Glencoe Textbook 11 Pre-calculus 2023.pdf

Glencoe Textbook 11 Pre-calculus 2023.pdf

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3. PRECALCULUS

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Storedina database ar retrieval system, without the
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transmission or rosdcast for tance ering

Sendallinguites to
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ISBN: 978-0-07-664183-3
MHID:0-07-664183

Printed inthe United State of America,
1213141516 avr 2120191817

5. Contents in Brief

Chaptor 0 Preparing for Precalculus
11 Functions from a Calculus Perspective
2. Power, Polynomial, and Rational Functions.
3 Exponential and Logarithmic Functions
4 Trigonometric Functions
5 Trigonometric Identities and Equations
6. Systems of Equations and Matrices.

7 Conic Sections and Parametric Equations
8 Vectors

9 Polar Coordinates and Complex Numbers.
10 Sequences and Series

11. Inferential Statistics

12 Limits and Derivatives.

Student Handbook

6. read authors ensure thatthe MacmilavMeGraw-Hll and Glencoe McGraw
mathematics programs are uy vertical aligned by beginning wit the end in

ming-sucess in Algebra 1 and beyond. By “backnapping" the content from the high schol

Programs, al of our mathemati programs are el rte in hir scope and sequence,

Lead Authors
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7. Program Authors

> Luajean Bryan
Mathematics Teacher

Waele igh Soboot
Généland Tennessee

sd llos alto students

D Vixen Hovsepian
Professor of Mathematics
Flo Hondo Colo
Wit Calor

2009 Temes Tocher othe Yer

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8. Consultants and Reviewers

hese professionals wor instrumental in providing valuable input and
suggestions fr improving the effectiveness ofthe mathematics instruction

| Consultants

Preparation for
Advanced Placement

Eizabetn W Black
MathematesTeacter

Green Hg Sol
Greenwich, Comectia

Dido Ross
Loa Teacher for Advance Placement
amer

Plug High School

Plage Tes

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Test Preparation
Christopher Black
Drecor

Cole HN Coaching
roe, Comectut

Graphing Calculator

uth Casey

‘Patna ieuctoe
(Teachers Teaching wit Tecnology)
Franko, Kentucky

ory J. Cumming
Ferrer Present, National Couns
of Superior of Mathematics
inl nis

Jane Bray Nelson
insite

Santa Fe Colege
Gaines, ona

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‘Sara Fe Cage
Gane, Fos
Pre-Engineering
Coes Baine
Spiel, Oregon

‘redo, Sldavin PE.
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Apart, Georgia

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Penelope Sather
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10. reparing for Precalculus

et Started on Chapter O re

=Protest a
1 Sets Ps
0-2 Operations with Complex Numbers Po
0-3 Quadratic Functions and Equations Po
0-4 nth Roots and Real Exponents pa
0-5 Systems of Linear Equations and Inequalities Pie
0-6 Matrix Operations Ps
0-7 Probability with Permutations and Combinations pa
0-8 Statistics P32

= Posttest Pa

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11. Calculus Perspective

Get Ready for Chapter 1

14

12

13

14

15

15

17

Functions
‘Analyzing Graphs of Functions and Relations.
Continuity, End Behavior, and Limits
Extrema and Average Rates of Change

‘= Mid-Chapter Quiz

Parent Functions and Transformations
{Extent Graphing Technology Lab Nonlinear inequalities

Function Operations and Composition of Functions

Inverso Relations and Functions
{extent Graphing Tecnology Lab Casi eres sng Parable Equations

ASSESSMENT
Study Guide and Review

Practice Test

= Connect to AP Calculus: Rate of Change at a Point

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12. Power, Polynom

al
and Rational Functions

Gt Ready for Chapter 2 a
2-1. Power and Radical Functions %
Explore: Graphing Technology Lab Behavior of Graphs %
2-2 Polynomial Functions. ”
RR Extend: Graphing Technology Lab Hidden Behavior of Graphs 108
2-3 The Remainder and Factor Theorems 109
= Mid-Chapter Quiz ms
2-4. Zeros of Polynomial Functions me
2-5. Rational Functions. 190
2-6 Nonlinear inequalities 141
ASSESSMENT
‘= Study Guide and Review 18
Practico Test 1
‘= Connect to AP Calculus: Area Under a Curve 154

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13. Exponential and

Logarithmic Functions

Get Ready for Chapter 3 158
3-1 Exponential Functions 158
il Extend: Graphing Technology Lab Financial Literacy: Exponential Funct 170
3-2 Logarithmic Functions m
3-3. Properties of Logarithms 181
‘= Mid-Chapter Quiz 19
3-4. Exponential and Logarithmic Equations 190
Eten: Graphing Technology Lab Exponent and Logic Inequalities 1988
3-5 Modeling with Nonlinear Regression 200
ASSESSMENT
Study Guide and Review au
Practice Test as
2 Connect to AP Calculus: Approximating Rates of Change 216

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14. Trigonometric Functions

et Ready Cater
4-1. Right Triangle Trigonometry
4-2. Degrees and Radans
143 Tigonomet Functions onthe Uni Cirle
Be: raping Technology ab Graig Se Fun Parma
4-4 Graphing Sine and Cosine Functions
{ten Groping Tetolgy Lab Sons nd Direc! Sis
‘Mi. chapter Quiz
4-5 Graphing Other Trigonometric Functions

46 Inverse Trigonometric Functions.

22 ee eee 8383

4-7. The Law of Sines and the Law of Cosines.

ASSESSMENT
‘= Study Guide and Review

1m Practice Test

+ Connect to AP Calculus: Related Rates

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15. Get Ready for Chapter 5
5-1. Trigonometric Identities

5-2 Verifying Tigonometric Identities

5-3. Solving Trigonometric Equations.
fl Extend: Graphing Technology Lab Solving Tigon

Inequalities
‘= Mid-Chapter Quiz

5-4 Sum and Difference Identities
A Eten: Graphing Technology Lab Red

dents

5-5. Multiple-Angle and Product-to-Sum Identities,

ASSESSMENT
Study Guide and Review

Practice Test

"= Connect to AP Calculus: Rate of Change for Sine and Cosine

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16. ystems of Equations

ind Matrices

‘Get Ready for Chapter 6
6-1. Multivariable Linear Systems and Row Operations

6-2. Matrix Multiplication, Inverses, and Determinants,
[Extend Graphing Technology Lab Determinants and vas of Polygons

6-3. Solving Linear Systems Using Inverses and Cramer's Rule
Il Extend:Graphing Technology Lab Matices and Crypoarety

= Mid-Chapter Quiz
6-4. Partial Fractions
6-5 Linear Optimization

ASSESSMENT
Study Guide and Review

Practice Test

+ Connect to AP Calculus: Nonlinear Optimization

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17. onic Sections and

Parametric Equations

Get Ready for Chapter 7
7-1 Parabolas
7-2. Elipses and Circles
7-3 Hyperbolas
‘= Mid-Chapter Quiz
7-4. Rotations of Conic Sections
fl Extend: Graphing Technology Lab Systems of Nonlinear Equations

7-5. Parametric Equations
[Extend Graphing Technology Lab Moding wih Parameti Equations

ASSESSMENT
Study Guide and Review

= Practice Test

‘= Connect to AP Calculus: Solids of Revolution

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18. ‘Get Ready for Chapter 8
8-1. Introduction to Vectors

8-2. Vectors in the Coordinate Plane
8-3 Dot Products and Vector Projections
‘= Mid-Chapter Quiz

8-4 Vectors in Three-Dimensional Space
Resten Graphing Tecnology Lab Yeo Tersomatan Matic

8-5 Dot and Cross Products of Vectors in Space

ASSESSMENT
‘= Study Guide and Review

1m Practice Test

‘= Connect to AP Calculus: Vector Fields.

