The period of the function
Graphs, MET2 2023 VCAA 18 MC
Graphs, MET2 2023 VCAA 1 MC
The amplitude,
Calculus, MET2 2021 VCAA 5
Part of the graph of
- State the period of
. (1 mark)
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- State the minimum value of
, correct to three decimal places. (1 mark)
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-
Find the smallest positive value of
for which . (1 mark)--- 3 WORK AREA LINES (style=lined) ---
- State the value of
such that for all . (1 mark)
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- i. Find an antiderivative of
in terms of . (1 mark)
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- ii. Use a definite integral to show that the area bounded by
and the -axis over the interval is equal above and below the -axis for all values of . (3 marks)
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- Explain why the maximum value of
cannot be greater than 2 for all values of and why the minimum value of cannot be less than –2 for all values of . (1 mark)
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- Find the greatest possible minimum value of
. (1 mark)
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Graphs, MET2 2021 VCAA 1 MC
The period of the function with rule
Functions, MET1 2021 VCAA 3
Consider the function
- State the range of
. (1 mark)
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- State the period of
. (1 mark)
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- Solve
for . (3 marks)
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Trigonometry, MET2-NHT 2019 VCAA 2
The wind speed at a weather monitoring station varies according to the function
where
- What is the amplitude and the period of
? (2 marks)
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- What are the maximum and minimum wind speeds at the weather monitoring station? (1 mark)
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- Find
, correct to four decimal places. (1 mark)
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- Find the average value of
for the first 60 minutes, correct to two decimal places. (2 marks)
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A sudden wind change occurs at 10 am. From that point in time, the wind speed varies according to the new function
where
- Find the smallest value of
, correct to four decimal places, such that and are equal and are both increasing at 10 am. (2 marks)
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- Another possible value of
was found to be 31.4358Using this value of
, the weather monitoring station sends a signal when the wind speed is greater than 38 km/h.i. Find the value of
at which a signal is first sent, correct to two decimal places. (1 mark)
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ii. Find the proportion of one cycle, to the nearest whole percent, for which
. (2 marks)
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- Let
and .
The transformation maps the graph of onto the graph of .State the values of
, , and , in terms of where appropriate. (3 marks)
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Graphs, MET2-NHT 2019 VCAA 2 MC
Calculus, MET2 2019 VCAA 3
During a telephone call, a phone uses a dual-tone frequency electrical signal to communicate with the telephone exchange.
The strength,
Part of the graph of
- State the period of the function. (1 mark)
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- Find the values of
where for the interval . (1 mark)
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- Find the maximum strength of the dual-tone frequency signal, correct to two decimal places. (1 mark)
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- Find the area between the graph of
and the horizontal axis for . (2 marks)
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Let
and
- Find the values of
and given that has the same area calculated in part d. (2 marks)
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- The rectangle bounded by the line
, the horizontal axis, and the lines and has the same area as the area between the graph of and the horizontal axis for one period of the dual-tone frequency signal.Find the value of
. (2 marks)
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Graphs, MET2 2019 VCAA 1 MC
Let
The period and range of
and and and and and
Graphs, MET2 2018 VCAA 11 MC
The graph of
The value of
Algebra, MET2 2018 VCAA 1 MC
Let
The period of this function is
- 1
- 2
- 3
- 4
- 5
Graphs, MET2 2017 VCAA 1 MC
Let
The period and range of this function are respectively
π π π π π
Graphs, MET1 SM-Bank 27
The graph shown is
- Write down the value of
. (1 mark)
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- Find the value of
. (1 mark)
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- Copy or trace the graph into your writing booklet.
On the same set of axes, draw the graph
for . (2 marks)
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Algebra, MET2 2010 VCAA 1 MC
The function with rule
Graphs, MET2 2016 VCAA 2 MC
Let
The period and range of this function are respectively
Algebra, MET2 2012 VCAA 1 MC
The function with rule
Functions, MET1 2006 VCAA 4
For the function
- write down the amplitude and period of the function. (2 marks)
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- sketch the graph of the function
on the set of axes below. Label axes intercepts with their coordinates.
Label endpoints of the graph with their coordinates. (3 marks)
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Functions, MET1 2010 VCAA 4a
Write down the amplitude and period of the function
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Functions, MET1 2011 VCAA 3a
State the range and period of the function
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Algebra, MET2 2014 VCAA 1
The population of wombats in a particular location varies according to the rule
- Find the period and amplitude of the function
. (2 marks)
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- Find the maximum and minimum populations of wombats in this location. (2 marks)
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- Find
. (1 mark)
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- Over the 12 months from 1 March 2013, find the fraction of time when the population of wombats in this location was less than
. (2 marks)
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Graphs, MET2 2013 VCAA 1
Trigg the gardener is working in a temperature-controlled greenhouse. During a particular 24-hour time interval, the temperature
- 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
- The line through points
and is a tangent to the graph of at point
-
- Find
when (1 mark)
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- Show that the value of
is (1 mark)
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- Find
In further planning for the garden, Trigg uses a transformation of the plane defined as a dilation of factor
- Let
and be the image, under this transformation, of the points and respectively.
- Find the values of
and if and (2 marks)
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- Find the coordinates of the point
(1 mark)
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- Find the values of
Graphs, MET2 2015 VCAA 1 MC
Let
The period and range of this function are respectively
Algebra, MET2 2013 VCAA 1 MC
The function with rule