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TRANSCRIPT
C O R E - P L U S M A T H E M A T I C S P R O J E C T
Scope & Sequencea l g e b r a a n d f u n c t i o n s
s t a t i s t i c s a n d p r o b a b i l i t y
g e o m e t r y a n d t r i g o n o m e t r y
d i s c r e t e m a t h e m a t i c s
ContemporaryMathematicsin ContextA Unified Approach
C O R E - P L U S M A T H E M A T I C S P R O J E C T
Scope and Sequence
ContemporaryMathematicsin ContextA Unified ApproachArthur F. CoxfordJames T. FeyChristian R. HirschHarold L. SchoenGail BurrillEric W. HartBrian A. KellerAnn E. WatkinswithMary Jo MessengerBeth E. RitsemaRebecca K. Walker
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher.
Send all inquiries to:Glencoe McGraw-Hill8787 Orion PlaceColumbus, Ohio 43240-4027
ISBN 1-57039-895-X Contemporary Mathematics in ContextScope & Sequence
2 3 4 5 6 7 8 9 079 03 02 01
Glencoe/McGraw-Hill
This project was supported, in part, by the National Science Foundation.The opinions expressed are those of the authors and not necessarily those of the Foundation.
C P M P S c o p e a n d S e q u e n c e 5
Project DirectorChristian R. HirschWestern Michigan University
Project Co-DirectorsArthur F. CoxfordUniversity of Michigan
James T. FeyUniversity of Maryland
Harold L. SchoenUniversity of Iowa
Senior Curriculum DevelopersGail BurrillUniversity of Wisconsin-Madison
Eric W. HartWestern Michigan University
Brian A. KellerMichigan State University
Ann E. WatkinsCalifornia State University, Northridge
Professional Development CoordinatorBeth RitsemaWestern Michigan University
Evaluation CoordinatorSteven W. ZiebarthWestern Michigan University
Advisory BoardDiane BriarsPittsburgh Public Schools
Jeremy KilpatrickUniversity of Georgia
Kenneth RuthvenUniversity of Cambridge
David A. SmithDuke University
Edna VasquezDetroit Renaissance High School
Curriculum Development ConsultantsAlverna ChampionGrand Valley State University
Cherie CornickWayne County Alliance for Mathematics andScience
Edgar Edwards (Formerly) Virginia State Department ofEducation
Kenneth RossUniversity of Oregon
Richard ScheafferUniversity of Florida
Martha SiegelTowson University
Edward SilverUniversity of Pittsburgh
Lee StiffNorth Carolina State University
Paul ZornSt. Olaf College
Collaborating TeachersEmma AmesOakland Mills High School, Maryland
Cheryl Bach HeddenSitka High School, Alaska
Mary Jo MessengerHoward County Public Schools, Maryland
Valerie MillsAnn Arbor Public Schools, Michigan
Jacqueline StewartOkemos High School, Michigan
Michael VerkaikHolland Christian High School, Michigan
Marcia WeinholdKalamazoo Area Mathematics and ScienceCenter, Michigan
Graduate AssistantsCos FiUniversity of Iowa
Sarah FieldUniversity of Iowa
Kelly FinnUniversity of Iowa
Judy FlowersUniversity of Michigan
Johnette MassonUniversity of Iowa
Chris RasmussenUniversity of Maryland
Heather ThompsonIowa State University
Bettie TruittUniversity of Iowa
Roberto VillarubiUniversity of Maryland
Rebecca WalkerWestern Michigan University
Ed WallUniversity of Michigan
Technical CoordinatorJames LaserWestern Michigan University
Production and Support StaffKelly MacLeanJennifer RosenboomWendy WeaverKathryn WrightTeri ZiebarthWestern Michigan University
Catherine KernUniversity of Iowa
Software DevelopersJim FlandersColorado Springs, Colorado
Eric KamischkeInterlochen, Michigan
About the Core-Plus Mathematics ProjectThe Core-Plus Mathematics Project (CPMP) was funded by the National Science Foundationto develop student and teacher materials for a comprehensive Standards-based high school mathematics curriculum. Courses 1–3 comprise a core curriculum appropriate for all students.Course 4 continues the preparation of students for college mathematics.
