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2017 VCE Maths Methods Mini Test 9
Adapted for Year 11. Unit 1 & 2.
Number of marks: 7
Reading time: 1 minute
Writing time: 11 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 a function \(f\), where \(f(-x) = f(x)\), is shown below.
The graph has \(x\)-intercepts at \((a, 0)\), \((b, 0)\), \((c, 0)\) and \((d, 0)\) only.
The area bound by the curve and the \(x\)-axis on the interval \([a, d]\) is
- A. \(\int_a^d f(x)dx\)
- B. \(\int_a^b f(x)dx - \int_b^c f(x)dx + \int_c^d f(x)dx\)
- C. \(2\int_a^b f(x)dx + \int_b^c f(x)dx\)
- D. \(2\int_a^b f(x)dx - 2\int_b^{b+c} f(x)dx\)
- E. \(\int_a^b f(x)dx + \int_c^b f(x)dx + \int_d^c f(x)dx\)
The graphs of \(f: [0, \frac{\pi}{2}] \to R, f(x) = \cos(x)\) and \(g: [0, \frac{\pi}{2}] \to R, g(x) = \sqrt{3}\sin(x)\) are shown below.
The graphs intersect at \(B\).
The ratio of the area of the shaded region to the area of triangle \(OAB\) is
- A. \(9:8\)
- B. \(\sqrt{3}-1 : \frac{\sqrt{3}\pi}{8}\)
- C. \(8\sqrt{3}-3 : 3\pi\)
- D. \(\sqrt{3}-1 : \frac{\sqrt{3}\pi}{4}\)
- E. \(1 : \frac{\sqrt{3}\pi}{8}\)
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.
For events (A) and (B) from a sample space, (Pr(A|B) = frac{1}{5}) and (Pr(B|A) = frac{1}{4}). Let (Pr(A cap B) = p).
a. Find (Pr(A)) in terms of (p). 1 mark
b. Find (Pr(A' cap B')) in terms of (p). 2 marks
c. Given that (Pr(A cup B) le frac{1}{5}), state the largest possible interval for (p). 2 marks
End of examination questions
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