Chapter 1Resource Masters
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ISBN: 0-07-868229-0 Advanced Mathematical ConceptsChapter 1 Resource Masters
1 2 3 4 5 6 7 8 9 10 XXX 13 12 11 10 09 08 07 06
© Glencoe/McGraw-Hill iii Advanced Mathematical Concepts
Vocabulary Builder . . . . . . . . . . . . . . . . . vii-x
Lesson 1-1Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Lesson 1-2Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Lesson 1-3Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Lesson 1-4Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 10Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Lesson 1-5Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 13Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Lesson 1-6Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 16Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Lesson 1-7Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 19Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Lesson 1-8Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 22Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Chapter 1 AssessmentChapter 1 Test, Form 1A . . . . . . . . . . . . . . 25-26Chapter 1 Test, Form 1B . . . . . . . . . . . . . . 27-28Chapter 1 Test, Form 1C . . . . . . . . . . . . . . 29-30Chapter 1 Test, Form 2A . . . . . . . . . . . . . . 31-32Chapter 1 Test, Form 2B . . . . . . . . . . . . . . 33-34Chapter 1 Test, Form 2C . . . . . . . . . . . . . . 35-36Chapter 1 Extended Response
Assessment . . . . . . . . . . . . . . . . . . . . . . . . 37Chapter 1 Mid-Chapter Test . . . . . . . . . . . . . . 38Chapter 1 Quizzes A & B . . . . . . . . . . . . . . . . 39Chapter 1 Quizzes C & D. . . . . . . . . . . . . . . . 40Chapter 1 SAT and ACT Practice . . . . . . . 41-42Chapter 1 Cumulative Review . . . . . . . . . . . . 43
SAT and ACT Practice Answer Sheet,10 Questions . . . . . . . . . . . . . . . . . . . . . . . A1
SAT and ACT Practice Answer Sheet,20 Questions . . . . . . . . . . . . . . . . . . . . . . . A2
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A3-A17
Contents
© Glencoe/McGraw-Hill iv Advanced Mathematical Concepts
A Teacher’s Guide to Using theChapter 1 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file theresources you use most often. The Chapter 1 Resource Masters include the corematerials needed for Chapter 1. These materials include worksheets, extensions,and assessment options. The answers for these pages appear at the back of thisbooklet.
All of the materials found in this booklet are included for viewing and printing inthe Advanced Mathematical Concepts TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-x include a student study tool that presents the key vocabulary terms from the chapter. Students areto record definitions and/or examples for eachterm. You may suggest that students highlight orstar the terms with which they are not familiar.
When to Use Give these pages to studentsbefore beginning Lesson 1-1. Remind them toadd definitions and examples as they completeeach lesson.
Study Guide There is one Study Guide master for each lesson.
When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can alsobe used in conjunction with the Student Editionas an instructional tool for those students whohave been absent.
Practice There is one master for each lesson.These problems more closely follow the structure of the Practice section of the StudentEdition exercises. These exercises are ofaverage difficulty.
When to Use These provide additional practice options or may be used as homeworkfor second day teaching of the lesson.
Enrichment There is one master for eachlesson. These activities may extend the conceptsin the lesson, offer a historical or multiculturallook at the concepts, or widen students’perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for usewith all levels of students.
When to Use These may be used as extracredit, short-term projects, or as activities fordays when class periods are shortened.
© Glencoe/McGraw-Hill v Advanced Mathematical Concepts
Assessment Options
The assessment section of the Chapter 1Resources Masters offers a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessments
Chapter Tests• Forms 1A, 1B, and 1C Form 1 tests contain
multiple-choice questions. Form 1A isintended for use with honors-level students,Form 1B is intended for use with average-level students, and Form 1C is intended foruse with basic-level students. These tests aresimilar in format to offer comparable testingsituations.
• Forms 2A, 2B, and 2C Form 2 tests arecomposed of free-response questions. Form2A is intended for use with honors-levelstudents, Form 2B is intended for use withaverage-level students, and Form 2C isintended for use with basic-level students.These tests are similar in format to offercomparable testing situations.
All of the above tests include a challengingBonus question.
• The Extended Response Assessmentincludes performance assessment tasks thatare suitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided for assessment.
Intermediate Assessment• A Mid-Chapter Test provides an option to
assess the first half of the chapter. It iscomposed of free-response questions.
• Four free-response quizzes are included tooffer assessment at appropriate intervals inthe chapter.
Continuing Assessment• The SAT and ACT Practice offers
continuing review of concepts in variousformats, which may appear on standardizedtests that they may encounter. This practiceincludes multiple-choice, quantitative-comparison, and grid-in questions. Bubble-in and grid-in answer sections are providedon the master.
• The Cumulative Review provides studentsan opportunity to reinforce and retain skillsas they proceed through their study ofadvanced mathematics. It can also be usedas a test. The master includes free-responsequestions.
Answers• Page A1 is an answer sheet for the SAT and
ACT Practice questions that appear in theStudent Edition on page 65. Page A2 is ananswer sheet for the SAT and ACT Practicemaster. These improve students’ familiaritywith the answer formats they may encounterin test taking.
• The answers for the lesson-by-lesson masters are provided as reduced pages withanswers appearing in red.
• Full-size answer keys are provided for theassessment options in this booklet.
© Glencoe/McGraw-Hill vi Advanced Mathematical Concepts
Chapter 1 Leveled Worksheets
Glencoe’s leveled worksheets are helpful for meeting the needs of everystudent in a variety of ways. These worksheets, many of which are foundin the FAST FILE Chapter Resource Masters, are shown in the chartbelow.
• Study Guide masters provide worked-out examples as well as practiceproblems.
• Each chapter’s Vocabulary Builder master provides students theopportunity to write out key concepts and definitions in their ownwords.
• Practice masters provide average-level problems for students who are moving at a regular pace.
• Enrichment masters offer students the opportunity to extend theirlearning.
primarily skillsprimarily conceptsprimarily applications
BASIC AVERAGE ADVANCED
Study Guide
Vocabulary Builder
Parent and Student Study Guide (online)
Practice
Enrichment
4
5
3
2
Five Different Options to Meet the Needs of Every Student in a Variety of Ways
1
© Glencoe/McGraw-Hill vii Advanced Mathematical Concepts
Reading to Learn MathematicsVocabulary Builder
NAME _____________________________ DATE _______________ PERIOD ________
This is an alphabetical list of the key vocabulary terms you will learn in Chapter 1.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term.
Vocabulary Term Foundon Page Definition/Description/Example
abscissa
absolute value function
best-fit line
boundary
coinciding lines
composite
composition of functions
constant function
correlation coefficient
domain
(continued on the next page)
Chapter
1
© Glencoe/McGraw-Hill viii Advanced Mathematical Concepts
Reading to Learn MathematicsVocabulary Builder (continued)
NAME _____________________________ DATE _______________ PERIOD ________
Vocabulary Term Foundon Page Definition/Description/Example
family of graphs
function
function notation
goodness of fit
greatest integer function
half plane
iterate
iteration
linear equation
linear function
linear inequality
(continued on the next page)
Chapter
1
© Glencoe/McGraw-Hill ix Advanced Mathematical Concepts
Reading to Learn MathematicsVocabulary Builder (continued)
NAME _____________________________ DATE _______________ PERIOD ________
Vocabulary Term Foundon Page Definition/Description/Example
model
ordinate
parallel lines
Pearson-product momentcorrelation
perpendicular lines
piecewise function
point-slope form
prediction equation
range
regression line
relation
(continued on the next page)
Chapter
1
© Glencoe/McGraw-Hill x Advanced Mathematical Concepts
Reading to Learn MathematicsVocabulary Builder (continued)
NAME _____________________________ DATE _______________ PERIOD ________
Vocabulary Term Foundon Page Definition/Description/Example
scatter plot
slope
slope intercept form
standard form
step function
vertical line test
x-intercept
y-intercept
zero of a function
Chapter
1
© Glencoe/McGraw-Hill 1 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
Relations and FunctionsA relation is a set of ordered pairs. The set of first elementsin the ordered pairs is the domain, while the set of secondelements is the range.
Example 1 State the domain and range of the following relation.{(5, 2), (30, 8), (15, 3), (17, 6), (14, 9)}Domain: {5, 14, 15, 17, 30}Range: {2, 3, 6, 8, 9}You can also use a table, a graph, or a rule torepresent a relation.
Example 2 The domain of a relation is all odd positive integersless than 9. The range y of the relation is 3 more than x,where x is a member of the domain. Write the relationas a table of values and as an equation. Then graph therelation.Table: Equation: Graph:
y � x � 3
A function is a relation in which each element of the domain ispaired with exactly one element in the range.
Example 3 State the domain and range of each relation. Thenstate whether the relation is a function.a. {(�2, 1), (3, �1), (2, 0)}
The domain is {�2, 2, 3} and the range is {�1, 0, 1}. Eachelement of the domain is paired with exactly oneelement of the range, so this relation is a function.
b. {(3, �1), (3, �2), (9, 1)}The domain is {3, 9}, and the range is {�2, �1, 1}. In thedomain, 3 is paired with two elements in the range, �1and �2. Therefore, this relation is not a function.
Example 4 Evaluate each function for the given value.a. ƒ(�1) if ƒ(x) � 2x3 � 4x2 � 5x
ƒ(�1) � 2(�1)3 � 4(�1)2 � 5(�1) x � �1� �2 � 4 � 5 or 7
b. g(4) if g(x) � x4 � 3x2 � 4g(4) � (4)4 � 3(4)2 � 4 x � 4
� 256 � 48 � 4 or 212
1-1
x y
1 4
3 6
5 8
7 10
© Glencoe/McGraw-Hill 2 Advanced Mathematical Concepts
Relations and FunctionsState the domain and range of each relation. Then state whetherthe relation is a function. Write yes or no.
1. {(�1, 2), (3, 10), (�2, 20), (3, 11)} 2. {(0, 2), (13, 6), (2, 2), (3, 1)}
3. {(1, 4), (2, 8), (3, 24)} 4. {(�1, �2), (3, 54), (�2, �16), (3, 81)}
5. The domain of a relation is all even negative integers greater than �9.The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation.Then graph the relation.
Evaluate each function for the given value.6. ƒ(�2) if ƒ(x) � 4x3 � 6x2 � 3x 7. ƒ(3) if ƒ(x) � 5x2 � 4x � 6
8. h(t) if h(x) � 9x9 � 4x4 � 3x � 2 9. ƒ(g � 1) if ƒ(x) � x2 � 2x � 1
10. Climate The table shows record high and low temperatures for selected states.a. State the relation of the data as a set of
ordered pairs.
b. State the domain and range of the relation.
c. Determine whether the relation is a function.
PracticeNAME _____________________________ DATE _______________ PERIOD ________
1-1
Record High and Low Temperatures ( °F)State High Low
Alabama 112 �27Delaware 110 �17Idaho 118 �60Michigan 112 �51New Mexico 122 �50Wisconsin 114 �54
Source: National Climatic Data Center
© Glencoe/McGraw-Hill 3 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-1
Rates of ChangeBetween x � a and x � b, the function f (x) changes by f (b) � f (a).The average rate of change of f (x) between x � a and x � b is definedby the expression
.
Find the change and the average rate of change of f(x) in the given range.
1. f (x) � 3x � 4, from x � 3 to x � 8
2. f (x) � x2 � 6x � 10, from x � 2 to x � 4
The average rate of change of a function f (x) over aninterval is the amount the function changes per unitchange in x. As shown in the figure at the right, theaverage rate of change between x � a and x � b represents the slope of the line passing through thetwo points on the graph of f with abscissas a and b.
3. Which is larger, the average rate of change of f (x) � x2 between 0 and 1 or between 4 and 5?
4. Which of these functions has the greatest average rate of change between 2 and 3: f (x) � x ; g(x) � x2; h(x) � x3 ?
5. Find the average rate of change for the function f (x) � x2 in each interval.a. a � 1 to b � 1.1 b. a � 1 to b � 1.01 c. a � 1 to b � 1.001
d. What value does the average rate of change appear to be approaching as the value of b gets closer and closer to 1?
The value you found in Exercise 5d is the instantaneous rate ofchange of the function. Instantaneous rate of change has enormousimportance in calculus, the topic of Chapter 15.
6. Find the instantaneous rate of change of the function f (x) � 3x2
as x approaches 3.
f (b) � f (a)��
(b � a)
© Glencoe/McGraw-Hill 4 Advanced Mathematical Concepts
Composition of FunctionsOperations of Two functions can be added together, subtracted,Functions multiplied, or divided to form a new function.
Example 1 Given ƒ(x) � x2 � x � 6 and g(x) � x � 2, find eachfunction.
a. (ƒ � g)(x) b. (ƒ � g)(x)( ƒ � g)(x) � ƒ(x) � g(x) ( ƒ � g)(x) � ƒ(x) � g(x)
� x2 � x � 6 � x � 2 � x2 � x � 6 � (x � 2)� x2 � 4 � x2 � 2x � 8
c. (ƒ � g)(x) d. ��gƒ
��(x)( ƒ � g)(x) � ƒ(x) �g(x)
� (x2 � x � 6)(x � 2)� x3 � x2 � 8x � 12
Functions can also be combined by using composition. Thefunction formed by composing two functions ƒ and g is calledthe composite of ƒ and g, and is denoted by ƒ � g. [ƒ � g](x) isfound by substituting g(x) for x in ƒ(x).
