Thank you for visiting Mathematical Methods @ Lyndale. I hope this blogger-website has been of some benefit to you throughout this year in your VCE studies
Sunday, 26 October 2014
Sunday, 21 September 2014
Mathematical Methods - 15 Exam Tips and General advice
A compilation of tips and general advice, that may assist you in your studies for Mathematical Methods CAS Units 3 and 4, Exams 1&2 2014
PREPARING FOR THE EXAM:
Mark down questions you were unable to do or had difficulty doing, and then add these to your bound reference post doing a few questions which are similar to the one you got stuck on - Tip by "Nightseeker"
DURING THE EXAM:
Profile of EulerFan101
1) Read and re-read the question (especially in the Extended response section of Exam to make sure you are not missing anything
2) Pay attention to the marking scheme. E.g. a 1 mark question will only usually requirecalculator syntax alongside the answer to gain the mark, whereas a 2-3 mark question would need some working out in addition with calculator syntax out to obtain full marks
EDIT: NEVER WRITE DOWN CALCULATOR SYNTAX
3)
In the extended response section pay close attention to the question number and letter, sometimes* you would use different values for unknowns though they are in the same question
Example:
(My comments will be italics)
1) A function is as following;
a) Find a and b, if the graph passes through (x,y) and (x,y)I have found a=2, and b=4
a ii) Find the minimum and maximum
b) Find the derivative of this function
Now it is important that I don't use the values a=2, and b=4 here, as though it's in the same question, this segment is under the letter (b) whereas we were told a=2 and b=4 in segment (a)
Instead I would find the derivative as;
If segment (b) said "Find the derivative of this function with the answers gained in Part (a)" or if it had said at the start of the question "A function is as following... where a =2, and b=4" THEN I would use a=2, and b=4 for part B, and in the latter scenario, for the entirety of the question
- End example-
This is especially important when doing Probability questions
*Comment by EulerFan101"Let's say you have a function f(x)=ax^2 + bx. If we know that a=2b will ALWAYS be true based on some logic (such as geometry rules), it is assumed you will use this in any future part. BUT, if they say for a single part that a point is (x, y), and from this you find a=2b, you shouldn't use this in future parts. Hope that made sense. "
4) When finding the inverse of a function, make sure to write the domain of the inverse especially if the original function is expressed as;
5) Pay attention to the part of the question which tells you to either
a) Express to (x) decimal places
b) Leave your answer in exact form
You do lose marks for not rounding up to the required amount of decimal places
If it doesn't specify, leave your answer in exact form
6)
7) Some questions may require you to find the range of a function, whilst giving you a domain
E.g. Find the range for the following function
You may instinctively substitute the values of the domain into the function to gain the range as;
However this is not correct!!
The correct range would be
The best thing to do if you encounter a question like this is to sketch the graph on a graphics calculator for the given domain and work out the minimum and maximum values from there
This will give you the correct range
8)
9) Do NOT write down calculator syntax when doing Probability questions, or in any question for that matter, you will not get the method marks, Write binomial and normal distribution notation instead
Example Q:
Find probability where x>2, where n=10, p=0.53
Correct notation;
X~Bi(10,0.53), Pr(X>2)=
NOT
binomCDF(10,0.53,3,10)
10)
11)
12) Alternative way to find Area of a triangle:
,
Where 'b' and 'c' are side lengths
13) You can find the intersection points of a function and it's inverse, by making the function equal to x.
14) You can quickly find what the inverse of a function looks like by sketching the function on the right-bottom hand corner of the page and then folding it in
15) Spend only a maximum of 30 minutes on the Multiple choice section of Exam 2. You should aim to utilize a full 1 hour and 20 minutes on the Extended response and then spend the last 5-10 minutes checking over the paper.
