2024 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 asymptote(s) of the graph of \( y = \log_e(x + 1) - 3 \) are
- A. \( x = -1\) only
- B. \( x = 1\) only
- C. \( y = -3\) only
- D. \( x = -1\) and \( y = -3 \)
A function \( g: \mathbb{R} \to \mathbb{R} \) has the derivative \( g'(x) = x^3 - x \).
Given that \( g(0) = 5 \), the value of \( g(2) \) is
- A. 2
- B. 3
- C. 5
- D. 7
A discrete random variable \( X \) is defined using the probability distribution below, where \( k \) is a positive real number.
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Pr(X = x) | 2k | 3k | 5k | 3k | 2k |
Find \( \Pr(X < 4 \mid X > 1) \).
- A. \(\frac{13}{15}\)
- B. \(\frac{11}{13}\)
- C. \(\frac{4}{5}\)
- D. \(\frac{8}{15}\)
If \( \int_a^b f(x)\,dx = -5 \) and \( \int_a^c f(x)\,dx = 3 \), where \( a < b < c \), then \( \int_b^c 2f(x)\,dx \) is equal to
- A. -16
- B. 16
- C. -4
- D. 4
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 \( y = e^x \cos(3x) \).
Find \( \frac{dy}{dx} \). 1 mark
b. Let \( f(x) = \log_e(x^3 - 3x + 2) \). Find \( f'(3) \). 2 marks
Consider the simultaneous linear equations
\( 3k x - 2y = k + 4 \)
\( (k - 4)x + ky = -k \)
where \( x, y \in \mathbb{R} \) and \( k \) is a real constant.
Determine the value of \( k \) for which the system of equations has no real solution. 3 marks
End of examination questions
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