Example 2 Given ƒ(x) � 3x2 � 2x � 1 and g(x) � 4x � 2,find [ƒ � g](x) and [g � ƒ](x).
[ ƒ � g](x) � ƒ(g(x))� ƒ(4x � 2) Substitute 4x � 2 for g(x).� 3(4x � 2)2 � 2(4x � 2) � 1 Substitute 4x � 2 for x in ƒ(x).� 3(16x2 � 16x � 4) � 8x � 4 � 1� 48x2 � 56x � 15
[ g � ƒ](x) � g( ƒ(x))� g(3x2 � 2x � 1) Substitute 3x2 � 2x � 1 for ƒ(x).� 4(3x2 � 2x � 1) � 2 Substitute 3x2 � 2x � 1 for x in g(x).� 12x2 � 8x � 2
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
1-2
��ƒg��(x) � �g
ƒ((xx))
�
� �x2 �
x �x
2� 6�
� �(x �
x3�
)(x2� 2)
�
� x � 3, x � �2
© Glencoe/McGraw-Hill 5 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
Composition of Functions
Given ƒ(x) � 2x2 � 8 and g(x) � 5x � 6, find each function.1. ( ƒ � g)(x) 2. ( ƒ � g)(x)
3. ( ƒ � g)(x) 4. ��ƒg��(x)
Find [ƒ � g](x) and [g � ƒ](x) for each ƒ(x) and g(x).5. ƒ(x) � x � 5 6. ƒ(x) � 2x3 � 3x2 � 1
g(x) � x � 3 g(x) � 3x
7. ƒ(x) � 2x2 � 5x � 1 8. ƒ(x) � 3x2 � 2x � 5g(x) � 2x � 3 g(x) � 2x � 1
9. State the domain of [ ƒ � g](x) for ƒ(x) � �x� �� 2� and g(x) � 3x.
Find the first three iterates of each function using the given initial value.10. ƒ(x) � 2x � 6; x0 � 1 11. ƒ(x) � x2 � 1; x0 � 2
12. Fitness Tara has decided to start a walking program. Her initial walking time is 5 minutes. She plans to double her walking time and add 1 minute every 5 days. Provided that Tara achieves her goal, how many minutes will she be walkingon days 21 through 25?
1-2
© Glencoe/McGraw-Hill 6 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-2
1�2
Applying Composition of FunctionsBecause the area of a square A is explicitly determined by the lengthof a side of the square, the area can be expressed as a function of onevariable, the length of a side s: A � f (s) � s2. Physical quantities areoften functions of numerous variables, each of which may itself be afunction of several additional variables. A car’s gas mileage, forexample, is a function of the mass of the car, the type of gasolinebeing used, the condition of the engine, and many other factors, eachof which is further dependent on other factors. Finding the value ofsuch a quantity for specific values of the variables is often easiest byfirst finding a single function composed of all the functions and thensubstituting for the variables.
The frequency f of a pendulum is the number of complete swings thependulum makes in 60 seconds. It is a function of the period p of thependulum, the number of seconds the pendulum requires tomake one complete swing: f ( p) � .
In turn, the period of a pendulum is a function of its length L in centimeters: p(L) � 0.2�L� .
Finally, the length of a pendulum is a function of its length � at 0°Celsius, the Celsius temperature C, and the coefficient of expansion eof the material of which the pendulum is made:L(�, C, e) � �(1 � eC).1. a. Find and simplify f( p(L(�, C, e))), an expression for the
frequency of a brass pendulum, e = 0.00002, in terms of itslength, in centimeters at 0°C, and the Celsius temperature.
b. Find the frequency, to the nearest tenth, of a brass pendulumat 300°C if the pendulum’s length at 0°C is 15 centimeters.
2. The volume V of a spherical weather balloon with radius r is
given by V(r) � �r3. The balloon is being inflated so that the
radius increases at a constant rate r(t) � t � 2, where r is in
meters and t is the number of seconds since inflation began.a. Find V(r(t))
b. Find the volume after 10 seconds of inflation. Use 3.14 for �.
4�3
60�p
© Glencoe/McGraw-Hill 7 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
Graphing Linear EquationsYou can graph a linear equation Ax � By � C � 0, where Aand B are not both zero, by using the x- and y-intercepts. To findthe x-intercept, let y � 0. To find the y-intercept, let x � 0.
Example 1 Graph 4x � y � 3 � 0 using the x- and y-intercepts.Substitute 0 for y to find the x-intercept. Thensubstitute 0 for x to find the y-intercept.
x-intercept y-intercept4x � y � 3� 0 4x � y � 3 � 04x � 0 � 3� 0 4(0) � y � 3 � 0
4x � 3� 0 y � 3 � 04x� 3 y � 3x� �34�
The line crosses the x-axis at ��34�, 0� and the y-axis at (0, 3).
Graph the intercepts and draw the line that passes throughthem.
The slope of a nonvertical line is the ratio of the change inthe y-coordinates of two points to the corresponding change inthe x-coordinates of the same points. The slope of a line can beinterpreted as the ratio of change in the y-coordinates to thechange in the x-coordinates.
Example 2 Find the slope of the line passing throughA(�3, 5) and B(6, 2).
m � �xy
2
2
�
�
xy
1
1�
� �62�
�(�
53)� Let x1 � �3, y1 � 5, x2 � 6, and y2 � 2.
� ��93� or ��3
1�
1-3
SlopeThe slope m of a line through two points (x1, y1) and (x2, y2) is given by
m � �yx
2
2
�
�
yx
1
1�.
© Glencoe/McGraw-Hill 8 Advanced Mathematical Concepts
Graphing Linear Equations
Graph each equation using the x- and y-intercepts.1. 2x � y � 6 � 0 2. 4x � 2y � 8 � 0
Graph each equation using the y-intercept and the slope.
3. y � 5x � �12� 4. y � �12� x
Find the zero of each function. Then graph the function.
5. ƒ (x) � 4x � 3 6. ƒ(x) � 2x � 4
7. Business In 1990, a two-bedroom apartment at RemingtonSquare Apartments rented for $575 per month. In 1999, thesame two-bedroom apartment rented for $850 per month.Assuming a constant rate of increase, what will a tenant pay for a two-bedroom apartment at Remington Square in the year 2000?
PracticeNAME _____________________________ DATE _______________ PERIOD ________
1-3
© Glencoe/McGraw-Hill 9 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-3
Inverses and Symmetry1. Use the coordinate axes at the right to graph the
function f(x) � x and the points A(2, 4), A′(4, 2),B(–1, 3), B′(3, –1), C(0, –5), and C′(–5, 0).
2. Describe the apparent relationship between the graph of the function f(x) � x and any two points with interchanged abscissas and ordinates.
3. Graph the function f(x) � 2x � 4 and its inverse f –1(x) on the coordinate axes at the right.
4. Describe the apparent relationship between the graphs you have drawn and the graph of the function f(x) � x.
Recall from your earlier math courses that two points P and Q are said to be symmetric about line � provided that P and Q are equidistant from � and on a perpendicular through �.The line � is the axis of symmetry and P and Q are images of each other in �. The image of the point P(a, b) in the line y � x is the point Q(b, a).
5. Explain why the graphs of a function f (x) and its inverse, f –1(x),are symmetric about the line y � x .
© Glencoe/McGraw-Hill 10 Advanced Mathematical Concepts
Writing Linear EquationsThe form in which you write an equation of a line depends on the information you are given. Given the slope and y-intercept, or given the slope and one point on the line, theslope-intercept form can be used to write the equation.
Example 1 Write an equation in slope-intercept form for each linedescribed.
a. a slope of �23� and a y-intercept of �5
Substitute �23� for m and �5 for b in the generalslope-intercept form.y � mx � b → y � �23�x � 5.
The slope-intercept form of the equation of the line is y � �23�x � 5.
b. a slope of 4 and passes through the pointat (�2, 3)Substitute the slope and coordinates of thepoint in the general slope-intercept form of alinear equation. Then solve for b.
y � mx � b3 � 4(�2) � b Substitute �2 for x, 3 for y, and 4 for m.
11 � b Add 8 to both sides of the equation.
The y-intercept is 11. Thus, the equation for the line is y � 4x �11.
When you know the coordinates of two points on a line,you can find the slope of the line. Then the equation of theline can be written using either the slope-intercept or thepoint-slope form, which is y � y1 � m(x � x1).
Example 2 Sales In 1998, the average weekly first-quartersales at Vic’s Hardware store were $9250. In 1999,the average weekly first-quarter sales were$10,100. Assuming a linear relationship, find theaverage quarterly rate of increase.
(1, 9250) and (5, 10,100) Since there are two data points, identify the twocoordinates to find the slope of the line.Coordinate 1 represents the first quarter of 1998and coordinate 5 represents the first quarter of1999.
Thus, for each quarter, the average sales increase was $212.50.
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
1-4
m � �y
x2
2
�
�
y
x1
1�
� �10,1050��
19250�
� �8540� or 212.5
© Glencoe/McGraw-Hill 11 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
Writing Linear EquationsWrite an equation in slope-intercept form for each line described.
1. slope � �4, y-intercept � 3 2. slope � 5, passes through A(�3, 2)
3. slope � �4, passes through B(3, 8) 4. slope � �43�, passes through C(�9, 4)
5. slope � 1, passes through D(�6, 6) 6. slope � �1, passes through E(3, �3)
7. slope � 3, y-intercept � �34� 8. slope � �2, y-intercept � �7
9. slope � �1, passes through F(�1, 7) 10. slope � 0, passes through G(3, 2)
11. Aviation The number of active certified commercial pilots has been declining since 1980, as shown in the table.a. Find a linear equation that can be used as a model
to predict the number of active certified commercial pilots for any year. Assume a steady rate of decline.
b. Use the model to predict the number of pilots in the year 2003.
1-4
Number of ActiveCertified Pilots
Year Total
1980 182,097
1985 155,929
1990 149,666
1993 143,014
1994 138,728
1995 133,980
1996 129,187Source: U. S. Dept. of Transportation
© Glencoe/McGraw-Hill 12 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-4
Finding Equations From AreaA right triangle in the first quadrant is bounded by the x-axis, the y-axis, and a line intersecting both axes. Thepoint (1, 2) lies on the hypotenuse of the triangle. Thearea of the triangle is 4 square units.
Follow these instructions to find the equation of the line containing the hypotenuse. Let m represent the slope of the line.
1. Write the equation, in point-slope form, of the line containing thehypotenuse of the triangle.
2. Find the x-intercept and the y-intercept of the line.
3. Write the measures of the legs of the triangle.
4. Use your answers to Exercise 3 and the formula for the area of atriangle to write an expression for the area of the triangle interms of the slope of the hypotenuse. Set the expression equal to4, the area of the triangle, and solve for m .
5. Write the equation of the line, in point-slope form, containing thehypotenuse of the triangle.
6. Another right triangle in the first quadrant has an area of4 square units. The point (2, 1) lies on the hypotenuse. Find theequation of the line, in point-slope form, containing thehypotenuse.
7. A line with negative slope passes through the point (6, 1). A triangle bounded by the line and the coordinate axes has an areaof 16 square units. Find the slope of the line.
© Glencoe/McGraw-Hill 13 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
1-5
Writing Equations of Parallel and Perpendicular Lines• Two nonvertical lines in a plane are parallel if and only if
their slopes are equal and they have no points in common.
• Graphs of two equations that represent the same line aresaid to coincide.
• Two nonvertical lines in a plane are perpendicular if andonly if their slopes are negative reciprocals.
Example 1 Determine whether the graphs of each pair ofequations are parallel, coinciding, or neither.a. 2x � 3y � 5 b. 12x � 6y � 18
6x � 9y � 21 4x � �2y � 6
Write each pair of equations in slope-intercept form.
a. 2x � 3y � 5 6x � 9y � 21y � �23�x � �53� y � �23�x � �3
7�
The lines have the same slope but different y-intercepts, so they are parallel.
Example 2 Write the standard form of the equation of theline that passes through the point at (3, �4) andis parallel to the graph of x � 3y � 4 � 0.
Any line parallel to the graph of x � 3y � 4 � 0will have the same slope. So, find the slope of thegraph of x � 3y � 4 � 0.
m � ��BA�
� ��13� A � 1, B � 3
Use the point-slope form to write the equation ofthe line.
y � y1 � m(x � x1)
y � (�4) � ��13�(x � 3) x1 � 3, y1 � �4, m � ��13�
y � 4 � � �13� x � 13y � 12 � �x � 3 Multiply each side by 3.
x � 3y � 9 � 0 Write in standard form.
b. 12x � 6y � 18 4x � �2y � 6y � �2x � 3 y � �2x � 3
The equations are identical, so thelines coincide.
© Glencoe/McGraw-Hill 14 Advanced Mathematical Concepts
Writing Equations of Parallel and Perpendicular Lines
Determine whether the graphs of each pair of equations areparallel, perpendicular, coinciding, or none of these.
1. x � 3y � 18 2. 2x � 4y � 83x � 9y � 12 x � 2y � 4
3. �3x � 2y � 6 4. x � y � 62x � 3y � 12 3x � y � 6
5. 4x � 8y � 2 6. 3x � y � 92x � 4y � 8 6x � 2y � 18
Write the standard form of the equation of the line that is parallelto the graph of the given equation and that passes through thepoint with the given coordinates.
