VCE Maths Methods Trigonometry 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 period of the function \( f(x) = 3\cos(2x + \pi) \) is
- A. \(2\pi\)
- B. \( \pi \)
- C. \( \frac{2\pi}{3} \)
- D. 2
- E. 3
The UV index, \(y\), for a summer day in Melbourne is illustrated in the graph below, where \(t\) is the number of hours after 6 am.
The graph is most likely to be the graph of
- A. \(y = 5 + 5\cos\left(\frac{\pi t}{7}\right)\)
- B. \(y = 5 - 5\cos\left(\frac{\pi t}{7}\right)\)
- C. \(y = 5 + 5\cos\left(\frac{\pi t}{14}\right)\)
- D. \(y = 5 - 5\cos\left(\frac{\pi t}{14}\right)\)
- E. \(y = 5 + 5\sin\left(\frac{\pi t}{14}\right)\)
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.
The graph of \( y = f(x) \), where \( f : [0, 2\pi] \rightarrow \mathbb{R},\ f(x) = 2\sin(2x) - 1 \), is shown below.
a. On the axes above, draw the graph of \( y = g(x) \), where \( g(x) \) is the reflection of \( f(x) \) in the horizontal axis. 2 marks
b. Find all values of \( k \) such that \( f(k) = 0 \) and \( k \in [0, 2\pi] \). 3 marks
c. Let \( h : D \rightarrow \mathbb{R},\ h(x) = 2\sin(2x) - 1 \), where \( h(x) \) has the same rule as \( f(x) \) with a different domain. The graph of \( y = h(x) \) is translated \( a \) units in the positive horizontal direction and \( b \) units in the positive vertical direction so that it is mapped onto the graph of \( y = g(x) \), where \( a, b \in (0, \infty) \).
i. Find the value for \( b \). 1 mark
ii. Find the smallest positive value for \( a \). 1 mark
iii. Hence, or otherwise, state the domain, \( D \), of \( h(x) \). 1 mark
End of examination questions
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