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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

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 BriefMM3: 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://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/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 graph y= log2xon her graphing

calculator. She typed in y= 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= log2x and

y= log(2x) are totally different by looking at the graphs.

a). Show that y= log2xand y= log(2x) are different by sketching the graph of y= log2xusingwhat you learned in previous lessons. Then sketch what your grapher shows to be the graph

of y= log(2x) .b. Now show that they are different by converting both of them to exponential form.

ForumNext week.

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Week 4

Term 1

2012


1. Limits and Differentiation:

http://www.intmath.com/differentiation/1-

limits-and-differentiation.php

2. Mmmmmhhhthe derivative from first

principles:


derivative-first-principles.php

3. Differentiation using power rule:


derivative-first-principles.php

4. Product and Quotient Rules:


derivatives-products-quotients.php

5. Chain Rule:


derivative-powers-of-function.php

6. Anti-differentiation:

http://www.intmath.com/integration/2-

indefinite-integral.php

I will be wise to complete the exercise after going

through

Practical Components1. Do as many questions of Ex 9C, 9D & 9E from Yr

11 Methods Ebook.

These exercises are on Differentiation Techniques

and basics of Integration.

QuizNext Week.


Review different techniques of differentiation (first principles, product,

quotient and chain rule)

Find the anti-derivative by rule Derive the original function from the gradient function

Goals

http://www.intmath.com/differentiation/1-limits-and-differentiation.phphttp://www.intmath.com/differentiation/1-limits-and-differentiation.phphttp://www.intmath.com/differentiation/1-limits-and-differentiation.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://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/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/integration/2-indefinite-integral.phphttp://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.intmath.com/integration/2-indefinite-integral.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.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/3-derivative-first-principles.phphttp://www.intmath.com/differentiation/1-limits-and-differentiation.phphttp://www.intmath.com/differentiation/1-limits-and-differentiation.php

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A:

Use the Java Applet on this link for this investigation:

http://www.intmath.com/differentiation/differentiation-java-applet-polynomials.php

Use the applet to graph various functions (at least one each from Linear, Quadratic and Cubic). Copy the graph of the

original function and the graph of its derivative, play with the slider to study when the function is increasing, decreasingand stationary. Record your observations/findings.

ForumDiscuss how you would explain the meaning of derivative to a primary school kid.

You may use examples, but keep in mind that you are talking to a primary school kid

who has never heard about this before.
http://www.intmath.com/differentiation/differentiation-java-applet-polynomials.phphttp://www.intmath.com/differentiation/differentiation-java-applet-polynomials.phphttp://www.intmath.com/differentiation/differentiation-java-applet-polynomials.php

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Week 5

Term 1

2012


1. Read through the notes from Chapter 7 (7E &

7F) from MM12 Quest ebook (Maths Quest 12


on various techniques used to find the

derivatives of exponential and logarithmic

functions. Familiarise yourself on how to use

the class-pad to find the derivatives.Section 7E: is on derivatives of various forms of

exponential functions. Study the derivation at the start of

this section on using the First Principles to compute the

derivative of ex

. Go through the worked examples 16-19(these examples use Chain Rule to work out various

derivatives.

Section 7F: is on derivatives of logarithmic functions.

Study the derivation at the start of the section. Go

through examples 20-23 (they all use Chain Rule).

2. More examples:

http://www.cliffsnotes.com/study_guide/Differ

entiation-of-Exponential-and-Logarithmic-

Functions.topicArticleId-39909,articleId-

39885.html

3. Read with care:http://www.intmath.com/differentiation-

transcendental/6-derivative-exponential.php

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

transcendental/5-derivative-logarithm.php

Practical Components1. Do as many questions of Ex 7E & Ex 7F from Yr 12

Methods Ebook.2. Do the questions under Exercises found in this

doc:

http://sydney.edu.au/stuserv/documents/maths

_learning_centre/derivativeofexp_logs.pdf

(Some really good examples can be found here!)

3. Attempt all questions you find on derivatives of

log and exponential functions from the website

listed under 3 in Theoretical Component.

QuizOn cLc under Quizzes folder.


Find the derivatives of exponential functions of the forms

= , = , = () .

Find the derivative of logarithmic functions of the form y = log Use the class-pad calculators to find the derivatives of exponential and

logarithmic functions.

