2016 Student MAM Course Outline (Version 1)

7/21/2019 2016 Student MAM Course Outline (Version 1)

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Subject structure and assessment details

To achieve all outcomes students will draw on key knowledge and key skillsoutlined in the VCAA Mathematical Methods Study Design (Accreditation period!"# $ !"%&'

• School$assessed Coursework or )nit * contributes "+ per cent to thestudy Score

• School$assessed Coursework or )nit , contributes "+ per cent to thestudy Score

• The two end o year e-aminations contribute ## per cent to the studyscore'

.or each unit the student is re/uired to demonstrate achievement o three

outcomes' As a set these outcomes encompass all o the selected areas o study

or each unit' .or each o )nit * and )nit , the outcomes apply to the content

rom the areas o study selected or that unit'

)nit *0Assessment Tasks or Unit 3 consist o:

An A!!"#CAT#O$ TA%& based on content rom the .unctions and 1raphs andAlgebra areas o study' The outcomes are to be assessed across the applicationtask.

OUTCOME% Marks

AllocatedOutcome 1

De2ne and e-plain key concepts as speci2ed in the

content rom the areas o study3 and apply a range o

related mathematical routines and procedures'

"4

Outcome 2

Apply mathematical processes in non$routine conte-ts3

including situations re/uiring problem$solving3 modelling

or investigative techni/ues or approaches3 and analyse

and discuss these applications o mathematics'

!

Outcome 3

Select and appropriately use numerical3 graphical3

symbolic and statistical unctionalities o technology to

develop mathematical ideas3 produce results and carry

out analysis in situations re/uiring problem$solving3

modelling or investigative techni/ues or approaches'

"4

Total VCAA marks 4!



)nit ,0Assessment Tasks or Unit 4 consist o:

Two MO'E""#$()!*O+"EM %O"V#$( TA%&%3 which we will call analysis tasks

" and ' The three outcomes will be assessed across these tasks'

The task designated A$A",%#% TA%& 1 will consist o a set o short answer and

e-tended response /uestions covering material rom chapters " 5 6'

The task designated A$A",%#% TA%& 2 will consist o a set o multiple choice

and e-tended response /uestions related to the 7robability and Statistics(chapters "! 5 ",& area o study'

8utcomes

.or each unit the student is re/uired to demonstrate achievement o threeoutcomes' As a set these outcomes encompass all o the selected areas o studyor each unit' .or each o )nit * and )nit , the outcomes apply to the contentrom the areas o study selected or that unit'

OUTCOME% Marks

Allocated

A

Outcome 1De2ne and e-plain key concepts as speci2ed in the content rom the areas

o study3 and apply a range o related mathematical routines and

procedures'

"4 %+

Outcome 2

Apply mathematical processes in non$routine conte-ts3 including situations

re/uiring problem$solving3 modelling or investigative techni/ues or

approaches3 and analyse and discuss these applications o mathematics'

! "

"

Outcome 3

Select and appropriately use numerical3 graphical3 symbolic and statistical

unctionalities o technology to develop mathematical ideas3 produce

results and carry out analysis in situations re/uiring problem$solving3

modelling or investigative techni/ues or approaches'

"4 +

%

Total VCAA marks 4!

School Assessed CourseworkU$#T T,!E O-

TA%&

'ATE O-

TA%&

VCAA

MA*&

%

TEC.$O"O(,

%TATU%

)nit

*

Application

Task

Chapters "3 and *

To /e announced 4! Assessment

component will

be CAS activenut no

bound reerence

book will be

allowed')nit

,

Analysis Task

"

Chapters " to

6

To /e announced 4 CAS Active

Summary book

)nit

,

Analysis Task

Chapters "!to ",

To /e announced 4 CAS Active

Summary book



!"# )nits * and , MAM 9earning Se/uence TimelineAny changes (due to unoreseen circumstances& to this timeline will be

communicated via student sharepoint and:or email'

;eek Date Content <mportant dates to

consider#nitio

n

201

*! =ov

5 , Dec

"'3 "'*3 "',>oliday >omework ?-pectations0 .inish as much o ?- "'$"', as you can over the

holidays'

Term

1

1

6:!"