Practice this sort of time management on all of your practice papers
Exam checklist: Maths Methods exam checklist
Get a print out of these tips:
"Paul's Mathematical Methods - Pre-Exam 2 Advice for 2012"
ATARnotes: Mathematical Methods Guides and Tips
PREPARING FOR THE EXAM:
Mark down questions you were unable to do or had difficulty doing, and then add these to your bound reference post doing a few questions which are similar to the one you got stuck on - Tip by "Nightseeker"
DURING THE EXAM:
Profile of EulerFan101
1) Read and re-read the question (especially in the Extended response section of Exam to make sure you are not missing anything
2) Pay attention to the marking scheme. E.g. a 1 mark question will only usually require
EDIT: NEVER WRITE DOWN CALCULATOR SYNTAX
3)
In the extended response section pay close attention to the question number and letter, sometimes* you would use different values for unknowns though they are in the same question
Example:
(My comments will be italics)
1) A function is as following;
a) Find a and b, if the graph passes through (x,y) and (x,y)I have found a=2, and b=4
a ii) Find the minimum and maximum
b) Find the derivative of this function
Now it is important that I don't use the values a=2, and b=4 here, as though it's in the same question, this segment is under the letter (b) whereas we were told a=2 and b=4 in segment (a)
Instead I would find the derivative as;
If segment (b) said "Find the derivative of this function with the answers gained in Part (a)" or if it had said at the start of the question "A function is as following... where a =2, and b=4" THEN I would use a=2, and b=4 for part B, and in the latter scenario, for the entirety of the question
- End example-
This is especially important when doing Probability questions
*Comment by EulerFan101"Let's say you have a function f(x)=ax^2 + bx. If we know that a=2b will ALWAYS be true based on some logic (such as geometry rules), it is assumed you will use this in any future part. BUT, if they say for a single part that a point is (x, y), and from this you find a=2b, you shouldn't use this in future parts. Hope that made sense. "
4) When finding the inverse of a function, make sure to write the domain of the inverse especially if the original function is expressed as;
5) Pay attention to the part of the question which tells you to either
a) Express to (x) decimal places
b) Leave your answer in exact form
You do lose marks for not rounding up to the required amount of decimal places
If it doesn't specify, leave your answer in exact form
6)
7) Some questions may require you to find the range of a function, whilst giving you a domain
E.g. Find the range for the following function
You may instinctively substitute the values of the domain into the function to gain the range as;
However this is not correct!!
The correct range would be
The best thing to do if you encounter a question like this is to sketch the graph on a graphics calculator for the given domain and work out the minimum and maximum values from there
This will give you the correct range
8)
9) Do NOT write down calculator syntax when doing Probability questions, or in any question for that matter, you will not get the method marks, Write binomial and normal distribution notation instead
Example Q:
Find probability where x>2, where n=10, p=0.53
Correct notation;
X~Bi(10,0.53), Pr(X>2)=
NOT
binomCDF(10,0.53,3,10)
10)
11)
12) Alternative way to find Area of a triangle:
,Where 'b' and 'c' are side lengths
13) You can find the intersection points of a function and it's inverse, by making the function equal to x.
14) You can quickly find what the inverse of a function looks like by sketching the function on the right-bottom hand corner of the page and then folding it in
15) Spend only a maximum of 30 minutes on the Multiple choice section of Exam 2. You should aim to utilize a full 1 hour and 20 minutes on the Extended response and then spend the last 5-10 minutes checking over the paper.
