Contentsmathsbooks.net/Maths Quest 11 Methods/By Chapter/TEACHER ENDMATTER.pdf–factor theorem 3E The remainder and factor theorems (page 121) 3F Factorising cubic polynomials (page

Teacher edition supplementary

material

ContentsCONTENTSNotes for the teacher . . . . . . . . . . . . . . . . . . . . 566

Teacher edition textbookTeacher edition CD-ROMMaths Quest Web site supportAssessment advice

Curriculum grid . . . . . . . . . . . . . . . . . . . . . . . 567

Work program . . . . . . . . . . . . . . . . . . . . . . . . . 573

Sample assessment template . . . . . . . . . . . . . . 596

TEACHER ENDMATTER Page 565 Friday, January 10, 2003 1:06 PM

566

M a t h e m a t i c a l M e t h o d s U n i t s 1 a n d 2

Notes for the teacher

Teacher edition textbook

In this textbook, you will find everything contained inthe student textbook plus the following Curriculum andassessment materials:

1. Curriculum grid

This grid matches the content of

Maths Quest 11 Mathe-matical Methods

to the study design dot points of theVCE 2000 Units 1 and 2 Mathematical Methods course.The curriculum grid illustrates how all dot points arethoroughly covered with appropriate sections of chaptersand investigations listed. A word file of this documentcan be found on the Teacher edition CD-ROM in theCurriculum and assessment folder.

2. Work program

The work program provides a complete overview of theresources available in the

Maths Quest 11 MathematicalMethods

package. It is organised in grid form for eachchapter for easy reference. Each row in the grid showsthe range of material available for each section within achapter. This material includes:

Column 1: section titles, number of worked examples,exercises of questions, Summary, Chapter review

Column 2: graphics calculator tips (GC tips), investi-gations, career profiles, History of mathematics

Column 3: SkillSHEETs, WorkSHEETs, ‘Test yourself’multiple choice questions, Topic tests

Column 4: Technology applications (Excel spreadsheets,Mathcad files, Cabri Geometry files, Graphics calcu-lator programs)

Column 5: Matching study design dot points.

A word file of this document can be found on theTeacher edition CD-ROM in the Curriculum and assess-ment folder.

3. Sample assessment template

This template is also provided as a word file on theTeacher edition CD-ROM in the Curriculum and assess-ment folder. It can be easily edited to suit your needs.

Teacher edition CD-ROM

The accompanying Teacher edition CD-ROM containsall material found on the student CD-ROM with thefollowing extras:1. Full solutions to the WorkSHEETs in Word 97 format

for easy editing.2. Topic tests (2 per chapter) with full solutions in Word

97 format for easy editing.3. Word files for the Curriculum and assessment

materials (Curriculum grid, Work program andSample assessment template).

Maths Quest

Web site support

The

Maths Quest

Web site will provide further assess-ment materials such as investigations, analysis tasks andpractice examinations.

www.jaconline.com.au/maths

Assessment advice for VCE Units 1 and 2Mathematical Methods

To satisfactorily complete each unit, students arerequired to demonstrate achievement of the followingthree outcomes.

Outcome 1

Define and explain key concepts as specified in thecontent from the ‘Functions and graphs’, ‘Algebra’,‘Calculus’ and ‘Probability’ areas of study, and to applya range of related mathematical routines and procedures.

Assessment tasks: assignments, tests, summary or review notes

Outcome 2

Apply mathematical processes in non-routine contextsand to analyse and discuss these applications of math-ematics.

Assessment tasks: projects, short written responses, problem-solving tasks, modelling tasks

Outcome 3

Use technology to produce results and carry out analysisin situations requiring problem-solving, modelling orinvestigative techniques or approaches.

Assessment tasks: effective and appropriate use of technology in tasks used to assess Outcomes 1 and 2.

Assessment tasks are to be part of the regular teachingand learning program and should be completed mainlyin class and within a limited timeframe.

Maths Quest 11 Mathematical Methods

offers a range oftasks for assessment purposes. These include:• investigations (projects, problem-solving tasks,

modelling tasks)• WorkSHEETs which can be used as assignments

(note that answers are not supplied with the studentCD-ROM)

• topic tests• exercise questions on the CD-ROM which can be

copied and pasted into word files, then tailored toprovide further assessment task material

• interactive technology tasks which provide a com-prehensive resource to cover the requirements ofOutcome 3

• further assessment materials on the

Maths Quest

Website.


http://www.jaconline.com.au/maths

Te a c h e r e d i t i o n s u p p l e m e n t a r y m a t e r i a l

567

Maths Quest

11 Mathematical Methods — Curriculum grid

Unit 1

1. Functions and graphs

Study design dot points Sections/

Investigations

• Pythagoras’ theorem and its application to finding the distance between two points

1I Distance between two points (page 37)

Approximating curve length using linear equations

(page 41)

• calculation of coordinates of the midpoint of a line segment

1J Midpoint of a segment (page 42)

• gradients of parallel and perpendicular lines 1D Equations of the form

y

=

mx

+

c

(page 21)1G Perpendicular lines (page 32)

• finding equations of straight lines from given information

1D Equations of the form

y

=

mx

+

c

(page 21)1H Formula for finding the equation of a straight line (page 33)1K Linear modelling (page 44)

• graphs and their use to express and interpret relationships

3L Modelling (page 149)6B Relations and graphs (page 267)6C Domain and range (page 273)6D Types of relations (including functions) (page 282)6F Special types of function (page 289)6G Circles (page 296)6H Functions and modelling (page 300)

• sketch graphs of straight lines, quadratics and cubics (including the use of simple transformations)

1C Gradient of a straight line (page 13)1D Equations of the form

y

=

mx

+

c

(page 21)1E Sketching linear graphs using intercepts (page 24)

Quadratic graphs – turning point form

(page 81)2H Quadratic graphs – turning point form (page 82)2I Quadratic graphs – intercepts method (page 86)2K Simultaneous quadratic and linear equations (page 99)3I Cubic graphs – intercepts method (page 134)

Repeated factors

(page 139)3J Cubic graphs – using translation (page 140)6B Relations and graphs (page 267)6C Domain and range (page 273)6D Types of relations (including functions) (page 279)

• domain and range of functions of a real variable

3K Domain, range, maximums and minimums (page 144)6C Domain and range (page 273)6D Types of relations (including functions) (page 279)6E Function notation (page 284)6F Special types of function (page 289)6G Circles (page 296)6H Functions and modelling (page 300)

• the 'vertical line test' and its use to determine whether a relation is a function

6D Types of relations (including functions) (page 279)6F Special types of function (page 289)6G Circles (page 296)

• circles with equations of the form (

x

−

a

)

2

+

(

y

−

b

)

2

=

r

2

as examples of relations that are not functions

A special relation

(page 295)6G Circles (page 296)


568


2. Algebra


Investigations

• substitution in and rearrangement of formulas 1A Solving linear equations (page 2)1B Rearrangement and substitution (page 6)2H Quadratic graphs – turning point form (page 82)

• identification of key features of polynomials: variables, coefficients, degree, and so on

3A Polynomials (page 110)

• the use of notation

y

=

f

(

x

); substitution and evaluation of

f

(

a

), where

a

is real3D Polynomial values (page 119)6E Function notation (page 284)

• expansion of quadratics and cubics from factors

2A Expanding quadratic expressions (page 56)3B Expanding (cubics)(page 113)

• factorisation– connections between factors, solutions and

corresponding graphs

2I Quadratic graphs – turning point form (page 82)3I Cubic graphs – intercepts method (page 134)

Repeated factors

(page 139)

– quadratic trinomials 2B Factorising quadratic trinomials (page 59)2C Factorising by completing the square (page 62)

– factor theorem 3E The remainder and factor theorems (page 121)3F Factorising cubic polynomials (page 124)

– factorisation of a cubic with a least one factor of the form (

x

−

a

) where

a

is an integer

3F Factorising cubic polynomials (page 124)3G Sum and difference of two cubes (page 128)

• quadratic equations: obtaining rational solutions or approximations to solutions by systematic trial and error, by graphing, by simple iteration; obtaining rational and irrational solutions by completion of the square (for cases where the coefficient of

x

2

is 1 only) and by the quadratic formula

2D Solving quadratic equations – Null Factor Law (page 65)

Fixed point iteration

(page 69)2E Solving quadratic equations – completing the square (page 70)

Solving x

2

+

bx

+

c

=

0

(page 71)2F The quadratic formula (page 73)

The formula that ‘doesn’t work’!

(page 77)2J Using graphs to solve quadratic equations (page 97)

• use and interpretation of the discriminant to identify the number of solutions

2G The discriminant (page 78)

The formula that ‘doesn’t work’!

(page 77)

• completion of the square method to finding maximum or minimum values of quadratic functions

2H Quadratic graphs – turning point form (page 82)

• cubic equations and their solution by any of the following methods – graphing (including cases which do not

have three solutions)– systematic trial and error– algebraic methods; for example,

factorisation of cubics that have at least one integer solution

Solving cubic equations using graphs

(page 133)3H Cubic equations (page 130)

• solution of two linear simultaneous equations, and one linear and one quadratic equation, by numerical, graphical or algebraic methods

1F Simultaneous equations (page 27)

Using matrices to solve simultaneous equations

(page 31)2K Simultaneous quadratic and linear equations (page 99)

• the development of polynomial models for sets of data; for example, by the use of finite difference tables

3L Modelling (page 149)

Fitting a model exactly

(page 155)3M Finite differences (page 156)

• index laws 4A Index laws (page 168)4B Negative and rational powers (page 174)


Te a c h e r e d i t i o n s u p p l e m e n t a r y m a t e r i a l

569

3. Calculus


Investigations

• concepts of rates of change;– practical examples of instantaneous rates of

change; for example, speedometer readings, revolutions counters

– practical examples of average rates of change; for example, average speed on a bush walk, average slope of a hill from bottom to top

7A Identifying rates (page 312)7B Constant rates (page 317)7C Variable rates (page 322)7D Average rates of change (page 325)7E Instantaneous rates (page 330)

• rate of change of a linear function: use of gradient as a measure of rate of change

7B Constant rates (page 317)

• graphs and the interpretation to rates of change; for example, where the rate of change is positive, negative, or zero

7B Constant rates (page 317)7C Variable rates (page 322)

• average rate of change: use of the gradient of a chord of a graph to describe average rate of change of

y

=

f

(

x

) with respect to

x

, over a given interval

7D Average rates of change (page 325)

