Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Maths On Track: Assessment Task
Name:
Date of Task:
Duration of Task: from 5 x 50 minute periods of class time
Time allocated: (250 minutes) in class under examination conditions.
Instructions
This SAC (school assessed coursework) is a problem solving task in which you are
required to make practical application of the theory, primarily from the rates of
change area of study, although some theory from other areas of study may be
required. You must answer all questions.
You should use your graphics calculator and you must clearly indicate how that
technology was used. Evidence for this maybe provided either in written form
(screen dumps for example), or through verbal communication with your teacher
who can observe your appropriate use of technology. It is your responsibility to
provide clear evidence of appropriate use of technology.
You may take into the SAC:
1) Your text book, 2) your summary book, 3) your graphics calculator.
Marks will not be given for the answers alone. In some cases you will need to
discuss the results you get, explaining both your reasoning and your working out.
This questions section of this paper has been printed single sided to
give you extra working space for each question (if needed).
Preparation for this SAC
On the following pages you have been provided with maps of the Australian Grand
Prix Albert Park circuit. Each of these maps provides you with different information
about the circuit, including layout and scale. You will need to refer to this information
to answer the questions in this SAC.
Before the SAC it will be useful for you to:
1. Identifying the relative speeds of each turn (which is slowest, fastest etc.)
2. Calculate the approximate distances between turns using the scale given on the
second map.
3. Use the following background information and maps to familiarise yourself with
the Grand Prix Circuit.
Complete all questions. Show all working out. Describe your use of technology
Page 1
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Background Information
Below is the layout of the Australian Grand Prix, Albert Park Circuit. The track
consists of 16 turns of varying difficulty for the driver. There are also straight
stretches along which very high speeds can be attained.
The circuit is 5303 metres in length. The Lap Record is held by Michael Schumacher
who, in 2004 completed one lap in 1:24.125 (1 minute 24.125 seconds) in his Ferrari,
with a top speed of 325 km hr
(http://www.formula1.com/races/in_detail/australia_787/). The Grand Prix runs for 58
laps totalling 307.574 km.
(Image Source: http://en.wikipedia.org/wiki/Image:Circuit_Albert_Park.svg)
Copyright statement from image page:
“I, the copyright holder of this work, hereby release it into the public domain. This
applies worldwide.
In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions,
unless such conditions are required by law.”)
Web Resources:
http://www.grandprix.com.au/ (Excellent map with a scale can be found on this site)
http://www.f1-fansite.com/circuits/albert-park.asp
http://www.f1corporate.com/content/f1-race-tracks
Complete all questions. Show all working out. Describe your use of technology
Page 2
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
http://www.formula1.com/races/in_detail/australia_787/
http://www.f1complete.com/index.php?option=content&task=view&id=7858
Complete all questions. Show all working out. Describe your use of technology
Page 3
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Name:
Task Questions
1.
a)
What is the average speed around the Australian Grand Prix track for one lap
(not the first or last lap)?
b)
Rate turns 1 to 16 from fastest to slowest. Justify your ordering.
c)
What is the fastest section of the track? Why? Estimate the average speed of this
section.
d)
What is the slowest section of the track? Why? Estimate the average speed of this
section.
Complete all questions. Show all working out. Describe your use of technology
Page 4
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
2. a) Following a series of speed trials, the following speed-time graph was generated
representing one lap of the track. Mark on the graph the turns represented.
b) Construct you own speed (in km/hr) – time (in seconds) graph for the track
assuming constant acceleration between the turns.
Complete all questions. Show all working out. Describe your use of technology
Page 5
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
3. a) Use the graph from 2. a) to calculate the acceleration at:
i) t = 25
ii) t = 40
b) Calculate the area under your graph in 2 b). What does this area represent? Use
your calculation to comment on the accuracy of your velocity-time graph.