.ri onlyIntroduction

2 " .eb $

4 .eb

1.5, 2.2 [check holiday homework]3 % .eb $

" .eb

2.3, 2.4

Thu 11: House wimmin!

"arni#al

4 "4 .eb

$ "6

.eb

2.5, 2.$

%ri 1&: enior 'ound 'o(in

.eb

$ #

.eb3.2, 3.3, 3.4

6 6 .eb

5

, Mar

3.5, 3.$, )ui* +"h13- + Mar 5

"" Mar

// Task ssi!nment "om/onent ", Mar

$ "%

Mar

4.2, 4.3, 4.4 " Mar

$ 4

Mar// task returned, 4.5, 4.$

Tue 22: House thletics

"arni#al

>oliday >omework ?-pectations0

"' ?nsure all e-ercises rom Ch "$, are completed

' ?nsure that Ch "$, are all summarised in your summary book'



Term

2

1

"" Apr

$ "4

Apr

0 5.4 isection ethod (unit 1 text), 5.2,

5.32 "% Apr

$

Apr

5.4, 5.5, 5.$3 4 Apr

$ 6

Apr

$.2, $.3

on 25:n*ac ay

4 May $

# May $.4, $.5, $.$ 6 May $

"* May $., 13.4 6ewton 'a/hson ethod (unit 1

text)6 "# May

$ !May

ummarise "h 4$, 'e#ision, )ui* 2 +"h 4$-

* May

$ +

May.2, .3

7nit 1 0aminations

*! May

$

* @une.4, 8.2

7nit 1 0aminations

# @un $

"! @un

6o "lasses

Tue : 9T

'e/ort ritin! ay

10 "* @un $

"+ @un 8.3, 8.4

on 13: )ueen;s irthday

7nit 4 "ommences

11 ! @un $

, @un &.2, &.3, &.4

>oliday >omework ?-pectations0

"' ?nsure all e-ercises rom Ch 4$6 are completed

' ?nsure that Ch 4$6 are all summarised in your summary book'

Term

3

1

"" @ul $

"4 @ul 'e#ision

2 "% @ul $ @ul 1<.2, 1<.3, 1<.4



3 4 @ul $

6 @ul 'eturn nalysis Task 1, 11.2, 11.3

4 " Aug 5

4 Aug

11.4, 12.2, 12.3

% Aug $

" Aug 12.4, 12.5, 13.2

6 "4 Aug

$ "6

Aug

13.3, 13.4, 13.5

Aug

$ #

Aug14.2, 14.3, 14.4

6 Aug

$ Sep evision

4 Sep $

6 Sep 2<14 =" eam 1

10 " Sep

$ "#

Sep'eturn nalysis Task 2, 2<14 =" eam 2

>oliday >omework ?-pectations $ see B?nd o ear ?-amination evision 7lanner'Term

4

1

* 8ct $

+ 8ct 2<15 =" eam 1

2 "! 8ct

$ ",

8ct2<15 =" eam 2

3 "+ 8ct

$ "

8ct

4 , 8ct

$ %

8ct *" 8ct

$

, =ov

Tues 1: "u/ ay

6 + =ov $

"" =ov

SC>889 ASS?SS?D C8)S?;8ET.E A!!"#CAT#O$ TA%&

The application task will consist o linked components that ollow a common

theme 5

15An assinment comonent• will consist o a booklet with a set o /uestions worth ,! marks that

will contribute !F towards each studentGs 2nal score or the

application task' (that is "! marks out o the total possible o "!!

marks available in total or school assessed coursework&



• will be available to be downloaded rom Student Share7oint rom

6am on Monday + March' <t is each studentGs responsibility to print

the assignment component booklet'

• which must be submitted to your class teacher by "'*!pm on .riday

"" March' 9ate submission will only be considered in e-ceptional

circumstances'

• .ailure to submit the assignment component booklet will result in a

Hero score or the assignment component o the Application Task'

• ;orking space is provided throughout the assignment component

booklet' All /uestions must be answered in the spaces provided'

