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Teacher edition supplementary
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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.
TEACHER ENDMATTER Page 566 Friday, January 10, 2003 1:06 PM
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)
TEACHER ENDMATTER Page 567 Friday, January 10, 2003 1:06 PM
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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
2. Algebra
Study design dot points Sections/
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)
TEACHER ENDMATTER Page 568 Friday, January 10, 2003 1:06 PM
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
Study design dot points Sections/
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)
TEACHER ENDMATTER Page 569 Friday, January 10, 2003 1:06 PM
570
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
Unit 2
1. Functions and graphs
Study design dot points Sections/
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)
Study design dot points Sections/
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
5B The unit circle (page 212)
– 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
)
= −
15B The unit circle (page 212)
– 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---
TEACHER ENDMATTER Page 570 Friday, January 10, 2003 1:06 PM
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------
TEACHER ENDMATTER Page 571 Friday, January 10, 2003 1:06 PM
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)
TEACHER ENDMATTER Page 572 Friday, January 10, 2003 1:06 PM
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 573
WO
RK
PR
OG
RA
M
Cha
pter
1L
inea
r fu
nctio
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
Solv
ing
linea
r eq
uatio
ns
(pag
e 2)
WE
1a-
c, 2
a-c
Ex
1A S
olvi
ng li
near
equ
atio
ns
(pag
e 5)
Exc
el: E
quat
ion
solv
er (
page
5)
GC
pro
gram
: Equ
atio
n so
lver
(pa
ge 5
)M
athc
ad: E
quat
ion
solv
er (
page
5)
•Su
bstit
utio
n in
and
re
arra
ngem
ent o
f fo
rmul
as
Rea
rran
gem
ent a
nd su
bstit
utio
n (p
age
6)W
E 3
a-c,
4a-
b, 5
Ex
1B R
earr
ange
men
t and
su
bstit
utio
n (p
age
9)
Car
eer
profi
le: R
ick
Mor
ris
(pag
e 12
)M
athc
ad: R
earr
angi
ng e
quat
ions
(pa
ge 9
)M
athc
ad: S
ubst
itutio
n (p
age
9)•
Subs
titut
ion
in a
nd
rear
rang
emen
t of
form
ulas
Gra
dien
t of
a st
raig
ht li
ne
(pag
e 13
)W
E 6
, 7, 8
a-b
Ex
1C G
radi
ent o
f a st
raig
ht li
ne
(pag
e 16
)
Skil
lSH
EE
T 1.
1: U
sing
gra
dien
t to
find
the
valu
e of
a
para
met
er (
page
20)
Mat
hcad
: Gra
dien
t of
a st
raig
ht li
ne
(pag
e 16
)E
xcel
: Gra
dien
t of
a st
raig
ht li
ne (
page
16)
GC
pro
gram
: Gra
dien
t of
a st
raig
ht li
ne
(pag
e 16
)C
abri
geo
met
ry: G
radi
ent o
f a s
trai
ght l
ine
(pag
e 16
)
•Sk
etch
gra
phs
of s
trai
ght
lines
Equ
atio
ns o
f the
form
y =
mx
+ c
(pag
e 21
)E
x 1D
Equ
atio
ns o
f th
e fo
rm
y =
mx
+ c
(pag
e 21
)
Wor
kSH
EE
T 1.
1 (p
age
23)
Mat
hcad
: Lin
ear
grap
hs (
page
21)
Exc
el: L
inea
r gr
aphs
(pa
ge 2
1)G
C p
rogr
am: G
uess
the
equa
tion
(pag
e 22
)
•G
radi
ents
of
para
llel a
nd
perp
endi
cula
r lin
es•
Sket
ch g
raph
s of
str
aigh
t lin
es•
Find
ing
equa
tions
of
stra
ight
lin
es f
rom
giv
en in
form
atio
n
Sket
chin
g lin
ear
grap
hs u
sing
in
terc
epts
(pa
ge 2
4)W
E 9
, 10,
11
Ex
1E S
ketc
hing
line
ar g
raph
s us
ing
inte
rcep
ts (
page
26)
GC
tip:
Fin
ding
x-
and
y-in
terc
epts
(pa
ge 2
6)M
athc
ad: G
radi
ent o
f a
stra
ight
line
(p
age
26)
Cab
ri g
eom
etry
: Gra
dien
t of a
str
aigh
t lin
e (p
age
26)
•Sk
etch
gra
phs
of s
trai
ght
lines
TEACHER ENDMATTER Page 573 Friday, January 10, 2003 1:06 PM
574 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
Sim
ulta
neou
s eq
uatio
ns
(pag
e 27
)W
E 1
2, 1
3, 1
4, 1
5E
x 1F
Sim
ulta
neou
s eq
uatio
ns
(pag
e 30
)
Inve
stig
atio
n: U
sing
mat
rice
s to
so
lve
sim
ulta
neou
s equ
atio
ns
(pag
e 31
)
Mat
hcad
: Sim
ulta
neou
s lin
ear
equa
tions
– gr
aphi
cal m
etho
d (p
age
30)
Exc
el: S
imul
tane
ous
linea
r eq
uatio
ns–
grap
hica
l met
hod
(pag
e 30
)M
athc
ad: S
imul
tane
ous
linea
r eq
uatio
ns
(pag
e 30
)C
abri
geo
met
ry: S
imul
tane
ous
linea
r eq
uatio
ns (
page
30)
Exc
el: S
imul
tane
ous
linea
r eq
uatio
ns
(pag
e 30
)G
C p
rogr
am: S
imul
tane
ous
linea
r eq
uatio
ns (
page
30)
•So
lutio
n of
two
linea
r si
mul
tane
ous
equa
tions
Perp
endi
cula
r lin
es (
page
32)
Ex
1G P
erpe
ndic
ular
line
s (p
age
32)
Skil
lSH
EE
T 1.
