SM3 Wks 2-8

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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.htm

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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.

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Week

Term

2012

4

1


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:


first-principles.php

4.Product and Quotient Rules:

http://www.intmath.com/differentiation/6-

derivatives-products-quotients.php

5.Chain Rule:


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.php

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Week 6

Term 1

2012


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


Find the derivatives of Trigonometrical functions of the forms

= , = , = .

Understand the use of class-pad calculators to find the derivatives of Trigfunctions.

Goals

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.pdf

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In class assignment to be completed

ForumNext week.

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Week 7

Term 1

2012


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.


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

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.php

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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.php

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Week 8

Term 1

2012


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.


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


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=relmfu

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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)

Documents

SM3 Wks 2-8