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19. olar Coordinates and

complex Numbers

Get Ready for Chapter 9
9-1. Polar Coordinates,

Explore: Graphing Technology Lab lnvesigate Graphs of Polar Equations
9-2. Graphs of Polar Equations

9-3. Polar and Rectangular Forms of Equations
‘= Mid-Chapter Quiz
9-4. Polar Forms of Conic Sections

9-5 Complex Numbers and DeMoivre's Theorem

ASSESSMENT
Study Guide and Review

Practice Test

2 Connect to AP Calculus: Arc Length

20. ‘Get Ready for Chapter 10
10-1 Sequences, Seres, and Sigma Notation

10-2 Arithmetic Sequences and Series

10-3 Geometric Sequences and Series
Estena: Graphing Technology Lab Continued Fractions

‘= Mid-Chapter Quiz
10-4 Mathematical Induction
10-5 The Binomial Theorem

10-8 Functions as infinite Series
L Estena: Spreadsheet Lab Detectng Paton in Data

ASSESSMENT
Study Guide and Review

= Practice Test

‘= Connect to AP Calculus: Riemann Sum

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21. Get Ready for Chapter 11

11-1 Descriptive Statistics ss
11-2 Probability Distributions: 654
11-3 The Normal Distribution om
{fg Extend: Graphing Technology Lab Transforming Skewed Data 5
11-4 The Central Limit Theorem us
‘= Mid-Chapter Quiz 695,
11-5 Confidence intervals C1
11-8 Hypothesis Testing m
11-7 Correlation and Linear Regression ns
fl Extend: Graphing Technology Lab Median-Ft Lines Ta
ASSESSMENT
Study Guide and Review 7
= Practice Test Ta
2 Connect to AP Calculus: Population Proportions m

22. its and Derivatives

‘Get Ready for Chapter 12
12-1 Estimating Limits Graphically

a

12-2 Evaluating Limits Algebraicaly 7

Explore: Graphing Technology Lab The Slope of a Curve
12-3 Tangent Lines and Velocity

‘= Mid-Chapter Quiz
12-4 Derivatives.

12-5 Area Under a Curve and Integration

23 a à aa

12-8 The Fundamental Theorem of Calculus

ASSESSMENT
‘= Study Guide and Review

‘= Practice Test

2 Connect to AP Calculus: The Chain Rule

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23. Student Handbook

Reterence
Key Concepts m
Selected Answers and Solutions Re
SGlossary/Glosario ord
Index am
‘Tigonometrc Functions and Identities Inside Back Cover
Formulas Inside Back Cover
Symbols Inside Back Cover

24. Preparing for Precalculus

th L

Chapter 0 lessons on

You can use this chapter in various ways.

+ Begin the schoo! year by taking the Pretest. you need
_adaitional review, complete the lessons in this chapter. T
very that you have successfully reviewed the topics, take

+ As you work trough the tx, you may ind that there are
topics you need to review. When ths happens, complete the
individual lessons that you need.

+ Use this chapter or reference, When you have questions

about any ofthese topics, Ml back o this chapter o review
‘definitions or key concepts.

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25. Get Started on the Chapter

You wl review several new concepts, ki, and vocabulary terms as you study
Chapter 0, To get read, identity important terms and organize your resources.

Pretest r
01 Sets rs
2. Operations wih Complex Numbers rs
03 uadrat Func and Equations mo
04 FA Roos ad Real Spore cn
05 Systems of near Eunos an equalities me
06. Mat Operations rs
(0-7 Probab with Permutations and Combinations mas
08 States Pee
Postes LA
ReviewVocabulary
Engl Español completa the square p.PI2 completo e cuadrado
Set ps canto oot p.PI4 rizenésina
lament 9.3 elemento Principal rot_p. P14 ral prnchal
subset p.P3 scout stom of quae. p. PIB. sitema de ecuaciones
unies set .P3 conto universal substvion method. p.P18. mé de ustución
complement _ p.FS complemento liminaton meted P18. método de elminación
‘wien Pd unn at p.P23 mata
Inerscion PA interacción Gioment p.P23 elemento
empty st p.P4 conjunto vacio mension p.F23 dimensión
‘imaginary nt p.PS unas imagino cexperinent 9.728 experiment
complex number p.PB nümer complejo cal 9.28 factorial,
standard form _p.PB toma sind pemutaton . 29. pemutacén
Imaginary number p. PB mero imaginario combination p. P30 combinación
complexcojugates p.P7 conugados comple measure of central p.PS2 media de tendencia
pare p.PD. paroi tendency canal
ais ot symmety 9.8 je de sim measures of spread. 32. mecs de propagación
verter p.P9 vico equenc iu p. POM drin e trecuencis

EAS Pr

26. ‘se sentation ren ements of ach st The determine
‘wheter Da statement bet ste ture fa.

1 Liste atout number tes lat ae ls 22.
mel

2. sist ligues at res an ut grata an 6,
“tes

LG 0.1.25.0, 0" 8,5 7.8,6= 101,

Find echte ala.
a one acne

$ cor © Due

Samy.

REM INM
a 0er 10 (-34 3-242
CEA

temo wheter nc ton maimam minim a.
Tre ra vl fe nu rim, st te Coan

and ga le acta.
“ge
CEE TS
7
Sao e equation,
Brno 188-4500
mer PERTE

18. CARS Tucan val Vans og voa rare
rad y V= vt A vr gr pt
yaa iste bef arse ral veo cari
10000 wat wade ret ae ot cater 30

‘mts tan rus pecan 1047
Simply cach reson

a PF a ea
2 VER a ae

PES

nd

2 (nar
5 sa
a (a ne

2% J08S est mon ws tr Sar o ad wees gres o
510 pagare. se hat js a mae $72, Pow mary le
rec mowing? How many wre edo?

‘sav each stem of equations Ste meter artes

‘avo ec system ot nog te system as no sohn, ee
moin.

Byers Myers
yom? pas

Buyer esas
aies rie

mor mor me
Moe DORE DDE
Fd ac parution or comia.

LEA CA ah
ae me “a

48. CARS Tee rd ro nto un ama and ck
52 ut. Fd each po,

Palen)
De Pwo cian ea

Fd tho mean median, and mudo or each sto! ala Tan go
rame vir, and standard devon each pop

a (7,7,810,10,10 51. (05,04,02,05,02)

27. A 50 Moaton asia con Each in at cl an ment Ast
‘ae using cop otr an is write with ts lent sed within braces (

o [mmomeoms | Cm 05,989 28904)
4 | en mde ao | A= e re)
Tet AH Lenacderen

ETA LETEEKZAIKEEEN

re that Olinda an men of set, write Olinda A.

‘Ure set notation to write the elements of ech ee. Then determine whether the statement
about the set ru al.
2 Nisthe se of whole numbers greater han 12 and less than 16.18 € N

‘The clement in this et ar 13, 14, an 15,0 N = (13, 14,15), Because 15 an clement of
NAS Visa tue statement

1. Visthesetofvowels.g€ Y

‘The lement in is stare the tes 3, and w 50 V = [eLo ul. Because the ter
shot an clement of Y, a core statement sg € V Therefore, € Visa alo statement.

€: Mis the set of months that begin with. April € M
“The lement nh stare the months January June, and July so M = January June, fly.
Because the month of Apis not an clement a thst a correct statement is Apr € M
‘Therefore Apa € Misa alse statement

4 Xiethesetof numbers on adie. 4€ X

‘The elements in thinset ar 1,2,3,4,5,and 6,20 X= (12,3,
of FEN ate statement.

6). Because isan element

very clement fs is cnt ise he Bical ub oA an writen as
BEA The nivel et sth set ofall POS element for aston Allee soins
Suton are bc ofthe ner et

‘Suppose A =(0,1,2,3,45,6,7,8] and B= (1,23) Becuse 1 € 4,2 À and 3 A, BCA,

“Tho ot of elements in Uthat ae not clement fet called the complement of Bands wien.
8 nthe Venn diagram, the complement of all he shaded repos,

ag

28. EJ J
A

E
a

se
SE
Seen:
at

GB re mono 1508

Let U=(0,1,2,3,4,5 6,78 91,A=U1,45,7,8,91.8=(5,71,C=11,5,7,8,D= 2,3,
raten

a. State whether BC Als treo false.
5-67 1.457,89

True 5 € À and7 € A, soallof he cements of
into.

also elements of A. Therefore, Bisa

1 State whether C Dis true ole.
PSA] D=23
Fake € D,sonatallof he clement o re n D. Therefore, Eis nota subset of D.

Find at
et he clement of that ar notin A

ALES — U=V1234567,89

SA = 02,361.
4 Bo
ef the clement of Uthat are not in D.
D=23 U-012345.62.89

So.0'=/01,4,5,67,89.

Unions and intersections The union of sets A and E weten À U Bla new et
conseting ofall ofthe clement hat ae in either À or 8 The intersection of sts À and B,
‘writen À Bla new st contin of ment found in A and BI two ses have o elements
in common, thei Intersecin is called the empty et and is writen as 2 or ()

Let 12,345,657 8, R= (4,6) 5=4,5,6,7.and T=)

a Find RUS, 7
‘The union of Rand isthe set ofl elements a
bat belong 5, orto both sets.

So RUS= 245,671 ©

D Find ens. m
"The interscction of Rand he set fall A
lens found in both Rand 5.

SRS =(46. (‘)

e Find Tas.

‘Because there ae no elements that belong to both Tand $, he intersection of and Sis the
empty set 0,75 = 2.

