MM1 Wks2-8

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Week 2

Term 1

2012

Theoretical Components

You shall make brief notes or copy examples as you

go through these links and text books.

Read:

http://www.karlscalculus.org/calc1.htmland

http://www.trottermath.net/personal/realn

osys.htmlon Number System;

http://www.mathsisfun.com/operation-

order-pemdas.htmlon Order of Operations

& attempt the 8 questions you will find on

this page. http://www.mathsisfun.com/algebra/substit

ution.htmlon Substitution & attempt the 10

questions at the bottom of this page.

Read through the examples from Combridge

3 Unit (text book, pages 1-7) on the Basics of

Algebra (Simplification, Expansion,

Factorisation)

Read through the Example on Changing the

Subject of the Formula (page 13, Cambridge

3 Unit).

Practical Components

Do the following exercises:

attempt questions from Exercises 1A, 1B & 1C

on the Basics of Algebra (Combridge 3 Unit

(text book), pages 1-7)

attempt Questions 9 of Exercise 1F

(Cambridge, page 15)

For all of the above, keep a record of your work in

your exercise book (they will be checked by a teacher)

Optional:

Click on this link and select Section 1 to get more

practises:

http://www.algebasics.com/index.html

Complete the investigation exercise on Real Number

System (Available oncLc)

QuizEvery even week there is a quiz, they contribute to 10% of your final grade.

By the end of this week, you should be able to:

understand the structure, properties and behaviour of real numbers;

be competent in operations involving real numbers;

re-arrange a given expression to change the subject of formula; simplify algebraic expressions involving like and unlike terms;

expand & simplify binomials and trinomials;

factorise expressions involving multiple terms.

Goals

ForumEvery week there is a requirement to participate in the online forum.

Learning BriefMM1 : Matrices,

Sequences &

Mensuration
http://www.karlscalculus.org/calc1.htmlhttp://www.karlscalculus.org/calc1.htmlhttp://www.trottermath.net/personal/realnosys.htmlhttp://www.trottermath.net/personal/realnosys.htmlhttp://www.trottermath.net/personal/realnosys.htmlhttp://www.mathsisfun.com/operation-order-pemdas.htmlhttp://www.mathsisfun.com/operation-order-pemdas.htmlhttp://www.mathsisfun.com/operation-order-pemdas.htmlhttp://www.mathsisfun.com/operation-order-pemdas.htmlhttp://www.mathsisfun.com/algebra/substitution.htmlhttp://www.mathsisfun.com/algebra/substitution.htmlhttp://www.mathsisfun.com/algebra/substitution.htmlhttp://www.mathsisfun.com/algebra/substitution.htmlhttp://www.algebasics.com/index.htmlhttp://www.algebasics.com/index.htmlhttps://clc.act.edu.au/UserLogin.asp?GroupId=37226https://clc.act.edu.au/UserLogin.asp?GroupId=37226https://clc.act.edu.au/UserLogin.asp?GroupId=37226https://clc.act.edu.au/UserLogin.asp?GroupId=37226http://www.algebasics.com/index.htmlhttp://www.mathsisfun.com/algebra/substitution.htmlhttp://www.mathsisfun.com/algebra/substitution.htmlhttp://www.mathsisfun.com/operation-order-pemdas.htmlhttp://www.mathsisfun.com/operation-order-pemdas.htmlhttp://www.trottermath.net/personal/realnosys.htmlhttp://www.trottermath.net/personal/realnosys.htmlhttp://www.karlscalculus.org/calc1.html

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Week

Term

2012

3

1


Introduction to matrices:

http://bit.ly/u9SwC6

e-book 1: Maths Quest 12: Further Mathematics

Chapter 16

View e-lesson-tutorial on worked examples 5and 9

e-book 2: Maths Quest 11: Mathematical Methods

CAS Chapter 7

View e-lesson-tutorial on worked examples1, 3, and 5

A(BC)=(AB)C

A(B+C)=AB+AC

(A+B)C=AC+BC

k(AB)=(kA)B(Ak)B=A(kB)

(AB)k=A(Bk)


Matrix Representation

e-book 1: Exercise 16A

Addition, subtraction and scalar multiplication

e-book 1: Exercise 16B;

e-book 2: Exercise 7A

Multiplication

e-book 1: Exercise 16C;

e-book 2: Exercise 7B

QuizGo to the cLc to complete this weeks quiz. Make sure you only take the quiz once you have

worked through all the Theory and Practical for the week.

