2022 VCE Maths Methods Mini Test 1
Number of marks: 10
Reading time: 2 minutes
Writing time: 15 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 period of the function \( f(x) = 3\cos(2x + \pi) \) is
- A. \(2\pi\)
- B. \( \pi \)
- C. \( \frac{2\pi}{3} \)
- D. 2
- E. 3
The graph of \( y = \frac{1}{(x + 3)^2} + 4 \) has a horizontal asymptote with the equation
- A. \( y = 4 \)
- B. \( y = 3 \)
- C. \( y = 0 \)
- D. \( x = -2 \)
- E. \( x = -3 \)
The gradient of the graph of \( y = e^{3x} \) at the point where the graph crosses the vertical axis is equal to
- A. 0
- B. \( \frac{1}{e} \)
- C. 1
- D. e
- E. 3
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 \( y = 3x e^{2x} \).
Find \( \frac{dy}{dx} \). 1 mark
b. Find and simplify the rule of \( f'(x) \), where \( f : \mathbb{R} \rightarrow \mathbb{R},\ f(x) = \frac{\cos(x)}{e^x} \). 2 marks
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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