Additional sheets o loose paper will not be assessed'

• Students may work on the assignment component during class time

and it may also be completed as homework'

• Students may not ask any teacher a /uestion directly taken rom

the assessment component booklet' Students may ask a teacher

any /uestion rom their te-tbook that is associated with any

/uestion taken rom the assessment component booklet' <n other

words teachers will only give indirect: non$speci2c assistance withthe assignment component'

25 A Test comonent

• will consist o a booklet with a set o /uestions worth ,! marks that

will contribute %!F towards each studentGs 2nal score or the

application task' (that is ,! marks out o the total possible o "!!

marks available in total or school assessed coursework&'

• will be completed under normal e-am conditions with "! minutes

reading time and #! minutes writing time in the period ,

assessment session on a date to be announced'• Students will be supplied with the VCAA Mathematical Methods

ormula sheet'

• 9anguage dictionaries will not be allowed'

• Students will be permitted to bring one CAS calculator and:or one

scienti2c calculator'

• A bound reerence book will not be allowed

• All students are e-pected to sit or the task on the scheduled date

as it has the same status as an oIcial end o year e-amination'

8nly in e-treme circumstances should a student not sit or the task

on the scheduled date and they would need to provide a medical

certi2cate to justiy their absence' <t is e-pected that any studentsin this position would notiy the school as early as possible o the

circumstances so that appropriate arrangements can be made'

• .ailure to provide a medical certi2cate or an absence will result in a

Hero score or the task' Students who have an oIcial school activity

on the scheduled date should liaise with their class teacher well in

advance o the session in order to make appropriate alternative

arrangements'

T.E A$A",%#% TA%&%



Joth tasks will be conducted under the ollowing general conditions0

• ?ach task will comprise "! minutes reading time and #! minutes writingtime to be ollowed by a eedback component o one period'

• The oIcial VCAA ormula sheet will be provided'

• 9anguage dictionaries are not permitted'

All students are e-pected to sit or the task on the scheduled date as it has the

same status as an oIcial end o year e-amination' 8nly in e-treme

circumstances should a student not sit or the task on the scheduled date and

they would need to provide a medical certi2cate to justiy their absence'

<t is e-pected that any students in this position would notiy the school as earlyas possible o the circumstances so that appropriate arrangements can be made'

.ailure to provide a medical certi2cate or an absence will result in a Hero score

or that dayGs task'

Students who have an oIcial school activity on the scheduled date o a task

should liaise with their class teacher well in advance o the date o the session in

order to make appropriate alternative arrangements'

.or the task designated A$A",%#% TA%& 1 the ollowing additional conditions

will apply0

• Students will be permitted to bring an approved CAS calculator and:or ascienti2c calculator'

• Students will be permitted to bring one bound reerence3 te-t (which may

be annotated&3 lecture pad or e-ercise book into the session' The resourcemust conorm to the oIcial VCAA guidelines as outlined later in thisdocument'

• The task will cover work rom Chapters " to 6 (including both theJisection method and the =ewton aphson method& o the te-tbook'

• The task will consist o a set o short answer and e-tended response

/uestions covering material rom chapters " 5 6'

.or the task designated A$A",%#% TA%& 2 the ollowing additional conditions

will apply0

• Students will be permitted to bring an approved CAS calculator and:or a

scienti2c calculator'

• Students will be permitted to bring one bound reerence3 te-t (which may

be annotated&3 lecture pad or e-ercise book into the session' The resourcemust conorm to the oIcial VCAA guidelines as outlined later in thisdocument'

• =ote that the BCheckpoints book cannot be used as a reerence te-t inthis assessment'

• The task will consist o a set o multiple choice and e-tended response/uestions related to the 7robability and Statistics (chapters "! 5 ",& areao study'



VCAA ASS?SSM?=T

The award o satisactory completion or a unit is based on a decision that the

student has demonstrated achievement o the set o outcomes speci2ed or the

unit' This decision will be based on the teacherGs assessment o the studentGs

overall perormance on assessment tasks designated or the unit'

Assessment o le7els o achie7ement

The studentGs level o achievement or )nits * and , will be determined byschool$assessed coursework and two end$o$year e-aminations'

