MGSC MATHEMATICAL METHODS CAS 3 & 4 2015
Welcome
Congratulations on choosing to study Maths Methods 3 & 4 at MGSC in 2015.
We hope you enjoy a challenging and rewarding year. Remember all we can ask is for you
to do your best. The most successful students are those who work consistently throughout the
year.
This year we will be encouraging the sharing of resources via our school Google Drive using
this link:
https://drive.google.com/a/mgsc.vic.edu.au/folderview?id=0B4EXkSp5TCc6ODRCTEduV3hV
ekk&usp=sharing
We also have a presence on our MGSC Maths Homework Club wikispace
https://mgscmathshomeworkclub.wikispaces.com/Year+12#
The remainder of this document will focus on defining the other important information you
need to know including: course content, assessments, timeline, topics, exercises, etc.
All the best. 
Mr Hughes & Mrs Hutchins
1
Areas of Study
 Functions and Graphs
 Algebra
 Calculus
 Probability
Each area contributes approximately 25% to overall assessment.
Refer to Study Design
http://www.vcaa.vic.edu.au/Documents/vce/mathematics/mathsstd.pdf
Assessment
Exam 1 = 22%
Exam 2 = 44%
SACs = 34%
1 hour Tech free, no reference material
2 hours Tech active, one bound reference book
Unit 3 SACs out of 60
Unit 4 SACs out of 40
Textbook
Essential Mathematical Methods 3 & 4 CAS (ClassPad Version)
Additional Text
Study on VCE Maths Methods CAS Units 3&4
2015 SACs
Unit 3
SAC 1
SAC 2
SAC 3
1 period
2/3 periods
1 period
Test 1
Application Task
Test 2
Term 1
Term 2
Term 2
Week 6
Week 3
Week 6
2 periods
2 periods
Analysis 1
Analysis 2
Term 3
Term 3
Week 1
Week 7
Unit 4
SAC 4
SAC 5
Assumed knowledge (Work from Year 10 and below)
1
Times tables (incl 0 X tables)
2
Basic number skills, esp BODMAS, fractions, decimals, brackets, integers
3
Know basic algebra skills such as how to expand eg
4
Know how to factorise a quadratic
5
Know how to work with (x,y) coordinates in correct order
6
Know how to simplify basic surds eg
7
Recognise simple powers eg 53 = 125, 64 = 26
8
Know how to apply the null factor law (not the “7” factor law) and use the quadratic formula
9
Know all index & log laws
10
Know basic mensuration skills – Pythagoras, SOHCAHTOA, similar triangles
11
Basic measurement formulae – Area & perimeter of square, rectangle, circle, Volume & surface area of
cube.
2
(a  b)2  a 2  b2
484
Glossary of question words
1.
Find, evaluate, calculate, solve
Working out is required.
2.
What is
Working out is required.
3.
Write Down
No, or minimal working required
4.
Show, prove
5.
State
6.
Sketch
Use the information in the question to
arrive at a given result. You cannot
assume what you are being asked to
show.
Similar to write down. No, or minimal
working required
A graph is needed
7.
Hence
8.
Hence, or otherwise
9.
Label
10. When
You must use the result of the previous
question to answer the next question
You may use the result of the previous
question to answer the next question or
you can use another method
Information must be placed on a graph
or diagram, in the correct place
The answer is usually time
11. How many
The answer is a number
12. Give an exact answer
Exact answers required. Do not evaluate
as an approximate decimal.
14. How long?
Eg 1/2 = 0.5 is acceptable
1/3 = 0.3333… is not acceptable
A written explanation is required. Avoid
rewording the question.
The answer is usually time
15. How far?
The answer is usually a distance
16. Given, if
These words usually mean a conditional
probabilityquestion
13. Explain
3
Unit 3
Functions and relations
WEEKS 1 and 2 ( Headstart 2014 – Mon 24 Nov – 5 Dec 2014)

Quick overview of areas of study, course outline, assessment and school assessed coursework
Set Notation, Identifying and describing relations and functions
p4 Ex1A 1, 2, 5, 6
p12 Ex1B 1, 3, 4, 5, 8, 9 eso,10, 11, 12, 13, 14

Implied Domain / Hybrid functions / Mapping / One-to-one fns / Odd and Even fns
p16 Ex1C 1, 2, 3, 5, 6d, 7abcdef 8, 9, 11,12,15,16