2: R
ecip
roca
ls
and
nega
tive
reci
proc
als
(pag
e 32
)
GC
pro
gram
: Ang
le b
etw
een
two
lines
(p
age
32)
•G
radi
ents
of
para
llel a
nd
perp
endi
cula
r lin
es
Form
ula
for
findi
ng th
e eq
uatio
n of
a s
trai
ght l
ine
(pag
e 33
)W
E 1
6, 1
7 E
x 1H
For
mul
a fo
r fin
ding
the
equa
tion
of a
str
aigh
t lin
e (p
age
35)
Wor
kSH
EE
T 1.
2 (p
age
36)
Mat
hcad
: Equ
atio
n of
a s
trai
ght l
ine
(pag
e 35
)C
abri
geo
met
ry: E
quat
ion
of a
str
aigh
t lin
e (p
age
35)
Exc
el: E
quat
ion
of a
str
aigh
t lin
e (p
age
35)
•Fi
ndin
g eq
uatio
ns o
f st
raig
ht
lines
fro
m g
iven
info
rmat
ion
Dis
tanc
e be
twee
n tw
o po
ints
(p
age
37)
WE
18
Ex
1I D
ista
nce
betw
een
two
poin
ts (
page
38)
GC
tip:
Rep
eate
d ca
lcul
atio
n of
th
e di
stan
ce b
etw
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
TEACHER ENDMATTER Page 574 Friday, January 10, 2003 1:06 PM
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 575
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)
TEACHER ENDMATTER Page 575 Friday, January 10, 2003 1:06 PM
576 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
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
TEACHER ENDMATTER Page 576 Friday, January 10, 2003 1:06 PM
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
)
TEACHER ENDMATTER Page 577 Friday, January 10, 2003 1:06 PM
578 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
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
TEACHER ENDMATTER Page 578 Friday, January 10, 2003 1:06 PM
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
)
TEACHER ENDMATTER Page 579 Friday, January 10, 2003 1:06 PM
580 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
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
TEACHER ENDMATTER Page 580 Friday, January 10, 2003 1:06 PM
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 581
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
)
TEACHER ENDMATTER Page 581 Friday, January 10, 2003 1:06 PM
582 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
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
--------
---
TEACHER ENDMATTER Page 582 Friday, January 10, 2003 1:06 PM
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 583
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---
TEACHER ENDMATTER Page 583 Friday, January 10, 2003 1:06 PM
584 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
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
)
TEACHER ENDMATTER Page 584 Friday, January 10, 2003 1:06 PM
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
TEACHER ENDMATTER Page 585 Friday, January 10, 2003 1:06 PM
586 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
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
)
TEACHER ENDMATTER Page 586 Friday, January 10, 2003 1:06 PM
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 587W
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
TEACHER ENDMATTER Page 587 Friday, January 10, 2003 1:06 PM
588 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
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
)
TEACHER ENDMATTER Page 588 Friday, January 10, 2003 1:06 PM
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 589W
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
------
TEACHER ENDMATTER Page 589 Friday, January 10, 2003 1:06 PM
590 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
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
)
TEACHER ENDMATTER Page 590 Friday, January 10, 2003 1:06 PM
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 591W
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
)
TEACHER ENDMATTER Page 591 Friday, January 10, 2003 1:06 PM
592 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
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
TEACHER ENDMATTER Page 592 Friday, January 10, 2003 1:06 PM
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 593
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
)
TEACHER ENDMATTER Page 593 Friday, January 10, 2003 1:06 PM
594 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
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
TEACHER ENDMATTER Page 594 Friday, January 10, 2003 1:06 PM
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 595
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
)
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596 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
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
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