Contri/ution to 8nal assessment

School$assessed coursework or )nit * will contribute "+ per cent and or )nit ,

will contribute "+ per cent to the study score' )nits * and , will also be assessed

by two end$o$year e-aminations3 which together will contribute ## per cent to

the study score'

E9amination 1

Students are re/uired to respond to a collection o short$answer and some

e-tended$answer /uestions covering all areas o the study' The task is designedto assess studentsG knowledge o mathematical concepts3 their skills in carrying

out mathematical algorithms and their ability to apply concepts and skills in

standard ways without the use o technology'

The task will be completed under the ollowing conditions0

• Duration0 one hour

• Date0 end$o$year

• =o calculators3 CAS or notes o any kind are permitted' A sheet o ormulas

will be provided with the e-amination'

• The e-amination will contribute per cent to the study score'

E9amination 2

Students are re/uired to respond to a collection o multiple$choice /uestions and

e-tended$answer /uestions involving multi$stage solutions o increasing

comple-ity' Student access to an approved graphics calculator will be assumed

by the setting panel' The task is designed to assess studentsG ability to

understand and communicate mathematical ideas3 and to interpret3 analyse and

solve both routine and non$routine problems'

The task will be completed under the ollowing conditions0

• Duration0 two hours

• Date0 end$o$year

• An approved CAS calculator3 a scienti2c calculator and one boundreerence3 te-t (which may be annotated& or lecture pad3 may be broughtinto the e-amination' A sheet o ormulas will be provided with thee-amination'

• The e-amination will contribute ,, per cent to the study score'

8T>? )S?.)9 ?S8)C?S

S)MMA J88E 1)<D?9<=?S $ details o how your summary book should be

structured'

ASS?SSM?=T 78T8C89S $ details o protocols associated with the marking o

SACGs'

http://student.balwynhs.vic.edu.au/Maths/MathsSubject/year12mathematics/Shared%20Documents/Forms/AllItems.aspx?RootFolder=%2FMaths%2FMathsSubject%2Fyear12mathematics%2FShared%20Documents%2FMathematical%20Methods%20(CAS)%20Unit%203_4%2FSummary%20Book%20Guidelines

http://student.balwynhs.vic.edu.au/Maths/MathsSubject/year12mathematics/Shared%20Documents/Forms/AllItems.aspx?RootFolder=%2FMaths%2FMathsSubject%2Fyear12mathematics%2FShared%20Documents%2FMathematical%20Methods%20(CAS)%20Unit%203_4%2FMathematical%20Methods%20Assessment%20Protocols

http://student.balwynhs.vic.edu.au/Maths/MathsSubject/year12mathematics/Shared%20Documents/Forms/AllItems.aspx?RootFolder=%2FMaths%2FMathsSubject%2Fyear12mathematics%2FShared%20Documents%2FMathematical%20Methods%20(CAS)%20Unit%203_4%2FSummary%20Book%20Guidelines

http://student.balwynhs.vic.edu.au/Maths/MathsSubject/year12mathematics/Shared%20Documents/Forms/AllItems.aspx?RootFolder=%2FMaths%2FMathsSubject%2Fyear12mathematics%2FShared%20Documents%2FMathematical%20Methods%20(CAS)%20Unit%203_4%2FMathematical%20Methods%20Assessment%20Protocols



!"# $"% ST)D D?S<1= 5 amongst other inormation this contains speci2c

inormation regarding what work is e-aminable'

@AC 79)S 5 electronic version o the te-tbook

TOPIC 1

CHAPTER 1 – SOLVING EQUATIONS

EXERCISE RECOMMENDED QUESTIONS

Pr!ti"e C#n"#$i%te M"ter

0 1.2 >olynomials 1 t# 1&' 1!e* 1+!* 1,* 1-!*

1.* &/* &&

&0* &

0 1.3 Tri! symmetry

>ro/erties

1* 0* +' -* 1/* 1!e* 1 1,* 1-

0 1.4 Tri! e?uations and

!eneral solutions

1* 0* +* ,* -' .* 11* 10* 1+!* 1, 1.* &/

0 1.5 @iteral e?uations

and simultaneous

e?uations

1* 0* +* * ,* .' 11!* 1&* 10* 1+* 1!*

1-* &/'

&1

TOPIC &

CHAPTER & – 2UNCTIONS AND GRAPHS



2.2 >olynomial Aunctions &* * * -* 1/ 10* 1* 1* 1,* &1 &0

2.3 Bther al!e(raic

Aunctions

&* 0* +*, .* 1/* 1&* 1* 1+ 1.