• instantaneous rates of change– defining the (instantaneous) rate of change

as given by the gradient of the graph at a given point

– linear functions as examples of constant rate of change

– quadratics and cubic functions as examples of variable rates of change

7B Constant rates (page 317)7E Instantaneous rates (page 330)

• relating the gradient function to features of the original function

7F Motion graphs (page 335)7G Relating the gradient function to the original function

(page 343)7H Relating velocity-time graphs to position-time graphs

(page 344)

• applying rates of change in motion graphs– construction and interpretation of

displacement-time and velocity-time graphs– informal treatment of the relationship

between displacement-time and velocity-time graphs

7F Motion graphs (page 335)7H Relating velocity-time graphs to position-time graphs

(page 344)

• the measurement of rates of change of polynomials: finding successive numerical approximations to the gradient of a polynomial function at a point by taking another point very close to it on the graph of the function and finding the gradient of the line joining the two points, and then repeating this procedure (leading to informal treatment of limits)

7I Rates of change of polynomials (page 352)


570


4. Probability

Unit 2

1. Functions and graphs


Investigations

• random experiments, events and event spaces 10A Introduction to probability (page 424)

• probability as an expression of long run proportion

10A Introduction to probability (page 424)

• probability of simple and compound events 10B Calculating probabilities (page 428)

• Venn diagrams, probability tables and tree diagrams

Sets and Venn diagrams; Using sets to solve practical problems (link to CD-ROM from page 428)

10C Tree diagrams and lattice diagrams (page 434)10D The Addition Law of probabilities (page 440)10E Karnaugh Maps and probability tables (page 446)10F Conditional probability (page 452)10G Independent events (page 457)

• the addition rule for probabilities 10D The Addition Law of probabilities (page 440)

• conditional probability and independence; the multiplication rule for independent events

10F Conditional probability (page 452)10G Independent events (page 457)

• simulation using simple generators such as coins, dice, spinners, random number tables and computers

10H Simulation (page 464)

• display and interpretation of results of simulations

10H Simulation (page 464)


Investigations

Circular (trigonometric) functions

• revision of trigonometric ratios and their applications to right-angled triangles

5A Trigonometric ratios: revision (page 206)

• exact values of sin and cos of 30

o

, 45

o

and 60

o

5B The unit circle (page 212)

• radians: definition, conversion between radians and degrees

5C Radians (page 218)

• unit circle– definition of sine, cosine and tangent


– special relationships sin

2

x

+

cos

2

x

=

1 and that

−

1

≤

sin

x

≤

1,

−

1

≤

cos

x

≤

15E Identities (page 229)

– special values; for example,sin(0)

=

0, cos (

π

)

= −


– symmetry properties: sin(

π

±

x

), cos(

π

±

x

), sin(2

π

±

x

), cos(2

π

±

x

)5D Symmetry (page 223)

• exact values of sin and cos for integer

multiples of . , ,

5D Symmetry (page 223)5H Solving trigonometric equations (page 246)5I Applications (page 251)

π6--- π

4--- π

3--- π

2---


Te a c h e r e d i t i o n s u p p l e m e n t a r y m a t e r i a l 571

2. Algebra (See Unit 1)

3. Calculus

• graphs of circular (trigonometric) functions of the form y = a sin(bx), y = a cos(bx), for simple cases of a and b, and the graph of y = tan x

5F Sine and cosine graphs (page 234)Sine and cosine graphs (page 235)5G Tangent graphs (page 242)Tangent graphs (page 242)5H Solving trigonometric equations (page 246)5I Applications (page 251)

• the identity tan (x) = 5E Identities (page 229)

• simple illustrations of the application of circular (trigonometric) functions; for example, tidal heights, sound waves, biorhythms, ovulation cycles, temperature fluctuations during a day

5I Applications (page 251)

• recognition and interpretation of period and amplitude

5F Sine and cosine graphs (page 234)Sine and cosine graphs (page 235)5G Tangent graphs (page 242)Tangent graphs (page 242)5I Applications (page 251)

• solution of simple equations of the form f (x) = B, using both exact and approximate values, where f is sin, cos or tan, on a given domain, by graphical methods or by using a calculator

5H Solving trigonometric equations (page 246)5I Applications (page 251)

Exponential functions

• graphs of y = 10x and y = 2x, and solving indicial equations related to these graphs by calculator or by graphical methods

4C Indicial equations (page 178)4D Graphs of exponential functions (page 182)4F Solving logarithmic equations (page 191)

• graph of y = log10 x using calculator-generated values and the relationship of the graph to that of y = 10x ; informal discussion of their inverse relationship

Logarithmic graphs (page 194)

• simple applications of exponential functions 4G Applications of exponential and logarithmic functions (page 195)

A world population model (page 185)The Richter scale (page 199)

Study design dot points Sections/Investigations

• the derivative as the gradient of the graph at a point and its representation by a gradient function

8C Differentiation using first principles (page 371)

• notation for derivatives: , f ′(x), ( f (x)) 8C Differentiation using first principles (page 371)

• first principles to find the gradient function for f (x) = x2 and f (x) = x3

8C Differentiation using first principles (page 371)

• first principles, graphical or numerical approaches to justify rules for finding the gradient functions of other polynomials

8C Differentiation using first principles (page 371)Secants and tangents (page 371)

x( )sinx( )cos

----------------

dydx------ d

dx------


572 M a t h e m a t i c a l M e t h o d s U n i t s 1 a n d 2

4. Probability

• derivatives of simple polynomials by rule 8D Finding derivatives by rule (page 375)Graphs of derivatives (page 380)

• applications of differentiation– finding rates of change

9A Rates of change (page 396)

– determining maximum or minimum points for quadratic and cubic functions graphically and analytically and their application to simple maximum/minimum problems

9C Solving maximum and minimum problems (page 409)When is a maximum not a maximum? (page 414)

– using turning points to assist in sketching graphs of simple polynomials

9B Sketching graphs containing stationary points (page 403)

• antidifferentiation as the reverse process of differentiation– developing rules for antiderivatives of

simple polynomials– identifying families of curves with the same

gradient function

Antidifferentiation (page 381)8E Antidifferentiation by rule (page 382)8F Deriving the original function from the gradient function

(page 385)9D Applications of antidifferentiation (page 417)

Study design dot points Sections/Investigations

• addition and multiplication principles 11A Addition and multiplication principles (page 476)

• permutations: concept of ordered samples, nPr 11B Permutations (page 481)Identification cards (page 484)11D Permutations using nPr (page 488)11E Permutations using restrictions (page 496)11F Arrangements in a circle (page 500)

• combinations: concept of unordered samples, nCr

11G Combinations using nCr (page 501)

• evaluation of nPr and nCr and establishing that nPr =

nCr × r!11D Permutations using nPr (page 488)11E Permutations using restrictions (page 496)11F Arrangements in a circle (page 500)11G Combinations using nCr (page 501)

• the relationship of combinations to Pascal's triangle

Pascal’s triangle (page 506)

• applications of permutations and combinations to probability, including an informal treatment of examples involving binomial and hypergeometric probabilities

11H Applications of probability (page 509)



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een

two

poin

ts (

page

37)

Inve

stig

atio

n: A

ppro

xim

atin

g cu

rve

leng

th u

sing

line

ar

equa

tions

(pa

ge 4

1)

Mat

hcad

: Dis

tanc

e be

twee

n tw

o po

ints

(p

age

38)

Exc

el: D

ista

nce

betw

een

two

poin

ts

(pag

e 38

)G

C p

rogr

am: D

ista

nce

betw

een

two

poin

ts

(pag

e 38

)C

abri

Geo

met

ry: D

ista

nce

betw

een

two

poin

ts (

page

38)

•A

pplic

atio

n of

Pyt

hago

ras’

th

eore

m to

find

ing

the

dist

ance

bet

wee

n tw

o po

ints

Mid

poin

t of

a se

gmen

t (p

age

42)

WE

19

Ex

1J M

idpo

int o

f a

segm

ent

(pag

e 43

)

Mat

hcad

: Mid

poin

t of

a se

gmen

t (pa

ge 4

3)E

xcel

: Mid

poin

t of

a se

gmen

t (pa

ge 4

3)G

C p

rogr

am: M

idpo

int o

f a

segm

ent

(pag

e 43

)C

abri

geo

met

ry: M

idpo

int o

f a

segm

ent

(pag

e 43

)

•C

alcu

latio

n of

the

coor

dina

tes

of th

e m

idpo

int

of a

line

seg

men

t



Lin

ear

mod

ellin

g (p

age

44)

WE

20,

21

Ex

1K L

inea

r m

odel

ling

(pag

e 46

)

Mat

hcad

: Sim

ulta

neou

s lin

ear

equa

tions

(p

age

46)

Exc

el: S

imul

tane

ous

linea

r eq

uatio

ns

(pag

e 46

)

•Fi

ndin

g eq

uatio

ns o

f st

raig

ht

lines

fro

m g

iven

info

rmat

ion

Sum

mar

y (p

age

48)

Cha

pter

rev

iew

(pa

ge 4

9)–

Mul

tiple

cho

ice

Q1–

22–

Shor

t ans

wer

Q1–

21–

Ana

lysi

s Q

1–4

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

54)

Topi

c te

sts

(2)



WO

RK

PR

OG

RA

M

Cha

pter

2Q

uadr

atic

Fun

ctio

ns

Are

as o

f st

udy:

Uni

t 1

Func

tions

and

gra

phs,

Alg

ebra

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Exp

andi

ng q

uadr

atic

ex

pres

sion

s (p

age

56)

WE

1a-

d, 2

Ex

2A E

xpan

ding

qua

drat

ic

expr

essi

ons

(pag

e 58

)

Skil

lSH

EE

T 2

.1: E

xpan

ding

pe

rfec

t squ

ares

(pa

ge 5

8)Sk

illS

HE

ET

2.2

: Exp

andi

ng

diff

eren

ce o

f sq

uare

s (p

age

58)

GC

pro

gram

: E

xpan

ding

(pa

ge 5

8)M

athc

ad:

Exp

andi

ng (

page

58)

•E

xpan

sion

of

quad

ratic

s fr

om f

acto

rs

Fact

oris

ing

quad

ratic

trin

omia

ls

(pag

e 59

)W

E 3

a-e,

4a-

bE

x 2B

Fac

tori

sing

qua

drat

ic

trin

omia

ls (

page

61)