Topic: Matrices

understand the structure, properties and behaviour of matrices be competent in basic manipulations of matrices

Matrix representation, nomenclature

Arithmetic work with matrices

- Addition, subtraction, scalar multiplication- Multiplication

Goals

ForumNEXT WEEK

Learning BriefMM1 Number Patterns,

Relations, Functions

Give examples to verify that the commutative,

associative and distributive laws hold for addition

and scalar multiplication with matrices.

Check for subtraction (see p819 e-book 1, p 333 e-

book 2)

Investigation
http://bit.ly/u9SwC6http://bit.ly/u9SwC6http://bit.ly/u9SwC6

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2012

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e-book 1: Maths Quest 12: Further Mathematics

Chapter 16

View e-lesson-tutorial on worked examples

11

e-book 2: Maths Quest 11: Mathematical Methods

CAS Chapter 7

View e-lesson-tutorial on worked examples 7

and 9

Multiplying matrices:

Watch -http://bit.ly/v7IOnj

More practice with worked examples -

http://bit.ly/py6ch3

Multiplicative inverse:

Watch -http://bit.ly/sJnHea

Read -http://bit.ly/zFF0gz

Watch -http://bit.ly/AgZMWE

Read -http://bit.ly/w3h691

Solving Matrix Equations:

Watch -http://bit.ly/xpXJNX


Multiplicative inverse and solving matrix equations

e-book 1: Exercise 16C, 16D;

e-book 2: Exercise 7C

Online quiz for practice

http://bit.ly/drGF4H

Part A - Determine by using examples whether the

commutative law holds for matrix multiplication.

Part B - Create 2 matrices that relate how many

combined classes you and 2 different class mates

share. If you add them together what does the

answer actually tell you? What if you add one of

your matrices and one of your friends?

QuizNEXT WEEK

Topic: Matrices

understand the structure, properties and behaviour of matrices

be competent in basic manipulations of matrices

At the end of this week you should be able to explain, what is an identity matrix,

what are determinants, and what is a multiplicative inverse?

Goals

ForumForum topic this week - For the matrix multiplication example shown in the forum, come up

with a UNIQUE (which means no one else in the forum has already said it) context for it.

Learning BriefMM1 Matrices,

sequences and

mensuration

Investigation
http://bit.ly/v7IOnjhttp://bit.ly/v7IOnjhttp://bit.ly/v7IOnjhttp://bit.ly/py6ch3http://bit.ly/py6ch3http://bit.ly/sJnHeahttp://bit.ly/sJnHeahttp://bit.ly/sJnHeahttp://bit.ly/zFF0gzhttp://bit.ly/zFF0gzhttp://bit.ly/zFF0gzhttp://bit.ly/AgZMWEhttp://bit.ly/AgZMWEhttp://bit.ly/AgZMWEhttp://bit.ly/w3h691http://bit.ly/w3h691http://bit.ly/w3h691http://bit.ly/xpXJNXhttp://bit.ly/xpXJNXhttp://bit.ly/xpXJNXhttp://bit.ly/drGF4Hhttp://bit.ly/drGF4Hhttp://bit.ly/drGF4Hhttp://bit.ly/xpXJNXhttp://bit.ly/w3h691http://bit.ly/AgZMWEhttp://bit.ly/zFF0gzhttp://bit.ly/sJnHeahttp://bit.ly/py6ch3http://bit.ly/v7IOnj

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2012

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As this is a really important component of the unit,

we will only be looking at one concept this week.