The modulus function
p23 Ex 1D all, p40

Sums and products p24 Ex 1E 1c 2 ab
Composite functions p30 Ex 1F 1ef, 3ae, 4, 5, 7, 8,10, 12,13

Inverse Functions
p33Ex 1G 1, 2, 4, 5eso, 6, 7, 8
To be submitted: Applications p35 Ex1H 3, 4, 5
Students are to complete the following questions
Ch Review M/C 1, 2, 3, 5-10 Short Answer 1ace, 2, 3, 5ace, 7, 8 Extended Response 3, 5, 6, 11
Holiday Work – The following questions must be attempted by all students undertaking
Mathematical Methods(CAS) Units 3 & 4 in 2015.
Your class teacher will collect this work at the end of the second week of Term 1 2015.
Correct all answers. Highlight or mark in red any questions you have difficulty with.
Revising linear functions
Ex 2A 1adgi, 2acf, 3, 7, 9
Ex 2C 1ab, 2ad, 3ac, 4a, 7, 8c, 9b, 11, 12, 15, 20
Ex 2E 1, 2, 4
Ex 2F 1a, 2, 3, 5
Ex 2G 1, 3
Polynomial functions
Ex 4A 2ab, 3ab, 4a, 7, 13ae, 18ac
Ex 4B 1ad, 2aei, 3ag, 4ag, 5ab, 7, 9
P158 Work through examples 20, 21
Ex 4G 1, 2
p167 Chapter Review 1-10
Revision of Functions
Chapter 8
p282 Ex 8.1
1, 4, 10, 3, 18, 19, 20, 21, 24, 25, 27, 28, 33, 35, 36, 37, 39, 40, 42, 43,
53, 54, 59, 60, 62, 63, 64*, 65, 67
p292 Ex 8.2
1, 2, 4, 12
CHAPTER REVIEW p 40 M/C 7-10
S/A(technology-free questions) 2, 3, 4, 5 ESO, 6-10 Extended Response 6, 11
4
Solving Systems of simultaneous linear equations in two variables
WEEK 3 (including Yr 12 CAMP) (WEEK 1 2015)
Students must review using CAS to enter matrices p60 and 61

Solving systems of linear simultaneous equations in two variables
p68 Ex 2F 6, 8
Simultaneous linear equations with more than two variables
P65 Ex 2G 1d, 2, 4a, 5, 7
Families of functions (Transformations)
WEEKS 4 and 5 (WEEK 2 and 3 2015)

Graphing functions y= xn p85 Ex3A 1, 2, 3, 4
Transformations: Dilations – p89 Ex3B 6 all

Reflections- p91 Ex3C 3
Translations – p94 Ex3D 4

Combinations of Transformations p98 Ex3E 1 ESO 2, 4, 5 p102
Ex3F 1-6 ESO

Using Matrices for transformations p109 Ex 3G 4, 5, 6, 8, 9, 12

Determining the rule p111 Ex3H all

Addition of ordinates p113 Ex3I 1, 4, 5

Graphing inverse functions p117 Ex3J 1eso, 2, 3eso, 4, 5
Students are to complete the following questions as part of preparation for SAC One
CHAPTER REVIEW p 122-124 M/C 1-10
S/A(technology-free questions) ESO E/R 1,3, 4, 6
Polynomial Functions
WEEKS 6, 7, 8 (WEEKS 4, 5, 6 2015)
(Completed prior to the start of the year – preliminary work:
Polynomials Ex 4A 2ab, 3ab, 4a, 7, 13ae, 18ac Ex 4B 1ad, 2aei, 3ag, 4ag, 5ab, 9
Ex 4G 1, 2 p 153 Chapter Review Multiple Choice 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

Determining the rule for a parabola p143 Ex 4C all
Functions of the form
n  N p149 Ex4D 1 LHS, 3 ,4 5 a e
f ( x)  a( x  h) n  k

