smc-753-75-Trig functions

Graphs, MET2 2020 VCAA 20 MC

Let , where , be a function with the property

for all

Let be a function where the range of is .

A possible interval for is

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♦♦♦ Mean mark 18%.

Graphs, MET2 2020 VCAA 13 MC

The transformation that maps the graph of onto the graph of is

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♦♦♦ Mean mark 26%.

Functions, MET2-NHT 2019 VCAA 17 MC

The graph of the function is obtained from the graph of the function with rule by a dilation of factor from the -axis, a dilation of factor from the -axis, a reflection in the -axis and a translation of units in the positive direction, in that order.

The range and period of are respectively

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Graphs, MET2 2008 VCAA 18 MC

Let The graph of is transformed by a reflection in the -axis followed by a dilation of factor 4 from the -axis.

The resulting graph is defined by

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♦♦ Mean mark 36%.

Graphs, MET2 2009 VCAA 12 MC

A transformation that maps the curve with equation onto the curve with equation is given by

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Calculus, MET2 2016 VCAA 1

Let .

Find the period and range of . (2 marks)

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State the rule for the derivative function . (1 mark)

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Find the equation of the tangent to the graph of at . (1 mark)

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Find the equations of the tangents to the graph of that have a gradient of 1. (2 marks)

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The rule of can be obtained from the rule of under a transformation , such that

Find the value of and the value of . (3 marks)

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Find the values of , such that . (2 marks)

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MARKER’S COMMENT: Including round brackets rather than square ones was a common mistake.

♦ Mean mark part (d) 50%.

♦♦ Mean mark part (e) 27%.

♦ Mean mark part (f) 50%.

Graphs, MET2 2013 VCAA 1

Trigg the gardener is working in a temperature-controlled greenhouse. During a particular 24-hour time interval, the temperature is given by , where is the time in hours from the beginning of the 24-hour time interval.

State the maximum temperature in the greenhouse and the values of when this occurs. (2 marks)

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State the period of the function (1 mark)

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Find the smallest value of for which (2 marks)

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For how many hours during the 24-hour time interval is (2 marks)

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Trigg is designing a garden that is to be built on flat ground. In his initial plans, he draws the graph of for and decides that the garden beds will have the shape of the shaded regions shown in the diagram below. He includes a garden path, which is shown as line segment

The line through points and is a tangent to the graph of at point

1. Find when (1 mark)
  
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2. Show that the value of is (1 mark)
  
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In further planning for the garden, Trigg uses a transformation of the plane defined as a dilation of factor from the -axis and a dilation of factor from the -axis, where and are positive real numbers.

Let and be the image, under this transformation, of the points and respectively.
1. Find the values of and if and (2 marks)
  
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2. Find the coordinates of the point (1 mark)
  
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i.
ii.
i.
ii.

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b.

e.i.

e.ii.

f.i.

♦♦♦ Mean mark part (f)(i) 14%.

♦♦♦ Mean mark part (f)(ii) 12%.

f.ii.