Feeling lazy!http://www.youtube.com/

watch?v=xTeV1IOIyJY&feat

ure=related

Goals

http://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.intmath.com/differentiation-transcendental/6-derivative-exponential.phphttp://www.intmath.com/differentiation-transcendental/6-derivative-exponential.phphttp://www.intmath.com/differentiation-transcendental/6-derivative-exponential.phphttp://www.intmath.com/differentiation-transcendental/5-derivative-logarithm.phphttp://www.intmath.com/differentiation-transcendental/5-derivative-logarithm.phphttp://www.intmath.com/differentiation-transcendental/5-derivative-logarithm.phphttp://sydney.edu.au/stuserv/documents/maths_learning_centre/derivativeofexp_logs.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/derivativeofexp_logs.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/derivativeofexp_logs.pdfhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://www.youtube.com/watch?v=xTeV1IOIyJY&feature=relatedhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/derivativeofexp_logs.pdfhttp://sydney.edu.au/stuserv/documents/maths_learning_centre/derivativeofexp_logs.pdfhttp://www.intmath.com/differentiation-transcendental/5-derivative-logarithm.phphttp://www.intmath.com/differentiation-transcendental/5-derivative-logarithm.phphttp://www.intmath.com/differentiation-transcendental/6-derivative-exponential.phphttp://www.intmath.com/differentiation-transcendental/6-derivative-exponential.phphttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.html

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Maths Joke:

The functions are sitting in a bar, chatting (how fast they go to zeroat infinity etc.). Suddenly, one cries "Beware! Derivation is coming!"All immediately hide themselves under the tables, only theexponential sits calmly on the chair.

The derivation comes in, sees a function and says "Hey, you don'tfear me?"

"No, I'am e to x", says the exponential self-confidently."Well" replies the derivation "but who says I differentiate along x?"

Objective

To observe the nature of the derivative

Method

For , find the gradient of the tangent at , using modelling techniques

from your graphing calculator. The domain is restricted to 3 3.

Repeat for , and the rest of the functions. You may record your results in a tabular form.

Use the above to write a statement about the derivative of the general exponential

.

ForumNext week.

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Week 6

Term 1

2012


1. Read through the notes from Chapter 7 (7G)

from MM12 Quest ebook (Maths Quest 12



derivatives of various trig functions. Familiarise

yourself on how to use the class-pad to find the

derivatives.

2. Websites on Derivatives of Trig functions:

http://www.cliffsnotes.com/study_guide/Differ

entiation-of-Exponential-and-Logarithmic-

Functions.topicArticleId-39909,articleId-

39885.html

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

transcendental/1-derivative-sine-cosine-

tangent.php

Practical Components1. Do as many questions of Ex 7G from Yr 12

Methods Ebook.

2. Attempt all questions you find on derivatives of

log and exponential functions from the website

listed under 2 in Theoretical Component.

PREPARE FOR YOUR IN-CLASS.

QuizNext week.


Find the derivatives of various Trig functions with and without a

ClassPad.

Find the derivatives of functions involving trig, logs and exponents

DO YOUR REVISION + WORK ON TAKE-HOME SECTION OF

THE IN-CLASS ON MODELLING/APLICATIONS OF

EXPONENTIAL FUNCTIONS.

IN-CLASS SCHEDULE:

LINES 1 ON THURSDAY(15/3; 12:00-1:00)

LINE 7 ON THURSDAY

(15/3; 11:00-12:00)

LINE 3 ON FRIDAY (16/3;

2:30-3:30)

Goals

http://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://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.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.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.htmlhttp://www.cliffsnotes.com/study_guide/Differentiation-of-Exponential-and-Logarithmic-Functions.topicArticleId-39909,articleId-39885.html

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COMPLETE THE TAKE HOME SECTION OF THE IN-CLASS. THIS IS

PART OF THE ASSESSMENT, i.e. YOUR TAKE-HOME COMPONENT

WILL BE COLLECTED AND MARKED.

YOU MAY BRING HANDWRITTEN NOTES AND EXAMPLES TO IN-

CLASS COMPONENT.

IN-CLASS COMPONENT: THERE WILL BE 4 QUESTIONS ON

APPLICATIONS/MODELLING OF EXPONENTIAL FUNCTIONS.

TAKE-HOME COMPONENT IS AVAILABLE ON CLC MM3

HOMEPAGE.

ForumPREPARE YOURSELF FOR YOUR IN-CLASS BY COMPLETING THE TAKE

HOME COMPONENT.

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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=ODwkTt0RMDg&feature=relmfu

3. Read through the notes from Chapter 9 (9D)

from MM12 Quest ebook (Maths Quest 12



approximate area under the curve.

Practical Components

1. Do few questions in Ex 9A in Yr 12 MethodsEbook (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.

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 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 using

definite integral

IN-CLASS ASSESSMENT:

ANY ONE WHO HAS NOT

YET COMPLETED THE TASK

SHOULD SEE SHEIKH ASAP

TO AVOID

DISAPPOINTMENT!

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!

F

O

R

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.

NOTE: This question is related to concept of Integral Calculus, and is one of the popular types

of question you would see in ASTs Short Response Paper.
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 Components

1. Do few 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 few 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 your notes,

you may copy the examples and watch the

tutorials)

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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