2016 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.
The linear function \(f: D \to R, f(x) = 5 - x\) has range \([-4, 5)\).
The domain \(D\) is
- A. \((0, 9]\)
- B. \((0, 1]\)
- C. \([5, -4)\)
- D. \([-9, 0)\)
- E. \([1, 9)\)
Let \(f: R \to R, f(x) = 1 - 2\cos\left(\frac{\pi x}{2}\right)\).
The period and range of this function are respectively
- A. 4 and \([-2, 2]\)
- B. 4 and \([-1, 3]\)
- C. 1 and \([-1, 3]\)
- D. \(4\pi\) and \([-1, 3]\)
- E. \(4\pi\) and \([-2, 2]\)
Part of the graph \(y = f(x)\) of the polynomial function \(f\) is shown below.
\(f'(x) < 0\) for
- A. \(x \in (-2, 0) \cup (\frac{1}{3}, \infty)\)
- B. \(x \in (-9, \frac{100}{27})\)
- C. \(x \in (-\infty, -2) \cup (\frac{1}{3}, \infty)\)
- D. \(x \in (-2, \frac{1}{3})\)
- E. \(x \in (-\infty, -2] \cup (1, \infty)\)
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 \(y = \frac{\cos(x)}{x^2+2}\). Find \(\frac{dy}{dx}\). 2 marks
b. Let \(f(x) = x^2e^{5x}\). Evaluate \(f'(1)\). 2 marks
Let \(f: (-\infty, \frac{1}{2}] \to R\), where \(f(x) = \sqrt{1-2x}\).
a. Find \(f'(x)\). 1 mark
b. Find the angle \(\theta\) from the positive direction of the x-axis to the tangent to the graph of \(f\) at \(x = -1\), measured in the anticlockwise direction. 2 marks
End of examination questions
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