Practice this sort of time management on all of your practice papers
Exam checklist: Maths Methods exam checklist
Get a print out of these tips:
"Paul's Mathematical Methods - Pre-Exam 2 Advice for 2012"
ATARnotes: Mathematical Methods Guides and Tips
Monday, 8 September 2014
Free trial exams
Links to free trial exams:
Engage education:MATHS METHODS PRACTICE EXAMS
"Puffy Publications 2011 - Maths Methods - ATARNotes Trial Examination"
"LLeong VCE Units 3&4 Mathematical Methods Practice Exam - ATARNotes"
Note: To access the ATARNotes practice exams you must have an account
"Puffy Publications 2011 - Maths Methods - ATARNotes Trial Examination"
"LLeong VCE Units 3&4 Mathematical Methods Practice Exam - ATARNotes"
Note: To access the ATARNotes practice exams you must have an account
Saturday, 30 August 2014
VCAA Past Exam Probability questions
Probability questions taken from past Maths Methods CAS Exam 2 papers
VCAA Past Exam Probability: Questions
- Thank you to "SLionsCricket" for helping compile the majority of this PDF file
VCAA Past Exam Probability: Answers
- Compiled by "SLionsCricket"
VCAA Past Exam Probability: Questions
- Thank you to "SLionsCricket" for helping compile the majority of this PDF file
VCAA Past Exam Probability: Answers
- Compiled by "SLionsCricket"
Sunday, 24 August 2014
The Continuous and Normal distributions
Continuous Probability distributions:
Introduction to Continuous Probability distributions
Continuous Probability distributions_1
Continuous Probability distributions_2
-http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htm
The Normal Probability distribution:
The Normal distribution
"Practice with Normal Distribution and Standard Deviation"
Haese Mathematics: The Normal distribution
Normal distribution
McGraw Hill: Normal distribution
Unfortunately, as of yet, answers could not be found for most of the PDF's. But we may stumble across them in the near future, in which case the links to them will be published here:
Introduction to Continuous Probability distributions
Continuous Probability distributions_1
Continuous Probability distributions_2
-http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htm
The Normal Probability distribution:
The Normal distribution
"Practice with Normal Distribution and Standard Deviation"
Haese Mathematics: The Normal distribution
Normal distribution
McGraw Hill: Normal distribution
Unfortunately, as of yet, answers could not be found for most of the PDF's. But we may stumble across them in the near future, in which case the links to them will be published here:
Sunday, 17 August 2014
Binomial distribution and Markov chains
Note: More 'Markov chain' questions may be added in the near future
Expected value:
"Practice with Expected value"
Binomial distribution:
"Worksheet: Binomial Distribution Problems"
"Worksheet: Binomial Distribution"
"Binomial distribution worksheet"
"Binomial distribution worksheet":2
CIMT: Binomial distribution
Markov chains:
"Markov chain exercises"
Markov chains - Link found by "SLionsCricket"
Expected value:
Binomial distribution:
"Worksheet: Binomial Distribution"
"Binomial distribution worksheet"
"Binomial distribution worksheet":2
CIMT: Binomial distribution
Markov chains:
"Markov chain exercises"
Markov chains - Link found by "SLionsCricket"
Sunday, 13 July 2014
Calculus: Compilation of practice exams/tests
A compilation of Calculus practice exams, and tests. Note that the majority of things posted are only links to websites and you will need to find the tests yourselves (some tests may be repeats) , as If I were to post them one by one they would take up too much space
AP calculus practice exams
Sample test; ATAR Notes
Calculus I Old Final exams
Sample tests
Calculus readiness test
Calculus.org
Practice Calculus Readiness Test
Sample test; ATAR Notes
Calculus I Old Final exams
Sample tests
Calculus readiness test
Calculus.org
Practice Calculus Readiness Test
Sunday, 6 July 2014
Finding the Area using integrals
Sketch the graph, and solve for the following integrals:
.gif)
- Questions made by 'tape-side'. Answers will be published soon
Definite Integrals
Applications of Integrals
Integration Worksheet
Itute: Calculus worksheet 9
- Questions made by 'tape-side'. Answers will be published soon