7. 2x � y � 5 � 0; (0, 4) 8. 3x � y � 3 � 0; (�1, �2) 9. 3x � 2y � 8 � 0; (2, 5)
Write the standard form of the equation of the line that isperpendicular to the graph of the given equation and that passesthrough the point with the given coordinates.10. 2x � y � 6 � 0; (0, �3) 11. 2x � 5y � 6 � 0; (�4, 2) 12. 3x � 4y � 13 � 0; (2, 7)
13. Consumerism Marillia paid $180 for 3 video games and 4 books. Three monthslater she purchased 8 books and 6 video games. Her brother guessed that she spent $320. Assuming that the prices of video games and books did not change,is it possible that she spent $320 for the second set of purchases? Explain.
PracticeNAME _____________________________ DATE _______________ PERIOD ________
1-5
© Glencoe/McGraw-Hill 15 Advanced Mathematical Concepts
NAME _____________________________ DATE _______________ PERIOD ________
Enrichment1-5
Reading Mathematics: Question AssumptionsStudents at the elementary level assume that the statements intheir textbooks are complete and verifiably true. A lesson on thearea of a triangle is assumed to contain everything there is to knowabout triangle area, and the conclusions reached in the lesson arerock-solid fact. The student’s job is to “learn” what textbooks have tosay. The better the student does this, the better his or her grade.
By now you probably realize that knowledge is open-ended and thatmuch of what passes for fact—in math and science as well as inother areas— consists of theory or opinion to some degree.
At best, it offers the closest guess at the “truth” that is now possible.Rather than accept the statements of an author blindly, the educated person’s job is to read them carefully, critically, and with anopen mind, and to then make an independent judgment of theirvalidity. The first task is to question the author’s assumptions.
The following statements appear in the best-selling text Mathematics: Trust Me!.Describe the author’s assumptions. What is the author trying to accomplish? Whatdid he or she fail to mention? What is another way of looking at the issue?
1. “The study of trigonometry is critically important in today’s world.”
2. “We will look at the case where x > 0. The argument where x ≤ 0 is similar.”
3. “As you recall, the mean is an excellent method of describing aset of data.”
4. “Sometimes it is necessary to estimate the solution.”
5. “This expression can be written .”1�x
© Glencoe/McGraw-Hill 16 Advanced Mathematical Concepts
Modeling Real-World Data with Linear FunctionsWhen real-world data are collected, the data graphed usually do notform a straight line. However, the graph may approximate a linearrelationship.
Example The table shows the amount of freighthauled by trucks in the United States. Usethe data to draw a line of best fit and topredict the amount of freight that will becarried by trucks in the year 2010.
Graph the data on a scatter plot. Use the year as theindependent variable and the ton-miles as the dependentvariable. Draw a line of best fit, with some points on the lineand others close to it.
Write a prediction equation for the data. Select two points thatappear to represent the data. We chose (1990, 735) and (1993, 861).
Determine the slope of the line.
m � �y
x2
2
�
�
y
x1
1
� → �1896913
��
7139590� � �12
36� or 42
Use one of the ordered pairs, such as (1990, 735), and theslope in the point-slope form of the equation.
y � y1 � m(x � x1)y � 735 � 42(x � 1990)
y � 42x � 82,845
A prediction equation is y � 42x � 82,845. Substitute 2010 forx to estimate the average amount of freight a truck will haulin 2010.
y � 42x � 82,845y � 42(2010) � 82,845y � 1575
According to this prediction equation, trucks will haul 1575 billion ton-miles in 2010.
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
1-6
AmountYear (billions of
ton-miles)
1986 632
1987 663
1988 700
1989 716
1990 735
1991 758
1992 815
1993 861
1994 908
1995 921
U.S. Truck Freight Traffic
Source: Transportation in America
© Glencoe/McGraw-Hill 17 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
Modeling Real-World Data with Linear Functions
Complete the following for each set of data.a. Graph the data on a scatter plot.b. Use two ordered pairs to write the equation of a best-fit line.c. If the equation of the regression line shows a moderate or
strong relationship, predict the missing value. Explain whetheryou think the prediction is reliable.
1. a.
2. a.
1-6
U. S. Life Expectancy
Birth Number ofYear Years
1990 75.4
1991 75.5
1992 75.8
1993 75.5
1994 75.7
1995 75.8
2015 ?Source: National Centerfor Health Statistics
Population Growth
YearPopulation (millions)
1991 252.1
1992 255.0
1993 257.7
1994 260.3
1995 262.8
1996 265.2
1997 267.7
1998 270.3
1999 272.9
2010 ?Source: U.S. Census Bureau
© Glencoe/McGraw-Hill 18 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-6
Significant DigitsAll measurements are approximations. The significant digits of anapproximate number are those which indicate the results of a measurement.
For example, the mass of an object, measured to the nearest gram, is210 grams. The measurement 210 g has 3 significant digits. Themass of the same object, measured to the nearest 100 g, is 200 g. Themeasurement 200 g has one significant digit.
Several identifying characteristics of significant digits are listedbelow, with examples.
1. Non-zero digits and zeros between significant digits are significant. For example, the measurement 9.071 m has 4 significant digits, 9, 0, 7, and 1.
2. Zeros at the end of a decimal fraction are significant. The measurement 0.050 mm has 2 significant digits, 5 and 0.
3. Underlined zeros in whole numbers are significant. The measurement 104,000 km has 5 significant digits, 1, 0, 4, 0, and 0.
In general, a computation involving multiplication or division ofmeasurements cannot be more accurate than the least accuratemeasurement of the computation. Thus, the result of computationinvolving multiplication or division of measurements should berounded to the number of significant digits in the least accuratemeasurement.
Example The mass of 37 quarters is 210 g. Find the mass of one quarter.
mass of 1 quarter � 210 g � 37� 5.68 g
Write the number of significant digits for each measurement.
1. 8314.20 m 2. 30.70 cm 3. 0.01 mm 4. 0.0605 mg
5. 370,000 km 6. 370,000 km 7. 9.7 104 g 8. 3.20 10–2 g
Solve each problem. Round each result to the correct number of significant digits.
9. 23 m 1.54 m 10. 12,000 ft � 520 ft 11. 2.5 cm 25
12. 11.01 mm 11 13. 908 yd � 0.5 14. 38.6 m 4.0 m
210 has 3 significant digits.37 does not represent a measurement.Round the result to 3 significant digits.Why?
© Glencoe/McGraw-Hill 19 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
Piecewise Functions
Piecewise functions use different equations for differentintervals of the domain. When graphing piecewise functions,the partial graphs over various intervals do not necessarilyconnect.
Example 1 Graph ƒ(x) � �First, graph the constant function ƒ(x) � �1 for x �3. Thisgraph is a horizontal line. Because the point at (�3, �1) isincluded in the graph, draw a closed circle at that point.
Second, graph the function ƒ(x) � 1 � x for �2 � x 2.Because x � �2 is not included in this region of the domain,draw an open circle at (�2, �1). The value of x � 2 is includedin the domain, so draw a closed circle at (2, 3) since for ƒ(x) � 1 � x, ƒ(2) � 3.
Third, graph the line ƒ(x) � 2x for x � 4. Draw an open circleat (4, 8) since for ƒ(x) � 2x, ƒ(4) � 8.
A piecewise function whose graph looks like a set of stairs iscalled a step function. One type of step function is thegreatest integer function. The symbol �x� means thegreatest integer not greater than x. The graphs of stepfunctions are often used to model real-world problems such asfees for phone services and the cost of shipping an item of agiven weight.
The absolute value function is another piecewise function.Consider ƒ(x) � x. The absolute value of a number is alwaysnonnegative.
Example 2 Graph ƒ(x) � 2x � 2.
Use a table of values to determine points on the graph.
if x � �3if �2 � x � 2if x � 4
�11 � x2x
1-7
x 2x � 2 (x, ƒ(x))
�4 2�4 � 2 (�4, 6)
�3 2�3 � 2 (�3, 4)
�1.5 2�1.5 � 2 (�1.5, 1)
0 20 � 2 (0, �2)
1 21 � 2 (1, 0)
2 22 � 2 (2, 2)
© Glencoe/McGraw-Hill 20 Advanced Mathematical Concepts
Piecewise Functions
Graph each function.
1. ƒ(x) � � 2. ƒ(x) � �
3. ƒ(x) � �x� � 3 4. ƒ(x) � x � 1
5. ƒ(x) � 3�x� � 2 6. ƒ(x) � 2x � 1
7. Graph the tax rates for the different incomes by using a step function.
�2 if x �11 � x if �1 � x � 21 � x if x � 2
1 if x 2x if �1 x � 2�x � 3 if x � �2
PracticeNAME _____________________________ DATE _______________ PERIOD ________
1-7
Income Tax Rates for a Couple Filing Jointly
Limits of Taxable TaxIncome Rate
$0 to $41,200 15%
$41,201 to $99,600 28%
$99,601 to $151,750 31%
$151,751 to $271,050 36%
$271,051 and up 39.6%
Source: Information Please Almanac
© Glencoe/McGraw-Hill 21 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-7
Modus PonensA syllogism is a deductive argument in which a conclusion isinferred from two premises. Whether a syllogistic argument is validor invalid is determined by its form. Consider the following syllogism.
Premise 1: If a line is perpendicular to line m, then the slope of that line is ��35�.
Premise 2: Line � is perpendicular to line m.Conclusion: � The slope of line � is ��35�.
Any statement of the form, “if p, then q,” such as the statement inpremise 1, can be written symbolically as p → q. We read this “pimplies q.”
The syllogism above is valid because the argument form,
Premise 1: p → q (This argument says that if p__ imp_____lies q_____Premise 2: p_______ is true and p_ is true, then q_ mustConclusion: � q be true.)
is a valid argument form.
The argument form above has the Latin name modus ponens,which means “a manner of affirming.” Any modus ponens argumentis a valid argument.
Decide whether each argument is a modus ponens argument.
1. If the graph of a relation passes the vertical line test, then the relation is a function. The graph of the relation f (x) does not pass the vertical line test. Therefore, f (x) is not a function.
2. If you know the Pythagorean Theorem, you will appreciate Shakespeare.You do know the Pythagorean Theorem. Therefore, you will appreciateShakespeare.
3. If the base angles of a triangle are congruent, then the triangle is isosceles. The base angles of triangle ABC are congruent. Therefore,triangle ABC is isosceles.
4. When x � –3, x2 � 9. Therefore, if t � –3, it follows that t2 � 9.
5. Since x > 10, x > 0. It is true that x > 0. Therefore, x > 10.
© Glencoe/McGraw-Hill 22 Advanced Mathematical Concepts
Graphing Linear InequalitiesThe graph of y � ��13�x � 2 is a line that
separates the coordinate plane into two regions, called half planes. The line
described by y � ��13�x � 2 is called the
boundary of each region. If the boundary is part of a graph, it is drawn as a solid line.A boundary that is not part of the graph is drawn as a dashed line.
The graph of y > ��13�x � 2 is the region above
the line. The graph of y < ��13�x � 2 is the region
below the line.
You can determine which half plane to shade by testing apoint on either side of the boundary in the original inequality.If it is not on the boundary, (0, 0) is often an easy point totest. If the inequality is true for your test point, then shadethe half plane that contains the test point. If the inequality isfalse for your test point, then shade the half plane that doesnot contain the test point.
Example Graph each inequality.
a. x � y � 2 � 0
x � y � 2 0�y �x � 2
y x � 2 Reverse the inequalitywhen you divide ormultiply by a negative.
The graph doesinclude the boundary,so the line is solid.Testing (0, 0) in theinequality yields afalse inequality, 0 2.Shade the half planethat does not include(0, 0).
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
1-8
b. y � x � 1
Graph the equation with adashed boundary. Then test a point to determinewhich region is shaded.The test point (0, 0) yields the false inequality 0 > 1,so shade the region that does not include (0, 0).
y
O x
y > x – 1
© Glencoe/McGraw-Hill 23 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
Graphing Linear Inequalities
Graph each inequality.
1. x �2 2. y � �2x � 4
3. y 3x � 2 4. y � �x � 3�
5. y � �x � 2� 6. y ��12�x � 4
7. �34�x � 3 y �54�x � 4 8. �4 x � 2y � 6
1-8
© Glencoe/McGraw-Hill 24 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
1-8
Line Designs: Art and GeometryIteration paths that spiral in toward an attractor or spiral out froma repeller create interesting designs. By inscribing polygons withinpolygons and using the techniques of line design, you can createyour own interesting spiral designs that create an illusion of curves.
1. Mark off equal units on 2. Connect two points that 3. Draw the secondthe sides of a square. are equal distances from (adjacent) side of the
adjacent vertices. inscribed square.
4. Draw the other two sides 5. Repeat Step 1 for the 6. Repeat Steps 2, 3,of the inscribed square inscribed square. (Use the and 4 for the
same number of divisions). inscribed square.
7. Repeat Step 1 for the 8. Repeat Steps 2, 3, and 4, 9. Repeat the procedurenew square. for the third inscribed as often as you wish.
square.
10. Suppose your first inscribed square is a clockwise rotationlike the one at the right. How will the design you createcompare to the design created above, which used a counterclockwise rotation?
11. Create other spiral designs by inscribing triangles withintriangles and pentagons within pentagons.
© Glencoe/McGraw-Hill 25 Advanced Mathematical Concepts
Chapter 1 Test, Form 1A
NAME _____________________________ DATE _______________ PERIOD ________
Write the letter for the correct answer in the blank at the right ofeach problem.