C P M P S c o p e a n d S e q u e n c e 7
UNIFIED MATHEMATICSContemporary Mathematics in Context is a four-year unified curriculum thatreplaces the traditional Algebra-Geometry-Advanced Algebra/Trigonometry-Precalculus sequence. Each course features interwoven strands of algebra andfunctions, statistics and probability, geometry and trigonometry, and discretemathematics. Each of these strands is developed within focused units connectedby fundamental ideas such as symmetry, functions, matrices, and data analysisand curve-fitting. The largest number of units is devoted to algebra and functions.By encountering mathematics every year from a more mathematically sophisticatedpoint of view, students’ understanding of the strands deepen across the four-yearcurriculum. Mathematical connections between strands and ways of thinkingmathematically that are common across strands are emphasized. These mathe-matical habits of mind include visual thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures, reasoning withmultiple representations, and providing convincing arguments and proofs.
The algebra and functions strand develops student ability to recognize, represent,and solve problems involving relations among quantitative variables. Central tothe development is the use of functions as mathematical models. The key algebraicmodels in the curriculum are linear, exponential, power, polynomial, logarithmic,rational, and periodic functions. Each algebraic model is investigated in fourlinked representations—verbal, graphic, numeric, and symbolic—with the aid oftechnology. Attention is also given to modeling with systems, both linear andnonlinear, and to symbolic reasoning and manipulation.
The primary role of the statistics and probability strand is to develop student abilityto analyze data intelligently, to recognize and measure variation, and to understandthe patterns that underlie probabilistic situations. The ultimate goal is for students tounderstand how inferences can be made about a population by looking at a samplefrom that population. Graphical methods of data analysis, simulations, sampling,and experience with the collection and interpretation of real data are featured.
The primary goal of the geometry and trigonometry strand is to develop visualthinking and student ability to construct, reason with, interpret, and apply math-ematical models of patterns in visual and physical contexts. Activities includedescribing patterns with regard to shape, size, and location; representing patternswith drawings, coordinates, or vectors; predicting changes and invariants in shapes;and organizing geometric facts and relationships through deductive reasoning.
The discrete mathematics strand develops student ability to model and solveproblems involving enumeration, sequential change, decision making in finitesettings, and relationships among a finite number of elements. Topics includematrices, vertex-edge graphs, recursion, models of social decision making, andsystematic counting methods. Key themes are discrete mathematical modeling,existence (Is there a solution?), optimization (What is the best solution?), andalgorithmic problem solving (Can you efficiently construct a solution?).
Algebra and Functions
Geometry andTrigonometry
Statistics and Probability
Discrete Mathematics
8 C P M P S c o p e a n d S e q u e n c e
ORGANIZATION OF THE CURRICULUMThe first three courses in the Contemporary Mathematics in Context series provided a common core of broadly useful mathematics for all students. Theywere developed to prepare students for success in college, in careers, and indaily life in contemporary society. Course 4 formalizes and extends the coreprogram, with a focus on the mathematics needed to be successful in collegemathematics and statistics courses. Unit titles for the four-year curriculum aregiven in the following table.