Definite Integrals
Applications of Integrals
Integration Worksheet
Itute: Calculus worksheet 9
Tuesday, 24 June 2014
An integrated approach to integrals
Theory:
"CHAPTER 12 INTEGRATION" - (Link found by "SLionsCricket")
Integration in Mathematics
The definite integral
Questions:
INTEGRATION WORKSHEET 2
"Math 229 Integration Worksheet – Substitution Method"
Anti-Derivative Practice
Further Integration
"MATH 34B INTEGRATION"
"MATH 34B INTEGRATION: 2"
"MATH 34B INTEGRATION: 3"
"MATH 34B INTEGRATION: FINAL REVIEW"
Solutions:
"Math 229 Integration Worksheet – Substitution Method": SOLUTIONS
Anti-Derivative Practice: SOLUTIONS
"MATH 34B INTEGRATION": SOLUTIONS
"CHAPTER 12 INTEGRATION" - (Link found by "SLionsCricket")
Integration in Mathematics
The definite integral
Questions:
INTEGRATION WORKSHEET 2
"Math 229 Integration Worksheet – Substitution Method"
Anti-Derivative Practice
Further Integration
"MATH 34B INTEGRATION"
"MATH 34B INTEGRATION: 2"
"MATH 34B INTEGRATION: 3"
"MATH 34B INTEGRATION: FINAL REVIEW"
Solutions:
"Math 229 Integration Worksheet – Substitution Method": SOLUTIONS
Anti-Derivative Practice: SOLUTIONS
"MATH 34B INTEGRATION": SOLUTIONS
Wednesday, 11 June 2014
VCAA Applications of Differentiation problems
Applications of Differentiation questions taken from past Maths Methods CAS and Maths Methods exam papers
VCAA Applications of Differentiation questions
Monday, 9 June 2014
Saturday, 31 May 2014
Note
Practice exam's have been uploaded by Mr. MJ and the link to the website can be accessed via your compass school manager by clicking on the 'Resources' tab in the Maths methods folder, and following the instructions located in the 'EXAM REVISION' file
Wednesday, 28 May 2014
Saturday, 3 May 2014
Monday, 28 April 2014
Mc-Graw Hill: Trigonometric graphs and models
Mc-Graw Hill: Trigonometric graphs and modelling
Sample modelling question:
NON-CALC
A marker is placed on the surface of a beach, and is used to measure how far up the beach a wave reaches over a period of 24 hours. It was calculated that the following equation could be used to model this data
Where 'D' is the distance away from the marker, and 't' is measured in hours
a) What is the furthest distance and closest distance from the marker that the wave reaches
b) At what times does the wave reach the furthest distance from marker A
Susie picks a position on the beach to sunbathe where she is 7.5 meters from the marker, if the waves come any closer, she will get wet.
c) At what times can she sunbathe?
Answers:
a) Furthest distance= 15 Closest: 5
b) 4 AM
c) t<12 U t>20
Question made by 'tape-side'. Please feel free to comment if you believe I have made any errors, or if this question does not make sense
Sample modelling question:
NON-CALC
A marker is placed on the surface of a beach, and is used to measure how far up the beach a wave reaches over a period of 24 hours. It was calculated that the following equation could be used to model this data
Where 'D' is the distance away from the marker, and 't' is measured in hours
a) What is the furthest distance and closest distance from the marker that the wave reaches
b) At what times does the wave reach the furthest distance from marker A
Susie picks a position on the beach to sunbathe where she is 7.5 meters from the marker, if the waves come any closer, she will get wet.
c) At what times can she sunbathe?
Answers:
a) Furthest distance= 15 Closest: 5
b) 4 AM
c) t<12 U t>20
Question made by 'tape-side'. Please feel free to comment if you believe I have made any errors, or if this question does not make sense
Saturday, 19 April 2014
Sketching and finding the equation of trigonometric graphs
Lancester's schools: Graphs of trigonometric fucntions
Periodic functions
Sketch the graphs of the following functions.
1. y = cos(x− Ï€)
2. y = sin 2(x+ π)
3. y = 3cos(x+Ï€)
4. y = −3cos(x+Ï€)+2
5. Find a sin or cos function that has amplitude 2, period π, and for which f(0) = 2.
Sketch the graphs of the following functions, and find x-intercepts if they exist. If the following equations are hard to read, click and drag an equation into the the address bar, and the image should appear clearer
Periodic functions
Sketch the graphs of the following functions.