General Cubic p153 Ex4E 1 a c, 2 a e

Polynomials of higher degree p 155 Ex4F 1, 2

Determining Rules for polynomials p 159 EX4G 3 a, 4 b c d, 5a, 6a

Solutions of Literal Equations and systems of Equations p 164 Ex 4H 1LHS, 2, 3b, 4a c, 6, 8, 10, 13, 14,
16
Note: The relationship of f(x+y), f(x-y), f(xy) and f (x/y) to values of f(x) and f(y) for different values of f
Mathematical Methods CAS Notes page 41
Students are to complete the following questions as part of preparation for SAC One
Chapter Review p 168 M/C 1-10
P169 S/A (technology-free questions) 1ae, 2, 4ae, 5ac, 6ab, 8, E/R 2, 3 6, 7
Practice SAC
5
SAC TEST ONE
Exponential and Logarithmic Functions
f ( x)  a x p179 EX 5A 1-5 eso 6, 8

Graphing transformations of

The exponential function
f ( x)  e x p182 Ex 5B 1 ESO, 2a , 3

Exponential equations
p183 Ex5C 1agh 2abf 3agi 4 agi

Log functions – Log laws p190 Ex5D 1-12 select a sample, 13adh, 14, 15

Determining rules p194 Ex5E 1, 3, 5, 7, 8, 9
Inverses p200 Ex5G 1, 3beh, 5, 7eso, 9

Solutions of exponential functions p197 Ex 5F1aeijo, 2ade, 3c, 4c, 5ae, 6a, 9, 11

Exponential Growth and Decay p204 Ex 5H 1, 3, 4
Students are to complete the following questions as part of preparation for SAC Two
CHAPTER REVIEW p 206 M/C 1-10 p207 S/A(technology-free questions) 1a d e h, 2 b d, 3 d, 4a,
5 b d, 10,11 p208 E/R 1, 5, 9, 11
Calculus: Differentiation of Polynomials, Power Functions and Rational Functions
WEEKS 9,10 (WEEKS 7, 8 2015)

Gradient of curve at a point p300 Ex9A 1, 2, 5; p306 The derived function EX9B 1ab 2LHS, 3LHS, 610

p310 EX9C 1-2eso, 3, 8c, 9

Chain rule p315 Ex 9D all p317 (Note: CAS screen shot p 313 Derivative of f(g(x))) Ex9E 1-2ESO, 4
a, 6 b

Product Rule p320 Ex9F 1-9 ESO

Quotient Rule p322 Ex9G 1-3eso

Graphs of gradient function p326 Ex9H 1adefhiklnqr, 4, 7ai, bi
(Note: CAS screen shot p 326 Derivative of f(x)=│x│)
Holiday Work – Maths Notes
1-14, 16-27, 32-45, 47-50, 52, 57-60, 64-66, 68-73, 76-86, 89-92, 96-103, 106-116, 119, 120, 122, 123127, 132-136, 140-141, 143-145, 151, 152, 154, 155, 159, 160, 167, 169
Or Studyon Questions
1-65, 78-85, 87-89, 91-97, 116-126, 128 plus additional questions on website
6
TERM 2
WEEKS 11,12, 13 (WEEKS 9,10, 11 2015)

Quick Review Limits – p333Ex9I 1 Continuity p333 Ex 9I 2, 3a c, 4 Differentiability p338 Ex9J 1, 3, 6
ab

Miscellaneous p339 Ex9K 1, 2 -27 (selection)
Students are to complete the following questions as part of preparation for SACS Two and Three
CHAPTER REVIEW p 343 M/C 1-10 p344 S/A(technology-free questions) 1a d k, 3, 4 p345 E/R 1, 2, 3
SAC 2 (date to be confirmed) – Applications Task (approx 2– 3 lessons
Applications of Differentiation

Tangents/Normals p335 Ex10A 1, 3, 5, 6ae, 8b

Linear approximation p357 Ex10C 1-4, 7, 12

Stationary points p361Ex10D 1a g , 2b, 5, 9a c p368 Ex10E 2a c , 3ac, 10, 12, 13, 17

Absolute Max/Min p373 Ex10F 3, 4, 5, 7, 9 Maxima and Minima problems p379 Ex 10G 3, 4, 6, 7, 9

Rates of Change p381 Ex10H 1, 3, 4, 5, 7(Displacement, velocity and acceleration) Related Rates of
Change p385 Ex10I 1, 6,7,10

Families of functions p388 Ex 10J 1, 5, 9
CHAPTER REVIEW p 391 M/C 1-10 p393 S/A (technology-free questions) 1,4, 11, 12 E/R 2,15,27, 28
Circular (Trigonometric) Function

