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VCE Maths Methods Differential Calculus Mini Test 2
Adapted for Year 11. Unit 1 & 2.
Number of marks: 3
Reading time: 1 minute
Writing time: 5minutes
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 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
A function \( g \) is continuous on the domain \( x \in [a, b] \) and has the following properties:
• The average rate of change of \( g \) between \( x = a \) and \( x = b \) is positive.
• The instantaneous rate of change of \( g \) at \( x = \frac{a + b}{2} \) is negative.
Therefore, on the interval \( x \in [a, b] \), the function must be
- A. many-to-one
- B. one-to-many
- C. one-to-one
- D. strictly decreasing
- E. strictly increasing
The value of an investment, in dollars, after n months can be modelled by the function
\( f(n) = 2500 \times (1.004)^n \)
where \( n \in \{0, 1, 2, ...\} \).
The average rate of change of the value of the investment over the first 12 months is closest to
- A. $10.00 per month.
- B. $10.20 per month.
- C. $10.50 per month.
- D. $125.00 per month.
- E. $127.00 per month.
End of examination questions
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