Mat

hcad

: Fa

ctor

isin

g (p

age

61)

•Fa

ctor

isat

ion

– qu

adra

tic

trin

omia

ls

Fact

oris

ing

by c

ompl

etin

g th

e sq

uare

(pa

ge 6

2)W

E 5

a-b

Ex

2C F

acto

risi

ng b

y co

mpl

etin

g th

e sq

uare

(p

age

64)

GC

pro

gram

: Com

plet

ing

the

squa

re

(pag

es 6

3, 6

4)•

Fact

oris

atio

n –

quad

ratic

tr

inom

ials

Solv

ing

quad

ratic

equ

atio

ns —

N

ull F

acto

r L

aw (

page

65)

WE

6a-

d, 7

Ex

2D S

olvi

ng q

uadr

atic

eq

uatio

ns —

Nul

l Fac

tor L

aw

(pag

e 67

)

Inve

stig

atio

n: F

ixed

poi

nt

itera

tion

(pag

e 69

)W

orkS

HE

ET

2.1

(pa

ge 6

8)E

xcel

: Q

uadr

atic

equ

atio

ns (

page

67)

GC

pro

gram

: Q

uadr

atic

equ

atio

ns

(pag

e 67

)G

C p

rogr

am: F

ixed

poi

nt it

erat

ion

(pag

e 69

)

•So

lvin

g qu

adra

tic e

quat

ions

Solv

ing

quad

ratic

equ

atio

ns —

co

mpl

etin

g th

e sq

uare

(p

age

70)

WE

8a-

cE

x 2E

Sol

ving

qua

drat

ic

equa

tions

— c

ompl

etin

g th

e sq

uare

(pa

ge 7

2)

Inve

stig

atio

n:

Solv

ing

x2 +

bx +

c =

0 (

page

71)

Skil

lSH

EE

T 2

.3: S

olvi

ng

equa

tions

in th

e co

mpl

ete

squa

re f

orm

(pa

ge 7

2)Sk

illS

HE

ET

2.4

: Sim

plif

ying

su

rds

(pag

e 72

)

•So

lvin

g qu

adra

tic e

quat

ions

by

com

plet

ing

the

squa

re


Te a c h e r e d i t i o n s u p p l e m e n t a r y m a t e r i a l 577T

he q

uadr

atic

form

ula

(pag

e 73

)W

E 9

a-b

Ex

2F T

he q

uadr

atic

for

mul

a (p

age

75)

Inve

stig

atio

n: T

he f

orm

ula

that

‘d

oesn

't w

ork’

! (p

age

77)

Mat

hcad

: The

qua

drat

ic f

orm

ula

(pag

e 75

)M

athc

ad:

Qua

drat

ic r

oots

(pa

ge 7

5)M

athc

ad:

Cal

cula

ting

the

disc

rim

inan

t (p

age

77)

•So

lvin

g qu

adra

tic e

quat

ions

us

ing

the

quad

ratic

for

mul

a

The

dis

crim

inan

t (pa

ge 7

8)W

E 1

0, 1

1, 1

2, 1

3E

x 2G

The

dis

crim

inan

t (p

age

81)

GC

tip:

Rep

eate

d ca

lcul

atio

n of

th

e di

scri

min

ant (

page

80)

Inve

stig

atio

n: Q

uadr

atic

gra

phs

— tu

rnin

g po

int f

orm

(p

age

81)

Exc

el: C

alcu

latin

g th

e di

scri

min

ant

(pag

e 81

)M

athc

ad:

Cal

cula

ting

the

disc

rim

inan

t (p

age

81)

•U

se a

nd in

terp

reta

tion

of th

e di

scri

min

ant t

o id

entif

y th

e nu

mbe

r of

sol

utio

ns

Qua

drat

ic g

raph

s —

turn

ing

poin

t for

m (

page

82)

WE

14,

15

Ex

2H Q

uadr

atic

gra

phs

—

turn

ing

poin

t for

m (

page

84)

Wor

kSH

EE

T 2.

2 (p

age

85)

GC

pro

gram

: Com

plet

ing

the

squa

re

(pag

e 85

)•

Com

plet

ion

of th

e sq

uare

m

etho

d to

find

ing

max

imum

or

min

imum

val

ues

of

quad

ratic

fun

ctio

ns•

Sket

ch g

raph

s of

qua

drat

ics

(inc

ludi

ng th

e us

e of

sim

ple

tran

sfor

mat

ions

)•

Rea

rran

gem

ent o

f fo

rmul

asQ

uadr

atic

gra

phs

— in

terc

epts

m

etho

d (p

age

86)

WE

16a

-d, 1

7a-b

, 18a

-bE

x 2I

Qua

drat

ic g

raph

s —

in

terc

epts

met

hod

(pag

e 95

)

Mat

hcad

: Q

uadr

atic

gra

phs

— fa

ctor

ed

form

(pa

ge 9

5)E

xcel

: Q

uadr

atic

gra

phs

— fa

ctor

ed f

orm

(p

age

95)

Mat

hcad

: Q

uadr

atic

gra

phs

— g

ener

al

form

(pa

ge 9

5)E

xcel

: Q

uadr

atic

gra

phs

— g

ener

al f

orm

(p

age

95)

•Sk

etch

gra

phs

of q

uadr

atic

s•

Fact

oris

atio

n –

conn

ectio

ns

betw

een

fact

ors,

sol

utio

ns

and

corr

espo

ndin

g gr

aphs

Usi

ng g

raph

s to

sol

ve q

uadr

atic

eq

uatio

ns (

page

97)

Ex

2J U

sing

gra

phs

to s

olve

qu

adra

tic e

quat

ions

(p

age

98)

•So

lvin

g qu

adra

tic e

quat

ions

by

gra

phin

g

Sim

ulta

neou

s qu

adra

tic a

nd

linea

r eq

uatio

ns (

page

99)

WE

19a

-b, 2

0a-b

, 21a

-b, 2

2E

x 2K

Sim

ulta

neou

s qu

adra

tic

and

linea

r eq

uatio

ns

(pag

e 10

3)

Mat

hcad

: Si

mul

tane

ous

quad

ratic

and

lin

ear

equa

tions

(pa

ge 1

03)

Exc

el:

Sim

ulta

neou

s qu

adra

tic a

nd li

near

eq

uatio

ns (

page

103

)

•So

lutio

n of

one

line

ar a

nd

one

quad

ratic

equ

atio

n•

Sket

ch g

raph

s of

str

aigh

t lin

es, q

uadr

atic

s

Sum

mar

y (p

age

104)

Cha

pter

rev

iew

(pa

ge 1

06)

–M

ultip

le c

hoic

e Q

1–18

–Sh

ort a

nsw

er Q

1–14

–A

naly

sis

Q1–

3

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

108

)To

pic

test

s (2

)



WO

RK

PR

OG

RA

M

Cha

pter

3C

ubic

fun

ctio

ns

Are

as o

f st

udy:

Uni

t 1

Func

tions

and

gra

phs,

Alg

ebra

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Poly

nom

ials

(pa

ge 1

10)

Ex

3A P

olyn

omia

ls (

page

112

)H

isto

ry o

f mat

hem

atic

s:

Éva

rist

e G

aloi

s (p

age

111)

•Id

entifi

catio

n of

key

fea

ture

s of

pol

ynom

ials

Exp

andi

ng (

page

113

)W

E 1

a-b

Ex

3B E

xpan

ding

(pa

ge 1

13)

Mat

hcad

: E

xpan

ding

(pa

ge 1

13)

•E

xpan

sion

of

cubi

cs f

rom

fa

ctor

s

Lon

g di

visi

on o

f cu

bic

poly

nom

ials

(pa

ge 1

14)

WE

2a-

c, 3

Ex

3C L

ong

divi

sion

of

cubi

c po

lyno

mia

ls (

page

118

)

Mat

hcad

: Po

lyno

mia

l div

isio

n (p

age

118)

GC

pro

gram

: Pol

ynom

ial d

ivis

ion

(pag

e 11

8)

•

Poly

nom

ial v

alue

s (p

age

119)

WE

4a-

dE

x 3D

Pol

ynom

ial v

alue

s (p

age

120)

Wor

kSH

EE

T 3.

1 (p

age

120)

Mat

hcad

: Pol

ynom

ial d

ivis

ion

(pag

e 12

0)E

xcel

: C

ubic

val

uer

(pag

e 12

0)•

Subs

titut

ion

and

eval

uatio

n of

f(a)

whe

re a

is r

eal

The

rem

aind

er a

nd fa

ctor

th

eore

ms

(pag

e 12

1)W

E 5

a-b,

6E

x 3E

The

rem

aind

er a

nd fa

ctor

th

eore

ms

(pag

e 12

3)

GC

tip:

Cal

cula

ting

seve

ral

valu

es o

f a

func

tion

at o

nce

(pag

e 12

2)

Exc

el: C

ubic

val

uer

(pag

e 12

3)•

Fact

or th

eore

m

Fact

oris

ing

cubi

c po

lyno

mia

ls

(pag

e 12

4)W

E 7

a-c,

8E

x 3F

Fac

tori

sing

cub

ic

poly

nom

ials

(pa

ge 1

27)

Skil

lSH

EE

T 3.

1: R

evie

win

g th

e di

scri

min

ant (

page

124

)M

athc

ad:

Fact

oris

ing

(pag

e 12

7)E

xcel

: Po

lyno

mia

ls z

ero

sear

ch (

page

127

)•

Fact

oris

atio

n –

fact

or

theo

rem

•Fa

ctor

isat

ion

of a

cub

ic w

ith

at le

ast o

ne fa

ctor

of t

he fo

rm

(x −

a)

whe

re a

is a

n in

tege

rSu

m a

nd d

iffe

renc

e of

two

cube

s (p

age

128)

WE

9a-

bE

x 3G

Sum

and

dif

fere

nce

of

two

cube

s (p

age

129)

•Fa

ctor

isat

ion

of a

cub

ic w

ith

at le

ast o

ne fa

ctor

of t

he fo

rm

(x −

a)

whe

re a

is a

n in

tege

r


Te a c h e r e d i t i o n s u p p l e m e n t a r y m a t e r i a l 579C

ubic

equ

atio

ns (

page

130

)W

E 1

0, 1

1a-c

Ex

3H C

ubic

equ

atio

ns

(pag

e 13

2)

Inve

stig

atio

n: S

olvi

ng c

ubic

eq

uatio

ns u

sing

gra

phs

(pag

e 13

3)

Wor

kSH

EE

T 3.