2.4 "om(inations oA

Aunctions

1* 0* + ,* -* 11* 10* 1+ 1,

2.5 6onal!e(raic

Aunctions

1* 0* +* * -* 11* 1 1+!* 1!e* 1-* 1.3e4*

&1!* &

&

2.$ odellin! and

a//lications

1 * +* ,* 1/* 1& 10

http://student.balwynhs.vic.edu.au/Maths/MathsSubject/year12mathematics/Shared%20Documents/Forms/AllItems.aspx?RootFolder=%2FMaths%2FMathsSubject%2Fyear12mathematics%2FShared%20Documents%2FMathematical%20Methods%20(CAS)%20Unit%203_4%2F2016%20resources&InitialTabId=Ribbon.Document&VisibilityContext=WSSTabPersistence

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TOPIC 0

CHAPTER 0 COMPOSITE 2UNCTIONS* TRANS2ORMATIONS AND INVERSES



0 3.2 "om/osite

Aunctions and Aunctionale?uations

1* 0* +* ,* .* 11* 10* 1 1-

0 3.3 TransAormations 1* 0* + ,* .* 11* 1* 1 1,

0 3.4 TransAormations

usin! matrices

1* +* ,* -* 1/* 10 1+

0 3.5 In#erse !ra/hs and

relations

1* 0 +* %* ,3!* 1/* 1&* 1 1+

0 3.$ In#erse Aunctions 1* 0* + ,!e* .* 11* 10* 1+ 1,

TOPIC

CHAPTER L#rit56i! 4un!ti#n"



0 4.2 @o!arithm laws

and e?uations

1* 0* + ,!e* -!* .!e* 1/!*

1&* 10%78* 1!* -

1,

0 4.3 @o!arithmic scales 1* & 0* +* 1/ 10

0 4.4 Indicial e?uations 1!* &! 0!%* !* * ,!* -!* 1/*

1&

1

0 4.5 @o!arithmic !ra/hs 1* 0 +* * ,* -* .!* 1/*

1&* 1

1+* 1

0 4.$ //lication

/ro(lems

+* ,* .* 11* 10 1+

Unit 1 text 0 5.4

6umerical a//roimations

to roots oA /olynomial

e?uations +isection

method-

1* & ,* -* .* 113 N9A

TOPIC +

CHAPTER + Di44erentiti#n





0 5.2 'e#iew oA

diAAerentiation

1* 0* * * ,* . 113%* 1&!%* 1* 1+!*

1!* 1-* &/

&&

0 5.3 iAAerentiation oA

e/onential Aunctions

1* 0 +!e* !* -* 1/* 1&* 1 1+

0 5.4 //lications oAe/onential Aunctions 1 0* * -* 11 10

0 5.5 iAAerentiation oA

tri!onometric Aunctions

1!e* 0 +!e* * -* 1/* 1&* 1 1+

0 5.$ //lications oA


1* & +* * .* 11* 1 1

TOPIC

CHAPTER 2urt5er %i44erentiti#n n% ::$i!ti#n"



