(s) of \(k\) for which this system has no real solutions.
- A. \(k=-2\) only
- B. \(k=\frac{3}{2}\) only
- C. \(k=-2\) or \(\frac{3}{2}\)
- D. \(k\in \mathbb{R}\backslash\{-2,\frac{3}{2}\}\)
Which of the following sets represents a function that has an inverse function?
- A. \(\{(1, 3), (2, 0), (2, 1)\}\)
- B. \(\{(-1, 3), (2, 2), (3, 1)\}\)
- C. \(\{(-1, 3), (0, 1), (1, 3)\}\)
- D. \(\{(1, 0), (2, 3), (1, 3)\}\)
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.
a. Let \( y = x^2 \cos(x) \). Find \( \frac{dy}{dx} \). 1 mark
b. Let \( f(x) = 6\sqrt{x+1} + 5 \). Find the gradient of the tangent to \( y = f(x) \) at \( x = 8 \). 2 marks
Let \( g(x) \) be a function defined for \( x > -\frac{3}{2} \) so that \( g'(x) = \frac{1}{2x+3} \) and \( g(1) = 0 \). Find \( g(x) \). 2 marks
End of examination questions
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