29. Exercises

Use set notation to weite the elements ofeach se. Then
determine whether the statement about the sti trac or
false ro 1

1. [isthe set of whole number multiples ofthat are ess
than 5.15 €7

2. Kistheset of consonant eters in the English alphabet
hex

3. Lis these ofthe tai prime numbers. 9 € L

Vis the set of states inthe US, that border Georg
Alabama EV

[isthe et of natural numbers ss than 12.0 € N
Dis e ot ol days that start with. Sunday € D
A the et of ies ames that star with Ashley € A

‘athe set ofthe 48 continental states in he US.
Hawaii eS

For Exercises 9-24 use the following Informati
1eU=10,12,3,4.5,67,8,9,10-1, 12),
A=01,2.6,,10,12, B=(2 9,10, C=(0,1,6,9, 10),
D=0,5,10,E=0,3,6Land F= 029

Determine whether cach statement i tr ofl. Explain
yourresoning

aseD mera
M BcA ruca
1 sep mer
10er ser

Find each of the following, Bann 29

mo mu
mx mm DnE
a cor bur
zu Aus 2 408

‘Use the Ven diagram to find eh ofthe folowing,
Gamez,

2400 2 AnD
m. cup ar
2 Anann a aunuc

(Oros Seen des in Me Frans gym cls ech
Patti on cor spre as shown ne
thle es

a. LetB represent he set of basketball players, 5
represent the st of soccer player and V represent the
Sof volybal players Draw Wenn diagram of is
ut.

1 Find SV. What docs this set represent?

{Find What docs his et represent?

Find BUY. What docs this set represent?

32. ACADEMOS There are 26 students at West High School
tho take either calls or phys or bath, Each student
À represented by eter of the alphabet blow. Dawa
Ven dira ol his station es 200,

8 BEVERAGES Suppose you an set jul fom tree
possible Kids: appl, range, o rape or you can select
“soda from two possible nds, rand Ar Brand BI
ou an chow a ule ov soda t drink according othe
‘dalton Principe of Counting you have3 + 2005
possible choles Using notation that you have learned in
thislesson justify dhs result In what situation could tis
principle nt be applied?

GEOMETRY Use the figure to find the simplest name foreach
ofthe following.

a DEN = Hum
m DEDO 37 Inenninep
ma Men mn FU

Eu

30. ‘Operations with Complex Numbers

Imaginary and Complex Numbers The imaginary unit jis defined as the principal
une ot fT and cane writen a= YT. Te it ia power ofa shown bot
ts camer Be

ceo wie

[Notice thatthe pattern 1, 1,1. repens after he st fou sul In general the value of,
‘where sa whole number canbe found by dividing by and examining the render

a NewWocabuary [Keyconcept Powers of]

mag it “oma Rb een na

compe mbr

sm no mo
regar Dern CE
ana part

may mer Berre Aare
re agar number a en

aeons Amor

Simply

Sums leal numbers and real number multiples o belong to an extended syste number,
Snow a compl numbers À complex number sa number hat cn be wate nthe standard
form a +, where he el number sth el pat and the rel number isthe imaginary part.

Xa an 0 he comple mbes +0, pation
brea numb Thera mane a
compe nantes 1 the ea

Per SERRES

iam 0and Ducs or complex >
number is a pure imaginary number.

31. TechnologyTip
Cai mtr some
alten cir
‘ent no he ot ey
nem enden unse,

WatchOut!
amis rs Mae re
EE
a at cn

amb fede cat

‘Complex numbers canbe added and subtracted by performing the chosen operation o the reat
and imaginary parts separately.

Simpify
a 6-30+ 62440

B= 4(-2+ MAH D+ (3144) cop uam pre

Er Sos

à 0020-04-60

A ECC
er] Son

Many properties of real numbers, such as th Distributive Property are lo valid for complex
numbers. Because o is, complex number can be mulipl using similar techniques to hose
thatare used chen multiplying binomial

Simpify
Aia 12?

@-s0-49
2-390 40
PARTS)

a
Bars
(64594 50-16-2040 - 20
16-3
=n

D use Complex Conjugates Two comple nantn ofthe oma + ande „ae

“Complet outs cn be un Latina an mag
denominater. MAS te numero andthe denominator bythe comple cong of he
‘Senin

32. Exercises

Simplify. =)
Lee aes
ame um
sr ann
1.040 ae
Simplify. Er

8 6+29+(-4+69

1 7-4) 42-39
m. 05+9-2-9
2 ao 4-9
rum (1-639
Hart CoH)
18 (2449 +6-49
16 6+70=(-5+0

1, ELECTRICITY Engineers use imaginary number to expres
he wo dimensional quant ofaltemating current,
‘which involves bot ampltude and ange I these
Imaginary numbers is replaced with because engineers
se as a variable forthe etre quantity of cunt.
Impala te mexsur of how much hinderance there
{tothe low of the charge ina dat with ltemating
‘trent, Te impedanos In one par ol seres Grout
24 3 ohms and th impedanes in another par oh
cat 67.3 ohms, Add hese complex number to find
elta mpedane in he cet 0000

Simplify. Er
wer war
am mor

z armen 2 0400-0
a 6+502+60 2 (6470067
Simplify. fa)

ED re eno | onen compi une

FAECTNCITY The voltage E, current and impedance Zin à
ru ar related by E= 1-2 Find ie voltage in voll) in
‘acho the following circuits given the current and
Impedance.

114 Jam, 2=7- Goh

35 192 amp, Z=4- ohms

3% 1=5—sjamps,2=3+ 2) ohms

3. 1234 10jamps, 226 john

Solve each equation.

a s+se0 ÉRIC EN
m 2412-0 a +720
ae seno 43 32450720

{A ELECTROTY Theimpedance Zo circuit depends onthe
resistance R the eaciance due to capacita Xe and the
‘eacancedueto inductance Xy and can be wen sa
complex number R + (X= XT values in chins) for
[Xe and Xy in the stand second parts fa particular
ei ru ae shown.

Series Creuit

nx] A

1 Wit complex numbers hat represent he impedances
Inthe wo parts ofthe creat

1. Ada your answers from port ato find the ta
impedance inthe creat

+. Tie admin Sofa circus the measur of how ely
(he ir allows cuento low and ithe recprocs of
Impedance Find the admitance (in semens) ina cu
an impedance of 6+ Sahne.

Find values of x andy to make each equation tre.
MARGA 46 Sete 6
DEEE SH = 10-94
DEEE Te

Simple
SL @= ns +290 40

82 (1-30 200 -29
ae
CRETE TE)

33. Quadratic Functions and Equations

1 rap Quadra Functions he pho qual mt lt pl
rap a qundr funcion, graph ordered pairs at sty the funcion

TI choose integer values for xa evaluate te function foreach value

(Gy Newvocabuiary a +4 | ne | o
pa ol rames | à
ss 10-20-00
en + means [=
Ste ten 2] rosas
conga e sure OCT EE:
AS romana

IE Graph teresting coordinate pais and connect he points with a smooth curve

poes
vil

"The ais ofsymmety sine ha divide the parabola nto two
halves that are reflectons ofeach other Notice hat because the
parabola it symmetric about he aio symmetry points Band C
reunite the socoondinat of the vertex, and ey have te
Sime ycoordiate

‘The axis of symmetry intersects parabin at point called the
‘vertex The vertex ofthe graph at the rights AG, D.

KeyConcept Graph ofa Quadratic Function

Cone a+
Écrits

"Terms + cm.
+ Pesa

34. Use the axis of symmetry, yrintercept, and vertex to graph fl
BIE] Determine a, b, and c.

armée

$f | — orme.
ponte

TR Vue and 0 ind the equation ofthe axis of symmetry.
etn tt oy

FERRO sonst yee
fat Sms
The verte sat (2,4)

ED Find te intercepta it rection.
Because cm ~3, the condiates ofthe ynterept
am O3) The aus of symmetry is = 1, so the
rein ofthe intercepts (2,3)

Study ip | EEE Graph the axis of symmetry, vertex interop and its
eee eco ‘ection Fin nd raph ono mor ana pais
on ana e nthe flection: Ten coma he pints witha
pee meee Snooth curve.

Permanente

Een
ce

Mies]

4

"The y-cordiate ofthe vertex ofa qudrai funtion th maximum or minimum eau ofthe
faction. These valu represent the grt or east posible val that the function cn eh.