Course 1 Course 21 Patterns in Data 1 Matrix Models
2 Patterns of Change 2 Patterns of Location, Shape, and Size
3 Linear Models 3 Patterns of Association
4 Graph Models 4 Power Models
5 Patterns in Space and 5 Network OptimizationVisualization
6 Exponential Models 6 Geometric Form and Its Function
7 Simulation Models 7 Patterns in Chance
CAPSTONE Planning a Benefits CAPSTONE Forests, the Environment,Carnival and Mathematics
Course 3 Course 41 Multiple-Variable Models 1 Rates of Change
2 Modeling Public Opinion 2 Modeling Motion
3 Symbol Sense and 3 Logarithmic Functions and Algebraic Reasoning Data Models
4 Shapes and Geometric 4 Counting ModelsReasoning
5 Patterns in Variation 5 Binomial Distributions and Statistical Inference
6 Families of Functions 6 Polynomial and Rational Functions
7 Discrete Models of Change 7 Functions and Symbolic Reasoning
CAPSTONE Making the Best of It: 8 Space GeometryOptimal Forms and 9 InformaticsStrategies
10 Problem Solving, Algorithms, and Spreadsheets
C P M P S c o p e a n d S e q u e n c e 9
The following charts provide an overview of the mathematical content and flowof Courses 1– 4 in the Contemporary Mathematics in Context curriculum. Thecharts are organized by mathematical strand: algebra and functions, statistics andprobability, geometry and trigonometry, and discrete mathematics. Each of thefour strands has been divided into major categories, and under each of these categories you will find the mathematical topics developed in the curriculum.
Many cells in the grid have either a “● ” or a “+” to indicate the units in which each topic is covered. The “● ” indicates focus; this means that the topicis initially developed or is extended beyond its initial development or use. The“+” indicates connection, which means that a conceptual basis for the topic isdeveloped, the topic is briefly introduced, or the topic is revisited and usedwithout further development.
The Strand Charts
10 C P M P S c o p e a n d S e q u e n c e
ALG
EB
RA
AN
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UN
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ual
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12
34
56
7
●●
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12
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C P M P S c o p e a n d S e q u e n c e 11
ALG
EB
RA
AN
D F
UN
CT
ION
S
Po
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Exp
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12
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56
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12 C P M P S c o p e a n d S e q u e n c e
ALG
EB
RA
AN
D F
UN
CT
ION
S
Rati
on
al
Exp
ressio
ns a
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Sym
bo
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12
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C P M P S c o p e a n d S e q u e n c e 13
ALG
EB
RA
AN
D F
UN
CT
ION
S
Syste
ms o
f R
ela
tio
ns
Gra
ph
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sys
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s
Solv
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tem
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phic
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ary
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12
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14 C P M P S c o p e a n d S e q u e n c e
