2025 VCE Maths Methods Mini Test 2
Number of marks: 13
Reading time: 2 minutes
Writing time: 19 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 \( g : \mathbb{R} \rightarrow \mathbb{R} \) be defined by \( g(x) = 4x^3 - 3x^4 \).
a. Find the coordinates of both stationary points of \( g \). 2 marks
b. Sketch the graph of \( y = g(x) \) on the axes below, labelling the stationary points and axial intercepts with their coordinates. 2 marks
c. Complete the following gradient table with appropriate values of \( x \) and \( g'(x) \) to show that \( g \) has a stationary point of inflection. 2 marks
d. Find the average value of \( g \) between \( x = 0 \) and \( x = 2 \). 2 marks
e. Let \( h \) be the result after applying a sequence of transformations to \( g \), such that \( h \) has a stationary point of inflection at \( (1, 0) \) and a local maximum at \( (-1, 1) \). Write down a possible sequence of three transformations to map from \( g \) to \( h \). 3 marks
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f. Let \( X \sim \text{Bi}(4, p) \) be a binomial random variable. Show that \( \Pr(X \ge 3) = g(p) \) for all \( p \in [0, 1] \). 2 marks
End of examination questions
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