Review p212 Ex6A 1-4 ESO Unit circle p215 Ex 6B 1-4 ESO

Symmetry Properties p217 Ex 6C 1, 2bc, 3bc p218 Ex 6D ESO

Exact values p222 EX 6E 1-8 ESO,

Graphs of y  a sin( nx ) and y  a cos(nx) p226 Ex 6F 1-5, 7, 8

Transformations of trigonometric functions of the form y  f (x) to y  Af ( n( x  b))  c
p229 Ex 6G 1 -3 ESO, Finding x-intercepts p232 Ex 6H 1-2 ESO
(Note: CAS screen shot page 232 –using CAS to find x-axis intercepts)

Addition of ordinates p233 Ex 6I 1,3 Determining rules of Circular functions p235 Ex 6J 1-5,7,9

Tangent graphs p241 and Solutions of equations of the form sin( nx)  k cos( nx) EX 6K 1-2 eso, 3,
5eso, 10

Using CAS to solve trigonometric equations p246 Ex6L 1eso. Also cover General solution of trig
equations
(Note: CAS screen shot page 245 Check calculator is in Radian mode))
Identitiy cos x  sin
2

2
x  1 p249 Ex6M all
Applications p251 EX6N 1, 3, 5
Students are to complete the following questions as revision exercise
CHAPTER REVIEW p 254 M/C 1-10 p256S/A (technology-free questions) 1a d c g, 2 a d, 3ad, 4 b e, 5a c,
7a c
7
E/R 2, 3, 6
WEEKS 17, 18 (SAC 3 1 period date to be confirmed ) (WEEKS 15, 16 2015)
Calculus: Differentiation of Transcendental Functions

Derivative of ex p 406 Ex11A 1-4eso, 5

Derivative of Log p408 Ex11B 1 LHS , 2acefg , 3ae, 4-8

Applications p413 Ex11C 1, 2, 5a e, 8, 15, 17, 25, 28

Derivative of Trig p421 Ex11D 1-2eso 3 c d, 4 a b j, 5 a c f, 6b, 7b

Applications p425 Ex11E 1a f, 4, 7, 8, 11 CAS Calculator p426 Ex11F 1a d, 2b, 6a b c

Applications p430 Ex 11G 1, 3
Students are to complete the following questions as revision exercise
CHAPTER REVIEW p 432 M/C 1-10 p433 S/A (technology-free questions) 1a f h j , 2 a c, 4 a c, 9,10,
E/R 1, 3, 20, 23
WEEK 19 (EXAM WEEK) (WEEK 17, 2015)
8
Unit 4
WEEKS 20, 21 (WEEKS 18, 19, 2015)
Anti-differentiation (Integration)

Approximation leading to Integrals p445 Ex 12A 1 a b ,2, 4, 5, 8 b

Anti differentiation p 450 Ex 12B 1, 2, 3 c, 5, 6 (Note: CAS screen shot page 452)

Anti differentiation (ax +b)r p 454 Ex12C 1eso, 2eso, 4, 6 (Note: CAS screen shot page 453)
Anti differentiation ekx p 455 Ex 12D 1eso, 2eso, 4

Definite Integrals p 459 Ex12E 1eso, 2 eso, 3a, d, g, h, 4 eso, 5a, d

Area under a curve p 462 Ex12F 1a, 2f, 3eso, 6, 7, 9, 12

Integration of Circular Functions p465 Ex12 G 1eso, 2eso, 3, 4af, 5ad, 6
Holiday work - To be selected from:
Practice Exam Questions
Maths Notes and Revision Chapters: CAS Calculators Questions, Technology Free Questions and
Applications Questions ;Revision Chapters (Questions to be confirmed) Multiple Choice, Short answer and
Extended Response
Term 3
WEEK 22 (WEEK 20 2015)
Extra Revision this Term: Students can select exercises from Chapter 7 Functions Revisited

Miscellaneous exercises p469 Ex 12H 1LHS, 3LHS omit 3e, 6, 8ac, 11,15, 18 eso
(Integration by recognition) Homework – Heinemann CAS page 317 Ex 7.5 ( see HP/DSA)

Area between two curves p 474 Ex 12I 1, 2, 3 ad, 4-8

Applications of Integration p479 Ex 12J 1, 4, 6, 7, 12, 13, 14, 15, 18
Students are to complete the following questions as revision exercise
CHAPTER REVIEW p 487 M/C 1-10
SHORT ANSWER (technology-free questions) p488 1LHS, 2 ,4, 9,10, 14, 17, 20b d
EXTENDED RESPONSE 1, 3, 6, 12
WEEK 23 (WEEK 21 2015)
Discrete Random Variables and their probability distributions