ALG
EB
RA
AN
D F
UN
CT
ION
S
Alg
eb
raic
Syste
ms
Rea
l nu
mb
ers
and
th
eir
pro
per
ties
Mat
rice
s an
d t
hei
r p
rop
erti
es
Tran
sfo
rmat
ion
s an
d t
hei
r p
rop
erti
es
Vect
ors
an
d t
hei
r p
rop
erti
es
Co
mp
lex
nu
mb
ers
and
th
eir
pro
per
ties
Set
s an
d s
et o
per
atio
ns
Inte
ger
s m
od
n a
nd
th
eir
pro
per
ties
Calc
ulu
s U
nd
erp
inn
ing
s
Rat
es o
f ch
ang
e
Max
ima
and
min
ima
Lim
its
Seq
uen
ces
and
ser
ies
Loca
l lin
eari
ty
Der
ivat
ive
fun
ctio
ns
Acc
um
ula
tio
n o
f ch
ang
e
Are
a u
nd
er a
cu
rve
Def
init
e in
teg
ral
12
34
56
7
+
+●
●
++
+
Co
urs
e 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
7
+ ●
● ++
++
+ ●+
+ + +
12
34
56
7
● ++
++
+●
++
++
● ●
●
12
34
56
78
910
++ +
●
+●
●
●●
+● ●
●+
++
++
●+
++
++
++
●
●●
+● ● ●
+●
●Fo
cus
+C
on
nec
tio
ns
C P M P S c o p e a n d S e q u e n c e 15
STA
TIS
TIC
S A
ND
PR
OB
AB
ILIT
Y
Un
ivari
ate
Data
Nu
mb
er li
ne
(do
t) p
lots
Mea
sure
s o
f ce
nte
r an
d t
hei
r p
rop
erti
es: m
ean
, med
ian
Bas
ic s
hap
es
Ske
wn
ess
and
sym
met
ry
His
tog
ram
s
Clu
ster
s, g
aps,
an
d o
utl
iers
Box
plo
ts
Lin
ear
tran
sfo
rmat
ion
s o
f d
ata
Ste
m-a
nd
-lea
f p
lots
Ran
ge
and
inte
rqu
arti
le r
ang
e (I
QR
)
Mea
n a
bso
lute
dev
iati
on
(M
AD
)
Perc
enti
les
and
qu
arti
les
Sta
nd
ard
dev
iati
on
an
d it
s p
rop
erti
es
Freq
uen
cy t
able
s
Sta
nd
ard
ized
or
z-sc
ore
s
Co
nce
pt
of
dis
trib
uti
on
Biv
ari
ate
Data
Sca
tter
plo
ts a
nd
ass
oci
atio
n
Plo
ts a
nd
tre
nd
s ov
er t
ime
Su
m o
f sq
uar
ed d
iffer
ence
s
Cen
tro
id
Leas
t sq
uar
es r
egre
ssio
n li
nes
Err
ors
of
pre
dic
tio
n a
nd
res
idu
als
No
nlin
ear
reg
ress
ion
Infl
uen
tial
po
ints
Sp
earm
an’s
ran
k co
rrel
atio
n c
oef
fici
ent
Sca
tter
plo
t an
d c
orr
elat
ion
mat
rice
s
Pear
son’
s co
rrel
atio
n c
oef
fici
ent
r
Exp
lan
ato
ry a
nd
res
po
nse
var
iab
les
Lurk
ing
var
iab
les
Cau
se-a
nd
-eff
ect
rela
tio
nsh
ips
Log
an
d lo
g-l
og
tra
nsf
orm
atio
ns
12
34
56
7
● ●+
+●
+●
+●
+● ● ● ● ● ● ● +
●
●●
●+
++
● + +●
++
●
Co
urs
e 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
7 + + +●
+ ● ●
●+
+ ● ● ●+
●+ ●
● ● ● ● ● ● ●
12
34
56
7
++ + ●
++
++
+ + + + ● ●
●● +
++
+● +
+ +●
12
34
56
78
910
+ + + + + + + + + ● ●
● + ● ● ● ● +
+
●
●Fo
cus
+C
on
nec
tio
ns
16 C P M P S c o p e a n d S e q u e n c e
STA
TIS
TIC
S A
ND
PR
OB
AB
ILIT
Y
Pro
bab
ilit
y
No
rmal
dis
trib
uti
on
Sim
ula
tio
n
Ran
dom
dig
it ta
bles
and
ran
dom
num
ber
gene
rato
rs
Law
of
Larg
e N
um
ber
s
Empi
rica
l (ex
peri
men
tal)
and
theo
retic
al p
roba
bilit
ies
Ind
epen
den
t ev
ents
Bin
om
ial d
istr
ibu
tio
n
Geo
met
ric
(wai
tin
g-t
ime)
dis
trib
uti
on
Mu
ltip
licat
ion
Ru
le f
or
ind
epen
den
t ev
ents
Geo
met
ric
(are
a) m
od
els
Co
nd
itio
nal
pro
bab
ility
Exp
ecte
d v
alu
e
Rar
e ev
ents
Sam
plin
g d
istr
ibu
tio
ns
Mu
tual
ly e
xclu
sive
eve
nts
Ad
dit
ion
Ru
le f
or
mu
tual
ly e
xclu
sive
eve
nts
Cen
tral
Lim
it T
heo
rem
Pro
bab
ility
dis
trib
uti
on
Gen
eral
mu
ltip
licat
ion
ru
le
Bin
om
ial p
rob
abili
ty f
orm
ula
No
rmal
ap
pro
xim
atio
n t
o a
bin
om
ial
Infe
ren
tial
Sta
tisti
cs
Pop
ula
tio
n v
s. s
amp
le
Co
nfi
den
ce in
terv
als
Mar
gin
of
erro
r
Co
ntr
ol (
run
) ch
arts
Test
s of
sig
nific
ance
incl
udin
g Ty
pe I
and
Type
II e
rror
s
Sta
tistic
al s
igni
fican
ce
One
sam
ple
z-te
st f
or a
pro
port
ion
Gen
eral
izab
ility
of
resu
lts
Su
rveys
Ch
arac
teri
stic
s o
f a
wel
l-d
esig
ned
su
rvey
Sam
ple
su
rvey
vs.