Complete all questions. Show all working out. Describe your use of technology
Page 6
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
4. a) One of the most action packed sections of the circuit is the Jones chicane
located at turn one (a chicane is an S-shaped bend in a road used to slow
traffic). Using a map you have found in your research, and the data in the table
below, determine the deceleration at the Jones chicane given that the brakes
are applied for only 1.7 seconds.
Turn
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
max. speed
before turn
(km/hr)
305
—
182
—
—
283
—
—
280
—
292
—
296
232
238
Braking time
(Sec)
1.7
—
0.5
—
—
1.4
1.1
0.5
1.7
0.5
1.6
min. speed
on turn
(km/hr)
145
200
92
145
239
134
186
255
115
—
226
233
138
205
84
180
b) Compare this braking time with other turns (where the available data
allows). What turn has the fastest braking rate?
Complete all questions. Show all working out. Describe your use of technology
Page 7
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
Note: This is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Additional working space
Complete all questions. Show all working out. Describe your use of technology
Page 8
Specialist Mathematics Unit 4
Outcomes
Outcome 1
Define and
explain key terms
and concepts.
SAC 3 Applications of Integration
Area of Study
Integration
High
Key Knowledge & skills
3
2
Can calculate average and
instantaneous speeds (q1a)
Consistently, accurately, with no errors.
Apply a range of
related
mathematical
routines and
procedures.
Can construct a v-t graph
(q2b).
Consistently, accurately, with no errors.
Can use a vt graph to calculate
acceleration (q3a)
Consistently, accurately, with no errors.
(By hand as well
as using
appropriate
technology.)
Can use a v-t graph to
calculate distance (q3b)
Consistently, accurately, with no errors.
Can convert units
appropriately (q1a, 3, 4)
Consistently and accurately.
Outcome 2
Apply, analyse
and discuss
mathematical
processes.
Outcome 3
Select and
appropriately use
technology.
Key Knowledge and skills
Applies appropriate key
mathematical concepts to the
F1 circuit. (All questions)
Demonstrated understanding
of how mathematics used
related to the reality of the F1
context. (q1b,c,d;2a).
Key Knowledge and Skills
Uses technology
appropriately to solve
problems.
Medium
Generally with few
errors.
Generally successful
with only minor
errors.
Generally with few
errors.
Generally with few
errors.
Generally successful
with only minor
errors.
Marking Scheme
Low
Not Shown
1
0
Recognized processes
involved but had little
success in determining
achieving a result.
Recognized processes
involved but had many
inaccuracies.
Recognized processes
involved but had little
success in determining
achieving a result.
Recognized processes
involved but had little
success in determining
achieving a result.
Limited conversion or
conversion with many
errors or omissions.
Total
Could not
calculate speeds.
/3
Could not
construct graph.
/3
Could not
calculate
acceleration.
/3
Could not
calculate
acceleration.
/3
Did/could not
convert units.
/3
/15
9-10
6-8
3-5
Outcome One Total
1-2
Consistently and
accurately applied
key concepts with
few errors.
Consistently and
accurately related
mathematics to real
context.
Generally applied key
concepts with some
errors or omissions.
Generally applied key
concepts with some
errors or omissions.
Limited application with
many errors or
omissions.
Application not
demonstrated
/10
Generally related
mathematics to real
context with a few
errors or omissions
Some understanding
of connection with
some errors or
omissions.
Limited understanding
with many errors or
omissions.
No understanding
apparent.
/10
5
3-4
Effectively and
consistently used
appropriate
technology.
Generally used
appropriate
technology
effectively.
2
Some effective use of
appropriate
technology.
Outcome Two Total
1
Limited and/or
ineffective use of
technology.
0
/20
0
Did not use
technology
Outcome Three Total
Total
/5
/5
/40
s is an analysis task. You must show step by step working out. Also, you must explain your use of technology.
Year 11 Mathematical Methods Unit 2 Rates of Change
Problem Solving Application Task
© State of Victoria 2008
Alan Thwaites is involved in the Intel Teach Program and developed this portfolio, in collaboration with other teachers.
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Complete all questions. Show all working out. Describe your use of technology
Page 10