1. What are the domain and range of the relation {(�1, �2), (1, �2), (3, 1)}? 1. ________Is the relation a function? Choose yes or no.A. D � {�1, 1, 3}; R � {�2, 1}; yes B. D � {�2, 1}; R � {�1, 1, 3}; noC. D � {�1, �2, 3}; R � {�1, 1}; no D. D � {�2, 1}; R � {�2, 1}; yes
2. Given ƒ(x) � x2 � 2x, find ƒ(a � 3). 2. ________A. a2 � 4a � 3 B. a2 � 2a � 15 C. a2 � 8a � 3 D. a2 � 4a � 6
3. Which relation is a function? 3. ________A. B. C. D.
4. If ƒ(x) � �x �x
3� and g(x) � 2x � 1, find ( ƒ � g)(x). 4. ________
A. ��2x2
x��
83x � 3� B. ��2x2
x��
63x � 1� C. ��2x2
x��
53x � 3� D. �2x2
x�
�6x
3� 3�
5. If ƒ(x) � x2 � 1 and g(x) � �1x�, find [ ƒ � g](x). 5. ________
A. x � �1x� B. �x12� C. �
x21� 1� D. �
x12� � 1
6. Find the zero of ƒ(x) � ��23�x � 12. 6. ________A. �18 B. �12 C. 12 D. 18
7. Which equation represents a line perpendicular to the graph of x � 3y � 9? 7. ________A. y � ��13�x � 1 B. y � 3x � 1 C. y � �3x � 1 D. y � ��13�x � 1
8. Find the slope and y-intercept of the graph 2x � 3y � 3 � 0. 8. ________
A. m � �23�, b � �3 B. m � ��23�, b � �23�
C. m � 1, b � 2 D. m � ��23�, b � 1
9. Which is the graph of 3x � 2y � 4? 9. ________A. B. C. D.
10. Line k passes through A(�3, �5) and has a slope of ��13�. What is the 10. ________standard form of the equation for line k?A. �x � 3y � 18 � 0 B. x � 3y � 12 � 0C. x � 3y � 18 � 0 D. x � 3y � 18 � 0
11. Write an equation in slope-intercept form for a line passing through 11. ________A(4, �3) and B(10, 5).
A. y � �43�x � �235� B. y � ��43�x � �73� C. y � �43�x � �23
5� D. y � �43�x � �130�
Chapter
1
© Glencoe/McGraw-Hill 26 Advanced Mathematical Concepts
12. Write an equation in slope-intercept form for a line with a slope of �110� 12. ________
and a y-intercept of �2.A. y � 0.1x � 200 B. y � 0.1x � 2C. y � 0.1x � 20 D. y � 0.1x � 2
13. Write an equation in standard form for a line with an x-intercept of 13. ________2 and a y-intercept of 5.A. 2x � 5y � 25 � 0 B. 5x � 2y � 5 � 0C. 2x � 5y � 5 � 0 D. 5x � 2y � 10 � 0
14. Which of the following describes the graphs of 2x � 5y � 9 and 14. ________10x � 4y � 18?A. parallel B. coinciding C. perpendicular D. none of these
15. Write the standard form of the equation of the line parallel to 15. ________the graph of 2y � 6 � 0 and passing through B(4, �1).A. x � 4 � 0 B. x � 1 � 0 C. y � 1 � 0 D. y � 4 � 0
16. Write an equation of the line perpendicular to the graph 16. ________of x � 2y � 6 � 0 and passing through A(�3, 2).A. 2x � y � 4 � 0 B. x � y � 4 � 0C. x � 2y � 7 � 0 D. 2x � y � 8 � 0
17. The table shows data for vehicles sold by a certain automobile dealer 17. ________during a six-year period. Which equation best models the data in the table?
A. y � x � 945 B. y � 720C. y � 45x � 89,010 D. y � �45x � 945
18. Which function describes the graph? 18. ________A. ƒ(x) � x � 1 B. ƒ(x) � 2x � 1C. ƒ(x) � 2x � 1 D. ƒ(x) � �12�x � 1
19. The cost of renting a car is $125 a day. Write a 19. ________function for the situation where d represents the number of days.A. c(d) � 125d � �12
245� d B. c(d) � 125d � 1
C. c(d) � � D. c(d) � �20. Which inequality describes the graph? 20. ________
A. y x B. x � 1 yC. 2x � y 0 D. x 7
Bonus Find the value of k such that ��23� Bonus: ________
is a zero of the function ƒ(x) � �4x7� k�.
A. ��134� B. ��76� C. �16� D. �3
8�
125d if d � d125d � 1 if d � d
125d if d � d125d � 1 if d � d
Chapter 1 Test, Form 1A (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
Year 1994 1995 1996 1997 1998 1999
Number of Vehicles Sold 720 710 800 840 905 945
© Glencoe/McGraw-Hill 27 Advanced Mathematical Concepts
Chapter 1 Test, Form 1B
NAME _____________________________ DATE _______________ PERIOD ________
Write the letter for the correct answer in the blank at the right ofeach problem.
1. What are the domain and range of the relation {(4, �1), (4, 1), (3, 2)}? 1. ________Is the relation a function? Choose yes or no.A. D � {�1, 1, 2}; R � {1, 2}; no B. D � {4, 3, 2}; R � {�1, 1}; yesC. D � {4, 3}; R � {�1, 1, 2}; no D. D � {4, �1, 3, 2}; R � {1}; no
2. Given ƒ(x) � �x2 � 2x, find ƒ(�3). 2. ________A. 3 B. �15 C. 15 D. �10
3. Which relation is a function? 3. ________A. B. C. D.
4. If ƒ(x) � �x �1
2� and g(x) � 3x, find ( ƒ � g)(x). 4. ________
A. ��3x2
x��
62x � 1� B. ��3x2
x��
62x � 1� C. ��3x2
x��
62x � 1� D. �3x2
x�
�6x
2� 1�
5. If ƒ(x) � x2 � 1 and g(x) � x � 2, find [ ƒ � g](x). 5. ________A. x2 � 4 B. x2 � 5 C. x2 � 4x � 4 D. x2 � 4x � 5
6. Find the zero of ƒ(x) � �34�x � 12. 6. ________
A. �12 B. �16 C. 9 D. 16
7. Which equation represents a line perpendicular to the graph 7. ________of 2y � x � 2?A. y � �12�x � 2 B. y � �4x � 2 C. y � �2x � 1 D. y � ��12�x � 2
8. Find the slope and y-intercept of the graph of 5x � 3y � 6 � 0. 8. ________A. m � �12�, b � 4 B. m � �53�, b � 2
C. m � �35�, b � 4 D. m � 2, b � �12�
9. Which is the graph of 4x � 2y � 6? 9. ________
A. B. C. D.
10. Write an equation in standard form for a line with a slope of �12� and 10. ________passing through A(1, 2).A. x � 2y � 3 � 0 B. x � 2y � 3 � 0C. �x � 2y � 3 � 0 D. �x � 2y � 3 � 0
11. Which is an equation for the line passing through B(0, 3) and C(�3, 4)? 11. ________A. x � 3y � 9 � 0 B. 3x � y � 3 � 0C. 3x � y � 3 � 0 D. x � 3y � 9 � 0
Chapter
1
© Glencoe/McGraw-Hill 28 Advanced Mathematical Concepts
12. Write an equation in slope-intercept form for the line passing 12. ________through A(�2, 1) and having a slope of 0.5.A. y � 0.5x � 2 B. y � 0.5x C. y � 0.5x � 3 D. y � 0.5x � 1
13. Write an equation in standard form for a line with an x-intercept of 13. ________3 and a y-intercept of 6.A. 2y � x � 6 � 0 B. y � 2x � 6 � 0C. y � 2x � 3 � 0 D. 2y � x � 3 � 0
14. Which describes the graphs of 2x � 3y � 9 and 4x � 6y � 18? 14. ________A. parallel B. coinciding C. perpendicular D. none of these
15. Write the standard form of an equation of the line parallel to 15. ________the graph of x � 2y � 6 � 0 and passing through A(�3, 2).A. x � 2y � 1 � 0 B. x � 2y � 1 � 0C. x � 2y � 7 � 0 D. x � 2y � 7 � 0
16. Write an equation of the line perpendicular to the graph 16. ________of 2y � 6 � 0 and passing through C(4, �1).A. x � 4 � 0 B. x � 1 � 0 C. y � 1 � 0 D. y � 4 � 0
17. A laboratory test exposes 100 weeds to a certain herbicide. 17. ________Which equation best models the data in the table?
Week 0 1 2 3 4 5
Number of Weeds Remaining 100 82 64 39 24 0
A. y � 100 B. y � x � 100 C. y � 20x � 5 D. y � �20x � 100
18. Which function describes the graph? 18. ________A. ƒ(x) � x B. ƒ(x) � 2xC. ƒ(x) � x � 2 D. ƒ(x) � �12�x
19. The cost of renting a washer and dryer is $30 for the first month, $55 19. ________for two months, and $20 per month for more than two months, up to one year. Write a function for the situation where m represents the number of months.
A. c(m) � � B. c(m) � �C. c(m) � 20m � 30 D. c(m) � 30(m � 1) � 55(m � 2) � 20(m � 3)
20. Which inequality describes the graph? 20. ________A. y � �2xB. ��12� x � 1� yC. y � �2x � 1D. y � �2x � 1
Bonus For what value of k will the graph of 2x � ky � 6 be Bonus: ________perpendicular to the graph of 6x � 4y � 12?
A. ��43� B. �43� C. �3 D. 3
30 if 0 � m � 155 if 1 m � 220m if 2 m
30 if 0 � m 155 if 1 � m 220m if 2 � m 12
Chapter 1 Test, Form 1B (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
© Glencoe/McGraw-Hill 29 Advanced Mathematical Concepts
Chapter 1 Test, Form 1C
NAME _____________________________ DATE _______________ PERIOD ________
Write the letter for the correct answer in the blank at the right ofeach problem.
1. What are the domain and range of the relation {(2, 2), (4, 2), (6, 2)}? 1. ________Is the relation a function? Choose yes or no.A. D � {2}; R � {2, 4, 6}; yes B. D � {2}; R � {2, 4, 6}; noC. D � {2, 4, 6}; R � {2}; no D. D � {2, 4, 6}; R � {2}; yes
2. Given ƒ(x) � x2 � 2x, find ƒ(4). 2. ________A. 0 B. �8 C. 8 D. 24
3. Which relation is a function? 3. ________A. B. C. D.
4. If ƒ(x) � x � 3 and g(x) � 2x � 4, find ( ƒ � g)(x). 4. ________A. 3x � 7 B. �x � 7 C. �x � 1 D. 3x � 1
5. If ƒ(x) � x2 � 1 and g(x) � 2x, find [ ƒ � g] (x). 5. ________A. 2x2 � 2 B. 2x2 � 1 C. x2 � 4x � 4 D. 4x2 � 1
6. Find the zero of ƒ(x) � 5x � 2. 6. ________A. �25� B. �2 C. 2 D. ��25�
7. Which equation represents a line perpendicular to the graph of 7. ________2x � y � 2?A. y � ��12�x � 2 B. y � 2x � 2 C. y � �2x � 2 D. y � �12�x � 2
8. Find the slope and y-intercept of the graph of 3x � 2y � 8 � 0. 8. ________A. m � �38�, b � 4 B. m � �53�, b � 2
C. m � �32�, b � 4 D. m � 2, b � �12�
9. Which is the graph of x � y � 1? 9. ________A. B. C. D.
10. Write an equation in standard form for a line with a slope of �1 10. ________passing through C(2, 1).A. x � y � 3 � 0 B. x � y � 3 � 0C. �x � y � 3 � 0 D. x � y � 3 � 0
11. Write an equation in standard form for a line passing through 11. ________A(�2, 3) and B(3, 4).A. 5x � y � 17 � 0 B. x � y � 1 � 0C. x � 5y � 19 � 0 D. x � 5y � 17 � 0
Chapter
1
© Glencoe/McGraw-Hill 30 Advanced Mathematical Concepts
12. Write an equation in slope-intercept form for a line with a slope of 2 12. ________and a y-intercept of 1.A. y � �2x � 1 B. y � 2x � 2 C. y � �12�x � 3 D. y � 2x � 1
13. Write an equation in standard form for a line with a slope of 2 and 13. ________a y-intercept of 3.A. 2x � y � 3 � 0 B. �12�x � y � 3 � 0C. 2x � y � 3 � 0 D. �2x � y � 3 � 0
14. Which of the following describes the graphs of 2x � 3y � 9 and 14. ________6x � 9y � 18?A. parallel B. coincidingC. perpendicular D. none of these
15. Write the standard form of the equation of the line parallel to the 15. ________graph of x � 2y � 6 � 0 and passing through C(0, 1).A. x � 2y � 2 � 0 B. x � 2y � 2 � 0C. 2x � y � 2 � 0 D. 2x � y � 2 � 0
16. Write an equation of the line perpendicular to the graph of x � 3 and 16. ________passing through D(4, �1).A. x � 4 � 0 B. x � 1 � 0 C. y � 1 � 0 D. y � 4 � 0
17. What does the correlation value r for a regression line describe 17. ________about the data?A. It describes the accuracy of the data.B. It describes the domain of the data.C. It describes how closely the data fit the line.D. It describes the range of the data.
18. Which function describes the graph? 18. ________A. ƒ(x) � � x � 1 � B. ƒ(x) � � x � 1 �C. ƒ(x) � � x � � 1 D. ƒ(x) � � x � � 1
19. A canoe rental shop on Lake Carmine charges $10 19. ________for one hour or less or $25 for the day. Write a functionfor the situation where t represents time in hours.