cen
sus
Sam
ple
siz
e
Sim
ple
ran
do
m s
amp
le
Bia
s in
su
rvey
met
ho
d
Res
po
nse
rat
e
12
34
56
7
++
● ● ● ● ● + + ●
Co
urs
e 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
7 + ● ● + ● ● ● ● ● + ●
+
12
34
56
7
●
+
+ ++
+ +●
+ ● ● + ●
●+
● ●
● +
●+
● ● ● ● ● ●
12
34
56
78
910
● ● + + ++
++
+●
++
++
++
● ● ● + + ● ●
●
● ● ● + + ● ● ● ● + + + ● ●
●Fo
cus
+C
on
nec
tio
ns
C P M P S c o p e a n d S e q u e n c e 17
STA
TIS
TIC
S A
ND
PR
OB
AB
ILIT
Y
Exp
eri
men
ts
Ch
arac
teri
stic
s o
f a
wel
l-d
esig
ned
exp
erim
ent
Trea
tmen
ts, c
on
tro
l gro
up
s, r
and
om
as
sig
nm
ent,
an
d r
eplic
atio
n
So
urc
e o
f b
ias
and
co
nfo
un
din
g, i
ncl
ud
ing
p
lace
bo
eff
ect
and
blin
din
g
Ran
do
miz
atio
n t
est
Larg
e sa
mp
le t
est
for
a d
iffer
ence
bet
wee
n
two
pro
po
rtio
ns
12
34
56
7C
ou
rse 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
71
23
45
67
12
34
56
78
910
● ● ● ● ●
●Fo
cus
+C
on
nec
tio
ns
18 C P M P S c o p e a n d S e q u e n c e
GE
OM
ET
RY
AN
D T
RIG
ON
OM
ET
RY
Th
ree-d
imen
sio
nal
Sh
ap
es
Reg
ula
r (P
lato
nic
) so
lids
Rig
ht
po
lyg
on
al p
rism
s an
d p
yram
ids
Co
nes
an
d c
ylin
der
s
Ske
tch
ing
sh
apes
Rig
idit
y
Bila
tera
l sym
met
ry
Cro
ss s
ecti
on
s
Co
nto
ur
dia
gra
ms
Su
rfac
es
Su
rfac
es o
f re
volu
tio
n
Cyl
ind
rica
l su
rfac
es
Tw
o-d
imen
sio
nal
Sh
ap
es
Def
init
ion
s o
f p
oly
go
ns
Cha
ract
eris
tics
of p
olyg
ons
and
spec
ial q
uadr
ilate
rals
Bila
tera
l an
d r
ota
tio
nal
sym
met
ry
Tran
slat
ion
al s
ymm
etry
An
gle
su
ms
of
po
lyg
on
s
Tess
ella
tio
ns
Co
ng
ruen
ce
Pro
per
ties
of
par
alle
log
ram
s
Sim
ilari
ty
Mo
del
ing
pla
ne
shap
es w
ith
co
ord
inat
es
Tria
ng
ula
r an
d q
uad
rila
tera
l lin
kag
es
Measu
res
Are
a
Peri
met
er
Pyt
hag
ore
an T
heo
rem
Volu
me
Su
rfac
e ar
ea
Rad
ian
an
d d
egre
e m
easu
re
An
gu
lar
velo
city
Lin
ear
velo
city
12
34
56
7
+● ● ● ● ● ● ● ● ● ● ● ● + +
+●
++
● ● ● ● +
Co
urs
e 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
7
+
●+
++
++
++
++
●+
●
●
+ ●
++
+● +
● ● ●
12
34
56
7
●
++
+ ●
+●
+●
++
+ ++
+
+●
++ +
+
12
34
56
78
910
+ + ● ● ● ● ● ● ●
++ +
●+
++
++
++ +
++
++
●●
●
●Fo
cus
+C
on
nec
tio
ns
C P M P S c o p e a n d S e q u e n c e 19
GE
OM
ET
RY
AN
D T
RIG