2 (p

age

132)

Mat

hcad

: So

lvin

g cu

bic

equa

tions

(pa

ges

130,

132

)M

athc

ad:

Cub

ic r

oots

(pa

ge 1

32)

GC

pro

gram

: So

lvin

g cu

bic

equa

tions

(p

age

132)

•C

ubic

equ

atio

ns a

nd th

eir

solu

tion

by a

lgeb

raic

m

etho

ds (

fact

oris

atio

n of

cu

bics

that

hav

e at

leas

t one

in

tege

r so

lutio

n)•

Cub

ic e

quat

ions

and

thei

r so

lutio

n by

gra

phin

gC

ubic

gra

phs

— in

terc

epts

m

etho

d (p

age

134)

WE

12a

-c, 1

3E

x 3I

Cub

ic g

raph

s —

in

terc

epts

met

hod

(pag

e 13

8)

Inve

stig

atio

n: R

epea

ted

fact

ors

(pag

e 13

9)M

athc

ad:

Cub

ic g

raph

s —

fac

tore

d fo

rm

(pag

e 13

8)E

xcel

: C

ubic

gra

phs

— f

acto

red

form

(p

age

138)

Mat

hcad

: C

ubic

gra

phs

— g

ener

al f

orm

(p

ages

137

, 138

)E

xcel

: C

ubic

gra

phs

— g

ener

al f

orm

(p

age

138)

•Sk

etch

gra

phs

of c

ubic

s•

Con

nect

ions

bet

wee

n fa

ctor

s, s

olut

ions

and

co

rres

pond

ing

grap

hs

Cub

ic g

raph

s —

usi

ng

tran

slat

ion

(pag

e 14

0)W

E 1

4a-c

Ex

3J C

ubic

gra

phs

— u

sing

tr

ansl

atio

n (p

age

143)

Mat

hcad

: C

ubic

gra

phs

— b

asic

for

m

(pag

es 1

40, 1

43)

Exc

el:

Cub

ic g

raph

s —

bas

ic f

orm

(pa

ges

140,

143

)

•Sk

etch

gra

phs

of c

ubic

s us

ing

sim

ple

tran

sfor

mat

ions

Dom

ain,

rang

e, m

axim

ums

and

min

imum

s (p

age

144)

WE

15,

16

Ex

3K D

omai

n, r

ange

, m

axim

ums

and

min

imum

s (p

age

147)

GC

tip:

Tur

ning

poi

nts

(pag

e 14

5)Sk

illS

HE

ET

3.2:

Int

erva

l no

tatio

n (p

ages

144

, 147

)•

Dom

ain

and

rang

e of

fu

nctio

ns o

f a

real

var

iabl

e

Mod

ellin

g (p

age

149)

WE

17,

18,

19

Ex

3L M

odel

ling

usin

g te

chno

logy

(pa

ge 1

52)

Car

eer

profi

le: A

shle

y H

anno

n (p

age

154)

Inve

stig

atio

n: F

ittin

g a

mod

el

exac

tly (

page

155

)

Exc

el:

Mod

ellin

g (p

ages

151

, 152

, 153

, 15

5)M

athc

ad:

Lin

ear

mod

ellin

g (p

age

152)

Mat

hcad

: Q

uadr

atic

mod

ellin

g (p

age

152)

Mat

hcad

: C

ubic

mod

ellin

g (p

ages

151

, 15

3)

•D

evel

opm

ent o

f po

lyno

mia

l m

odel

s fo

r se

ts o

f da

ta

Fini

te d

iffe

renc

es (

page

156

)W

E 2

0, 2

1E

x 3M

Fin

ite d

iffe

renc

es

(pag

e 15

9)

•D

evel

opm

ent o

f po

lyno

mia

l m

odel

s fo

r se

ts o

f da

ta u

sing

fin

ite d

iffe

renc

e ta

bles

Sum

mar

y (p

age

161)

Cha

pter

rev

iew

(pa

ge 1

63)

–M

ultip

le c

hoic

e Q

1–18

–Sh

ort a

nsw

er Q

1–15

–A

naly

sis

Q1–

2

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

166

)To

pic

test

s (2

)



WO

RK

PR

OG

RA

M

Cha

pter

4E

xpon

entia

l and

loga

rith

mic

fun

ctio

ns

Are

as o

f st

udy:

Uni

t 2

Func

tions

and

gra

phs,

Alg

ebra

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Inde

x L

aws

(pag

e 16

8)W

E 1

a-d,

2, 3

a-b,

4E

x 4A

Ind

ex la

ws

(pag

e 17

2)

Mat

hcad

: In

dice

s (p

age

172)

•In

dex

law

s

Neg

ativ

e an

d ra

tiona

l pow

ers

(pag

e 17

4)W

E 5

a-b,

6a-

b, 7

a-b

Ex

4B N

egat

ive

and

ratio

nal

pow

ers

(pag

e 17

7)

Skil

lSH

EE

T 4

.1: N

egat

ive

and

ratio

nal p

ower

s (p

age

177)

Mat

hcad

: N

egat

ive

and

ratio

nal p

ower

s (p

ages

176

, 177

)•

Inde

x la

ws

Indi

cial

equ

atio

ns (

page

178

)W

E 8

a-c,

9, 1

0, 1

1E

x 4C

Ind

icia

l equ

atio

ns

(pag

e 18

1)

Mat

hcad

: E

quat

ion

solv

er (

page

181

)M

athc

ad:

Indi

cial

equ

atio

ns (

page

181

)•

Solv

ing

indi

cial

equ

atio

ns

Gra

phs o

f exp

onen

tial f

unct

ions

(p

age

182)

WE

12,

13

Ex

4D G

raph

s of

exp

onen

tial

func

tions

(pa

ge 1

84)

Inve

stig

atio

n: A

wor

ld

popu

latio

n m

odel

(pa

ge 1

85)

Skil

lSH

EE

T 4.

2: S

ubst

itutio

n in

ex

pone

ntia

l fun

ctio

ns

(pag

e 18

4)W

orkS

HE

ET

4.1

(pag

e 18

4)

Exc

el:

Exp

onen

tial f

unct

ions

(pa

ge 1

84)

Mat

hcad

: E

xpon

entia

l fun

ctio

ns

(pag

e 18

4)G

C p

rogr

am:

Exp

onen

tial f

unct

ions

(p

age

184)

Exc

el: W

orld

pop

ulat

ion

•G

raph

s of

y =

10x a

nd y

= 2

x ,

and

solv

ing

indi

cial

eq

uatio

ns r

elat

ed to

thes

e gr

aphs

by

grap

hica

l met

hods

Log

arith

ms

(pag

e 18

6)W

E 1

4a-b

, 15a

-b, 1

6, 1

7a-b

Ex

4E L

ogar

ithm

s (p

age

189)

Car

eer

Pro

file:

Alis

on

Hen

ness

y (p

age

186)

Mat

hcad

: L

ogar

ithm

law

s (p

age

187)

Mat

hcad

: L

ogar

ithm

s to

any

bas

e (p

age

189)

Solv

ing

loga

rith

mic

equ

atio

ns

(pag

e 19

1)W

E 1

8, 1

9, 2

0, 2

1E

x 4F

Sol

ving

loga

rith

mic

eq

uatio

ns (

page

193

)

Inve

stig

atio

n: L

ogar

ithm

ic

grap

hs (

page

194

)W

orkS

HE

ET

4.2

(pag

e 19

3)E

xcel

: L

ogar

ithm

ic g

raph

s (p

age

194)

•So

lvin

g in

dici

al e

quat

ions

by

calc

ulat

or•

The

gra

ph o

f y

= lo

g 10

x an

d

its r

elat

ions

hip

with

y =

10x

; in

form

al d

iscu

ssio

n of

thei

r in

vers

e re

latio

nshi

p



Ext

ensi

on —

Log

arith

mic

gr

aphs

(lin

k to

CD

-RO

M o

n pa

ge 1

94)

WE

1, 2

, 3E

x 4.

1 L

ogar

ithm

ic g

raph

s

App

licat

ions

of e

xpon

entia

l and

lo

gari

thm

ic f

unct

ions

(p

age

195)

WE

22a

-c, 2

3a-c

Ex

4G A

pplic

atio

ns o

f ex

pone

ntia

l and

loga

rith

mic

fu

nctio

ns (

page

197

)

Inve

stig

atio

n: T

he R

icht

er s

cale

(p

age

199)

Mat

hcad

: The

Ric

hter

sca

le (

page

199

)•

Sim

ple

appl

icat

ions

of

expo

nent

ial f

unct

ions

Sum

mar

y (p

age

200)

Cha

pter

rev

iew

(pa

ge 2

02)

–M

ultip

le c

hoic

e Q

1–17

–Sh

ort a

nsw

er Q

1–10

–A

naly

sis

Q1

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

204

)To

pic

test

s (2

)



WO

RK

PR

OG

RA

M

Cha

pter

5C

ircu

lar

func

tions

Are

as o

f st

udy:

Uni

t 2

Func

tions

and

gra

phs,

Alg

ebra

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Tri

gono

met

ric

ratio

s: R

evis

ion

(pag

e 20

6)W

E 1

a-c,

2E

x 5A

Tri

gono

met

ric

ratio

re

visi

on (

page

208

)

Skil

lSH

EE

T 5

.1: T

rigo

nom

etry

re

view

1 (

page

208

)Sk

illS

HE

ET

5.2

: Tri

gono

met

ry

revi

ew 2

(pa

ge 2

08)

•R

evis

ion

of tr

igon

omet

ric

ratio

s an

d th

eir

appl

icat

ions

to

rig

ht-a

ngle

d tr

iang

les

The

uni

t cir

cle

(pag

e 21

2)W

E 3

a-b,

4a-

d, 5

a-c

Ex

5B T

he u

nit c

ircl

e (p

age

217)

Wor

kSH

EE

T 5.