A. c(t) � � B. c(t) � �C. c(t) � 10t D. c(t) � 25 � 10t
20. Which inequality describes the graph? 20. ________A. y � x � 2B. 2x � 1 yC. x � y 2D. y x � 2
Bonus For what value of k will the graph of Bonus: ________6x � ky � 6 be perpendicular to the graphof 2x � 6y � 12?A. �12� B. 4 C. 2 D. 5
10 if 0 � t 125 if 1 � t 24
10 if t � 125 if 1 � t
Chapter 1 Test, Form 1C (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
© Glencoe/McGraw-Hill 31 Advanced Mathematical Concepts
Chapter 1 Test, Form 2A
NAME _____________________________ DATE _______________ PERIOD ________
1. State the domain and range of the relation 1. ________________{(�2, �1), (0, 0), (1, 0), (2, 1), (�1, 2)}. Then state whether the relation is a function. Write yes or no.
2. If ƒ(x) � 2x2 � x, find ƒ(x � h). 2. ________________
3. State the domain and range of the 3. ________________relation whose graph is shown. Then state whether the relation is a function.Write yes or no.
Given ƒ(x) � x � 3 and g(x) � �x2
1� 9� , find each function.
4. (ƒ � g)(x) 4. ________________
5. [ g � ƒ ](x) 5. ________________
6. Find the zero of ƒ(x) � 4x � �23�. 6. ________________
Graph each equation.7. 4y � 8 � 0 7.
8. y � ��13�x � 2 8.
9. 3x � 2y � 2 � 0 9.
10. Depreciation A car that sold for $18,600 new in 1993 is 10. _______________valued at $6000 in 1999. Find the slope of the line through the points at (1993, 18,600) and (1999, 6000). What does this slope represent?
Chapter
1
© Glencoe/McGraw-Hill 32 Advanced Mathematical Concepts
11. Write an equation in slope-intercept form for a line that 11. __________________passes through the point C(�2, 3) and has a slope of �23�.
12. Write an equation in standard form for a line passing 12. __________________through A(2, 1) and B(�4, 3).
13. Determine whether the graphs of 4x � y � 2 � 0 and 13. __________________2y � 8x � 4 are parallel, coinciding, perpendicular, ornone of these.
14. Write the slope-intercept form of the equation of the line 14. __________________that passes through C(2, �3) and is parallel to the graph of 3x � 2y � 6 � 0.
15. Write the standard form of the equation of the line that 15. __________________passes through C(3, 4) and is perpendicular to the line that passes through E(4, 1) and F(�2, 4).
16. The table displays data for a toy store’s sales of a specific 16. __________________toy over a six-month period. Write the prediction equation in slope-intercept form for the best-fit line. Use the points (1, 47) and (6, 32).
Graph each function.17. ƒ(x) � 2� x � 1 � � 2 17.
18. ƒ(x) � � 18.
Graph each inequality.19. �2 x � 2y 4 19.
20. y � �� x � 1 � � 2 20.
Bonus If ƒ(x) � �x� �� 2� and ( ƒ � g)(x) � � x � , find g(x). Bonus: __________________
x � 3 if x � 02x if x 0
Chapter 1 Test, Form 2A (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
Month 1 2 3 4 5 6Number of Toys Sold 47 42 43 38 37 32
© Glencoe/McGraw-Hill 33 Advanced Mathematical Concepts
Chapter 1 Test, Form 2B
NAME _____________________________ DATE _______________ PERIOD ________
1. State the domain and range of the relation {(�3, 1), (�1, 0), 1. __________________(0, 4), (�1, 5)}. Then state whether the relation is a function.Write yes or no.
2. If ƒ(x) � 3x2 � 4, find ƒ(a � 2). 2. __________________
3. State the relation shown in the graph 3. __________________as a set of ordered pairs. Then state whetherthe relation is a function. Write yes or no.
Given ƒ(x) � x2 � 4 and g(x) � �x �
12
�, find each function.
4. �ƒg((xx))
� 4. __________________
5. �g � ƒ�(x) 5. __________________
6. Find the zero of ƒ(x) � ��23�x � 8. 6. __________________
Graph each equation.
7. x � 2 � 0 7.
8. y � 3x � 2 8.
9. 2x � 3y � 6 � 0 9.
10. Retail The cost of a typical mountain bike was $330 in 1994 and $550 in 1999. Find the slope of the line through the points at (1994, 330) and (1999, 550). What 10. __________________does this slope represent?
Chapter
1
© Glencoe/McGraw-Hill 34 Advanced Mathematical Concepts
11. Write an equation in slope-intercept form for a line that 11. __________________passes through the point A(4, 1) and has a slope of ��12�.
12. Write an equation in standard form for a line with an 12. __________________x-intercept of �3 and a y-intercept of 4.
13. Determine whether the graphs of 3x � 2y � 5 � 0 and 13. __________________y � ��23�x � 4 are parallel, coinciding, perpendicular, or
none of these.
14. Write the slope-intercept form of the equation of the 14. __________________line that passes through A(�6, 5) and is parallel to the line x � 3y � 6 � 0.
15. Write the standard form of the equation of the line that 15. __________________passes through B(�2, 3) and is perpendicular to the graph of 2y � 6 � 0.
16. A laboratory tests a new fertilizer by applying it to 100 16. __________________seeds. Write a prediction equation in slope-intercept form for the best-fit line. Use the points (1, 8) and (6, 98).
Week 1 2 3 4 5 6
Number of Sprouts 8 20 42 61 85 98
Graph each function.17. ƒ(x) � �2x 17.
18. ƒ(x) � x � 1 18.
Graph each inequality.19. x � 1 � y 19.
20. y 2x � 1 20.
Bonus If ƒ(x) � �x� +� 2� and (g � ƒ)(x) � x � 1, find g(x). Bonus: __________________
Chapter 1 Test, Form 2B (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
© Glencoe/McGraw-Hill 35 Advanced Mathematical Concepts
Chapter 1 Test, Form 2C
NAME _____________________________ DATE _______________ PERIOD ________
1. State the domain and range of the relation {(�1, 0), (0, 2), (2, 3), 1. __________________(0, 4)}. Then state whether the relation is a function. Write yes or no.
2. If ƒ(x) � 2x2 � 1, find ƒ(3). 2. __________________
3. State the relation shown in the graph 3. __________________as a set of ordered pairs. Then state whether the relation is a function. Write yes or no.
Given ƒ(x) � x � 3 and g(x) � x2, find each function.4. ( g � ƒ)(x) 4. __________________
5. [ƒ � g](x) 5. __________________
6. Find the zero of ƒ(x) � 4x � 5. 6. __________________
Graph each equation.7. y � x � 1 7.
8. y � 2x � 2 8.
9. 2y � 4x � 1 9.
10. Appreciation An old coin had a value of $840 in 1991 10. __________________and $1160 in 1999. Find the slope of the line through the points at (1991, 840) and (1999, 1160). What does this slope represent?
Chapter
1
© Glencoe/McGraw-Hill 36 Advanced Mathematical Concepts
11. Write an equation in slope-intercept form for a line that 11. __________________passes through the point A(0, 5) and has a slope of �12�.
12. Write an equation in standard form for a line passing 12. __________________through B(2, 4) and C(3, 8).
13. Determine whether the graphs of x � 2y � 2 � 0 and 13. __________________�3x � 6y � 5 � 0 are parallel, coinciding, perpendicular,or none of these.
14. Write the slope-intercept form of the equation of the line 14. __________________that passes through D(�2, 3) and is parallel to the graph of 2y � 4 � 0.
15. Write the standard form of the equation of the line that 15. __________________passes through E(2, �2) and is perpendicular to the graph of y � 2x � 3.
16. The table shows the average price of a new home in a 16. __________________certain area over a six-year period. Write the prediction equation in slope-intercept form for the best-fit line. Use the points (1994, 102) and (1999, 125).
Graph each function.17. ƒ(x) � �� x � 17.
18. ƒ(x) � � 18.
Graph each inequality.19. y � 3x � 1 19.
20. y � x � � 1 20.
Bonus What value of k in the equation Bonus: __________________2x � ky � 2 � 0 would result in a slope of �13�?
2 if x � 0x if x 0
Chapter 1 Test, Form 2C (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
Year 1994 1995 1996 1997 1998 1999Price (Thousands
102 105 115 114 119 125of Dollars)
© Glencoe/McGraw-Hill 37 Advanced Mathematical Concepts
Chapter 1 Open-Ended Assessment
NAME _____________________________ DATE _______________ PERIOD ________
Instructions: Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include allrelevant drawings and justify your answer. You may show yoursolution in more than one way or investigate beyond therequirements of the problem.
1. a. The graphs of the equations y � 2x � 3, 2y � x � 11, and 2y � 4x � 8 form three sides of a parallelogram. Complete the parallelogram by writing an equation for the graph that forms the fourth side. Justify your choice.
b. Explain how to determine whether the parallelogram is a rectangle. Is it a rectangle? Justify your answer.
c. Graph the equations on the same coordinate axes. Is the graph consistent with your conclusion?
2. a. Write a function ƒ(x).
b. If g(x) � 2x2 � 1, does (ƒ � g)(x) � ( g � ƒ)(x)? Justify your answer.
c. Does (ƒ � g)(x) � ( g � ƒ)(x)? Justify your answer.
d. Does (ƒ � g)(x) � ( g � ƒ)(x)? Justify your answer.
e. Does ��ƒg��(x) � ��ƒ
g��(x)?
f. What can you conclude about the commutativity of adding,subtracting, multiplying, or dividing two functions?
3. Write a word problem that uses the composition of two functions.Give an example of the composition and solve. What does the answer mean? Use the domain and range in your explanation.
Chapter
1
© Glencoe/McGraw-Hill 38 Advanced Mathematical Concepts
1. State the domain and range of the relation {(�3, 0), (0, �2), 1. __________________(1, 1), (0, 3)}. Then state whether the relation is a function.Write yes or no.
2. Find ƒ(�2) for ƒ(x) � 3x2 � 1. 2. __________________
3. If ƒ(x) � 2(x � 1)2 � 3x, find ƒ(a � 1). 3. __________________
Given ƒ(x) � 2x � 1 and g(x) � �21x2� , find each function.
4. ��ƒg��(x) 4. __________________
5. [ƒ � g](x) 5. __________________
Graph each equation.6. x � 2y � 4 6.
7. x � �3y � 6 7.
8. Find the zero of ƒ(x) � 2x � 5. 8. __________________
9. Write an equation in standard form for a line passing 9. __________________through A(�1, 2) and B(3, 8).
10. Sales The initial cost of a new model of calculator was 10. __________________$120. After the calculator had been on the market for two years, its price dropped to $86. Let x represent the number of years the calculator has been on the market,and let y represent the selling price. Write an equation that models the selling price of the calculator after any given number of years.
Chapter 1 Mid-Chapter Test (Lessons 1-1 through 1-4)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
1. State the domain and range of the relation 1. __________________{(2, 3), (3, 3), (4, �2), (5, �3)}. Then statewhether the relation is a function. Write yes or no.
2. State the relation shown in the graph 2. __________________as a set of ordered pairs. Then state whether the graph represents a function. Write yes or no.
3. Evaluate ƒ(�2) if ƒ(x) � 3x2 � 2x. 3. __________________
Given f(x) � 2x � 3 and g(x) � 4x2, find each function.4. (ƒ � g)(x) 4. __________________
5. [ƒ � g](x) 5. __________________
Graph each equation.1. y � ��32�x � 1 1.
2. 4x � 3y � 6 2.
3. Find the zero of the function ƒ(x) � 3x � 2. 3. __________________4. Write an equation in slope-intercept form for the line that
passes through A(9, �2) and has a slope of ��23�. 4. __________________5. Write an equation in standard form for the line that passes
through B(�2, �2) and C(4, 1). 5. __________________
Chapter 1, Quiz B (Lessons 1-3 and 1-4)
NAME _____________________________ DATE _______________ PERIOD ________
Chapter 1, Quiz A (Lessons 1-1 and 1-2)
NAME _____________________________ DATE _______________ PERIOD ________
© Glencoe/McGraw-Hill 39 Advanced Mathematical Concepts
Chapter
1
Chapter
1
Determine whether the graphs of each pair of equations are parallel, coinciding, perpendicular, or none of these.
1. 3x � y � 7 1. __________________2y � 6x � 4
2. y � �13�x � 1 2. __________________x � 3y � 11
3. Write an equation in standard form for the line that 3. __________________passes through A(�2, 4) and is parallel to the graph of 2x � y � 5 � 0.
4. Write an equation in slope-intercept form for the line that 4. __________________passes through B(3, 1) and is perpendicular to the line through C(�1, 1) and D(1, 7).
5. Demographics The table shows data for the 10-year 5. __________________growth rate of the world population. Predict the growth rate for the year 2010. Use the points (1960, 22.0) and (2000, 12.6).
Graph each function.1. ƒ(x) � x � 1 1.
2. ƒ(x) � � 2.