KeyConcep! Maximum and Minimum Vales

Dean maf + br cota po
2 ete ha mm nen a > 0,0

ine
wy
we
a romero eee 1e pan nee Pe
Lee re

ID] Pro | 1ssono | Quadra funcions and équations

35. “The domain of» quadratic function all ral numbers. Te ange will cre al el numbers
les than o galt he maximum vlc oral al numbers gente han or qual o the minimum
value

‘studyTip \
ah ?| Considers = + 120-411.

encens | | a Determine whether the function has a maximum or minime value

ani ot

Chers Forts function, = ~3. Because a negative, he graph opens down and to function has a

daa]

Find the maximum or minimum value ofthe function.

‘The maximum value the function i the coordinate of he vertex. To find ie cordiates
‘ofthe vertex fist find the equation ofthe aus osymumery.

a+ Coctel nero

Sty
Lopilato brida Because ih equation of the ai of sentry is = 2, he coodiat ofthe verte is? You
Any 2 bcos ‘ean now find the coordinate ofthe vertex, or maximum value the function by evaluating
Here he orginal function for = 2
uE AD= + 12+ ot

f2)= 307+ 20411 a2

masa ty

i
Tieren, fi) has a maximum value 25

+. State the domain and range ofthe función.

“The domain ofthe function al el numbers or. The range ofthe function al ral
numbers les than or equal to th maximum value 23 0ry = 23

Solve Quadratic Equations quad eaten otomí oque of degre
The standard form of quadratic equation sex" + br + ¢=0, where #0. The factors af
_quadatic polynomial cn be used to solve the red quadratic equation. Solving quadratic
‘uations by factoring Ian application ofthe Zero Product Property.

KoyConcept Zero Product Property

Fu ant = ar =, rh an Dean

Solves? —8r+12=0by factoring.

Resto Ouen

2-00 Fc

2220 of 2-620 amor
xe? zus soy

‘The solutions ofthe equation ae and 6.

36. Another method fr solving quadeai equations io complete the square.

oytoncopt, Conte the Sue ]

ms te sa y u ers em + low pa,
EOE rar a pecera

ETE son vertes.

ET AS

oa Solves? Ar + 12 0 by completing the square.
Contig Sane Wan Giga

‘ocr ear. ae at ot ie mb
a mat aereas

E (3)
a) ia mel atu

roza Yi or m2 VÍ tre.
=37 027 rca

“me solutions ofthe equation ae approimaey 027 and 373

Completing the square canbe used to develop a neral formula that an be used to save any
drain of the form a + br +e 0, now a the

KeyConcept Quadrate Formula ]

aa ac atin el a om a+ Bi 0 hey em

r Solver? -Ar+15=0by using the Quadratic Formula.

Erz Out om

coe a = ‘Replace ami, beth 4, and c wth 15
„ua u
„u u
„ad VAN Te
-22/m sms,

"The sohtions are 2 + ViTiand 2 - VIT.

PAZ | Lesson 03 | Quadratic Function and Equations

37. Exercises

(Graph exch equation by making able of values.)
1 feet +546 2m
a potes um
amer-ı-e um

7. BASEBALL A ater its a baba wit an ia sped of
0 fot per second Ihe nil high ofthe all 35 fet
above the ground, he funtion d() = 8 — 162 +35,
‘model the bals height above the ground in fetas a
Function a ine in seconds. Graph he function wang
table of valves Samos)

Use the ans of yecto y intercepta vertex to graph
each Fenton, 12

CESSE ete
Were TE
A m Were

14. HEALTH The normal systolic pressure Pin milmeters
‘of mercury (mm Hg) fora woman can be modeled by
i) = 0012? + 005% + 107, where is age in years.
ama
Find the axis of symmetry, yinterept, and vertex for

the graph of Pt

1. Graph te) ing the values you ound in part +

Determine whether each function has a masimu oF
mime value. Then ind the value ofthe maximum or
minimum and state the domain and range ofthe
Function. En

6

M fn tas A
Wer E
NN

Solve each equation by factoring. Bro
2 pp 5=0
2 Aw? + 190-540
maires 248 -16-0

Solve each equation by completing the square. Ko

Murten MARIO
a Pate 2 p-y-9-o
@:-:-7-0 ae

Solve each equation by using the Quadratic Formula.
Gares

A)
m. Hm = m 8-549=
ma ato o are

A1: PHOTOGRAPHY Jocelyn wants o frame a
photograph that has a are of 20 square inches with
trflorm width of mating between te Photograph and
the edge ofthe ame as shown.

EI

‘Write an equation to model he situation the length
nd width ofthe mating must be inches By 10
Inches, spectively to iti the tame

Graph the related function.

Whats the with ofthe exposed part ofthe matting x?

Solve each equation
45-690 eto no
Mimo Meine
Me AmO 74320

M F-44720 0 w+ 6-30

MR. PETS A rectangular turtle pens fet ong by 4 et wide
“The penis enlarge by increasing the length and ith
y a equal amount inorder to double its area What are
the dimensions ofthe new pen?

DUMBER THEORY Use a quadratic equation to find two real
‘numbers tht satisfy each situation or show that no such
umber exist

1. Their sum is ~17 and thei produc 172.
82 Their sum i7 and thei products 4.

$2 Their sum is -9and thei product 24
BR Their sum is 12and her products 28.

==> + Y

38. Objective

QD rie mms

nth Roots and Real Exponents

1 Samy Radical sure oa number og fo qual cam of at nan
Forexample, dis square root of 16 because for 4 = 16 ln general a nd bare eal,
numbers and a positive integer greater han LE" = a, then an mh tot of

KoyConcept ath Root of a Number.

Lat er ma ae per a

Premiers
+ Hanan tapé ot a ag ne gs
‘opi el ai et by ea ees Y wee ls nl erase is rc

Some examples of th roots are sed below

vis recta een et
MT asco pr a pn ar

A AUT sen nannte

‘Whether a adil expression has postive and/or nativ rot is dependent upon the value o he
radican and whether the index seven oo

E
cria
ac | oras De ae a
EEE IA

‘Because thee korea number hat can be rise tothe fouth power to produce 121,
{FIAT isnot a al number

39. Study Tip
ese Malo a à
‘yee ee Ten,

‘Sear a ee

Koyconcept Basie Properties of Radicals

ut aan Dal be ete a pre, neste ie gra Bn wen tl oro
ele dat ele cesos gr an Ter Pe one ps e

Proc VV

cnr fe

When you find an even rot ofan even power an the results an dd power, you must use the
aboot value ofthe result o ensure that the answers nonnative

AS
Simply
ar

Wa fahr

Note that? ia ich rot of Because the inde is even and the exponent is dd, you
must use the abra val of?

coe

(iar

E
=

cause the indes even and the exponent is dd, yo must use the absolute alu of
ar

er
nn

Notice that VER soy a ral number when y nonneative. Therefore its not necessary
une able vac

PE
ee

Because the index sod ts not necessary tous absolute vale,

Ga "a

40. sity
tearm n

isch

So, VB = This process can be usd 1 determine the exponential form for any ih oot. You an
‘termine oponen! om or ay ih ot ng Da propa shown blo.

KeyConcept Rational Exponents ]
Dar RCA SAT mp tm ne pte pe gr a, on
+ he Si tie rra rm tt Dx a

DETTES

Aa

4
dios

4
watt centre
athe VE Sn

ET

IND] Pte | esson 0. | min Roots and al Exponents

41. rate on)
„va 2 vom
E «E
sv CAT
ve av
Simpy emma
CRETE LAIT
nor PA
1 Var hzie = 2"
ar DE
Simpy m
ma a faba)
10 CT a VER
a 2%

2A. BOATING The motion comfort ratio M fa out given by
Me — 2,

asser +038)

here Disthe water displacement of the boat in pounds,

Bistheboat'sbeam or id et, Wisthe bat

length in fet atthe watering and À she bout overall

length infect The higher the rato, the greater the evel

‘of comfort experienced by those onboard as the boat

‘encounters waves. =e")

“a. Find the mation comfort rato of the boat shown,

— a

la. Find the beam ofa oat othe nearest fot with a
‘comfort ratio of 27 that displaces 15,000 pounds of
‘water has a watertine length of 304 fet and an
verle of 323 fc

24 CARS Te value fa car deprcates or decines over
Ihe cour oft useful e The new value Vand the
Orginal value ofa car are elated bythe formula
Vs oft ~ 1) where ris the ate of deprecation per
year ands the number af years Suppose the current
Value of use car $12000 What would be te value
‘ofthe car after 8 months atan anna deprecation ate
Ss

value
mad a
mt ayi

28. MUSIC The not progression of the welv tone sales
‘comprised of a sel of half tones In order for an
instrument be “in tune” the frequency of each note has.
an optimum rato with the frequency of mide, called
the perfect Is

mass

he optimum frequency rir, xpd a dec,
can becalaated using = (YA)? here e the amber
‘otha ones the note above tr perfect It. nung
thenateiel.

