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8/2/2019 SM3 Wks 2-8
1/10
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8/2/2019 SM3 Wks 2-8
2/10
Week 3
Term 1
2012
Theoretical Components
1. Read through the notes from Chapter 5 (5D &
5G) from MM11 Quest ebook (Maths Quest 11
Mathematical Methods) and make your notes
on various graphs of exponential and
logarithmic functions. Try graphing various
functions using your classpad calculator, and
observe the changes when you change values of
a or x.
2. Go through the characteristics of exponential
functions:
http://www.regentsprep.org/Regents/math/alg
trig/ATP8b/exponentialFunction.htm
3. Go through the characteristics of exponential
functions:
http://www.regentsprep.org/Regents/math/alg
trig/ATP8b/logFunction.htm
4. Youtube video on exponential functions:
http://www.khanacademy.org/video/exponenti
al-growth-functions?topic=algebra-worked-
examples-2
5. Youtube video on logarithmic functions:
http://www.khanacademy.org/video/graphing-
logarithmic-functions?topic=developmental-
math-3
Practical Components1. Do as many questions of Ex 5D & Ex 5G from Yr
11 Methods Ebook.2. Complete the sets of questions in the following
links (it would be wise to keep a record of what
you have done):
http://www.regentsprep.org/Regents/math/algtr
ig/ATP8b/logexpractice.htm
http://www.regentsprep.org/Regents/math/algtr
ig/ATP8b/logpractice.htm
You may want to refresh your graphing skills in Ch3
of:http://edu.casio.com/products/classpad/cp_v304/dat
a/CP330_ver306_Soft_E.pdf
QuizOn cLc under Quizzes folder.
By the end of this week, you should be able to:
Graph functions of the form () = () = log
Identify how the features of these basic graph changes under reflection,
translation and dilation Understand the relationship between an exponential and a logarithmic
function.
Goals
Learning BriefSM3: Integral Calculusand Special Functions
http://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htmhttp://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.regentsprep.org/Regents/math/algtrig/ATP8b/logexpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logexpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logexpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logpractice.htmhttp://edu.casio.com/products/classpad/cp_v304/data/CP330_ver306_Soft_E.pdfhttp://edu.casio.com/products/classpad/cp_v304/data/CP330_ver306_Soft_E.pdfhttp://edu.casio.com/products/classpad/cp_v304/data/CP330_ver306_Soft_E.pdfhttp://edu.casio.com/products/classpad/cp_v304/data/CP330_ver306_Soft_E.pdfhttp://edu.casio.com/products/classpad/cp_v304/data/CP330_ver306_Soft_E.pdfhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logexpractice.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logexpractice.htmhttp://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.khanacademy.org/video/graphing-logarithmic-functions?topic=developmental-math-3http://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.khanacademy.org/video/exponential-growth-functions?topic=algebra-worked-examples-2http://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htmhttp://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htm8/2/2019 SM3 Wks 2-8
3/10
Marta was convinced that there had to be some way to graphy = log2x on her graphing
calculator. She typed iny = log(2x) and hit EXE.
It WORKED! Marta yelled in triumph.
Whaaaaat? said Celeste. I think y = log2x and y = log(2x ) are totally different, and I bet we can
prove it by converting both of them to exponential form.Yeah, I think youre wrong, Marta, said Sophia. I think we can prove y = log2 x and y
= log(2x ) are totally different by looking at the graphs.
a). Show thaty = log2x andy = log(2x ) are different by sketching the graph ofy = log2x using what you
learned in previous lessons. Then sketch what your grapher shows to be the graph ofy = log(2x ) .
b. Now show that they are different by converting both of them to exponential form.
ForumNext week.
8/2/2019 SM3 Wks 2-8
4/10
Week
Term
2012
4
1
Theoretical Components
1.Limits and Differentiation:
http://www.intmath.com/differentiation/1-limits-and-
differentiation.php
2.Remember - the derivative from first principles:
http://www.intmath.com/differentiation/3-derivative-
first-principles.php
3.Differentiation using power rule:
http://www.intmath.com/differentiation/3-derivative-
first-principles.php
4.Product and Quotient Rules:
http://www.intmath.com/differentiation/6-
derivatives-products-quotients.php
5.Chain Rule:
http://www.intmath.com/differentiation/7-derivative-
powers-of-function.php
6.Anti-differentiation:
http://www.intmath.com/integration/2-indefinite-
integral.php
Practical Com onents
1. Look at the examples in the links to the left.2. Refresh your mind with a selection of the
problems from Maths Quest 12 Maths Methods
Chapter 7: (which you can read)
7C Power Rule,
7D Chain Rule,
7H - Product Rule,
7I Quotient Rule
Explain why
is not a fraction.
1 x A4 page to be handed in.
QuizNext week
By the end of this week, you should have:
Reviewed different techniques of differentiation (first principles, product,
quotient and chain rule)
Found the anti-derivative by rule Been able to work out the original function from the gradient function
Goals
ForumRemember the Forum participation now counts toward your attendance.