1 (p

age

217)

Exc

el:

The

uni

t cir

cle

(pag

e 21

7)C

abri

Geo

met

ry: T

he u

nit c

ircl

e (p

age

217)

GC

pro

gram

: T

he u

nit c

ircl

e (p

age

217)

•E

xact

val

ues

of s

in a

nd c

os

(and

tan)

of

30°,

45° a

nd 6

0°•

Uni

t cir

cle

– de

finiti

on o

f si

ne, c

osin

e an

d ta

ngen

t; sp

ecia

l val

ues

Rad

ians

(pa

ge 2

18)

WE

6a-

b, 7

a-b,

8a-

b, 9

a-b

Ex

5C R

adia

ns (

page

222

)

GC

tip:

Deg

rees

and

rad

ians

(p

age

219)

GC

pro

gram

: D

egre

es a

nd r

adia

ns

(pag

e 22

2)M

athc

ad: D

egre

es a

nd r

adia

ns (

page

222

)

•R

adia

ns: d

efini

tion,

co

nver

sion

bet

wee

n ra

dian

s an

d de

gree

s

Sym

met

ry (

page

223

)W

E 1

0a-d

, 11a

-d, 1

2a-b

Ex

5D S

ymm

etry

(pa

ge 2

27)

Car

eer

Pro

file:

Bro

nwyn

L

ayco

ck (

page

228

)E

xcel

: T

he u

nit c

ircl

e (p

ages

223

, 227

)C

abri

Geo

met

ry: T

he u

nit c

ircl

e (p

ages

22

3, 2

27)

Mat

hcad

: U

nit c

ircl

e sy

mm

etry

(pa

ges

223,

227

)M

athc

ad: T

he u

nit c

ircl

e (p

ages

223

, 227

)

•E

xact

val

ues

of s

in a

nd c

os

(and

tan)

for

inte

ger

mul

tiple

s of

.

, ,

•U

nit c

ircl

e –

sym

met

ry

prop

ertie

s

Iden

titie

s (p

age

229)

WE

13a

-b, 1

4, 1

5a-b

, 16a

-dE

x 5E

Ide

ntiti

es (

page

232

)

Inve

stig

atio

n: F

urth

er

trig

onom

etri

c id

entit

ies

(pag

e 23

3)

•U

nit c

ircl

e –

spec

ial

rela

tions

hips

sin

2 x +

cos

2 x =

1

and

that

−1

≤ si

n x

≤ 1,

−1

≤ co

s x

≤ 1

•T

he id

entit

y ta

n(x)

=

π 6---π 4---

π 3---π 2---

xsi

nx

cos

--------

---



Sine

and

cos

ine

grap

hs

(pag

e 23

4)W

E 1

7a-c

, 18a

-b, 1

9E

x 5F

Sin

e an

d co

sine

gra

phs

(pag

e 23

9)

Inve

stig

atio

n: S

ine

and

cosi

ne

grap

hs (

page

235

)W

orkS

HE

ET

5.2

(pag

e 24

1)M

athc

ad:

Sine

gra

phs

(pag

e 23

9)E

xcel

: Si

ne g

raph

s (p

age

239)

Mat

hcad

: C

osin

e gr

aphs

(pa

ge 2

39)

Exc

el:

Cos

ine

grap

hs (

page

239

)G

C p

rogr

am:

Tri

g. g

raph

s (p

age

239)

Cab

ri G

eom

etry

: Si

ne a

nd c

osin

e gr

aphs

(p

age

239)

•G

raph

s of

cir

cula

r (t

rigo

nom

etri

c) f

unct

ions

of

the

form

y =

a s

in (

bx)

and

y =

a co

s (b

x), f

or s

impl

e ca

ses

of a

and

b

•R

ecog

nitio

n an

d in

terp

reta

tion

of p

erio

d an

d am

plitu

de

The

gra

ph o

f y

= ta

n x

(pag

e 24

2)W

E 2

0a-b

, 21

Ex

5G T

ange

nt g

raph

s (p

age

245)

Inve

stig

atio

n: T

ange

nt g

raph

s (p

age

242)

Mat

hcad

: Tan

gent

gra

phs

(pag

e 24

5)E

xcel

: Ta

ngen

t gra

phs

(pag

e 24

5)G

C p

rogr

am:

Tri

gono

met

ric

grap

hs

(pag

e 24

5)

•T

he g

raph

of

y =

tan

x•

Rec

ogni

tion

and

inte

rpre

tatio

n of

per

iod

and

ampl

itude

Ext

ensi

on —

Fur

ther

tr

igon

omet

ric

grap

hs (

link

to

CD

-RO

M f

rom

pag

e 24

5)W

E 1

a-b

Ex

5.1

Furt

her

trig

onom

etri

c gr

aphs

Solv

ing

trig

onom

etri

c eq

uatio

ns (

page

246

)W

E 2

2, 2

3a-b

, 24

Ex

5H S

olvi

ng tr

igon

omet

ric

equa

tions

(pa

ge 2

50)

Exc

el: T

rigo

nom

etri

c eq

uatio

ns (

page

250

)M

athc

ad:

Solv

ing

sine

equ

atio

ns

(pag

e 25

0)M

athc

ad:

Solv

ing

cosi

ne e

quat

ions

(p

age

250)

Mat

hcad

: So

lvin

g ta

ngen

t equ

atio

ns

(pag

e 25

0)

•So

lutio

n of

sim

ple

equa

tions

of

the

form

f(x)

= B

, usi

ng

both

exa

ct a

nd a

ppro

xim

ate

valu

es, w

here

f is

sin

, cos

or

tan,

on

a gi

ven

dom

ain,

by

grap

hica

l met

hods

or

by

usin

g a

calc

ulat

or•

Exa

ct v

alue

s of

sin

and

cos

(a

nd ta

n) f

or in

tege

r

mul

tiple

s of

.

, ,

•G

raph

s of

cir

cula

r (t

rigo

nom

etri

c) f

unct

ions

of

the

form

y =

a s

in (

bx)

and

y =

a co

s (b

x), f

or s

impl

e ca

ses

of a

and

b, a

nd th

e gr

aph

of y

= ta

n x

π 6---π 4---

π 3---π 2---



App

licat

ions

(pa

ge 2

51)

WE

25

Ex

5I A

pplic

atio

ns (

page

253

)

Exc

el:

Tri

g. E

quat

ions

(pa

ge 2

53)

Mat

hcad

: So

lvin

g si

ne e

quat

ions

(p

age

253)

Mat

hcad

: So

lvin

g co

sine

equ

atio

ns

(pag

e 25

3)

•Si

mpl

e ill

ustr

atio

ns o

f th

e ap

plic

atio

n of

cir

cula

r (t

rigo

nom

etri

c) f

unct

ions

•E

xact

val

ues

of s

in a

nd c

os•

Gra

phs

of c

ircu

lar

(tri

gono

met

ric)

fun

ctio

ns –

si

ne a

nd c

osin

e•

Rec

ogni

tion

and

inte

rpre

tatio

n of

per

iod

and

ampl

itude

Sum

mar

y (p

age

255)

Cha

pter

rev

iew

(25

9)–

Mul

tiple

cho

ice

Q1–

24–

Shor

t ans

wer

Q1–

11–

Ana

lysi

s Q

1–2

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

262

)To

pic

test

s (2

)


Te a c h e r e d i t i o n s u p p l e m e n t a r y m a t e r i a l 585W

OR

K P

RO

GR

AM

Cha

pter

6R

elat

ions

and

fun

ctio

ns

Are

a of

stu

dy: U

nit 1

Fu

nctio

ns a

nd g

raph

s

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Set n

otat

ion

(pag

e 26

4)W

E 1

a-d

Ex

6A S

et n

otat

ion

(pag

e 26

6)

Rel

atio

ns a

nd g

raph

s (p

age

267)

WE

2a-

b, 3

Ex

6B R

elat

ions

and

gra

phs

(pag

e 27

0)

GC

tip:

Plo

tting

poi

nts

(pag

e 27

2)E

xcel

: Plo

tting

rel

atio

ns (

page

271

)•

Sket

ch g

raph

s of

str

aigh

t lin

es, q

uadr

atic

s•

Gra

phs

and

thei

r us

e to

ex

pres

s an

d in

terp

ret

rela

tions

hips

Dom

ain

and

rang

e (p

age

273)

WE

4a-

c, 5

a-b,

6a-

d, 7

a-b

Ex

6C D

omai

n an

d ra

nge

(pag

e 27

7)

Inve

stig

atio

n: I

nter

estin

g re

latio

ns (

page

279

)Sk

illS

HE

ET

6.1

: Dom

ain

and

rang

e (p

age

277)

Wor

kSH

EE

T 6.

1 (p

age

278)

•D

omai

n an

d ra

nge

of

func

tions

of

a re

al v

aria

ble

•Sk

etch

gra

phs

of s

trai

ght

lines

, qua

drat

ics

and

cubi

cs•

Gra

phs

and

thei

r us

e to

ex

pres

s an

d in

terp

ret

rela

tions

hips

Type

s of

rel

atio

ns (

incl

udin

g fu

nctio

ns)

(pag

e 27

9)W

E 8

a-c,

9a-

cE

x 6D

Typ

es o

f re

latio

ns

(inc

ludi

ng f

unct

ions

) (p

age

282)

•T

he ‘v

ertic

al li

ne te

st’ a

nd it

s us

e to

det

erm

ine

whe

ther

a

rela

tion

is a

fun

ctio

n•

Dom

ain

and

rang

e of

fu

nctio

ns o

f a

real

var

iabl

e•

Sket

ch g

raph

s of

str

aigh

t lin

es, q

uadr

atic

s an

d cu

bics

•G

raph

s an

d th

eir

use

to

expr

ess

and

inte

rpre

t re

latio

nshi

ps



Func

tion

nota

tion

(pag

e 28

4)W

E 1

0a-d

, 11a

-c, 1

2a-b

, 13a

-bE

x 6E

Fun

ctio

n no

tatio

n (p

age

288)

Skil

lSH

EE

T 6

.2: S

ubst

itutio

n (p

age

288)

Skil

lSH

EE

T 6.

3: T

rans

posi

tion

of e

quat

ions

(pa

ge 2

88)

Mat

hcad

: Fu

nctio

n no

tatio

n (p

age

288)

Mat

hcad

: Si

ngle

fun

ctio

n gr

aphe

r (p

age

288)

Mat

hcad

: Sq

uare

roo

t gra

phs

(pag

e 28

8)E

xcel

: Sq

uare

roo

t gra

phs

(pag

e 28

8)

•T

he u

se o

f no

tatio

n y

= f(

x);

subs

titut

ion

and

eval

uatio

n of

f(a

), w

here

a is

rea

l •

Dom

ain

and

rang

e of

fu

nctio

ns o

f a

real

var

iabl

e

Spec

ial t

ypes

of

func

tion

(pag

e 28

9)W

E 1

4a-c

, 15a

-c, 1

6a-b

, 17a

-bE

x 6F

Spe

cial

type

s of

func

tion

(pag

e 29

2)

GC

tip:

Pie

cew

ise

defin

ed

func

tions

(pa

ge 2

94)

Inve

stig

atio

n: A

spe

cial

rela

tion

(pag

e 29

5)

Wor

kSH

EE

T 6.