Read: Ebook 1 Maths Quest 12 : Further

Mathematics Chap 16 Section E

Watch : Solving equations

http://bit.ly/rWrOE5

Dont forget to start your assignment this week!


Multiplicative inverse and solving matrix equations

Ebook 1: 16E

Complete as many as you need to make sure you are

getting this concept correct. Make sure you ask for

directions or to see an example in your Face 2 Face

session if you need it.

Dont forget to start your assignment this week!

Find the determinant of the matrix

What does this result mean in terms of solving

matrix equations?

QuizQuiz on the cLc

By the end of this week you should be able to explain how to solve matrix

equations, and what role the inverse has in this process.

You should also be able to forming simultaneous equations from written

information. You should also be able to solve something like XA = B by hand where A

and B are 2 x 2 matrices

You should by now be able to use your CAS to enter matrices, perform

calculations on them and use it to find inverses and solve systems larger

than 2 unknowns.

Goals

ForumNEXT WEEK

Learning BriefMM1 Numbers

Patterns Relations and

Functions
http://bit.ly/rWrOE5http://bit.ly/rWrOE5http://bit.ly/rWrOE5

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2012

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This is a list of relevant chapter sections to matrices

so far.

This is our final week on matrices. You are to ensure

that you have understood these concepts.

Addition of matrices

subtraction of matrices

scalar multiplication of matrices

Multiplication of matrices (3x3 by hand),

higher order on CAS

identity matrix

determinants

multiplicative inversehow to use the multiplicative inverse,

identity and determinants

how to solve matrix equations, (and what

role the inverse has in this process)

solve something like AX = B by hand where

A and B are 2 x 2 matrices and know how to

solve higher order on your CAS

know the connections between

simultaneous equations, graphs of straight

lines and matrix equations ** (for this oneyou need to talk to Erin! if you haven't talked

to her already!)

**** Chapter 7D - has hints for your

assignment, particularly the INTERACTIVITY

called Matrices and Transformations! ****


Maths Quest 12 - Further Mathematics

Chapter 16 Sets 16A - 16 EParticularly the worded questions at the end of 16E

(matrices in context)

Maths Quest 11 - Mathematical Methods

Chapter 7 Sets 7A-7C

You have done some of these before, take this week

to complete and fully understand all work in these

sections.

ASK QUESTIONS!

Investi ation

There is an investigation on the cLc, read or print out

these questions and complete it in your investigation

folder.

This uses a lot of the concepts we have learnt in

matrices so far.

QuizNEXT WEEK

Topic: Matrices

understand the structure, properties and behaviour of matrices be competent in basic manipulations of matrices

HAVE YOU COMPLETED ALL MATRICE WORK?

Goals

Learning BriefMM1 - Numbers

Functions Patterns

Relations

ForumThis week the forum is in 2 parts - you must contribute your own question, and solve someone elses.

1. You need to submit a question from the text that has proved difficult for you.

2. You need to submit a solution to someone else's question

(you are restricted to answering only 1 question, but you may submit more than 1 if you like). You

cannot answer a question that has already been answered. The question can be on anything to do

with matrices so far.

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Week

Term

2012

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1

Topic: Sequences and Series. Unit Goal

understand and apply arithmetic and geometric sequences and seriesThis Week

General Patterns (concepts common to all patterns) Notation used in the unit Arithmetic Progressions (nth term, sum to n'th term, using both graphical and

algebraic representations )

CAS operations including setting up an e-activity

Goals


Functions Patterns

Relations

ForumNo Forum this week.

QuizThis weeks quiz is a summary of all matrices work. It will be available from Tuesday. You will be able

to take this quiz multiple times. I will check that you have completed this quiz by Tuesday 27th

March.


Website:http://mathdude.quickanddirtytips.com/what-

are-sequences-in-math.aspx

On this website.

What are arithmetic sequences? What are some really well known arithmetic

sequences you already know?