1. y = cos(x− Ï€)
2. y = sin 2(x+ π)
3. y = 3cos(x+Ï€)
4. y = −3cos(x+Ï€)+2
5. Find a sin or cos function that has amplitude 2, period π, and for which f(0) = 2.
Sketch the graphs of the following functions, and find x-intercepts if they exist. If the following equations are hard to read, click and drag an equation into the the address bar, and the image should appear clearer
Saturday, 12 April 2014
Solving trigonometric equations
Classzone: Solving trigonometric equations
Lancestor schools: Solving Trigonometric equations
The "Lancestor schools:Solving Trig. equations" site is a restricted PDF, hence you may not be able to print it. To unlock it do the following
Save the PDF file to your computer
Go on: http://convert.neevia.com/pdfconvert/
Upload then convert and download the presented file
Note: Be wary of advertisements and suspicious files
If the owner of the "Lancestor schools" file believes that I am interfering with copy rights, please do not hesitate to email me via the contact form located on the right. I will remove the link immediately upon request
Lancestor schools: Solving Trigonometric equations
The "Lancestor schools:Solving Trig. equations" site is a restricted PDF, hence you may not be able to print it. To unlock it do the following
Save the PDF file to your computer
Go on: http://convert.neevia.com/pdfconvert/
Upload then convert and download the presented file
Note: Be wary of advertisements and suspicious files
If the owner of the "Lancestor schools" file believes that I am interfering with copy rights, please do not hesitate to email me via the contact form located on the right. I will remove the link immediately upon request
Tuesday, 11 March 2014
Sunday, 9 March 2014
Tips for charging CAS calculator
Charging via computer too slow?
TRY THIS
The reason it takes a while to charge on a computer is because the current going through the computer and into the CAS calculator is very low
By connecting your CAS calculator to an A/C adapter, the current output is considerably higher, and your CAS calculator may be fully charged in only a period of 2 hours, whereas it would take almost a day to charge via the computer
Requirements:
A/C adapter in which you can plug USB cables into (can be purchased/ may come with your phone)
(http://www.amazon.com/Cosmos-Adapter-Charger-shuffle-classic/dp/B0052RM8T2 - $10 w/o P&H)
(http://www.greenplanetcollections.com/usb-power-a-c-adapter-cube-black/ - $5 w/o P&H)
CAS calculator USB cable
Method:
1. Plug USB cable into CAS calculator and connect this to the A/C Adapter
2. Plug the A/C adapter into a power socket
TRY THIS
The reason it takes a while to charge on a computer is because the current going through the computer and into the CAS calculator is very low
By connecting your CAS calculator to an A/C adapter, the current output is considerably higher, and your CAS calculator may be fully charged in only a period of 2 hours, whereas it would take almost a day to charge via the computer
Requirements:
A/C adapter in which you can plug USB cables into (can be purchased/ may come with your phone)
(http://www.amazon.com/Cosmos-Adapter-Charger-shuffle-classic/dp/B0052RM8T2 - $10 w/o P&H)
(http://www.greenplanetcollections.com/usb-power-a-c-adapter-cube-black/ - $5 w/o P&H)
CAS calculator USB cable
Method:
1. Plug USB cable into CAS calculator and connect this to the A/C Adapter
2. Plug the A/C adapter into a power socket
Practice papers and exams (Logarithmic and Exponential)
Click here for Exponential_and_Logarithmic_functions_worksheet_1
Click here for Exponential_and_Logarithmic_functions_worksheet_2
Click here for Exponential_and_Logarithmic_functions_worksheet_3
Click here for Exponential_and_Logarithmic_functions_worksheet_4
Click here for Exponential_and_Logarithmic_functions_practice_exam
Click here for Exponential_and_Logarithmic_functions_worksheet_2
Click here for Exponential_and_Logarithmic_functions_worksheet_3
Click here for Exponential_and_Logarithmic_functions_worksheet_4
Click here for Exponential_and_Logarithmic_functions_practice_exam
Sunday, 2 March 2014
Friday, 28 February 2014
Exponential and Logarithmic functions; Heinemann PDF
Located here:
http://pearson.com.au/media/651029/hvz_mm3_4casen.pdf
Unfortunately, answers to this chapter could not be found
Worksheets:
http://www.ms.uky.edu/ma109/fall_2012/fall_2012/activities/exponentialwkstSolutions.pdf
http://pearson.com.au/media/651029/hvz_mm3_4casen.pdf
Unfortunately, answers to this chapter could not be found
Worksheets:
http://www.ms.uky.edu/ma109/fall_2012/fall_2012/activities/exponentialwkstSolutions.pdf
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