2 (p

age

294)

Mat

hcad

: H

ybri

d fu

nctio

ns (

page

293

)M

athc

ad:

Cir

cula

r re

latio

ns (

page

295

)E

xcel

: C

ircu

lar

rela

tions

(pa

ge 2

95)

•T

he ‘v

ertic

al li

ne te

st’ a

nd it

s us

e to

det

erm

ine

whe

ther

a

rela

tion

is a

fun

ctio

n•

Dom

ain

and

rang

e of

fu

nctio

ns o

f a

real

var

iabl

e•

Gra

phs

and

thei

r us

e to

ex

pres

s an

d in

terp

ret

rela

tions

hips

Cir

cles

(pa

ge 2

96)

WE

18a

-c, 1

9a-b

Ex

6G C

ircl

es (

page

298

)

Mat

hcad

: C

ircl

e gr

aphs

(pa

ge 2

98)

Exc

el:

Cir

cle

grap

hs (

page

298

)•

Cir

cles

with

equ

atio

ns o

f th

e fo

rm (x

− a

) + (y

− b

)2 =

r2 as

ex

ampl

es o

f rel

atio

ns th

at a

re

not f

unct

ions

•T

he ‘v

ertic

al li

ne te

st’ a

nd it

s us

e to

det

erm

ine

whe

ther

a

rela

tion

is a

fun

ctio

n•

Dom

ain

and

rang

e of

fu

nctio

ns o

f a

real

var

iabl

e•

Gra

phs

and

thei

r us

e to

ex

pres

s an

d in

terp

ret

rela

tions

hips

Func

tions

and

mod

ellin

g (p

age

300)

WE

20a

-bE

x 6H

Fun

ctio

ns a

nd m

odel

ling

(pag

e 30

1)

•G

raph

s an

d th

eir

use

to

expr

ess

and

inte

rpre

t re

latio

nshi

ps•

Dom

ain

and

rang

e of

fu

nctio

ns o

f a

real

var

iabl

e

Sum

mar

y (p

age

303)

Cha

pter

rev

iew

(pa

ge 3

05)

–M

ultip

le c

hoic

e Q

1–25

–Sh

ort a

nsw

er Q

1–9

–A

naly

sis

Q1–

2

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

310

)To

pic

test

s (2

)



OR

K P

RO

GR

AM

Cha

pter

7R

ates

of

chan

ge

Are

a of

stu

dy: U

nit 1

C

alcu

lus

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Iden

tifyi

ng r

ates

(pa

ge 3

12)

WE

1a-

c, 2

a-b,

3E

x 7A

Ide

ntif

ying

rat

es

(pag

e 31

4)

Car

eer

profi

le:

Sean

McI

nnes

(p

age

316)

Skil

lSH

EE

T 7.

1: In

trod

uctio

n to

ra

tes

of c

hang

e (p

age

315)

•C

once

pts

of r

ates

of

chan

ge;

prac

tical

exa

mpl

es

Con

stan

t rat

es (

page

317

)W

E 4

a-c,

5a-

cE

x 7B

Con

stan

t rat

es

(pag

e 31

9)

Exc

el:

Plot

ting

rela

tions

(pa

ge 3

21)

•C

once

pts

of r

ates

of

chan

ge;

prac

tical

exa

mpl

es•

Gra

phs

and

the

inte

rpre

tatio

n to

rat

es o

f ch

ange

•R

ate

of c

hang

e of

a li

near

fu

nctio

n: u

se o

f gr

adie

nt a

s a

mea

sure

of

rate

of

chan

ge•

Inst

anta

neou

s ra

tes

of c

hang

e –

linea

r fun

ctio

ns a

s exa

mpl

es

of c

onst

ant r

ates

of

chan

ge

Var

iabl

e ra

tes

(pag

e 32

2)W

E 6

a-b

Ex

7C V

aria

ble

rate

s (p

age

323)

Exc

el:

Plot

ting

rela

tions

(pa

ge 3

24)

•C

once

pts

of r

ates

of

chan

ge;

prac

tical

exa

mpl

es•

Gra

phs

and

the

inte

rpre

tatio

n to

rat

es o

f ch

ange

Ave

rage

rat

es o

f ch

ange

(p

age

325)

WE

7, 8

, 9a-

eE

x 7D

Ave

rage

rat

es o

f ch

ange

(p

age

327)

Skil

lSH

EE

T 7.

2: G

radi

ent o

f a

stra

ight

line

(pa

ge 3

27)

Wor

kSH

EE

T 7.

1 (p

age

329)

Exc

el: G

radi

ent o

f a

chor

d (p

age

329)

Mat

hcad

: G

radi

ent o

f a

chor

d (p

age

329)

•A

vera

ge r

ate

of c

hang

e: u

se

of th

e gr

adie

nt o

f a

chor

d of

a

grap

h to

des

crib

e av

erag

e ra

te o

f ch

ange

of

y =

f(x)

w

ith r

espe

ct to

x, o

ver

a gi

ven

inte

rval

•C

once

pts

of r

ates

of

chan

ge;

prac

tical

exa

mpl

es o

f av

erag

e ra

tes

of c

hang

e



Inst

anta

neou

s ra

tes

(pag

e 33

0)W

E 1

0a-b

, 11

Ex

7E I

nsta

ntan

eous

rat

es

(pag

e 33

2)

GC

tip:

Dra

win

g a

tang

ent t

o a

curv

e (p

age

331)

Mat

hcad

: In

stan

tane

ous

rate

s (p

age

334)

Exc

el:

Inst

anta

neou

s ra

tes

(pag

e 33

4)•

Inst

anta

neou

s ra

tes

of

chan

ge•

Con

cept

s of

rat

es o

f ch

ange

; pr

actic

al e

xam

ples

of

inst

anta

neou

s ra

tes

of c

hang

e

Mot

ion

grap

hs (

page

335

)W

E 1

2a-d

, 13a

-d, 1

4E

x 7F

Mot

ion

grap

hs

(pag

e 33

8)

Skil

lSH

EE

T 7.

3: D

ispl

acem

ent

and

dist

ance

(pa

ge 3

38)

Skil

lSH

EE

T 7.

4: I

nter

val

nota

tion

(pag

e 34

0)W

orkS

HE

ET

7.2

(pag

e 34

2)

•A

pply

ing

rate

s of

cha

nge

in

mot

ion

grap

hs –

con

stru

ctio

n an

d in

terp

reta

tion

of

posi

tion-

time

and

velo

city

-tim

e gr

aphs

•R

elat

ing

the

grad

ient

fu

nctio

n to

fea

ture

s of

the

orig

inal

fun

ctio

n

Rel

atin

g th

e gr

adie

nt f

unct

ion

to th

e or

igin

al f

unct

ion

(pag

e 34

3)E

x 7G

Rel

atin

g th

e gr

adie

nt

func

tion

to th

e or

igin

al

func

tion

(pag

e 34

3)

GC

pro

gram

: G

radi

ent a

t a p

oint

(p

age

343)

Mat

hcad

: G

radi

ent a

t a p

oint

(pa

ge 3

43)

Exc

el:

Gra

dien

t at a

poi

nt (

page

343

)E

xcel

: Pl

ottin

g re

latio

ns (

page

343

)

•R

elat

ing

the

grad

ient

fu

nctio

n to

fea

ture

s of

the

orig

inal

fun

ctio

n

Rel

atin

g ve

loci

ty-t

ime

grap

hs

to p

ositi

on-t

ime

grap

hs

(pag

e 34

4)W

E 1

5, 1

6E

x 7H

Rel

atin

g ve

loci

ty-t

ime

grap

hs to

pos

ition

-tim

e gr

aphs

(pa

ge 3

46)

•A

pply

ing

rate

s of

cha

nge

in

mot

ion

grap

hs –

info

rmal

tr

eatm

ent o

f th

e re

latio

nshi

p be

twee

n po

sitio

n-tim

e an

d ve

loci

ty-t

ime

grap

hs•

Rel

atin

g th

e gr

adie

nt

func

tion

to f

eatu

res

of th

e or

igin

al f

unct

ion

Rat

es o

f cha

nge

of p

olyn

omia

ls

(pag

e 34

9)W

E 1

7a-c

, 18

Ex

7I R

ates

of

chan

ge o

f po

lyno

mia

ls (

page

352

)

Mat

hcad

: R

ates

of

chan

ge o

f po

lyno

mia

ls

(pag

e 35

2)E

xcel

: R

ates

of

chan

ge o

f po

lyno

mia

ls

(pag

e 35

2)

•T

he m

easu

rem

ent o

f ra

tes

of

chan

ge o

f po

lyno

mia

ls:

findi

ng s

ucce

ssiv

e nu

mer

ical

ap

prox

imat

ions

to th

e gr

adie

nt o

f a

poly

nom

ial

func

tion

at a

poi

nt (l

eadi

ng to

in

form

al tr

eatm

ent o

f lim

its)

Sum

mar

y (p

age

354)

Cha

pter

rev

iew

(pa

ge 3

56)

–M

ultip

le c

hoic

e 1–

16–

Shor

t ans

wer

1–8

–A

naly

sis

Q1

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

360

)To

pic

test

s (2

)



OR

K P

RO

GR

AM

Cha

pter

8D

iffe

rent

iatio

n

Are

a of

stu

dy: U

nit 2

C

alcu

lus

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Intr

oduc

tion

to li

mits

(p

age

362)

WE

1, 2

, 3E

x 8A

Int

rodu

ctio

n to

lim

its

(pag

e 36

5)

Inve

stig

atio

n: S

neak

ing

up o

n a

limit

(pag

e 36

6)Sk

illS

HE

ET

8.1

: Sub

stitu

ting

into

a f

unct

ion

(pag

e 36

5)

Lim

its o

f di

scon

tinuo

us,

ratio

nal a

nd h

ybri

d fu

nctio

ns

(pag

e 36

7)W

E 4

a-b,

5a-

b, 6

a-b

Ex

8B L

imits

of

disc

ontin

uous

, ra

tiona

l and

hyb

rid

func

tions

(p

age

369)

Dif

fere

ntia

tion

usin

g fir

st

prin

cipl

es (

page

371

)W

E 7

, 8a-

bE

x 8C

Dif

fere

ntia

tion

usin

g fir

st

prin

cipl

es (

page

374

)

Inve

stig

atio

n: S

ecan

ts a

nd

tang

ents

(pa

ge 3

71)

Skil

lSH

EE

T 8.