Review of probability, conditional probability, independent events
P516 Ex 14A Q1, 2, 3, 5, 7, 9, 13, 15, 17

Discrete random variables
P520 Ex 14B Q1, 3, 5, 6

Discrete probability distributions
P522 Ex 14C Q2, 3, 4, 5, 7
9

Expectation (Mean), Median, Mode and Variance
P531 Ex 14D Q1a c f, 3, 4, 6, 8, 9, 11, 13
Chapter Review p 536 MC1-10
Short Answer (technology free) p537 1, 2, 3, 4, 5a, 8, 10
Extended Response 1, 2, 6
WEEK 24, 25 (WEEKS 22, 23, 2015)

Practice SAC preparation
SAC 4 Analysis 1 during week 24
Binomial Distribution

p 696 Review combinations and permutations p697 Ex A1
p668 Ex A3 Binomial Theorem

Bernoulli Sequences and Binomial Distribution
P547 Ex 15A Q1, 2a, 3, 5, 6, 8, 9, 12, 16
(Note: CAS screen shot page 546)

The Graph of the Binomial Probability Distribution
P550 Ex 15B Q1, 3, 5, 7
E(X), Var(X) for the Binomial Probability Distribution
P555 Ex 15C Q1-7

Using CAS Calculator to find sample size
P556 Ex 15D 1, 4, 6
CHAPTER REVIEW p 559 M/C 1-10
SHORT ANSWER (technology-free questions) p 560 1, 3, 5, 7
EXTENDED RESPONSE 1, 3, 4, 6, 8
WEEK 26, 27 (WEEKS 24, 25, 2015)
Markov Chains

Using matrices to represent Conditional Probability
P567 Ex 16A Q 1, 2, 4, 5, 6

Markov Chains
P574 Ex 16B Q1, 3, 6, 7, 10

Steady state of a markov cahin
P582 Ex 16C Q 1, 2, 3, 5, 8
P587 Ex 16D Q 1, 3, 5, 6, 7
CHAPTER REVIEW p 590 M/C 1-10
SHORT ANSWER (technology-free questions) p 591 1, 3, 5, 7
EXTENDED RESPONSE 1, 3
Continuous Random Variables and their Probability Distribution

Continuous Random Variables
P601 Ex 17A Q 1, 2, 4, 6, 10, 13, 16,

Cumulative Distribution functions
P607 Ex 17B Q1-3

Mean, Median, Mode
P613 Ex 17C Q 1a d, 2 a d, 3, 4, 7, 8 14, 15, 17

Measures of Spread
P620 Ex 17D Q 1, 4, 6, 8, 10
Properties of Mean and Variance
P624 Ex 17E Q 1, 2, 4
10
CHAPTER REVIEW p 627 M/C 1-10
SHORT ANSWER (technology-free questions) p 629 1, 2, 3, 4, 5, 6, 7,10
EXTENDED RESPONSE 1, 2, 3
WEEK 28 (WEEKS 26 2015)
Normal Distribution

The Normal Distribution
P637 Ex 18A Q 1, 2, 3, 5, 8

Standardisation
Review    ,   2 ,   3
P642 Ex 18B Q 1, 2, 3, 4, 6, 8, 10, 12, 14

Determining Normal Probabilities
P648 Ex 18C Q 1ESO, 2ESO, 4 ad, 5, 8, 11, 12, 14, 16
(Note: CAS screen shot page 646)

Solving problems using normal distribution
P652 Ex 18D Q 1, 3, 4, 5, 6, 7, 10
CHAPTER REVIEW p 654 M/C 1-10
SHORT ANSWER (technology-free questions) p 656 1, 2, 5, 6, 8EXTENDED RESPONSE 1, 2, 3, 4, 5
WEEK 29 (WEEK 27 2015)
SAC 5 Analysis 2 (1-2 days)
REVISION
WEEK 30, 31 (End of Term) (WEEKS 28, 29 2015)
REVISION
Term 4
WEEKS 32 ,33 (WEEKS 30, 31 2015)
REVISION / PRACTICE EXAMS / OCTOBER TEST
11