Graph each inequality.3. 2x � y � 4 4. �3 x � 3y 6
x � 3 if x � 03x � 1 if x 0
Chapter 1, Quiz D (Lessons 1-7 and 1-8)
NAME _____________________________ DATE _______________ PERIOD ________
Chapter 1, Quiz C (Lessons 1-5 and 1-6)
NAME _____________________________ DATE _______________ PERIOD ________
© Glencoe/McGraw-Hill 40 Advanced Mathematical Concepts
Chapter
1
Chapter
1
Year 1960 1970 1980 1990 2000 2010
Ten-year 22.0 20.2 18.5 15.2 12.6 ?Growth Rate (%)Source: U.S. Bureau of the Census
© Glencoe/McGraw-Hill 41 Advanced Mathematical Concepts
Chapter 1 SAT and ACT Practice
NAME _____________________________ DATE _______________ PERIOD ________
After working each problem, record thecorrect answer on the answer sheetprovided or use your own paper.
Multiple Choice1. If 9 9 9 � 3 3 t, then t �
A 3B 9C 27D 81E 243
2. If 11! � 39,916,800, then �142!!� �
A 9,979,200B 19,958,400C 39,916,800D 79,833,600E 119,750,000
3. (�3)3 � (16)�12�
� (�1)5 �
A ��72�
B �24C �28D 32E �20
4. Which number is a factor of 15 26 77?A 4B 9C 36D 55E None of these
5. To dilute a concentrated liquid fabricsoftener, the directions state to mix 3 cups of water with 1 cup ofconcentrated liquid. How many gallons of water will you need to make 6 gallonsof diluted fabric softener?A 1�12� gallons B 3 gallons
C 2�12� gallons D 4 gallons
E 4�12� gallons
6. If a number between 1 and 2 is squared, the result is a number betweenA 0 and 1B 2 and 3C 2 and 4D 1 and 4E None of these
7. Seventy-five percent of 32 is what percent of 18?
A 1�13�%
B 13�13�%
C 17�79�%
D 75%
E 133�13�%
8. �23� � �56� � �112� � �78� �
A �153� B �2
549�
C �5254� D �32
14�
E �1225�
9. If 9 and 15 each divide M without aremainder, what is the value of M?A 30B 45C 90D 135E It cannot be determined from the
information given.
10. 145 � 32 �
A �53
1
2
4�
B 196C 143
D 75
E 57
Chapter
1
© Glencoe/McGraw-Hill 42 Advanced Mathematical Concepts
11. A long-distance telephone call costs$1.25 a minute for the first 2 minutesand $0.50 for each minute thereafter.At these rates, how much will a 12-minute telephone call cost?A $6.25B $6.75C $7.25D $7.50E $8.50
12. After has been simplified to a
single fraction in lowest terms,what is the denominator?A 33B 6C 12D 4E 11
13. Which of the following expresses theprime factorization of 24? A 1 2 2 3B 2 2 2 3C 2 2 3 4D 1 2 2 3 3E 1 2 2 2 3
14. �� �4 � � (�7) � � 2 � � � �6 � � (�3) �A �10B �4C �2D �14E 22
15. Which of the following statements istrue?A 5 � 3 4 � 6 � 26B 2 � 3 � 1 � 2 � 4 � 3 � 1C 3 � (5 � 2) 6 � 5(6 � 4) � �5D 2 (5 � 1) � 3 � 2 (4 � 1) � 19E (6 � 22) 5 � 3 � 2 (4 � 1) � �33
16. At last night’s basketball game, Ryanscored 16 points, Geoff scored 11 points,and Bruce scored 9 points. Together they scored �37� of their team’s points.What was their team’s final score?A 108B 96C 36D 77E 84
17–18. Quantitative ComparisonA if the quantity in Column A is
greaterB if the quantity in Column B is
greaterC if the two quantities are equalD if the relationship cannot be
determined from the informationgiven
0 � y � 1
Column A Column B
17.
18.
19. Grid-In What is the sum of thepositive odd factors of 36?
20. Grid-In Write �ab� as a decimal
number if a � �32� and b � �54�.
3�16��2�34�
Chapter 1 SAT and ACT Practice (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
1
y4 y5
0.01% 10�4
© Glencoe/McGraw-Hill 43 Advanced Mathematical Concepts
Chapter 1 Cumulative Review
NAME _____________________________ DATE _______________ PERIOD ________
1. Given that x is an integer and �1 x 2, state the relation 1. __________________represented by y � �4x � 1 by listing a set of ordered pairs.Then state whether the relation is a function. Write yes or no.(Lesson 1-1)
2. If ƒ(x) � x2 � 5x, find ƒ(�3). (Lesson 1-1) 2. __________________
3. If ƒ(x) � �x �1
4� and g(x) � x2 � 2, find [ƒ � g](x). (Lesson 1-2) 3. __________________
Graph each equation.4. x � 2y � 2 � 0 (Lesson 1-3) 4.
5. x � 2 � 0 (Lesson 1-3) 5.
6. Write an equation in standard form for the line that passes 6. __________________through A(�2, 0) and B(4, 3). (Lesson 1-4)
7. Write an equation in slope-intercept form for the line 7. __________________perpendicular to the graph of y � ��
13� x � 1 and passing
through C(2, 1). (Lesson 1-5)
8. The table shows the number of students in Anne Smith’s 8. __________________Karate School over a six-year period. Write the prediction equation in slope-intercept form for the best-fit line. Use the points (1994, 10) and (1999, 35). (Lesson 1-6)
9. Graph the function ƒ(x) � � . (Lesson 1-7) 9.
10. Graph the inequality y � x � � 1. (Lesson 1-8) 10.
�2x if x 01 if x � 0
Chapter
1
Year 1994 1995 1996 1997 1998 1999
Number of Students 10 15 20 25 30 35
BLANK
© Glencoe/McGraw-Hill A1 Advanced Mathematical Concepts
SAT and ACT Practice Answer Sheet(10 Questions)
NAME _____________________________ DATE _______________ PERIOD ________
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
© Glencoe/McGraw-Hill A2 Advanced Mathematical Concepts
SAT and ACT Practice Answer Sheet(20 Questions)
NAME _____________________________ DATE _______________ PERIOD ________
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
© G
lenc
oe/M
cGra
w-H
ill2
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Re
latio
ns
an
d F
un
ctio
ns
Sta
te t
he
dom
ain
an
d r
ang
e of
eac
h r
elat
ion
. Th
en s
tate
wh
eth
erth
e re
lati
on is
a f
un
ctio
n. W
rite
yes
or
no.
1.{(
�1,
2),
(3,
10)
, (�
2, 2
0), (
3, 1
1)}
2.{(
0, 2
), (
13, 6
), (
2, 2
), (
3, 1
)}D
�{�
2,�
1, 3
}, R
�{2
, 10,
11,
20}
;D
�{0
, 2, 3
, 13}
, R�
{1, 2
, 6};
noye
s
3.{(
1, 4
), (
2, 8
), (
3, 2
4)}
4.{(
�1,
�2)
, (3,
54)
, (�
2,�
16),
(3,
81)
}D
�{1
, 2, 3
}, R
�{4
, 8, 2
4};
D�
{�2,
�1,
3},
ye
sR
�{�
16,�
2, 5
4, 8
1}; n
o
5.T
he
dom
ain
of
a re
lati
on is
all
eve
n
y�
x�
4n
egat
ive
inte
gers
gre
ater
th
an�
9.
Th
e ra
nge
yof
th
e re
lati
on is
th
e se
t fo
rmed
by
addi
ng
4 to
th
e n
um
bers
in
th
e do
mai
n. W
rite
th
e re
lati
on a
s a
tabl
e of
val
ues
an
d as
an
equ
atio
n.
Th
en g
raph
th
e re
lati
on.
Eva
luat
e ea
ch f
un
ctio
n f
or t
he
giv
en v
alu
e.6.
ƒ(�
2) if
ƒ(x
)�4x
3�
6x2
�3x
7.ƒ(
3) if
ƒ(x
)�5x
2�
4x�
6�
1427
8.h
(t)
if h
(x)�
9x9
�4x
4�
3x�
29.
ƒ(g
� 1
) if
ƒ(x
)�x2
�2x
�1
9t9
�4t
4�
3t�
2g
2
10.C
lim
ate
Th
e ta
ble
show
s re
cord
hig
h a
nd
low
tem
pera
ture
s fo
r se
lect
ed s
tate
s.a.
Sta
te t
he
rela
tion
of
the
data
as
a se
t of
or
dere
d pa
irs.
{(11
2,�
27),
(110
,�17
), (1
18,�
60),
(112
,�51
), (1
22,�
50),
(114
,�54
)}
b.
Sta
te t
he
dom
ain
an
d ra
nge
of
th
e re
lati
on.
D�
{110
, 112
, 114
, 118
, 122
} R
�{�
60,�
54,�
51,�
50,�
27,�
17}
c.D
eter
min
e w
het
her
th
e re
lati
on is
a f
un
ctio
n.
no
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
1-1
xy
�2
2�
40
�6
�2
�8
�4 R
eco
rd H
igh
and
Lo
w T
emp
erat
ures
(°F
)S
tate
Hig
h Lo
w
Ala
bam
a11
2�
27D
elaw
are
110
�17
Idah
o11
8�
60M
ichi
gan
112
�51
New
Mex
ico
122
�50
Wis
cons
in11
4�
54S
our
ce:
Nat
iona
l Clim
atic
Dat
a C
ente
r
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A3 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill3
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-1
Ra
tes
of
Ch
an
ge
Bet
wee
n x
�a
and
x �
b, t
he
fun
ctio
n f
(x)
chan
ges
by f
(b)�
f(a)
.T
he
aver
age
rate
of
chan
geof
f(x
) be
twee
n x
�a
and
x �
bis
def
ined
by t
he
expr
essi
on
.
Fin
d t
he
chan
ge
and
th
e av
erag
e ra
te o
f ch
ang
e of
f(x
) in
th
e g
iven
ran
ge.
1.f(
x)�
3x�
4, f
rom
x�
3 to
x�
8 ch
ang
e: 1
5; a
vera
ge
rate
of
chan
ge:
3
2.f(
x)�
x2�
6x�
10, f
rom
x�
2 to
x�
4 ch
ang
e: 2
4; a
vera
ge
rate
of
chan
ge:
12
Th
e av
erag
e ra
te o
f ch
ange
of
a fu
nct
ion
f(x
) ov
er a
nin
terv
al is
th
e am
oun
t th
e fu
nct
ion
ch
ange
s pe
r u
nit
chan
ge in
x. A
s sh
own
in t
he
figu
re a
t th
e ri
ght,
th
eav
erag
e ra
te o
f ch
ange
bet
wee
n x
�a
and
x�
b re
pres
ents
th
e sl
ope
of t
he
lin
e pa
ssin
g th
rou
gh t
he
two
poin
ts o
n t
he
grap
h o
f f
wit
h a
bsci
ssas
aan
d b.
3.W
hic
h is
larg
er, t
he
aver
age
rate
of
chan
ge o
f f(
x)�
x2be
twee
n 0
an
d 1
or b
etw
een
4 a
nd
5?b
etw
een
4 an
d 5
4.W
hic
h o
f th
ese
fun
ctio
ns
has
th
e gr
eate
st a
vera
ge r
ate
of c
han
ge
betw
een
2 a
nd
3: f
(x)�
x ; g
(x)�
x2 ; h
(x)�
x3?
h(x
)5.
Fin
d th
e av
erag
e ra
te o
f ch
ange
for
th
e fu
nct
ion
f(x
)�x2
in e
ach
inte
rval
.a.
a�
1 to
b�
1.1
b.
a�
1 to
b�
1.01
c.a
�1
to b
�1.
001
2.1
2.01
2.00
1d
.W
hat
val
ue
does
th
e av
erag
e ra
te o
f ch
ange
app
ear
to b
e ap
proa
chin
g as
th
e va
lue
of b
gets
clo
ser
and
clos
er t
o 1?
2
Th
e va
lue
you
fou
nd
in E
xerc
ise
5dis
th
e in
stan
tan
eou
s ra
te o
fch
ange
of t
he
fun
ctio
n. I
nst
anta
neo
us
rate
of
chan
ge h
as e
nor
mou
sim
port
ance
in c
alcu
lus,
th
e to
pic
of C
hap
ter
15.
6.F
ind
the
inst
anta
neo
us
rate
ofch
ange
of t
he
fun
ctio
n f
(x)�
3x2
asx
appr
oach
es 3
.18
f (b
)�f
(a)
��
(b�
a)
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A4 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill5
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Co
mp
osi
tio
n o
f F
un
ctio
ns
Giv
en ƒ
(x)�
2x2
�8
and
g(x
)�5x
�6,
fin
d e
ach
fu
nct
ion
.1.
(ƒ�
g)(x
)2.
(ƒ�
g)(x
) 2
x2�
5x�
22
x2�
5x�
14
3.(ƒ
�g)
(x)
4.��ƒ g� �(x
)10
x3�
12x2
�40
x�
48�2 5x x2
��68
�, x
��6 5�
Fin
d [
ƒ �
g](
x)an
d [
g �
ƒ](
x)fo
r ea
ch ƒ
(x)
and
g(x
).5.
ƒ(x)
�x
�5
6.ƒ(
x)�
2x3
�3x
2�
1g(
x)�
x�
3g(
x)�
3xx
�2,
x�
254
x3�
27x2
�1,
6x3
�9x
2�
3
7.ƒ(
x)�
2x2
�5x
�1
8.ƒ(
x)�
3x2
�2x
�5
g(x)
�2x
�3
g(x)
�2x
�1
8x2
�34
x�
34, 4
x2�
10x
�1
12x2
�16
x�
10, 6
x2�
4x�
9
9.S
tate
th
e do
mai
n o
f [ƒ
�g]
(x)
for
ƒ(x)
��
x���
2�an
d g
(x)�
3x.
x�
� 32 �
Fin
d t
he
firs
t th
ree
iter
ates
of
each
fu
nct
ion
usi
ng
th
e g
iven
in
itia
l val
ue.