2: D

iffe

rent

iatin

g fr

om fi

rst p

rinc

iple

s (p

age

374)

Wor

kSH

EE

T 8.

1 (p

age

374)

Exc

el:

Gra

dien

t of

a se

cant

(pa

ge 3

71)

Mat

hcad

: G

radi

ent o

f a

seca

nt (

page

371

)•

The

der

ivat

ive

as th

e gr

adie

nt o

f th

e gr

aph

at a

po

int a

nd it

s re

pres

enta

tion

by a

gra

dien

t fun

ctio

n•

Not

atio

n fo

r de

riva

tives

:

, f′(x

),

(f(x

))

•Fi

rst p

rinc

iple

s to

find

the

grad

ient

fun

ctio

n fo

r f(

x) =

x2

and

f(x)

= x

3 •

Firs

t pri

ncip

les,

gra

phic

al o

r nu

mer

ical

app

roac

hes

to

just

ify

rule

s fo

r fin

ding

the

grad

ient

fun

ctio

ns o

f ot

her

poly

nom

ials

dy

dx

------

d dx

------



Find

ing

deri

vativ

es b

y ru

le

(pag

e 37

5)W

E 9

a-d,

10,

11,

12a

-d-T

ange

nts

and

norm

als

(pag

e 37

7)W

E 1

3a-b

Ex

8D F

indi

ng d

eriv

ativ

es b

y ru

le (

page

378

)

Inve

stig

atio

n: G

raph

s of

de

riva

tives

(pa

ge 3

80)

GC

tip:

Plo

tting

the

deri

vativ

e fu

nctio

n (p

age

380)

Mat

hcad

: D

eriv

ativ

es (

page

378

)M

athc

ad:

Gra

dien

t at a

poi

nt (

page

379

)E

xcel

: G

radi

ent a

t a p

oint

(pa

ge 3

79)

Mat

hcad

: Tan

gent

and

nor

mal

(pa

ge 3

79)

Exc

el:

Tang

ent a

nd n

orm

al (

page

379

)M

athc

ad: T

wo

func

tion

grap

her (

page

380

)E

xcel

: Tw

o fu

nctio

n gr

aphe

r (p

age

380)

Mat

hcad

: Fu

nctio

n an

d de

riva

tive

(pag

e 38

0)E

xcel

: Fu

nctio

n an

d de

riva

tive

(pag

e 38

0)

•D

eriv

ativ

es o

f si

mpl

e po

lyno

mia

ls b

y ru

le

Ant

idif

fere

ntia

tion

(pag

e 38

1)In

vest

igat

ion:

A

ntid

iffe

rent

iatio

n (p

age

381)

•A

ntid

iffe

rent

iatio

n as

the

reve

rse

proc

ess

of

diff

eren

tiatio

n –

deve

lopi

ng

rule

s fo

r an

tider

ivat

ives

of

sim

ple

poly

nom

ials

Ant

idif

fere

ntia

tion

by r

ule

(pag

e 38

2)W

E 1

4, 1

5, 1

6, 1

7E

x 8E

Ant

idif

fere

ntia

tion

by

rule

(pa

ge 3

84)

Wor

kSH

EE

T 8.

2 (p

age

384)

Mat

hcad

: Ant

idif

fere

ntia

tion

(pag

e 38

4)G

C p

rogr

am: A

ntid

iffe

rent

iatio

n (p

age

384)

•A

ntid

iffe

rent

iatio

n as

the

reve

rse

proc

ess

of

diff

eren

tiatio

n –

deve

lopi

ng

rule

s fo

r an

tider

ivat

ives

of

sim

ple

poly

nom

ials

; id

entif

ying

fam

ilies

of

curv

es

Der

ivin

g th

e or

igin

al f

unct

ion

from

the

grad

ient

fun

ctio

n (p

age

385)

WE

18,

19a

-b, 2

0E

x 8F

Der

ivin

g th

e or

igin

al

func

tion

from

the

grad

ient

fu

nctio

n (p

age

387)

•A

ntid

iffe

rent

iatio

n as

the

reve

rse

proc

ess

of

diff

eren

tiatio

n –

iden

tifyi

ng

fam

ilies

of

curv

es

Sum

mar

y (p

age

389)

Cha

pter

rev

iew

(pa

ge 3

91)

–M

ultip

le c

hoic

e Q

1–24

–Sh

ort a

nsw

er Q

1–12

–A

naly

sis

Q1–

2

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

394

)To

pic

test

s (2

)



OR

K P

RO

GR

AM

Cha

pter

9A

pplic

atio

ns o

f di

ffer

entia

tion

Are

a of

stu

dy: U

nit 2

C

alcu

lus

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Rat

es o

f ch

ange

(pa

ge 3

96)

WE

1a-

c, 2

a-d,

3a-

dE

x 9A

Rat

es o

f ch

ange

(p

age

399)

Skil

lSH

EE

T 9.

1: A

vera

ge ra

te o

f ch

ange

(pa

ge 3

99)

Skil

lSH

EE

T 9.

2: I

nsta

ntan

eous

ra

te o

f ch

ange

(pa

ge 4

00)

Mat

hcad

: Gra

dien

t bet

wee

n tw

o po

ints

on

a gr

aph

(pag

e 39

9)E

xcel

: G

radi

ent b

etw

een

two

poin

ts o

n a

grap

h (p

age

399)

•A

pplic

atio

ns o

f di

ffer

entia

tion

– fin

ding

rate

s of

cha

nge

Sket

chin

g gr

aphs

con

tain

ing

stat

iona

ry p

oint

s (p

age

403)

WE

4a-

b, 5

, 6E

x 9B

Ske

tchi

ng g

raph

s co

ntai

ning

sta

tiona

ry p

oint

s (p

age

407)

GC

tip:

Fin

ding

sta

tiona

ry

(tur

ning

) po

ints

(pa

ge 4

06)

Skil

lSH

EE

T 9

.3: R

evie

w o

f th

e di

scri

min

ant (

page

408

)Sk

illS

HE

ET

9.4:

Sol

ving

cub

ic

equa

tions

(pa

ge 4

08)

Mat

hcad

: Q

uadr

atic

gra

phs

(pag

e 40

7)E

xcel

: Q

uadr

atic

gra

phs

(pag

e 40

7)E

xcel

: C

ubic

gra

phs

(pag

e 40

7)M

athc

ad:

Cub

ic g

raph

s (p

age

407)

•A

pplic

atio

ns o

f di

ffer

entia

tion

– us

ing

turn

ing

poin

ts to

ass

ist i

n sk

etch

ing

grap

hs o

f si

mpl

e po

lyno

mia

ls

Solv

ing

max

imum

and

m

inim

um p

robl

ems

(pag

e 40

9)W

E 7

a-b,

8E

x 9C

Sol

ving

max

imum

and

m

inim

um p

robl

ems

(pag

e 41

2)

Inve

stig

atio

n: W

hen

is a

m

axim

um n

ot a

max

imum

? (p

age

414)

Wor

kSH

EE

T 9.

1 (p

age

413)

Mat

hcad

: Q

uadr

atic

gra

phs

(pag

e 41

2)E

xcel

: Q

uadr

atic

gra

phs

(pag

e 41

2)M

athc

ad:

Cub

ic g

raph

s (p

age

412)

Exc

el:

Cub

ic g

raph

s (p

age

412)

GC

pro

gram

: M

axim

um (

page

412

)G

C p

rogr

am:

Min

imum

(pa

ge 4

12)

•A

pplic

atio

ns o

f di

ffer

entia

tion

– de

term

inin

g m

axim

um o

r m

inim

um

poin

ts f

or q

uadr

atic

and

cu

bic

func

tions

gra

phic

ally

an

d an

alyt

ical

ly a

nd th

eir

appl

icat

ion

to s

impl

e m

axim

um/m

inim

um

prob

lem

s

App

licat

ions

of

antid

iffe

rent

iatio

n (p

age

415)

WE

9, 1

0a-b

Ex

9D A

pplic

atio

ns o

f an

tidif

fere

ntia

tion

(pag

e 41

7)

Wor

kSH

EE

T 9.

2 (p

age

418)

Mat

hcad

: Ant

idif

fere

ntia

tion

(pag

e 41

7)•

Ant

idif

fere

ntia

tion

as th

e re

vers

e pr

oces

s of

di

ffer

entia

tion

– de

velo

ping

ru

les

for

antid

eriv

ativ

es o

f si

mpl

e po

lyno

mia

ls

Sum

mar

y (p

age

419)

Cha

pter

rev

iew

(pa

ge 4

20)

–M

ultip

le c

hoic

e Q

1–12

–Sh

ort a

nsw

er Q

1–7

–A

naly

sis

Q1–

2

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

422

)To

pic

test

s (2

)



WO

RK

PR

OG

RA

M

Cha

pter

10

Intr

oduc

tory

pro

babi

lity

Are

a of

stu

dy: U

nit 1

Pr

obab

ility

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

Intr

oduc

tion

to p

roba

bilit

y (p

age

424)

WE

1, 2

, 3E

x 10

A E

stim

ated

pro

babi

lity

and

expe

cted

num

ber

of

outc

omes

(pa

ge 4

26)

Wor

kSH

EE

T 10

.1 (

page

427

)E

xcel

: L

ong

run

prop

ortio

n (p

age

424)

GC

pro

gram

: C

oin

flip

(pag

e 42

4)E

xcel

: O

ne d

ie (

page

424

)G

C p

rogr

am:

One

die

(pa

ge 4

24)

Exc

el:

Two

dice

(pa

ge 4

24)

GC

pro

gram

: Tw

o di

ce (

page

424

)

•R

ando

m e

xper

imen

ts, e

vent

s an

d ev

ent s

pace

s•

Prob

abili

ty a

s an

exp

ress

ion

of lo

ng r

un p

ropo

rtio

n

Ext

ensi

on —

Set

s an

d V

enn

diag

ram

s (l

ink

to C

D-R

OM

fr

om p

age

428)

