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VCE Maths Methods Integral Calculus Mini Test 4
Adapted for Year 11. Unit 1 & 2.
Number of marks: 5
Reading time: 1 minute
Writing time: 7 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.
If \(\int_1^8 f(x)dx = 5\), then \(\int_0^2 f(2(x+2))dx\) is equal to
- A. 12
- B. 10
- C. 8
- D. \(\frac{1}{2}\)
- E. \(\frac{5}{2}\)
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. Let \( g : \left( \frac{3}{2}, \infty \right) \rightarrow \mathbb{R},\ g(x) = \frac{3}{2x - 3} \).
Find the rule for an antiderivative of \( g(x) \). 1 mark
b. Evaluate \( \int_{0}^{1} f(x)\left(2f(x) - 3\right) dx \), where \( \int_{0}^{1} \left[f(x)\right]^2 dx = \frac{1}{5} \) and \( \int_{0}^{1} f(x)\, dx = \frac{1}{3} \). 3 marks
End of examination questions
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