2021 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 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
The graph of \( y = \log_e(x) + \log_e(2x) \), where \( x > 0 \), is identical, over the same domain, to the graph of
- A. \( y = 2\log_e\left(\frac{1}{2}x\right) \)
- B. \( y = 2\log_e(2x) \)
- C. \( y = \log_e(2x^2) \)
- D. \( y = \log_e(3x) \)
- E. \( y = \log_e(4x) \)
A box contains many coloured glass beads.
A random sample of 48 beads is selected and it is found that the proportion of blue-coloured beads in this sample is 0.125
Based on this sample, a 95% confidence interval for the proportion of blue-coloured glass beads is
- A. (0.0314, 0.2186)
- B. (0.0465, 0.2035)
- C. (0.0018, 0.2482)
- D. (0.0896, 0.1604)
- E. (0.0264, 0.2136)
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. Differentiate \( y = 2e^{-3x} \) with respect to \(x\). 1 mark
b. Evaluate \( f'(4) \), where \( f(x) = x\sqrt{2x+1} \). 2 marks
a. Sketch the graph of \( y = 1 - \frac{2}{x-2} \) on the axes below. Label asymptotes with their equations and axis intercepts with their coordinates. 3 marks
b. Find the values of \(x\) for which \( 1 - \frac{2}{x-2} \ge 3 \). 1 mark
End of examination questions
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