WE

1, 2

, 3a-

g, 4

a-c,

5a-

h, 6

a-d,

7

Ex

10.1

Set

s an

d V

enn

diag

ram

sU

sing

set

s to

sol

ve p

ract

ical

pr

oble

ms

(lin

k to

CD

-RO

M

from

pag

e 42

8)W

E 8

, 9, 1

0E

x 10

.2 U

sing

set

s to

sol

ve

prac

tical

pro

blem

s

•V

enn

diag

ram

s

Cal

cula

ting

prob

abili

ties

(pag

e 42

8)W

E 4

, 5a-

b, 6

a-b,

7a-

d, 8

a-b

Ex

10B

Cal

cula

ting

prob

abili

ties

(pag

e 43

2)

•Pr

obab

ility

of

sim

ple

and

com

poun

d ev

ents

Tre

e di

agra

ms

and

latti

ce

diag

ram

s (p

age

434)

WE

9a-

b, 1

0a-b

, 11a

-cE

x 10

C T

ree

diag

ram

s an

d la

ttice

dia

gram

s (p

age

437)

•T

ree

diag

ram

s



The

Add

ition

Law

of

prob

abili

ties

(pag

e 44

0)W

E 1

2, 1

3, 1

4, 1

5a-b

, 16a

-b, 1

7E

x 10

D A

dditi

on L

aw o

f pr

obab

ilitie

s (p

age

443)

Wor

kSH

EE

T 10

.2 (

page

445

)•

The

add

ition

rul

e fo

r pr

obab

ilitie

s•

Ven

n di

agra

ms

Kar

naug

h M

aps

and

prob

abili

ty

tabl

es (

page

446

)W

E 1

8, 1

9, 2

0a-b

Ex

10E

Kar

naug

h M

aps

and

prob

abili

ty ta

bles

(pa

ge 4

49)

•V

enn

diag

ram

s, p

roba

bilit

y ta

bles

Con

ditio

nal p

roba

bilit

y (p

age

452)

WE

21,

22a

-b, 2

3a-d

, 24a

-bE

x 10

F C

ondi

tiona

l pro

babi

lity

(pag

e 45

5)

Skil

lSH

EE

T 10

.1: C

ondi

tiona

l pr

obab

ility

(pa

ge 4

55)

•C

ondi

tiona

l pro

babi

lity

•V

enn

diag

ram

s, p

roba

bilit

y ta

bles

and

tree

dia

gram

s

Inde

pend

ent e

vent

s (p

age

457)

WE

25,

26,

27a

-b, 2

8a-c

, 29a

-bE

x 10

G I

ndep

ende

nt e

vent

s (p

age

461)

•In

depe

nden

ce; t

he

mul

tiplic

atio

n ru

le f

or

inde

pend

ent e

vent

s•

Tre

e di

agra

ms

Ext

ensi

on —

Sam

plin

g w

ithou

t re

plac

emen

t (lin

k to

C

D-R

OM

fro

m p

age

463)

WE

1a-

c, 2

a-d

Ex

10.3

Sam

plin

g w

ithou

t re

plac

emen

t

Skil

lSH

EE

T 1

0.2:

Sam

plin

g w

ithou

t rep

lace

men

t

Sim

ulat

ion

(pag

e 46

4)W

E 3

0a-b

, 31a

-bE

x 10

H S

imul

atio

n (p

age

467)

Mat

hcad

: R

ando

m n

umbe

rs (

page

467

)E

xcel

: R

ando

m n

umbe

rs (

page

467

)G

C p

rogr

am: R

ando

m n

umbe

rs (p

age

467)

•Si

mul

atio

n us

ing

sim

ple

gene

rato

rs s

uch

as c

oins

, di

ce, s

pinn

ers,

ran

dom

nu

mbe

r ta

bles

and

com

pute

rs•

Dis

play

and

inte

rpre

tatio

n of

re

sults

of

sim

ulat

ions

Sum

mar

y (p

age

469)

Cha

pter

rev

iew

(pa

ge 4

71)

–M

ultip

le c

hoic

e Q

1–11

–Sh

ort a

nsw

er Q

1–11

–A

naly

sis

Q1

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

474

)To

pic

test

s (2

)



WO

RK

PR

OG

RA

M

Cha

pter

11

Com

bina

tori

csA

rea

of s

tudy

: Uni

t 2

Prob

abili

ty

Sect

ion

GC

tip

s, I

nves

tiga

tion

s,

Car

eer

profi

les,

H

isto

ry o

f m

athe

mat

ics

Skill

SHE

ET

S,

Wor

kSH

EE

TS,

Tes

t yo

urse

lf,

Topi

c te

sts

(CD

-RO

M)

Tech

nolo

gy a

pplic

atio

ns

(CD

-RO

M)

Stud

y de

sign

dot

poi

nts

The

add

ition

pri

ncip

le

(pag

e 47

6)W

E 1

, 2M

ultip

licat

ion

prin

cipl

e (p

age

477)

WE

3, 4

a-c

Ex

11A

Add

ition

and

m

ultip

licat

ion

prin

cipl

e (p

age

479)

•A

dditi

on a

nd m

ultip

licat

ion

prin

cipl

es

Perm

utat

ions

(pa

ge 4

81)

WE

5, 6

, 7a-

bE

x 11

B P

erm

utat

ions

(p

age

483)

Inve

stig

atio

n: I

dent

ifica

tion

card

s (p

age

484)

•Pe

rmut

atio

ns: c

once

pt o

f or

dere

d sa

mpl

es

Fact

oria

ls (

page

485

)W

E 8

a-b,

9, 1

0E

x 11

C F

acto

rial

s (p

age

487)

GC

tip:

Fac

tori

als

(pag

e 48

6)In

vest

igat

ion:

Stir

ling'

s for

mul

a (p

age

486)

Wor

kSH

EE

T 11

.1 (

page

487

)E

xcel

: St

irlin

g's

form

ula

(pag

e 48

6)

Perm

utat

ions

usi

ng n P

r (p

age

488)

WE

11,

12,

13,

14

Ex

11D

Per

mut

atio

ns u

sing

n Pr

(pag

e 49

1)

GC

tip:

Per

mut

atio

ns

(pag

e 49

0)Sk

illS

HE

ET

11.1

: Cal

cula

ting

n Pr (

page

491

)M

athc

ad:

Com

bina

tori

cs (

page

491

)E

xcel

: C

ombi

nato

rics

(pa

ge 4

91)

•Pe

rmut

atio

ns: c

once

pt o

f or

dere

d sa

mpl

es, n P

r

•E

valu

atio

n of

n Pr

Perm

utat

ions

invo

lvin

g re

stri

ctio

ns (

page

493

)W

E 1

5, 1

6, 1

7, 1

8E

x 11

E P

erm

utat

ions

invo

lvin

g re

stri

ctio

ns (

page

496

)

•Pe

rmut

atio

ns: c

once

pt o

f or

dere

d sa

mpl

es, n P

r

•E

valu

atio

n of

n Pr

Arr

ange

men

ts in

a c

ircl

e (p

age

498)

WE

19,

20,

21

Ex

11F

Arr

ange

men

ts in

a c

ircl

e (p

age

500)

Wor

kSH

EE

T 11

.2 (

page

500

)•

Perm

utat

ions

: con

cept

of

orde

red

sam

ples

, n Pr

•E

valu

atio

n of

n Pr



Com

bina

tions

usi

ng n C

r (p

age

501)

WE

23,

24,

25a

-cE

x 11

G C

ombi

natio

ns u

sing

n Cr

(pag

e 50

4)

GC

tip:

Com

bina

tions

(p

age

501)

Skil

lSH

EE

T 11

.2: L

istin

g po

ssib

ilitie

s (p

age

505)

Mat

hcad

: C

ombi

nato

rics

(pa

ge 5

04)

Exc

el:

Com

bina

tori

cs (

page

504

)•

Com

bina

tions

: con

cept

of

unor

dere

d sa

mpl

es, n C

r

•E

valu

atio

n of

n Cr an

d

esta

blis

hing

that

n Pr =

n Cr ×

r!

Pasc

al’s

tria

ngle

(pa

ge 5

06)

Inve

stig

atio

n: P

asca

l's tr

iang

le

(pag

e 50

6)E

xcel

: Pa

scal

’s tr

iang

le (

page

506

)•

The

rel

atio

nshi

p of

co

mbi

natio

ns to

Pas

cal’s

tr

iang

le

App

licat

ions

of

prob

abili

ty

(pag

e 50

7)W

E 2

6, 2

7, 2

8, 2

9E

x 11

H A

pplic

atio

ns o

f pr

obab

ility

(pa

ge 5

09)

Mat

hcad

: C

ombi

nato

rics

(pa

ge 5

09)

Exc

el:

Com

bina

tori

cs (

page

509

)•

App

licat

ions

of p

erm

utat

ions

an

d co

mbi

natio

ns to

pr

obab

ility

, inc

ludi

ng a

n in

form

al tr

eatm

ent o

f ex

ampl

es in

volv

ing

bino

mia

l an

d hy

perg

eom

etri

c pr

obab

ilitie

s

Sum

mar

y (p

age

511)

Cha

pter

rev

iew

(pa

ge 5

12)

–M

ultip

le c

hoic

e Q

1–14

–Sh

ort a

nsw

er Q

1–19

–A

naly

sis

Q1–

2

‘Tes

t you

rsel

f’ m

ultip

le c

hoic

e qu

estio

ns (

page

514

)To

pic

test

s (2

)



Sample assessment templateVCE Mathematical Methods Unit

Task:

Student: Date:

Comments:

Outcome Criteria Allocated number of

marks

Student mark

Outcome 1Define and explain key concepts as specified in the content of the areas of study, and to apply a range of related mathematical routines and procedures.

1. Appropriate use of mathematical conventions, symbols and terminology

2. Definition and explanation of key concepts

3. Accurate application of mathematical skills and techniques

Outcome 2Apply mathematical processes in non-routine contexts and to analyse and discuss these applications of mathematics.

1. Identification of important information, variables and constraints

2. Application of mathematical ideas and content from the specified areas of study

3. Analysis and interpretation of results

Outcome 3Use technology to produce results and carry out analysis in situations requiring problem solving, modelling or investigative techniques or approaches.

1. Appropriate selection and effective use of technology

2. Application of technology

Total marks


Documents

Contentsmathsbooks.net/Maths Quest 11 Methods/By Chapter/TEACHER ENDMATTER.pdf–factor theorem 3E The remainder and factor theorems (page 121) 3F Factorising cubic polynomials (page