2018 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.
Let \(f:R \to R\), \(f(x) = 4\cos\left(\frac{2\pi x}{3}\right) + 1\).
The period of this function is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
The maximal domain of the function \(f\) is \(R\setminus\{1\}\).
A possible rule for \(f\) is
- A. \(f(x) = \frac{x^2 - 5}{x-1}\)
- B. \(f(x) = \frac{x+4}{x-5}\)
- C. \(f(x) = \frac{x^2+x+4}{x^2+1}\)
- D. \(f(x) = \frac{5-x^2}{1+x}\)
- E. \(f(x) = \sqrt{x-1}\)
Consider the function \(f:[a, b) \to R, f(x) = \frac{1}{x}\), where \(a\) and \(b\) are positive real numbers.
The range of \(f\) is
- A. \(\left[\frac{1}{a}, \frac{1}{b}\right)\)
- B. \(\left(\frac{1}{b}, \frac{1}{a}\right]\)
- C. \(\left[\frac{1}{b}, \frac{1}{a}\right)\)
- D. \(\left(\frac{1}{b}, \frac{1}{a}\right)\)
- E. \([a, b)\)
The point \(A(3, 2)\) lies on the graph of the function \(f\). A transformation maps the graph of \(f\) to the graph of \(g\), where \(g(x) = \frac{1}{2}f(x-1)\). The same transformation maps the point \(A\) to the point \(P\).
The coordinates of the point \(P\) are
- A. \((2, 1)\)
- B. \((2, 4)\)
- C. \((4, 1)\)
- D. \((4, 2)\)
- E. \((4, 4)\)
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. If \( y = (-3x^3 + x^2 - 64)^3 \), find \( \frac{dy}{dx} \). 1 mark
b. Let \( f(x) = \frac{e^x}{\cos(x)} \).
Evaluate \( f'(\pi) \). 2 marks
The derivative with respect to \(x\) of the function \( f: (1, \infty) \rightarrow \mathbb{R} \) has the rule \( f'(x) = \frac{1}{2} - \frac{1}{(2x-2)} \).
Given that \( f(2) = 0 \), find \( f(x) \) in terms of \(x\). 3 marks
End of examination questions
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