VCE Maths Methods Diff Calculus Mini Test 10
Number of marks: 8
Reading time: 1 minute
Writing time: 12 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.
a. Let \(y = \frac{\cos(x)}{x^2+2}\). Find \(\frac{dy}{dx}\). 2 marks
b. Let \(f(x) = x^2e^{5x}\). Evaluate \(f'(1)\). 2 marks
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
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