2: Approximate the optimum frequency rato ofthe
‘idle with he perfect Ist,

1. Without the ue of cleus approximate the
‘optimum frequency rato of the perfect th and the
eset It Jat your answer.

Simply.
Rn a Ve
a ae O (7
a VE a (A

EE "Y

42. tens lun.
Save tens of

Systems of Linear Equations
and Inequalities

Systems of Equations A system of equations is a set of wo or moe equations. To sl a

System of equations means to ind values forthe variables nthe equations hat make al ofthe
“uations tre. One way to solve a system of equations by graphing the equations on the same
‘ordinate plane. The pont of intersection ofthe grap ofthe equations represents the solution of
esse

‘Solve the system of equations by graphing.

‘Te ins inersct at he point (-2, 0). This ordered
aire the solution of estem.

EK amm na et
32-20 2-6 CETTE
Ber ‘so av

Algebraic methods are used to find exact solutions of systems of equations, One algebra method
{scaled the substitution method,

KoyConcept Substitution Method

BETH sore ogro ets ms ee:
‘Samat psn tn Sp st cbr tints nin not te Ten Be
Ces

{Use substitution to sole the system of equations.

240929
sin
ER s-:
pus
zu mm
EE vun seo tein
50)-MoeTheslton 80,2)

CHECK From he graph in Figure. 1, you can see thatthe ins intersect at the point G, 1)

43. You can use the elimination method 10 solve a system when one ofthe variables has the same
ofen in both uations.

‘KeyConcept Elimination Method

EEE me ew rtm antares es in cp
ET san egos enti cn rte on or eaten
EH sou oso recreate,

‘Use elimination to solve the system of equations.
15042920,
20-802

> 1
Wtenout D 200-2 BEER Mi

lon Armee wen yo A
neo x tc 12
Sema rg

‘onan ert sry Gent

== 150) +2y=20 cos

y-7 see

he soon 4,7.

You can we any of the methods or combination of the methods for solving systems of equations
in wo vas ske systems of uation in use variable

Solve the system of equations.

paises
COCA]
EN ere
Studyrip À BEI mime one var by using wo pis of equations
ne es cst res PE
nc es (presse IO Asi comme
Poston iene Kern m nm
en 18 m
=
ET Solve the system of two equations.
MZ cenamos
a
e hates

[BE substitute th two values int one at original uations oid
ty $2215 Goat!
SADA eta
203 Sites
The solutions, -2.3).

a] " Q

44. ‘StudyTip

Gras opens fanaa
rr
e re

‘The graphs of two equations do not always intesetat one pont. For example, system ficar
equations could contain parallel ines rte same ine In these css, system ol equations may

ave no sautonorinitely many solutions A stem has test one solution. thee
say one solution, the sytem a there ar int many solutions Ie stem
E here no solution, the y str inconsistent.

reese Dre) LUS
ra lp veut

e E E

Tee ES co

oo coo ronan

‘Solve each system of equations State whether the system i consistent and independent,
consistent and dependent o consistent.
ant

mayer

yen mi
pay =17
o

‘Because O 38 nota hs system has mo solution Therefore estem is inconsistent,
nd the equations in the system ae paral ines, as shown in Figure 032.

bartyen
ayas
Bor+ fy =48 tae
(hoe + y= 48)
0-0
Because D = Os always rc, there are an infinite numberof solutions. Therefor the system

As consent and dependent andthe equations in he system ave the ame graph, as shown,
in Figur 053.

Fun 052

pap lon | ns tun eons annus

45. D Systems of inequalities saving sytem of Ineualis mear fining al of te
ordered pie that satisfy the inequalities the system

KoyConcept Sahing Systems of Inequalities

E cre nay stag Da rc U ai gs aan > na
‘Sete gn rates nn >

E sey mnt a e Te wen ete.
TE omer ston o ii tg.

Solve the system o inequalities,
yzase-3
yee?

BEM Graph och inequality.
Use solid inet raph ach inegualiy since each
‘contain either = oF = Then hade the rien eher.
‘ove or below then that contains the coordinates
‘hat mate each inequality tue

ST ent the ego that is shaded foal ofthe
Inequalities.

‘The solution fy 2 051 is Regions Land 3.
"The solution ol y -2r + 7Ís Regions 2and 3.

Region 3 s part ofthe solution of bth inequalities, sot
{nthe solution ofthe system.

(CHECK You can use ts point fom the solution region to check your solution.
Seite Ihe and rales ofthe test point no the neues,

Y20S-3 y<-2+7
0205-3 02-20+7
ona sty

When the regions do na intersect, the system has no solution. Tht the solution sets the
empty set

Solve the system of inequalities,
years

eared

(Graph each ine and shade he egin ether above oe
below the ine hat makes he naar.

‘The solution of y <r ~ 8s Region L

‘The soliton ofy> 3x + is Region 2

>] cause the graphs ofthe inequalie donot overlap,
there aren pots in comman and theres 0 solution
to system

46. ses

Solve each system of equation by graphing, u)

DPEPES Bynes
yrnats. vase

area ayes
ar-y=10 es

Deren Qs
Best free

{Use substitution to solve each system of equations.
Ce

2 50-y=16
243

BR y=6x
raasty

M aro 5y=6
24322

126
array

18, J08S Connor works ata movi ret store coming $8
Per hour He also walks dogs for 10 per hour onthe
‘reskends, Connor worked 3 hours this wee and made
SI. How many hours did he work at he manie rental
Store How many hours dd he walk dogs over the
tweskend?

Use elimination to solve each system of equations.
Cr

Wzrry=s A]
se-y=15 re
16 ~ar + 10y=5 marrano
ze 15e 4
arty 18 5-0
wor ara
Solve each system of equations oma
menos mayo

aa.
ens Seremi
Meer? Bree?

Bryan dy
ya. az

manent @s-2+:-
yr. Srtytiens
tnt y= tyra

Solve cach system of equations. State wheather the system is
consisten and independent consistent and dependen, of
consistent 2

ae Bryn?
89 =7 zen
Een 19%
Wr sen syat
2 1sréymas EE
3092927 ay
sara
states
sy +=

38. CAMPING The Mountaineers Club held two camping trips
during the summer. Te lb rented tents and abia
{or the 30 members who went on the is ip. The hb
rented tent and 2 cabin fo the 6 members who went
‘onthe second tp IF the tens and cabins were led 0
pay on bot is, how many poopl can each ent
and each cabin accommodate? paros

Solve cach system of inequalities. If the system hat no
solation state o solution. 500.007

myers
yazıı

een
sayz

a yes car eyes
wor yaüsı-a

Ss Myst
were Yesos

45 ses Wysich
ya sauts

moya mit
veu nova
setys9 arte

4. ART Charlie can spend no more tan $228 onthe at
‘lub’ supply of brushes and paint. He needs at ess 20
brushes and 86 tubes of paint Graph the region hat
shows how many packages of ach tem canbe
purchased.)

P22 | Lesson 0 | systems of Linear Equations and Inequalities

47. Matrix Operations

‘constants in horizontal rows and vertical columns, sualy enclosed i brackets Each value in
‘he mais called an element. A matrix usual named sing an uppercase eter

A matrix can be described by its dimensions. A marx with m ows and columns sam X 1
‘mas which ie nd my Mat above sa 3 4 matrix bene has 3 ome and columns

& State the dimensions of A.

49 8 Because A has 2rows and 3columas,
zu af he dimensions of are 2 X 3.

% Find the value of y

Because the clement in ow I,
clu 3, he value aay is “18

‘Cerin matrices have speci ames. For ample a mat ha as on ron is ceda row mats, and

‘rte wih one corn. "Amat hat as he same number ro and cor
cm sou pa ak and a man which every cement ro calc eo a
si Û
wo. al

35 Los

“Two matrices re equal matics and ni euch lement of one matrix is equal fo the
comespondig element in the ther mati So matrix À and B shown below re equal matrices

Notice that for two matrices o be equal hy must have the same number o rows and columns

Ga q

48. ‘atx Operations Mares canbe add or braco fan ony y have the ae
dimensions.