0 $.2 The chain rule 1* 0* + ,!ei* -!e* 1/* 1&!*

1* 1

1-

0 $.3 The /roduct rule 1* 0* + ,3e58* -!* 1/* 1&* 1 1-

0 $.4 The ?uotient rule 1* 0 +3e58* ,!* .* 11* 10 1

0 $.5 "ur#e sketchin! &* * ,* .* 11!e* 10!* 1+ 1,

0 $.$ aimum and

minimum /ro(lems

1* & +* * -* 1/* 1&* 1 1+

0 $. 'ates oA chan!e 1* 0* * -* 1/* 1&* 1 1

Unit 1 text 0 13.4

"oordinate !eometry

a//lications oA

diAAerentiation +6ewton

'a/hson ethod-

,* - 13% N9A

TOPIC ,

CHAPTER , Anti%i44erentiti#n



0 .2 ntidiAAerentiation 1* 0* +* , 1/!* 11!e* 1&!e* 1*1* 1-

&/

0 .3 ntideri#ati#es oA

e/onential and


&* +* , .* 11* 10* 1+* 1- &/



0 .4 %amilies oA cur#es

and a//lications

0* * * ,* .!* 1& 1* 1!* 1,* 1.* &1 &0

TOPIC -

CHAPTER - Interti#n



0 8.2 The Aundamental

theorem oA inte!ral

calculus

1* 0* + ,* .* 1/!e* 11!e* 10*

1+

1,

0 8.3 reas under cur#es 1* 0 +* ,* .* 11* 10 1

0 8.4 //lications oA

inte!ration

1* &* * * -* 1/ 1&* 1* 1* 1- &1

TOPIC .

CHAPTER . L#rit56i! 4un!ti#n" u"in !$!u$u"



0 &.2 The deri#ati#e oA

the lo!arithmic Aunction

1* &* * ! ,!e* -!* .!* 1/!* 1&*

1* 1

1,

0 &.3 The inte!ral oA thelo!arithmic Aunction

&* * + ,* -!* 1/* 1&* 1* 1 1,

0 &.4 @o!arithmic

a//lication /ro(lems

1* & * * -* 1/* 1& 10

TOPIC 1/

CHAPTER 1/ Di"!rete rn%#6 ;ri3$e"



0 1<.2 iscrete random

#aria(les

1* &* * ,* -!* .!* 1/* 10* 1*

1+

1-

0 1<.3 easures oA

centre and s/read

1* &* * * - .!* 1/* 1&* 1* 1* 1- &/

0 1<.4 //lications oA

discrete random #aria(les

&* +* ,* .* 1/* 10* 1



TOPIC 11

CHAPTER 11 T5e 3in#6i$ %i"tri3uti#n



0 11.2 ernoulli trials 1 0* * +

0 11.3 The (inomial

distri(ution

1* 0* * ,* .* 1/!* 1&* 1+* 1 1,

0 11.4 //lications oAthe (inomial distri(ution

& 0* +* ,* .* 11 10

TOPIC 1&

CHAPTER 1& C#ntinu#u" :r#33i$it< %i"tri3uti#n"



0 12.2 "ontinuous

random #aria(les and

/ro(a(ility Aunction

&* +* ,* -!* 1/* 1&* 10 1+

0 12.3 The continuous

/ro(a(ility density

Aunction

1* & 0* * * .* 11 10

0 12.4 easures oA

centre and s/read Aor

continuous /ro(a(ility

Aunctions

&* * -* 1/* 10* 1 1

0 12.5 @inear

transAormations oA

continuous random

#aria(les

1* &* 0 +* -* 1/* 1&* 1 1+



TOPIC 10

CHAPTER 10 T5e n#r6$ %i"tri3uti#n



0 13.2 The normal

distri(ution and conAidence inter#als

0* ,* .* 11* 10 1

0 13.3 "alculatin!

/ro(a(ilities and the

standard normal

distri(ution

1 0* * * ,* .* 11* 10

0 13.4 The in#erse

normal distri(ution

1* 0* * -* 1/* 1&* 1 1

0 13.5 ied /ro(a(ilitya//lication /ro(lems

1 0* +* ,* .* 1& 10

TOPIC 1

CHAPTER 1 Stti"ti!$ in4eren!e



0 14.2 >o/ulation

/arameters and sam/le

statistics

1* &* * * - 1/* 1&* 1* 1- 1.

0 14.3 The distri(ution

oA /C

1* 0* + ,* .* 11* 10* 1+ 1,

0 14.4 "onAidenceinter#als

1* 0* +* .* 11* 10* 1+ 1-

