VCE Maths Methods Trigonometry Mini Test 5
Number of marks: 4
Reading time: 1 minute
Writing time: 6 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 period of the function with rule \( y = \tan\left(\frac{\pi x}{2}\right) \) is
- A. 1
- B. 2
- C. 4
- D. 2π
- E. 4π
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 \([-2, 2]\)
The graph of \(y = \tan(ax)\), where \(a \in R^+\), has a vertical asymptote \(x = 3\pi\) and has exactly one \(x\)-intercept in the region \((0, 3\pi)\).
The value of \(a\) is
- A. \(\frac{1}{6}\)
- B. \(\frac{1}{3}\)
- C. \(\frac{1}{2}\)
- D. \(1\)
- E. \(2\)
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
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.
End of examination questions
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