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8/2/2019 SM1 Wks3-8
1/6
Week
Term
2012
3
1
Theoretical Components
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)
Practical Components
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 BriefSM1 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/u9SwC68/2/2019 SM1 Wks3-8
2/6
Week
Term
2012
4
1
Theoretical Components
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
Practical Components
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 Inverses for 3x3 matrices are also important
for specialist mathematics. Research how to get the
inverse of a 3x3, and show by hand how to find the
inverse of0 2 11 3 12 4 1
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 BriefSM1 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/v7IOnj8/2/2019 SM1 Wks3-8
3/6
Week
Term
2012
5
1
Theoretical Components
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!
Practical Components
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 BriefSM1 Numbers Patterns
Functions and Relations
http://bit.ly/rWrOE5http://bit.ly/rWrOE5http://bit.ly/rWrOE58/2/2019 SM1 Wks3-8
4/6
Week
Term
2012
6
1
Theoretical Components
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! ****
Practical Components
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 BriefSM1 - 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.
8/2/2019 SM1 Wks3-8
5/6
Week
Term
2012
7
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
Learning BriefSM1 - Numbers
Functions Patterns
Relations
Forum No 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.
Theoretical Components
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.
I-5. Look at the graph for a sum to n-terms of an Arithmetic Series. What do you see?
Investigation
Practical Components
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.aspx8/2/2019 SM1 Wks3-8
6/6
Week
Term
2012
8
1
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
Learning BriefSM1 - Numbers
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)
Theoretical Components
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
Practical Components
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