ON
OM
ET
RY
Co
ord
inate
Mo
dels
an
d G
rap
hs
Co
ord
inat
e g
rap
hs
Geo
met
ry o
f fu
nct
ion
gra
ph
s
Slo
pe
of
a lin
e
Eq
uat
ion
s o
f lin
es
Slo
pes
of
par
alle
l an
d p
erp
end
icu
lar
lines
Dis
tan
ce a
nd
mid
po
int
form
ula
s
Co
ord
inat
e re
pre
sen
tati
on
of
tran
sfo
rmat
ion
s
Co
ng
ruen
ce a
nd
sim
ilari
ty
Mat
rix
rep
rese
nta
tio
n o
f p
oly
go
ns
Co
ord
inat
e p
roo
f
Vect
ors
3-d
imen
sio
nal
co
ord
inat
e g
rap
hs
Ske
tch
ing
su
rfac
es in
3-d
imen
sio
nal
sp
ace
Eq
uat
ion
s o
f su
rfac
es
Eq
uat
ion
s o
f p
lan
es
Trac
es o
f su
rfac
es
Tra
nsfo
rmati
on
s a
nd
Sym
metr
ies
Bila
tera
l an
d r
ota
tio
nal
sym
met
ry
Frac
tals
Tran
slat
ion
al s
ymm
etry
Tess
ella
tio
ns
Str
ip p
atte
rns
Iso
met
ric
tran
sfo
rmat
ion
s
Siz
e tr
ansf
orm
atio
ns
Mat
rix
rep
rese
nta
tio
n o
f tr
ansf
orm
atio
ns
Tran
sfo
rmat
ion
of
gra
ph
s an
d f
un
ctio
n r
ule
s
Co
mp
lex
nu
mb
er o
per
atio
ns
and
tra
nsf
orm
atio
ns
12
34
56
7
●●
++
●
+●
++
● ● ● ●
++
+
Co
urs
e 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
7
++
++
●● ● ● ● ● ● +
+
+ ● ●+
●
● ++
12
34
56
7
++
● ●
++
●
++
++
●+
++
+ ++
+
●●
12
34
56
78
910
++
+● ●
++
++
++
●+
+ ++
●
●+
+● ● ● ● ● +
++
+
+●
●+
+●
●Fo
cus
+C
on
nec
tio
ns
20 C P M P S c o p e a n d S e q u e n c e
GE
OM
ET
RY
AN
D T
RIG
ON
OM
ET
RY
Tri
go
no
metr
y
Peri
od
ic c
han
ge
Tria
ng
ula
r lin
kag
es w
ith
on
e va
riab
le s
ide
Trig
onom
etric
ratio
s an
d fu
nctio
ns (s
ine,
cos
ine,
and
tang
ent)
Ind
irec
t m
easu
rem
ent
(an
gle
s an
d le
ng
ths)
Cir
cula
r an
d p
erio
dic
mo
tio
n
Peri
od
Peri
od
ic m
od
els
Trig
on
om
etri
c g
rap
hs
Rad
ian
an
d d
egre
e m
easu
re
Am
plit
ud
e
Law
of
Co
sin
es
Law
of
Sin
es
Co
mp
on
ent
anal
ysis
of
vect
ors
Inve
rse
trig
on
om
etri
c fu
nct
ion
s
Trig
on
om
etri
c id
enti
ties
Trig
on
om
etri
c ra
tio
s an
d f
un
ctio
ns
(sec
ant,
co
seca
nt,
an
d c
ota
ng
ent)
Reaso
nin
g a
nd
Pro
of
Ind
uct
ive
reas
on
ing
Co
un
tere
xam
ple
s
Ded
uct
ive
reas
on
ing
Des
ign
ing
an
d p
rog
ram
min
g a
lgo
rith
ms
Co
ord
inat
e an
d a
nal
ytic
pro
of
Syn
thet
ic p
roo
f
Ass
um
pti
on
s in
pro
of
Prin
cip
les
of
log
ic
Co
nver
se
An
gle
rel
atio
ns
for
two
inte
rsec
tin
g li
nes
An
gle
rel
atio
ns
for