KeyConcept Adding and Subtracting Matrices.
Study Tp Tasso aw en mr ee a mtn ne
ey a + 8 ase
ie cp
EE Lo Ga -
= b 1 -
fe lee +
F6 ur
wane
2 1
[ab]
Bla y 2maticandClsa2 1 mat Since tee diendo ae ot these, ou
ace
|
Yona ay mty smn ils sl Wien yo doth, yooh
individual lent byte valued Sor
Find cach produc
a 7
sf 3
[ee > po as = 2
A ee
f 2 =
‘StudyTip nel 7 3
a oe va
Pe HN
Frs) 7. Ze Jos 12
a Ten re

IND] P24 | tessonos | matrix Operations

49. Watchout!
ar ur
Bone at Xin
ren
‘ne te wae
Sree castes ea

Many properties oral numbers also hold true for matrices A summary ofthese properties is
Hd low

KeyConcept Properties of Matrix Operations

Fo ay ans Aan Ci whe ar um ao m eed tr

a ra
Commie Property al Adon Aeon
Associate Property of Aion Usps cea rn
La Sater Drove Prop memes
ot Saar Diane Pope err

Multstep operations can be performed on matrices. The order ofthese operations is the same
‘vith el numbers.

rousrsour=[ 2 ]mar{t u 7]

of ss TS 0 J) ome
ss alts il
on le a] Se
min mew ra
mar arm urn“
mn

You cn use the same algebra method fr solving equations with real numbers t solve equations
th matrices

4x=a
xo jara

2 8 33 3)

Fe U Par

pus e

“6 u
12 3 no ca
“los vad

50. Real-WorldLink

re
‘Sorta wry
rca et
tes
see

Matrix equations can be sein el word situations.

Real-World Exam

‘messages, pictures and talked for the most minutes on their call phones each week The
verges forthe freshmen, sophomores, juniors, and seniors are shown.

2

2 eh text message costs $0.10, cach picture cot 07 and uch minute on the phone
‘costs $005 find he average wech cel phone costs fr each ls. Express your answer
seam

[BEM writes matrix equation fr the otal cost X Let represent the number of tests forall
clases, eps he number of pers, and Crop he number fal mins.

X= 0107 +0750 + 008

ER solve the equation.

sur +075 + ou San
a) py pe

00018 +075|$] +005] | sun
zl LG) le

200] [225] [815] [1240
250,300, aso, 1400
150 |* [525 |*|690/%| 1545
220) l225) [ss] Lass.

“The inal matixidicts average wockly cll phone cots or sch class. Therefore, o
average, ach rahman spent $124 each sophomoro spent 1400, ech juno spent S155,
nd enh senior spent S395,

ba If there are 10 freshmen, 180 sophomores, 230 Junior, and 30 seniors hat use cll
phones at Alison school use her survey result to estimate the otal numberof tet
messages sen pictures sen and minutes used onthe cel phone each week by these
students Express your answer as a mattis,

EI vta matrix equation fo the tota usage X Let represent freshen, represent
sophomore, present junio» and N represent seniors

= 100 + 1805 +250) +300N
ER sive the equation.

UF + 1805 + 250 + 30007
= 10920 3 MOSH 1895 4 17O]+250N5 7 17143002 3 190)
16350 3670 148400)

“The final mat indicats the average wecky total foreach ype of cll phone use
‘Therefore, there wer 16850 text 3670 pictures an 148,400 minutes used by these student.

[ras | ens | mc pets

51. Exercises

State the dimensions of each mtr. En

+3 2|2

E
a.
sans) fx]

Find the value of each element in

Ss m0
num s
somos 17

I

m
Em CEA ag
bay CE DEA
5 =
Find esch ft folowing or | 2 —10 |,

E

he mat dos not exist, write impossible, Bono
TS 1.21

wxer ww wre

1. BUSINESS A car dealership has two used cr lots. The
matices blow represent he number of canon cach ot
by age ange and type of while Wirte a matrix
showing the total number of car ofeach age range and
ec type on both ot En 2

258] [sam
tele] 57 ley=|o 48 sı
sal” Ls «m

Find each produc. nio
ads 7
3

2
2 mass
2

“#31 «E

24. SING Jesica ook hor wo children o th community
Swimming pool once a week or ix wee, The day
“mision Fes ae $10 fo acid and 5675 oran
Ada. Weitea 10% 3 mat wäh asclarmulple at
present the ttl cat of admin. What ls the toa
cot cane

"1%

Sp Sl

pas]
5 nf,
4 >)

Find each ofthe folowing if D =|

: sa
= Janse A oo o
1-2 6 0

wee xen
2.04 0-28

m D+E-r a. 20+n-

Lael

DE 18 xo Sana
à 5 prie cum

mixe sk

zı-x

‘Use matrices BD, and Fo solve for XI the matric
ea

elle: ot 5

HEAR sa

Avex ar

c-D=x

a x=D48

poes

F-2e+0)=x

A

SiG The table shows some ofthe women's style
‘rimming record.

o | ame | awe | nos
© _ Tommıans | Baie | braze

& Find the free between American and World
records exprese a a column mates

Halte dat in the table were expressed in seconds
and represented by a mati A, what mai expression
‘ould Be ued to conver all data o miter?

EA 927

52. stl ones of
sn epanneat.

Use permuto and
canon win
ota.

flag Newvocabulary
spa

(Brae sesos

Probability with Permutations

and Combinations

1 Sale Space An xin uan ving ans pity ads o
spac outomes The ot all panbleouones ea he sample space One meh
(hat Can be sed determine he me of possible outs of an experiments te
Fundamental Counting Ppl

KeyConcep! Fundamental Counting Principle

{etn bn ot vet As pri os mh en
ta psi ann Det Monel oes Os y o os

"The Fundamental Counting Principle can also be usd o find he number o possible outcomes
for tres or more vent or example, the number of ways that k events can ocur ls given by
Perens

Events with outcomes that donot ae ach the ar called independent event, and evens with
‘outcomes that do affect each the ar called dependent events,

2. À restaurant offers a diner special in which a customer can selec from one of

Because he selection of one mens tem doc ot affect the selection of any oer tem each
selections independent. To determine the number o possible dinner spas mul he
‘umber of ways uch tem canbe selected.

6-2+12-8=1152
“Therefore, there are 1152 diferent dinner pecas
1. Garett works fora bookstore. He arangin the five bestsellers fora shel display.

he cam place te books in any order how many different ways can Garrett arange
ebook?

“The selection ofthe book or he first postion affects ebooks avaiable or the second
poston, the selection forthe second poston affects the books avaiable forthe thd
poston and soon. So, he selectins ol books are dependent events.

‘There ae 5 books frm which to chaos for th fs positon, bok forthe second, for
{he thd, 2 for the fourth, and 1 for he Ah. To determine he total number of way hat
‘he book can be arranged, mulipl by the number o ways hat he books can be chosen
foreach position.

5
‘Therefor, ere are 120 possible ways for Gare to arrange the books.

‘The expression used in sample I to acute he number of arrangement of books, 54-3221,
canbe written a which sad factoria, The factorial of postive integer isthe product of
‘he positive integers les than or equal 0% nd is given by

MD 2e + L whee dt

53. Study Tip
Braune a rm,
ica
er ert en
Beeren
roses
sonner Marat

Permutations and Combinations The Fundamental Counting Principe can also be
used to determine the number of ways that objects an be arranged ina certain order An
Arrangement of abject called pertain ofthe oc

KeyConcept Permutations

Team ol parate l naj ten naa |The nımde peut bots en at
mon sine

An. eta

An alarm system requires à 7 code using the digit through 9 Each digit maybe used
only once.

2. How many diferent codes are possible?

‘The order ofthe numbers In the code is important, so this situation isa permutation of
10 gs taken ata time.

an ad at mme ca.

= 1098726508 om
coo tu
So, 604,80 codes ae possible

ba Ifacodeisrandomly generated, what the probability tha the fist thre digits are oda?

To ind the probability of theft thre digs being oda, ind the number of ways oct
thre odd digits and mul by the numberof ways to sic the remaining digits and then
vide by the tol posible codes

ray ee ii - ways to ds igi
ade

Pl thee digits are odo)

ans 0810 ae at

LT mon
a ms
o a

“Theos th probably or bout 008

Ga 9

54. Ina combination onde spa important. A combination of objects taken ata time calculated
by viding the numberof prmutatons by te numberof arrangements containing the same
laments and is denoted by cn

KeyConcept Combinations
Te number of cobra notes kn ata ie

‘The main difference bien a permuttin and a combination is whether order consider (as
in permstation) or not asin combination), For example, for jet FG and H taken io
tine, he permutation and combinations an sed below

tchat \
ee
en anna mu
Se pee =p
nat bee) Eh

In permutations EF different from FE. But in combinations, EF the same a FE.

“There ate seniors, juniors and 4 sophomores on the pep squad. Me Rinehart needs to
choose 12 students ot ofthe group to sell spirit buttons drin lunch.

