2016 VCE Maths Methods Mini Test 2
Number of marks: 11
Reading time: 2 minutes
Writing time: 16 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: mathbb{R} to mathbb{R}, f(x) = x^3 - 5x). Part of the graph of (f) is shown below.
a. Find the coordinates of the turning points. 2 marks
b. (A(-1, f(-1))) and (B(1, f(1))) are two points on the graph of (f).
i. Find the equation of the straight line through (A) and (B). 2 marks
ii. Find the distance (AB). 1 mark
c. Let (g: mathbb{R} to mathbb{R}, g(x) = x^3 - kx, k in mathbb{R}^+).
Let (C(-1, g(-1))) and (D(1, g(1))) be two points on the graph of (g).
i. Find the distance (CD) in terms of (k). 2 marks
ii. Find the values of (k) such that the distance (CD) is equal to (k + 1). 1 mark
d. The diagram below shows part of the graphs of (g) and (y = x). These graphs intersect at the points with the coordinates ((0, 0)) and ((a, a)).
i. Find the value of (a) in terms of (k). 1 mark
ii. Find the area of the shaded region in terms of (k). 2 marks
End of examination questions
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