thre
e in
ters
ecti
ng
lin
es
Para
llelis
m
Sim
ilari
ty c
on
dit
ion
s fo
r tr
ian
gle
s
Co
ng
ruen
ce c
on
dit
ion
s fo
r tr
ian
gle
s
Nec
essa
ry a
nd s
uffic
ient
con
ditio
ns fo
r pa
ralle
logr
ams
Geo
met
ric
con
stru
ctio
ns
Vect
or
pro
of
12
34
56
7
+
+
++
++
++
++
+ +
Co
urs
e 1
Co
urs
e 2
Co
urs
e 3
Co
urs
e 4
12
34
56
7
● ● ● ● ● ● ● ● ● ● +
++
++
++
++
++
+●
++
●+
●
12
34
56
7
+●
+ ++
●+ +
●
+●
+●
+● + ●
●●
+●
++
++
+
++
+●
++
++
+●
++
●+
●● ● ● ● ● ● ● ● ● ● ● ●
12
34
56
78
910
●●
●
++ ●
●
●●
+●
●
●+
+●
+●
●
+●
+ + ●
+● ● ●
++
++
++
++
++
++
++
++
++
+●
+ +●
●
++
++
●
●Fo
cus
+C
on
nec
tio
ns
C P M P S c o p e a n d S e q u e n c e 21
DIS
CR
ET
E M
AT
HE
MA
TIC
S
Vert
ex-E
dg
e G
rap
hs
Vert
ex-e
dg
e g
rap
h m
od
els
Dig
rap
hs
Ad
jace
ncy
mat
rice
s fo
r ve
rtex
-ed
ge
gra
ph
s
Eu
ler
pat
hs
and
cir
cuit
s
Gra
ph
co
lori
ng
Cri
tica
l pat
h a
nal
ysis
an
d P
ER
T c
har
ts
Tree
s an
d m
inim
al s
pan
nin
g t
rees
Sh
ort
est
pat
hs
Ham
ilto
nia
n p
ath
s an
d c
ircu
its
Recu
rsio
n a
nd
Ite
rati
on
Rep
rese
nta
tio
n u
sin
g t
he
wo
rds
NO
W a
nd
NE
XT
Rep
rese
nta
tio
ns
of
linea
r fu
nct
ion
s
Rep
rese
nta
tio
ns
of
exp
on
enti
al f
un
ctio
ns
Rec
urs
ion
eq
uat
ion
s (d
iffer
ence
eq
uat
ion
s)
Frac
tals
Co
mp
osi
tio
n o
f fu
nct
ion
s
Seq
uen
ces
and
ser
ies
Fun
ctio
n it
erat
ion
Fin
ite
diff
eren
ces
Fixe
d p
oin
ts
Gra
ph
ical
iter
atio
n
Matr
ices
Ad
jace
ncy
mat
rice
s fo
r ve
rtex
-ed
ge
gra
ph
s
Mat
rix
mo
del
s
Ro
w a
nd
co
lum
n s
um
s
Mat
rix
add
itio
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Sca
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mu
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Mat
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Iden
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mat
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Mat
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solu
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of
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12
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22 C P M P S c o p e a n d S e q u e n c e
DIS
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Item No. 39895 ISBN 1-57039-895-X