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2021 VCE Maths Methods Mini Test 3
Adapted for Year 11. Unit 1 & 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.
The maximum value of the function \( h: [0, 2] \to R, h(x) = (x-2)e^x \) is
- A. \(-e\)
- B. 0
- C. 1
- D. 2
- E. \(e\)
Consider the following four functional relations.
\( f(x) = f(-x) \quad -f(x) = f(-x) \quad f(x) = -f(x) \quad (f(x))^2 = f(x^2) \)
The number of these functional relations that are satisfied by the function \( f: R \to R, f(x) = x \) is
- A. 0
- B. 1
- C. 2
- D. 3
- E. 4
The probability of winning a game is 0.25
The probability of winning a game is independent of winning any other game.
If Ben plays 10 games, the probability that he will win exactly four times is closest to
- A. 0.1460
- B. 0.2241
- C. 0.9219
- D. 0.0781
- E. 0.7759
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.
Let \( f'(x) = x^3 + x \).
Find \( f(x) \) given that \( f(1) = 2 \). 2 marks
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
End of examination questions
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