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2016 VCE Maths Methods Mini Test 2
Adapted for Year 11. Unit 1 & 2.
Number of marks: 8
Reading time: 1 minute
Writing time: 13 minutes
Section B – Calculator Allowed
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 \(f: [0, 8\pi] \to R, f(x) = 2\cos\left(\frac{x}{2}\right) + \pi\).
a. Find the period and range of \(f\). 2 marks
b. State the rule for the derivative function \(f'\). 1 mark
c. Find the equation of the tangent to the graph of \(f\) at \(x = \pi\). 1 mark
d. Find the equations of the tangents to the graph of \(f: [0, 8\pi] \to R, f(x) = 2\cos\left(\frac{x}{2}\right) + \pi\) that have a gradient of 1. 2 marks
e. No longer in the curriulum.
f. Find the values of \(x, 0 \le x \le 8\pi\), such that \(f(x) = 2f'(x) + \pi\). 2 marks
End of examination questions
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