VCE Maths Methods Trigonometry Mini Test 2
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 \(f: R \to R, f(x) = 3\sin\left(\frac{2x}{5}\right) - 2\).
The period and range of \(f\) are respectively
- A. \(5\pi\) and \([-3, 3]\)
- B. \(5\pi\) and \([-5, 1]\)
- C. \(5\pi\) and \([-1, 5]\)
- D. \(\frac{5\pi}{2}\) and \([-5, 1]\)
- E. \(\frac{5\pi}{2}\) and \([-3, 3]\)
Let \( \cos(x) = \frac{3}{5} \) and \( \sin^2(y) = \frac{25}{169} \), where \( x \in \left[\frac{3\pi}{2}, 2\pi\right] \) and \( y \in \left[\frac{3\pi}{2}, 2\pi\right] \).
The value of \(\sin(x) + \cos(y)\) is
- A. \( \frac{8}{65} \)
- B. \( -\frac{112}{65} \)
- C. \( \frac{112}{65} \)
- D. \( -\frac{8}{65} \)
- E. \( \frac{64}{65} \)
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.
Consider the function \( g : \mathbb{R} \rightarrow \mathbb{R}, g(x) = 2 \sin(2x) \).
a. State the range of \(g\). 1 mark
b. State the period of \(g\). 1 mark
c. Solve \( 2 \sin(2x) = \sqrt{3} \) for \( x \in \mathbb{R} \). 3 marks
Shown below is part of the graph of a period of the function of the form \(y = \tan(ax+b)\).
The graph is continuous for \(x \in [-1, 1]\).
Find the value of \(a\) and the value of \(b\), where \(a > 0\) and \(0 < b < 1\). 3 marks
End of examination questions
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