10.ƒ
(x)�
2x�
6; x
0�
111
.ƒ(
x)�
x2�
1; x
0�
2�
4,�
14,�
343,
8, 6
3
12.F
itn
ess
Tara
has
dec
ided
to
star
t a
wal
kin
g pr
ogra
m. H
er
init
ial w
alki
ng
tim
e is
5 m
inu
tes.
Sh
e pl
ans
to d
oubl
e h
er
wal
kin
g ti
me
and
add
1 m
inu
te e
very
5 d
ays.
Pro
vide
d th
at
Tara
ach
ieve
s h
er g
oal,
how
man
y m
inu
tes
wil
l sh
e be
wal
kin
gon
day
s 21
th
rou
gh 2
5?95
min
utes
or
1 ho
ur 3
5 m
inut
es
1-2
© G
lenc
oe/M
cGra
w-H
ill6
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-2
1 � 2
Ap
ply
ing
Co
mp
osi
tio
n o
f F
un
ctio
ns
Bec
ause
th
e ar
ea o
f a
squ
are
Ais
exp
lici
tly
dete
rmin
ed b
y th
e le
ngt
hof
a s
ide
of t
he
squ
are,
th
e ar
ea c
an b
e ex
pres
sed
as a
fu
nct
ion
of
one
vari
able
, th
e le
ngt
h o
f a
side
s: A
�f(
s)�
s2 . P
hys
ical
qu
anti
ties
are
ofte
n f
un
ctio
ns
of n
um
erou
s va
riab
les,
eac
h o
f w
hic
h m
ay it
self
be
afu
nct
ion
of
seve
ral a
ddit
ion
al v
aria
bles
. Aca
r’s
gas
mil
eage
, for
exam
ple,
is a
fu
nct
ion
of
the
mas
s of
th
e ca
r, t
he
type
of
gaso
lin
ebe
ing
use
d, t
he
con
diti
on o
f th
e en
gin
e, a
nd
man
y ot
her
fac
tors
, eac
hof
wh
ich
is f
urt
her
dep
ende
nt
on o
ther
fac
tors
. Fin
din
g th
e va
lue
ofsu
ch a
qu
anti
ty f
or s
peci
fic
valu
es o
f th
e va
riab
les
is o
ften
eas
iest
by
firs
t fi
ndi
ng
a si
ngl
e fu
nct
ion
com
pose
d of
all
th
e fu
nct
ion
s an
d th
ensu
bsti
tuti
ng
for
the
vari
able
s.
Th
e fr
equ
ency
fof
a p
endu
lum
is t
he
nu
mbe
r of
com
plet
e sw
ings
th
epe
ndu
lum
mak
es in
60
seco
nds
. It
is a
fu
nct
ion
of
the
peri
od p
of t
he
pen
dulu
m, t
he
nu
mbe
r of
sec
onds
th
e pe
ndu
lum
req
uir
es t
om
ake
one
com
plet
e sw
ing:
f(p
)�.
In t
urn
, th
e pe
riod
of
a pe
ndu
lum
is a
fu
nct
ion
of
its
len
gth
Lin
ce
nti
met
ers:
p(L
)�0.
2�L�
.
Fin
ally
, th
e le
ngt
h o
f a
pen
dulu
m is
a f
un
ctio
n o
f it
s le
ngt
h �
at 0
°C
elsi
us,
th
e C
elsi
us
tem
pera
ture
C, a
nd
the
coef
fici
ent
of e
xpan
sion
eof
th
e m
ater
ial o
f w
hic
h t
he
pen
dulu
m is
mad
e:L
(�, C
, e)�
�(1
�eC
).
1.a.
Fin
d an
d si
mpl
ify
f(p(
L(�
, C, e
))),
an
exp
ress
ion
for
th
e fr
equ
ency
of
a br
ass
pen
dulu
m, e
= 0.
0000
2, in
ter
ms
of it
sle
ngt
h, i
n c
enti
met
ers
at 0
°C, a
nd
the
Cel
siu
s te
mpe
ratu
re.
f(p
(L(�
, C, e
)))�
b.
Fin
d th
e fr
equ
ency
, to
the
nea
rest
ten
th, o
f a
bras
s pe
ndu
lum
at 3
00°C
if t
he
pen
dulu
m’s
len
gth
at
0°C
is 1
5 ce
nti
met
ers.
77.2
sw
ing
s p
er m
inut
e2.
Th
e vo
lum
e V
of a
sph
eric
al w
eath
er b
allo
on w
ith
rad
ius
ris
give
n b
y V
(r)�
�r3 .
Th
e ba
lloo
n is
bei
ng
infl
ated
so
that
th
e
radi
us
incr
ease
s at
a c
onst
ant
rate
r(t
)�
t�2,
wh
ere
ris
in
met
ers
and
tis
th
e n
um
ber
of s
econ
ds s
ince
infl
atio
n b
egan
.a.
Fin
d V
(r(t
))
V(r
(t))
��
2�t2
�8�
t�
�
b.
Fin
d th
e vo
lum
e af
ter
10 s
econ
ds o
f in
flat
ion
. Use
3.1
4 fo
r �
.14
36.8
m3
32 � 3�
t3
�64 � 3
300
���(�
1���
0�.0�
0�0�0�2�
C�)�
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002C
)
60 � p
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A5 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill8
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Gra
ph
ing
Lin
ea
r E
qu
atio
ns
Gra
ph
eac
h e
qu
atio
n u
sin
g t
he
x- a
nd
y-i
nte
rcep
ts.
1.2x
�y
�6
�0
2.4x
�2y
�8
�0
Gra
ph
eac
h e
qu
atio
n u
sin
g t
he
y-in
terc
ept
and
th
e sl
ope.
3.y
�5x
��1 2�
4.y
��1 2�
x
Fin
d t
he
zero
of
each
fu
nct
ion
. Th
en g
rap
h t
he
fun
ctio
n.
5.ƒ
(x)�
4x�
3�3 4�
6.ƒ
(x)�
2x�
4�
2
7.B
usi
nes
sIn
199
0, a
tw
o-be
droo
m a
part
men
t at
Rem
ingt
onS
quar
e A
part
men
ts r
ente
d fo
r $5
75 p
er m
onth
. In
199
9, t
he
sam
e tw
o-be
droo
m a
part
men
t re
nte
d fo
r $8
50 p
er m
onth
.A
ssu
min
g a
con
stan
t ra
te o
f in
crea
se, w
hat
wil
l a t
enan
t pa
y fo
r a
two-
bedr
oom
apa
rtm
ent
at R
emin
gton
Squ
are
in t
he
year
200
0?ab
out
$88
1
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
1-3
© G
lenc
oe/M
cGra
w-H
ill9
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-3
Inve
rse
s a
nd
Sy
mm
etr
y1.
Use
th
e co
ordi
nat
e ax
es a
t th
e ri
ght
to g
raph
th
e fu
nct
ion
f(x
)�x
and
the
poin
ts A
(2, 4
), A
′(4, 2
),
B(–
1, 3
), B
′(3,–
1), C
(0,–
5), a
nd
C′(–
5, 0
).
2.D
escr
ibe
the
appa
ren
t re
lati
onsh
ip b
etw
een
th
e gr
aph
of
the
fun
ctio
n f
(x)�
xan
d an
y tw
o po
ints
w
ith
inte
rch
ange
d ab
scis
sas
and
ordi
nat
es.
Sam
ple
ans
wer
s: T
he p
oin
ts a
re m
irro
r im
ages
of
each
oth
er in
the
gra
ph
of
f(x)
�x;
the
po
ints
are
sym
met
ric
to e
ach
oth
er w
ith
resp
ect
to t
he g
rap
h o
f f(
x) �
x; t
he p
oin
ts a
reth
e sa
me
dis
tanc
e fr
om
but
on
op
po
site
sid
eso
f th
e g
rap
h o
f f(
x) �
x.
3.G
raph
th
e fu
nct
ion
f(x
)�2x
�4
and
its
inve
rse
f– 1(x
) on
th
e co
ordi
nat
e ax
es a
t th
e ri
ght.
4.D
escr
ibe
the
appa
ren
t re
lati
onsh
ip b
etw
een
th
e gr
aph
s yo
u h
ave
draw
n a
nd
the
grap
h o
f th
e fu
nct
ion
f(x
)�x.
S
amp
le a
nsw
ers:
The
y ar
e m
irro
r im
ages
o
f ea
ch o
ther
in t
he g
rap
h o
f f(
x) �
x; t
hey
inte
rsec
t f(
x) �
xat
the
sam
e p
oin
t an
d a
t th
e sa
me
ang
le.
Rec
all f
rom
you
r ea
rlie
r m
ath
cou
rses
th
at t
wo
poin
ts P
and
Q a
re s
aid
to b
e sy
mm
etri
c ab
out
lin
e �
prov
ided
th
at P
and
Q a
re e
quid
ista
nt
from
�an
d on
a p
erpe
ndi
cula
r th
rou
gh �
. T
he
lin
e �
is t
he
axis
of
sym
met
ryan
d P
and
Q a
re i
mag
es o
f ea
ch o
ther
in �
. Th
e im
age
of t
he
poin
t P
(a, b
) in
th
e li
ne
y�
xis
th
e po
int
Q(b
, a).
5.E
xpla
in w
hy
the
grap
hs
of a
fu
nct
ion
f(x
) an
d it
s in
vers
e, f
– 1(x
),ar
e sy
mm
etri
c ab
out
the
lin
e y
�x
.T
he g
rap
h o
f f– 1
(x) c
ons
ists
of
ord
ered
pai
rs f
orm
ed b
y in
terc
hang
ing
the
co
ord
inat
es o
f th
e o
rder
ed p
airs
of
f(x
).T
here
fore
, eac
h p
oin
t P
(a, b
) in
f(x
) has
an
imag
e Q
(b, a
) in
f– 1
(x) t
hat
is s
ymm
etri
c w
ith
it a
bo
ut t
he li
ne y
�x.
© G
lenc
oe/M
cGra
w-H
ill12
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-4
Fin
din
g E
qu
atio
ns
Fro
m A
rea
Ari
ght
tria
ngl
e in
th
e fi
rst
quad
ran
t is
bou
nde
d by
th
e x-
axis
, th
e y-
axis
, an
d a
lin
e in
ters
ecti
ng
both
axe
s. T
he
poin
t (1
, 2)
lies
on
th
e h
ypot
enu
se o
f th
e tr
ian
gle.
Th
ear
ea o
f th
e tr
ian
gle
is 4
squ
are
un
its.
Follo
w t
hes
e in
stru
ctio
ns
to f
ind
th
e eq
uat
ion
of
the
line
con
tain
ing
th
e h
ypot
enu
se. L
et m
rep
rese
nt
the
slop
e of
th
e lin
e.
1.W
rite
th
e eq
uat
ion
, in
poi
nt-
slop
e fo
rm, o
f th
e li
ne
con
tain
ing
the
hyp
oten
use
of
the
tria
ngl
e.y
�2
�m
(x�
1)2.
Fin
d th
e x-
inte
rcep
t an
d th
e y-
inte
rcep
t of
th
e li
ne.
x�in
terc
ept:
y�
inte
rcep
t: 2
�m
3.W
rite
th
e m
easu
res
of t
he
legs
of
the
tria
ngl
e.
and
2�
m
4.U
se y
our
answ
ers
to E
xerc
ise
3 an
d th
e fo
rmu
la f
or t
he
area
of
atr
ian
gle
to w
rite
an
exp
ress
ion
for
th
e ar
ea o
f th
e tr
ian
gle
inte
rms
of t
he
slop
e of
th
e h
ypot
enu
se. S
et t
he
expr
essi
on e
qual
to
4, t
he
area
of
the
tria
ngl
e, a
nd
solv
e fo
r m
.m
�– 2
5.W
rite
th
e eq
uat
ion
of
the
lin
e, in
poi
nt-
slop
e fo
rm, c
onta
inin
g th
eh
ypot
enu
se o
f th
e tr
ian
gle.
y�
2�
– 2(x
�1)
6.A
not
her
rig
ht
tria
ngl
e in
th
e fi
rst
quad
ran
t h
as a
n a
rea
of4
squ
are
un
its.
Th
e po
int
(2, 1
) li
es o
n t
he
hyp
oten
use
. Fin
d th
eeq
uat
ion
of
the
lin
e, in
poi
nt-
slop
e fo
rm, c
onta
inin
g th
eh
ypot
enu
se.
y�
1�
–(x
�2)
7.A
lin
e w
ith
neg
ativ
e sl
ope
pass
es t
hro
ugh
th
e po
int
(6, 1
). A
tria
ngl
e bo
un
ded
by t
he
lin
e an
d th
e co
ordi
nat
e ax
es h
as a
n a
rea
of 1
6 sq
uar
e u
nit
s. F
ind
the
slop
e of
th
e li
ne.
m�
–or
m�
–1 � 18
1 � 2
1 � 2
m�
2�
m
m�
2�
m
© G
lenc
oe/M
cGra
w-H
ill11
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Wri
tin
g L
ine
ar
Eq
ua
tio
ns
Wri
te a
n e
qu
atio
n in
slo
pe-
inte
rcep
t fo
rm f
or e
ach
lin
e d
escr
ibed
.