Show an example of a problem that you found hard and explain where you made a mistake
and how you corrected it.
Learning BriefSM3
Differentiation
Review
http://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/6-derivatives-products-quotients.phphttp://www.intmath.com/differentiation/6-derivatives-products-quotients.phphttp://www.intmath.com/differentiation/7-derivative-powers-of-function.phphttp://www.intmath.com/differentiation/7-derivative-powers-of-function.phphttp://www.intmath.com/differentiation/7-derivative-powers-of-function.phphttp://www.intmath.com/differentiation/7-derivative-powers-of-function.phphttp://www.intmath.com/differentiation/6-derivatives-products-quotients.phphttp://www.intmath.com/differentiation/6-derivatives-products-quotients.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.php8/2/2019 SM3 Wks 2-8
5/10
Week 6
Term 1
2012
Theoretical Components
1. You may want to cast your eyes over the
MathsQuest Methods Yr 12 Jacplus book Ch6
on Trig functions to remind yourself about
them.
2. Read MathsQuest Methods Yr 12 Ch 7G
regarding the derivatives of Trig functions.
3. Pay particular note to Worked example 24
this emphasizes that on the Classpad you have
to have it in the Radians mode to get the
correct answer for derivatives of Circular or
Trig functions.
4. Also look at:
http://sydney.edu.au/stuserv/documents/mat
hs_learning_centre/Dtrig.pdf
5. More examples (Derivatives of Trig functions
explained here)
http://www.intmath.com/differentiation-
transcendental/1-derivative-sine-cosine-
tangent.php
6. YouTube of Sine and Cosine Functions:
http://www.youtube.com/watch?v=LHqdbj9gOKg&feature=relmfu
http://www.youtube.com/watch?v=rCHFa_nXE
hA&feature=relmfu
Practical Components1. Do as many questions as you need of Ex 7G from
MathsQuest Yr 12 Methods JacPlus book.2. Do the Exercise 1 found in this doc:
http://sydney.edu.au/stuserv/documents/maths
_learning_centre/Dtrig.pdf
3. Do some of the trig questions that you have
previously skipped if you need more practice.
4. Remember that you have the assignment pre-
class work to finish in preparation for the in-class
work this week.
5. You may like to look at:
http://www.classpad.com.au/and look at theIntermediate menu working in main 141
Equation of the tangent to the Curve (so you how
to use the classpad.)
QuizNext week
By the end of this week, you should be able to:
Find the derivatives of Trigonometrical functions of the forms
= , = , = .
Understand the use of class-pad calculators to find the derivatives of Trigfunctions.
Goals
Learning BriefSM3: Integral Calculusand Special Functions
http://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://www.youtube.com/watch?v=LHqdbj9gOKg&feature=relmfuhttp://www.youtube.com/watch?v=LHqdbj9gOKg&feature=relmfuhttp://www.youtube.com/watch?v=LHqdbj9gOKg&feature=relmfuhttp://www.youtube.com/watch?v=rCHFa_nXEhA&feature=relmfuhttp://www.youtube.com/watch?v=rCHFa_nXEhA&feature=relmfuhttp://www.youtube.com/watch?v=rCHFa_nXEhA&feature=relmfuhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://www.classpad.com.au/http://www.classpad.com.au/http://www.classpad.com.au/http://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://www.youtube.com/watch?v=rCHFa_nXEhA&feature=relmfuhttp://www.youtube.com/watch?v=rCHFa_nXEhA&feature=relmfuhttp://www.youtube.com/watch?v=LHqdbj9gOKg&feature=relmfuhttp://www.youtube.com/watch?v=LHqdbj9gOKg&feature=relmfuhttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.phphttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/Dtrig.pdf8/2/2019 SM3 Wks 2-8
6/10
In class assignment to be completed
ForumNext week.
8/2/2019 SM3 Wks 2-8
7/10
Week 7
Term 1
2012
Theoretical Components
1. Study the examples on integrating special
functions:
Revisit all worked examples in Chapter 9
(9A).
Study Worked Examples (WE) 10-12 in
Chapter 9 (9B) on integrating special
functions (exponential, sine and cosine)
Study examples on basic integration
here:
http://www.intmath.com/integration/2-indefinite-integral.php
2. Watch these youtube video: Approximating
area under a curve using rectangles:
http://www.youtube.com/watch?v=vqSPGeYO2
UA&feature=relmfu
Exact Area under the curve using Definite
integral:
http://www.youtube.com/watch?v=ODwkTt0R
MDg&feature=relmfu3. Read through the notes from Chapter 9 (9D)
from MM12 Quest ebook (Maths Quest 12
Mathematical Methods) and make your notes
on various techniques used to find the
approximate area under the curve.
4. Look at the Resources folder about Simpsons
and Trapezoidal Rules for working out the areas
under curves read and make notes on rules
Practical Components
1. Do few questions in Ex 9A in Yr 12 Methods
Ebook (Q2, Q5, Q7, Q10, Q13, Q14).