2: How many ways can the 12 students be chosen?

rh tnt rat

om me

nun, mn

Dot non
eto ata
(evan ro Summer
cs rumor.
Dates me
Swe tc So, there are 180 ways that he 12 students can be chosen.

mo

Sms

1 Ifthe students ar randomly chosen, what the probability hat senior, junior and
A sophomeres wil be chosen?

ways to choose 4 seniors out 7: ¿Cy =

ways to choose juniors out of 56 =

co

‘ways to choos sophomores out of 46, =

por 178 ways to choose seniors, junior, and 4 sophomores

A P20 tonos | mobi with ermitas and Cantinas

55. Exercises

‘Use the Fundamental Counting Principle to determine the
‘numberof outcomes foreach event 22000

1. How many diferent shies ar available?

ASMA | to. gm. gay ck |

2. Fora particular model of at a dele offers sizes
engine, 2 types of tros 18 body colors, and
upholstery colors: How many diferent possiblities
ro tab for tht model?

out aci lla di and then spin lol pin
il gl sets, how many um ar pre”

4 ade ors 12 different ment, different cheeses, and
‘diferent breads, how many diferent sandwiches can be
made with Type of meat, typeof cheese, and type of
bread?

8. Anicecram shop ofes 2 flavors fc cream,

5 iront topping, nd diferent sizes How many
fret sundaes ar arabe?

& How many diferent topping pizzas are avaiable?

7. How many ways can diferent books be arranged on à
shelf the books can be ranged in any order?

(How many ways can eight cor bested in the
credit oa mie te leading actor must be ited st

Find each value. Ban

um m me
LE m wm
15 6% mi
WG roe 26

21, CLASS OFFERS At Grant Senior High choo, here are
15 names on the allot fr Junior classes Five will
elec form a class commie. Luna.

2. How many diferent commites can be formed?

2 Inhow many ways can the commie be formed if
‘ich student has diferent responsibly?

1 there ar 8 ges and 7 boy onthe allot whats the
probability tat comateeof2 boys and 3 gis
Formed?

22. ART An at gallery curator wants to eet four paintings
‘uo twenty to put cn display How many groups of
four painting an be chose?

ZA. PHONE NUMBERS In the United States standard acl
telephone number consist of digits where the i digit
cannot be 1 060.

a. Find the number of posites for telephone
ame

a. Find the probity of randomly selecting given
telephone number rm all the possible numbers.

+. How many different telephone numbers are posible if
only even gts are used?

& Find the probabili of chosing telephone number
in which ony even digs ar used.

{Find the number of posites for telephone numbers
‘the fist he digits ar 358, Whats the probably

‘of randomly choosing a telephone number in which
{he fate digits ao 5007

24. CARS Five cand are drawn rom standard deck of

Beards

2. Determine the number of posible var selections.

Find the probability ofan arrangement containing
Shears and Zehn.

& Find the probability of an arrangement containing
pers

& Find the probability fan arrangement containing
ace, Zack and hinge

A gumball machine contains ed (1), orange (N),9 purple
(7 white (Wand 5 yellow () gumball Tyson buys

3 pumballs Find each probability suming thatthe
‘machine dispenses 3 gumball at random al tone.

FSR) 2 PoWand1P)
Orinoco 2 Panama
2 PORO 2 PARA Wand 1)

31. COMPUTERS iui board with 20 computer chips
‘contains chips that are defective. 3 chips are selected
random, whats the probability that all are defective?

32. BOOKS Dan has twelve books on hi shelf tht he has not
rend inching seven novels and five biographies Ihe
‘wants to take four boos with him on vacation whats
the probably that he randomly select wo novels and
two biographies?

2. SCHOLARSIPS Twelve mal and 16 female students
have ben selected as equal qualifiers for college
bolis If the awarded recien ae tbe chosen
at rando what the probably that 3 wil be male
And willbe feral?

E »

56. Objective

© 4 Pommes
ctr and spread.

22

(E Newvocabutary
sas

art te
ma fen

Statistics

1 Messures ol Center and Spread sut ne ec ecg ra
intrpreing and presenting data. The Branch of satis that Jcuss on UNE,
summarieing, and playing datas krown a dere statisti. Data in ne trab or data
Type are called univariate data Tse dat can be decribed by a messure of central tendency
‘which represents the center or middle ofthe data The te mos common messes feta
tendency are mean, mean, and mode

‘A population isthe ere membership of people objets or events of interes to be analyzed. A
‘ample sa subst of» population. Te formula for mean usos to represent the data vas in.
‘Simple or population ro represent the sum eal values to represent the number of
talus, represent the population mean, to represent he sample mea.

KeyConcep! Measures of Central Tendency

us PR MAP man és dy mre ens
Pane Sante
Meson DR NAS a ee argo AÑ ac nap ió
Le
Mee tarmac pe met canal at

Find the man, median, and mode forthe data 14,7, 12,4, 15,20,2,3,5,15,10,4.

AAA te

=908

E

Moden 234457101233 1415.20

+

Zi yes

Mode The value hat occur most often in he set 4,0 the mode is 4.

aration describe the distribution of set of dat. Three measures of pred
rang, van, and standard deviation. The formulas for population variance snd standard
Écrit use = to represent the deviation e drone ans vale fom the population mean.
and 268 = to represen the sum ofthe squares of thse deviations Similar notations used for

‘Simple variance and standard deviation

KoyConcep! Measures of Spread

mem Demon bee ne
(eesti aver ast

oom

ess eee

St ms
itn atom e
Eros

57. StudyTip

Mann memes |
Perg
Feen ea
Er

‘The quz core fra las 2 students are shawn
2: Find the measures of prea forthe entire as. 1fefsfefe
Range mainun = minimum, DO DE
10-2008 DO
Variance Find themean ofthe dat ct
ES Mae
“te raras o
= 7Morsbo7A Sa
‘se the unwunded mean find he arses
pe PE
Er: arate ts
wur 5
ET HB Hunt
= 4566 or about 6 soi
Standard Deviation Take the square root of the variance
a= Vie
mas
8 Use the at column the gue scores find he measures of spread fra sample of
ess
Range The sample 9,6, 2,5 and 10. The range ft ample 10 208
IPN
vicio
es

Ina given st of data, the majority of the values fll within one standard deviation of the mean, and
lost alo te values wil fal within 2 standard deviations. The quiz scores in Example 2a had a
tenn of about 74 anda standard deviation of about 21, This can e strated grapes

tr a

E
“st eon

the que scores were compared with other scores throughout he country ona national st, this
‘dass would be considered sample allo the students who look the test À sample mean and a
Sample standard deviation need tobe calculate

When comparing dat sty itis important analyze the enter and prea ofeach distribution.
‘This Important because to ass of at can have the same sean but diferent spreads,

ae P33
u

58. EAU Metabolic rate the rate at which the Body consumes energy, measured in Calories
er 4 hours During a study on diet and exercise, the metabolic ates fortwo different groups
‘of men were observed: Which group has a greater aration in metabolic ates?

ve [ras [es [ioe [ee] [sr Lune | woe [si
es [ee [re [om [166 re | 169 ve [rot [en

Enter the data into Land L2 ona graphing calculator Press STAT] and select Var Sta rom
the CALC menu, res and] [LJ or an) {U2 select the Group 1 or Group 2 dota and press,
[es Record the vales for the sample mean, median Med, standard deviation Sx, and use
Iman minX to cause the ange

Group mean = 16039 Group? mean = 1604
range = 395, range = 247
standard deviton = 1002 standard deviation = 546
median = 16915 ~ 10290515915 median = 1723 = 47601605

Although the measures of center ar reasonably los, the standard deviation of 102 fr
‘Group ismuch larger than Group 2% value of 5.6. The range for Group 1 lo much ager
‘than that of Group 2. Therefore, here isa grater variation in metabolic ates in Group 1

StudyTip

Gus Enr Wena
vaca migra | 7 Organize Data Data cn be organized int a table called to show
etre how often each ta value or group af dat values, called a ‘appear ina data

[autonome | set The relative frequency of caw orto of ata within the cas tal the data. The

Parser” | ama gun rach sum lo ay an pron du, The

Palen ora cla isthe ai ofthe cumulative que of the lst all
flange pecar | the data

Inde Each clas can be described in several ways. The las wth is he range of vals for ach las
— Aloe caso lis the eat vale that cn belong specie as, and an per a ns he

) greatest vale that can belong toa specie dln.

FOOTBALL The winning sores forthe it 42 Super Bowls are shown below.

