2020 VCE Maths Methods Mini Test 3
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 graph of the function \(f: D \to R, f(x) = \frac{3x+2}{5-x}\), where \(D\) is the maximal domain, has asymptotes
- A. \(x = -5, y = -\frac{3}{2}\)
- B. \(x = -3, y = 5\)
- C. \(x = \frac{2}{3}, y = -3\)
- D. \(x = 5, y = 3\)
- E. \(x = 5, y = -3\)
Part of the graph of \(y = f'(x)\) is shown below.
The corresponding part of the graph of \(y = f(x)\) is best represented by
If \(f(x) = e^{g(x^2)}\), where \(g\) is a differentiable function, then \(f'(x)\) is equal to
- A. \(2xe^{g(x^2)}\)
- B. \(2xg(x^2)e^{g(x^2)}\)
- C. \(2xg'(x^2)e^{g(x^2)}\)
- D. \(2xg'(2x)e^{g(x^2)}\)
- E. \(2xg'(x^2)e^{g(2x)}\)
Items are packed in boxes of 25 and the mean number of defective items per box is 1.4
Assuming that the probability of an item being defective is binomially distributed, the probability that a box contains more than three defective items, correct to three decimal places, is
- A. 0.037
- B. 0.048
- C. 0.056
- D. 0.114
- E. 0.162
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.
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
Solve the equation \(2\log_2(x+5) - \log_2(x+9) = 1\). 3 marks
End of examination questions
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