2. Do few questions in Ex 9B in Yr 12 Methods
Ebook (Q2-4, Q7, Q10).
3. Do the following questions of Ex 9D from Yr 12
Methods Ebook:
Q1 after you have studied Worked
Example (WE) 18;
Q4 after going through WE19;
Q6 after going through WE20.
4. Use Resources Ex11I and Ex11J to do a
selection of problems on the Trapezoidal and
Simpsons Rules
QuizNext week.
By the end of this week, you should be able to:
Integrate various functions (by hand and by using ClassPad)
Understand the use of areas of rectangles to approximate the area under a
given curve between a defined interval including Simpsons and TrapezoidalRules
Understand the use of sigma notation and limits to approximate area under acurve
Relate the above to idea of finding an exact area under a given curve using
definite integral
IN-CLASS ASSESSMENT:
ANY ONE WHO HAS NOT
YET COMPLETED THE TASKS
SHOULD SEE TOBY ASAP
Goals
Learning BriefSM3: Integral Calculusand Special Functions
http://www.intmath.com/integration/2-indefinite-integral.phphttp://www.intmath.com/integration/2-indefinite-integral.phphttp://www.intmath.com/integration/2-indefinite-integral.phphttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.intmath.com/integration/2-indefinite-integral.phphttp://www.intmath.com/integration/2-indefinite-integral.php8/2/2019 SM3 Wks 2-8
8/10
1. Watch this mini-lecture on Integration:
http://www.intmath.com/integration/integration-mini-lecture-by-
substitution.php
2. Make your notes on the examples shown.
3. Provide additional 2 fully worked examples on Integration by
Substitution.
YOUNEEDTOGETYOURINVESTIGATIONS(FORW
EEKS3,4&5)CHECKEDBYANYMATHSTEACHER!
For
um
Each winter, the Snowy Mountains Authority makes regular measurements of the depth of snow
on the ground in a selected area near some of the major ski resorts. A local newspaper has
published the following graphs snow depth of the 2008 and 2010. Skiers and other visitors find
it interesting to compare the graphs for different years to debate which was the best year for
snow was and which was the worst.
Study the graphs shown below.
Decide which you think were the best and the worst of the years shown. Think about how you
might decide which year was the best for snow and which was the worst.
http://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.php8/2/2019 SM3 Wks 2-8
9/10
Week 8
Term 1
2012
Theoretical Components
1. Exact Area under the curve using Definite
integral:
http://www.youtube.com/watch?v=ODwkTt0R
MDg&feature=relmfu
AREA UNDER THE CURVE
http://www.rootmath.org/calculus/area-intro
FUNDAMENTAL THEOREM OF CALCULUS
http://www.rootmath.org/calculus/first-
fundamental-theorem-of-calculusPROPERTIES OF INTEGRATION
http://www.rootmath.org/calculus/properties-
of-integrals
2. Study examples on AREA under the curve:
http://www.intmath.com/applications-
integration/2-area-under-curve.php
3. Area between curves:
http://www.intmath.com/applications-
integration/3-area-between-curves.php
4. Notes on Area under the curve:
http://www.teacherschoice.com.au/maths_libr
ary/calculus/area_under_a_curve.htm
(Focus on the notes/explanations and the
examples, dont have to use Maths Helper Plus)
Practical ComponentsRead the examples and the introduction to the
following Exercises and do the following:
1. Do questions in Ex 9E in Yr 12 Methods Ebook (Q1
(a,d,g,j,m,p,s), Q2 (a,d,g,j,m,p), Q3, Q7-Q9).
2. Do questions in Ex 9F in Yr 12 Methods Ebook (Q3
(all-dont have to evaluate, just write an
expression for finding the area for each),
Q5(a,d,g), Q6).
3. Study the worked examples from Chapter 9H (on
Areas between two curves). Make notes, you
should copy the examples and watch thetutorials)
QuizOn cLc.
By the end of this week, you should be able to:
Integrate various functions (by hand and by using ClassPad), BOTH
INDEFINITE AND DEFINITE INTEGRALS
Understand the use of areas of rectangles to approximate the area under agiven curve between a defined interval
Understand the use of sigma notation and limits to approximate area under a
curve
Relate the above to idea of finding an exact area under a given curve (or
between curves) using definite integral
MINI-LECTURES:NOW RUNNING EVERY
WEDNESDAYS DURING
LUNCH TIME IN ROOM 23.
ALL WELCOME.
Goals
Learning BriefSM3: Integral Calculusand Special Functions
F
O
R
U
M
Next week.
http://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.rootmath.org/calculus/area-introhttp://www.rootmath.org/calculus/area-introhttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/properties-of-integralshttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/area-introhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfu8/2/2019 SM3 Wks 2-8
10/10
Consider the curve (2 1)
1. Integrate the function with respect to x
2. Calculate the Definite integral of this function between -1 and 1
ie (2 1)1
1
3. Explain what you find any why the result may not be what you expected.(hint try graphing on your classpad and splitting up areas)
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