35-39 16 29 16 4 14 24 16 21 32 2735 91 27 28 27 9 38 46 9
A2 20 88 20 37 82 30 49 27 35 4 23 34 20 48 92 2 21 29
2 Make a distribution table that shows the frequency and relative frequency of he data
EX Determine he number of cases and an appropriate cas interval. Th cores range
from 141955, so ue 5 dasses with alas interval of 10 points Make table Hg
‘the cs mi Bogin with 10 points and end ih 39 ponts.

TR ny the dat. Then calculate heave frequencies

sos [ut 5 [aveu
>> |mmm| «
> [mm] ®
oo [un a
sos [y 2

ED r2e en sus

59. LB Construct histogram for both the frequency distribution andthe relative frequency
Aistbation. The compare the graphs

Winning Scores ofthe Super Bowl Winning Scores ofthe Super Bow!

mm | «6 wen] Zoom
ms | » [inox] Zum
os | 2 [rue

4, Construct histogram for the culate
frequency dstbeton, Then compare the
Ah tothe graph of the frequency distibution,

‘The shape of the cumulative frequency
Ingram shows an increasing pattern
‘There à are innen nthe number of
teams scoring 01019 point fo the number
‘of teams scoring 200 9 point, Then there
ls very ite change nthe numberof ems
scoring 40 or moe points.

Ina sel dat, quate are values hat divide the data nt four equal pats
meno;

sot at oom at
upon inns

Ea "a

60. StudyTip

Cros Mears,
creer.
ee nee
‘saucy aes ase
‘or ere rg Oe
tne pe gar ome

aoe

‘This ive-mumber summary which includes the minimum vale lower quale, median, upper
quart and the maximum value of data se, provides anther numerical way of characterizing
{eto data. The iverumber summary can be described visually witha box and-ehinker plot
sto.

"Ts dference between the upper quart and lower quart calle the
Our are data that are more tha 15 tines the interquartile range beyond the upper or lower
quar,

Real-World En

EDUCATION The enrolment for tte univers in Ohio s shown. Display the data ing a
borand-whisker plot

CA ooo Ez]

et mans En

Een TO ar
ETS ea zai
ey Er

Gm an a

Ga) — ron rn sai | rase

‘woe ar

ies an

Dr EST | rs

ESA ‘eee Sey |
See Se El

Cm er

EM nd the maximum and minimum values, and draw a number ie that covers the ange
of data Then nd the median and the upper ad lower quarts Mark thse pints
And the extreme vales above the number Une,

vaste moro mm an o

ent any otis.
‘The interquartile ranges 22913 ~ 143165 or 8965. Thera no data values les.
than 143163 = 15(65965) or 142175. Theres ne data value pear than 22913 +
11585965) or 3550775. The evollment at The Ohio State University, 5256, an outer.

KITE Draw a box around the upper and lower quartiles, avert tne through the median,
nd us horizontal lines or hers 1 connect the lower value and th retest value
‘Batis ot an tie The greatest value tats not an our 5.

T .

Bros | sone suso

61. Exercises
Find the mean, median, and mode o each st of data.
Ga

1. (24,28,21, 37,31, 28 252,34 31

2 (6,87, 62 87, 68,98, 755487, 58,70, 76)

3 169,11,1,12,7,611,5,8,10,6)

4. PACING Crates of books ar being store The weight of
the crates pounds ae shown inthe able Ear

126 | wos [113 [ins | us

ep by Sp Sons begin on pago

HN PHONES The prices of 18 randomly selected
graphic novels at two stores are shown, Which stor has
greater variation in graphic novel prices? En

nase | 120 | 1585 | 1209 | 1208 | 2095

‘What ithe mean ofthe weight?
Find the median of the weights

+ 165 pounds added 1 each cate, how wil the mean
and median be affected?

Find the range, valance, and standar deviaton for each set
‘of data. Use the formula fora population. En à

($445 $5.50, $550, $630,578, $1.0, $1220 $1720)
(200,476,721, 57,152,158)

7. (57,57,56,55,53,49,44,40, 40,38)

(69,998,381, 992,405, 413,576, 44, 420,35, 402,446

CRE
tant at ba Basen)

‘Find the measures of spread fort eights ofthe
sstronomy students

Using the second row asa sample, ind the measures
‘of ped forthe sample ofthe astronomy students

10. MANUFACTURING Sample times, measured in number of
arging cles, fortwo brands of rechargeable batteries
‘reshown Which brand has greater vation in
lime? Cande

sa | ms | on | we | a
107 Le [so Le [os

GOT EE DEEE
ejolsfejefejelefejajo

Make distribution table ofthe data. Show the
Frequency lative roqueney cumulative frequency,
and cumulative lave uen.

1 Consnut histograms forthe frequency, lative
frequency, and cumulative rave quan
ita.

& Name the interval or intervals that describe the age of
most presidents upon aking oe.

8. SPORTS DRINGS Carls surveyed his finds t find the
‘number of bts of ports rinks that hey consume in.
an average week Display the data wing bow and
he plot. par

A E

14. DIVINO Kara surveyed 20 randomly selected students at
er school about how many miles hey drive in an
average day. The results are sown. Par

+ —

reer rary

2. What percent ofthe students drive more than 30 miles

inde

1 What the ineruarile range ofthe bow and-whisher
plot shoven?

& Doce a stent at Kars school havea beter chance of

meeting someone wh drives about the same mileage
{athe or she does 15 miles or 0 mis ae divin
day? Why?

EA #97

62. ‘se sentation re ements of ach st The taming

ar nement bet este fue faa
1 Mist st trata nunc mails tr san O

new

2. Stet el toes tres tan Aura an 60.
Tes

InB=01,2.3,0=01,23,45.8,0=1

ES OR stand Fd o mes

a onc 4 o0F

$ 0 ur

Samy.

Barmen RIRS

BB 10 (1+ K-62

Sao ecu.
CES
m. 254 4=0

10 Porra
18 21-30

18, RECREATION Te canta nd he cs ao veta
recreate ae oe = ~ N° eres te
gen per er ant nis te unta ee
rr veal reset vid à 567,00 at ob te
a be wie ar 6 mor a ru eaten inc

ta
‘init epson.

al a Ve
2 Vie a VF

38 | apuro | rot

PE a VS
FF 5
a 28

2. J08S Len nyt dig by $10 pr ar nd ht
lo pr ow. stewards haus an eared 80, ow any
ous se att our cay? How may ath?

‘Sao sach stom of equates Sate wer te sten
‘asset and dependent, coset and pede or
recast

waren
Pa ay 162=
CARE

ae res

‘Sav each ste of negate system as sota, sae
cr

sers Myers
peur Pur?
Sue wars
depa?
3
Fndeach ote towing A=| 2
‘i Ls
meh 4
muse mec mue
Fd each parution or contin,
LES Sr aK
am wh sa

48. AROS For ce ran rn om star dk 52
cars re each rta

2 PU sands)
BP en ard 2 tc cats)

‘de mean med, and mad for ach st a. Tan nd
‘ang, vane, nd Suna devon feck Pop.

2011229 48 04040408060808

64. unctions from a
alculus Perspective

A een
Ute ab es noe, =

69. aos sans

=a:

78. ‘i or Syme

(6 | seen 2 anorg cnet con

79. toser

80. D 18 son anorg rs turco

87. ety Poet ty

90. Dr seen | conn

94. (G2 teo in aio an un

98. Dos mr

115. Cu RD ARO

119. Function Operations and
Composition of Functions

121. nd amt Foran win ase Soman

122. Omen Comes inten

130. ty ne ts

(6 seen | more ton ns ncn,

132. LD 70 seen | eons ncn,

137. Eneeisen

138. Study Guide

139. Lesson-by-Lesson Review

140. ‘Study Guide and Review contes

141. [5 Pret estos ad Tasas «

142. ‘Applications and Problem Solving

146. Sea Poema eat

147. Soe a Poyremalenauy ung Es Sever

romana eats mth neal Sto Se

QD 102 seen 26 no

151. QD 106 | een 26 non

154. LD 102 | enon 23 | rose

162. Tn Pope pri ions

Sve sont tors Us nene ron

163. ‘seve opts Egos ig de on Prey

‘Gro Fan of eprom Fonsi

164. Soe Lune ate sr Or ne Progr

Soe pont ans

(Gt | onan 4 | rei an putes

165. ‘Se pana nn in ae Form

166. se Linens

ec rer Sots

(GO 108 | onan 4 | crea an topo tes

181. Us ws age ton Deen

182. Soe a Ran Tange

D 225 oman e | range gone

188. amar Bet DS an rca Dg Frm

QD 22 seman |

192. ep Si

194. PES

196. EE

201. Use ere ges pre one oes

206. i Per at rear toe

D 250 | enon 2 | rgorameic ron

211. xacises

216. (F260 | seen | cing ane a rine no