In the Brain Teaser Problem - he asks "Can youthink of a more efficient way to fully define an

arithmetic sequence other than simply writing out

all its elements?" think about this answer, and

then watch his solution on Youtube.(http://youtu.be/GLTCpI9esM0)

e-Book Further Maths Chapter 5

Read Section 5A. then complete T1

Read Section 5B. then complete T2

Read Section 5C. then complete T3

This weeks investigation is to connect the numeric and algebraic concepts of arithmetic sequences to their geometricrepresentations.

I-1. State the numeric sequence of 3 different arithmetic sequences (these can be from the text questions you have

completed, or you can come up with your own.)

I-2. State the algebraic rule for each sequence.

I-3. Graph each sequence, where the x-axis is the term number, and the y-axis is the value of the term.

I-4. What do you notice about these graphs? Make a general comment that describes the graphical representation of

an arithmetic sequence.

Investigation


Go to the e-Book Further Maths Chapter 5T1.

Set 5A (don't spend too long on this set if you are getting

the idea..... but do look at a few from each question. Also

pay particular attention to the worded questions 9-13)

T2.

On the right hand side of the e-book look in the

interactivities.

Complete the Number patters interactivity.

Set up an e-activity on your CAS. Instructions for this will

be given in classes this week, and in a special lunch timesession on Monday and Tuesday in Room 23.

Then questions from set 5B. (do half of these using e-

activity and half using algebraic methods)

T3.

Set 5C. (do half using e-activity on your CAS and half using

algebraic methods)
http://mathdude.quickanddirtytips.com/what-are-sequences-in-math.aspxhttp://mathdude.quickanddirtytips.com/what-are-sequences-in-math.aspxhttp://mathdude.quickanddirtytips.com/what-are-sequences-in-math.aspxhttp://mathdude.quickanddirtytips.com/what-are-sequences-in-math.aspxhttp://mathdude.quickanddirtytips.com/what-are-sequences-in-math.aspxhttp://mathdude.quickanddirtytips.com/what-are-sequences-in-math.aspx

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Topic: Sequences and Series. Unit Goal

understand and apply arithmetic and geometric sequences and seriesThis Week

Geometric Progressions TEST REVIEW---- test is on in WEEK 9. You will have an essential module - you MUST attend Wednesday Lunch Time in

the science lecture theatre for a summary of the terms work before your test

next week. If you cannot attend see ERIN.

Goals


Functions Patterns

Relations

ForumNO FORUM this week - Study for your exam instead!

QuizGo over all the quizzes from the past (weeks 3, 5 and 7) They have been opened up to allow for

practice sessions. Also refer to the PDF printed answers and my explanations (there are a few

quizzes with incorrect solutions so this is important to clarify)


YouTube - Sal Khan Introducing Geometric Sequences

http://youtu.be/pXo0bG4iAyg

e-Book Further Maths Chapter 5

Read Section 5D. then complete T1

Read Section 5E and 5F then complete T2

Read Section 5G. then complete T3

This weeks investigation is to connect the numeric and algebraic concepts ofgeometric sequences to their graphicalrepresentations.

I-1. State the numeric sequence of 3 different geometric sequences (these can be from the text questions you have

completed, or you can come up with your own.)

I-2. State the algebraic rule for each sequence. (remember to simplify fully)

I-3. Graph each sequence, where the x-axis is the term number, and the y-axis is the value of the term.

I-4. What do you notice about these graphs? Make a general comment that describes the graphical representation of a

geometric sequence.

Investigation


Go to the e-Book Further Maths Chapter 5T1.

Set 5D (don't spend too long on this set if you are getting

the idea..... but do look at a few from each question)

T2.

Set 5E and 5F. (do half of these using e-activity and half

using algebraic methods - this means add the geometric

sequence rules to your existing e-activity on your CAS or

create a new one) - MAKE SURE YOU SAVE IT!

T3.Set 5G Applications of Geometric sequences, these are

mostly worded questions, use your CAS as much as

possible, practice setting out your working.
http://youtu.be/pXo0bG4iAyghttp://youtu.be/pXo0bG4iAyghttp://youtu.be/pXo0bG4iAyg

Documents

MM1 Wks2-8