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VCE Maths Methods Differential Calculus Mini Test 10
Adapted for Year 11. Unit 1 & 2.
Number of marks: 4
Reading time: 1 minute
Writing time: 6 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.
Consider (f(x) = x^2 + frac{p}{x}, x neq 0, p in R).
There is a stationary point on the graph of (f) when (x = -2).
The value of (p) is
- A. (-16)
- B. (-8)
- C. (2)
- D. (8)
- E. (16)
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 \(f: (-\infty, \frac{1}{2}] \to R\), where \(f(x) = \sqrt{1-2x}\).
a. Find \(f'(x)\). 1 mark
b. Find the angle \(\theta\) from the positive direction of the x-axis to the tangent to the graph of \(f\) at \(x = -1\), measured in the anticlockwise direction. 2 marks
End of examination questions
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