1.sl
ope
��
4, y
-in
terc
ept
�3
2.sl
ope
�5,
pas
ses
thro
ugh
A(�
3, 2
)y
��
4x�
3y
�5x
�17
3.sl
ope
��
4, p
asse
s th
rou
gh B
(3, 8
)4.
slop
e�
�4 3� , p
asse
s th
rou
gh C
(�9,
4)
y�
�4x
�20
y�
�4 3� x�
16
5.sl
ope
�1,
pas
ses
thro
ugh
D(�
6, 6
)6.
slop
e�
�1,
pas
ses
thro
ugh
E(3
,�3)
y�
x�
12y
��
x
7.sl
ope
�3,
y-i
nte
rcep
t�
�3 4�8.
slop
e�
�2,
y-i
nte
rcep
t�
�7
y�
3x�
�3 4�y
��
2x�
7
9.sl
ope
��
1, p
asse
s th
rou
gh F
(�1,
7)
10.
slop
e�
0, p
asse
s th
rou
gh G
(3, 2
)y
��
x�
6y
�2
11.
Avi
ati
onT
he
nu
mbe
r of
act
ive
cert
ifie
d co
mm
erci
al
pilo
ts h
as b
een
dec
lin
ing
sin
ce 1
980,
as
show
n in
th
e ta
ble.
a.F
ind
a li
nea
r eq
uat
ion
th
at c
an b
e u
sed
as a
mod
el
to p
redi
ct t
he
nu
mbe
r of
act
ive
cert
ifie
d co
mm
erci
al
pilo
ts f
or a
ny
year
. Ass
um
e a
stea
dy r
ate
of d
ecli
ne.
Sam
ple
ans
wer
usi
ng (1
985,
155
,929
) and
(1
995,
133
,980
): y
��
2195
x�
4,51
3,00
4
b.
Use
th
e m
odel
to
pred
ict
the
nu
mbe
r of
pil
ots
in
the
year
200
3.S
amp
le p
red
icti
on:
11
6,41
9
1-4
Num
ber
of A
ctiv
eC
ertif
ied
Pilo
ts
Year
Tota
l
1980
182,
097
1985
155,
929
1990
149,
666
1993
143,
014
1994
138,
728
1995
133,
980
1996
129,
187
So
urce
:U. S
. Dep
t.
of T
rans
por
tatio
n
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A6 Advanced Mathematical Concepts
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A7 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill15
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
Enr
ichm
ent
1-5 Ho
w is
it d
one
? W
hy is
the
aut
hor
wri
ting
the
exp
ress
ion
inth
is f
orm
rat
her
than
ano
ther
?
Re
ad
ing
Ma
the
ma
tic
s: Q
ue
stio
n A
ssu
mp
tio
ns
Stu
den
ts a
t th
e el
emen
tary
leve
l ass
um
e th
at t
he
stat
emen
ts in
thei
r te
xtbo
oks
are
com
plet
e an
d ve
rifi
ably
tru
e. A
less
on o
n t
he
area
of
a tr
ian
gle
is a
ssu
med
to
con
tain
eve
ryth
ing
ther
e is
to
know
abou
t tr
ian
gle
area
, an
d th
e co
ncl
usi
ons
reac
hed
in t
he
less
on a
rero
ck-s
olid
fac
t. T
he
stu
den
t’s jo
b is
to
“lea
rn”
wh
at t
extb
ooks
hav
e to
say.
Th
e be
tter
th
e st
ude
nt
does
th
is, t
he
bett
er h
is o
r h
er g
rade
.
By
now
you
pro
babl
y re
aliz
e th
at k
now
ledg
e is
ope
n-e
nde
d an
d th
atm
uch
of
wh
at p
asse
s fo
r fa
ct—
in m
ath
an
d sc
ien
ce a
s w
ell a
s in
oth
er a
reas
— c
onsi
sts
of t
heo
ry o
r op
inio
n t
o so
me
degr
ee.
At
best
, it
offe
rs t
he
clos
est
gues
s at
th
e “t
ruth
” th
at is
now
pos
sibl
e.R
ath
er t
han
acc
ept
the
stat
emen
ts o
f an
au
thor
bli
ndl
y, t
he
edu
cate
d pe
rson
’s jo
b is
to
read
th
em c
aref
ull
y, c
riti
call
y, a
nd
wit
han
ope
n m
ind,
an
d to
th
en m
ake
an in
depe
nde
nt
judg
men
t of
th
eir
vali
dity
. Th
e fi
rst
task
is t
o qu
esti
on t
he
auth
or’s
ass
um
ptio
ns.
A
nsw
ers
will
var
y. S
amp
le a
nsw
ers
are
giv
en.
Th
e fo
llow
ing
sta
tem
ents
ap
pea
r in
th
e b
est-
selli
ng
tex
t M
ath
emat
ics:
Tru
st M
e!.
Des
crib
e th
e au
thor
’s a
ssu
mp
tion
s. W
hat
is t
he
auth
or t
ryin
g t
o ac
com
plis
h?
Wh
atd
id h
e or
sh
e fa
il to
men
tion
? W
hat
is a
not
her
way
of
look
ing
at
the
issu
e?
1.“T
he
stu
dy o
f tr
igon
omet
ry is
cri
tica
lly
impo
rtan
t in
tod
ay’s
wor
ld.”
Tha
t’s a
n o
pin
ion.
Cri
tica
lly im
po
rtan
t to
who
m?
The
aut
hor
sho
uld
bac
k th
is s
tate
men
t up
. It
soun
ds
like
the
auth
or
istr
ying
to
just
ify in
clud
ing
thi
s to
pic
in t
he b
oo
k.2.
“We
wil
l loo
k at
th
e ca
se w
her
e x
> 0.
Th
e ar
gum
ent
wh
ere
x ≤
0 is
sim
ilar
.”Is
it?
I wo
uld
like
to
hea
r th
e ar
gum
ent.
Per
hap
s it
get
s in
to s
om
est
icky
issu
es o
rra
ises
so
me
inte
rest
ing
po
ints
.The
auth
ora
ssum
esth
atIa
mno
tint
eres
ted,
but
Iam
.3.
“As
you
rec
all,
the
mea
n is
an
exc
elle
nt
met
hod
of
desc
ribi
ng
ase
t of
dat
a.”
I do
no
t re
call
that
. Whe
re a
nd w
hen
was
tha
tes
tab
lishe
d?
Wha
t d
oes
“ex
celle
nt”
mea
n? P
erha
ps
at
cert
ain
tim
es t
he m
ean
is e
xcel
lent
but
the
re a
re t
imes
w
hen
it is
no
t.4.
“Som
etim
es it
is n
eces
sary
to
esti
mat
e th
e so
luti
on.”
Whe
n is
it n
eces
sary
? W
hy is
it n
eces
sary
? It
so
und
s as
tho
ugh
the
auth
or
is t
ryin
g t
o a
void
say
ing
tha
t th
ere
are
nog
oo
d m
etho
ds
for
solv
ing
thi
s p
rob
lem
, or
that
the
re a
reso
me
met
hod
s b
ut t
he a
utho
r th
inks
I am
no
t ca
pab
le o
fun
der
stan
din
g t
hem
.5.
“Th
is e
xpre
ssio
n c
an b
e w
ritt
en
.”1 � x
© G
lenc
oe/M
cGra
w-H
ill14
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Wri
tin
g E
qu
atio
ns
of
Pa
ralle
l a
nd
Pe
rpe
nd
icu
lar
Lin
es
Det
erm
ine
wh
eth
er t
he
gra
ph
s of
eac
h p
air
of e
qu
atio
ns
are
par
alle
l, p
erp
end
icu
lar,
coin
cid
ing
, or
non
e of
th
ese.
1.x
�3y
�18
par
alle
l2.
2x�
4y�
8co
inci
din
g3x
�9y
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13.C
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Th
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late
r sh
e pu
rch
ased
8 b
ooks
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d 6
vide
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. Her
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ssu
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at t
he
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es o
f vi
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gam
es a
nd
book
s di
d n
ot c
han
ge,
is it
pos
sibl
e th
at s
he
spen
t $3
20 f
or t
he
seco
nd
set
of p
urc
has
es?
Exp
lain
. N
o; t
he li
nes
that
rep
rese
nt t
he s
itua
tio
n ar
e p
aral
lel.
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
1-5
Answers (Lesson 1-6)
© Glencoe/McGraw-Hill A8 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill18
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-6
Sig
nif
ica
nt
Dig
its
All
mea
sure
men
ts a
re a
ppro
xim
atio
ns.
Th
e si
gnif
ican
t d
igit
sof
an
appr
oxim
ate
nu
mbe
r ar
e th
ose
wh
ich
indi
cate
th
e re
sult
s of
a
mea
sure
men
t.
For
exa
mpl
e, t
he
mas
s of
an
obj
ect,
mea
sure
d to
th
e n
eare
st g
ram
, is
210
gram
s. T
he
mea
sure
men
t 21
0g
has
3 s
ign
ific
ant
digi
ts. T
he
mas
s of
the
sam
e ob
ject
, mea
sure
d to
the
nea
rest
100
g, i
s 20
0 g.
The
mea
sure
men
t 20
0 g
has
on
e si
gnif
ican
t di
git.
Sev
eral
iden
tify
ing
char
acte
rist
ics
of s
ign
ific
ant
digi
ts a
re li
sted
belo
w, w
ith
exa
mpl
es.
1.N
on-z
ero
digi
ts a
nd
zero
s be
twee
n s
ign
ific
ant
digi
ts a
re
sign
ific
ant.
For
exa
mpl
e, t
he
mea
sure
men
t 9.
071
m h
as 4
si
gnif
ican
t di
gits
, 9, 0
, 7, a
nd
1.2.
Zer
os a
t th
e en
d of
a d
ecim
al f
ract
ion
are
sig
nif
ican
t. T
he
mea
sure
men
t 0.
050
mm
has
2 s
ign
ific
ant
digi
ts, 5
an
d 0.
3.U
nde
rlin
ed z
eros
in w
hol
e n
um
bers
are
sig
nif
ican
t. T
he
mea
sure
men
t10
4,00
0km
has
5si
gnif
ican
tdi
gits
,1,0
,4,0
,an
d0.
In g
ener
al, a
com
puta
tion
invo
lvin
g m
ult
ipli
cati
on o
r di
visi
on o
fm
easu
rem
ents
can
not
be
mor
e ac
cura
te t
han
th
e le
ast
accu
rate
mea
sure
men
t of
th
e co
mpu
tati
on. T
hu
s, t
he
resu
lt o
f co
mpu
tati
onin
volv
ing
mu
ltip
lica
tion
or
divi
sion
of
mea
sure
men
ts s
hou
ld b
ero
un
ded
to t
he
nu
mbe
r of
sig
nif
ican
t di
gits
in t
he
leas
t ac
cura
tem
easu
rem
ent.
Exa
mp
le
Th
e m
ass
of 3
7 q
uar
ters
is
210
g. F
ind
th
e m
ass
of o
ne
qu
arte
r.
mas
s of
1 q
uar
ter
�21
0g
�37
�5.
68 g
Wri
te t
he
nu
mb
er o
f si
gn
ific
ant
dig
its
for
each
mea
sure
men
t.
1.83
14.2
0 m
2.
30.7
0 cm
3.
0.01
mm
4.
0.06
05 m
g 6
41
35.
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000
km
6.37
0,00
0 km
7.
9.7
�10
4 g
8.3.
20 �
10–2
g
35
23
Sol
ve e
ach
pro
ble
m. R
oun
d e
ach
res
ult
to
the
corr
ect
nu
mb
er o
f si
gn
ific
ant
dig
its.
9.23
m �
1.54
m
10.
12,0
00 f
t �
520
ft11
.2.
5 cm
�25
35
m2
23.1
63 c
m12
.11
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mm
�11
13
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� 0
.5
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m �
4.0
m
121.
1 m
m1,
820
yd15
0 m
2
210
has
3 s
ign
ific
ant
dig
its.
37
doe
s n
ot r
epre
sen
t a
mea
sure
men
t.R
oun
d t
he
resu
lt t
o 3
sign
ific
ant
dig
its.
Wh
y?
© G
lenc
oe/M
cGra
w-H
ill17
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Mo
de
ling
Re
al-
Wo
rld
Da
ta w
ith
Lin
ea
r F
un
ctio
ns
Com
ple
te t
he
follo
win
g f
or e
ach
set
of
dat
a.a.
Gra
ph
th
e d
ata
on a
sca
tter
plo
t.b
.U
se t
wo
ord
ered
pai
rs t
o w
rite
th
e eq
uat
ion
of
a b
est-
fit
line.
c.If
th
e eq
uat
ion
of
the
reg
ress
ion
lin
e sh
ows
a m
oder
ate
orst
ron
g r
elat
ion
ship
, pre
dic
t th
e m
issi
ng
val
ue.
Exp
lain
wh
eth
eryo
u t
hin
k th
e p
red
icti
on is
rel
iab
le.
1.a.
b.
Sam
ple
ans
wer
usi
ng (1
991,
75.
5) a
nd (1
994,
75.
7):
y�
0.07
x�
63.9
c.P
red
icti
on:
77.2
; the
pre
dic
tio
n is
no
t ve
ry r
elia
ble
b
ecau
se m
any
po
ints
are
off
the
line
.
2.a.
b.
Sam
ple
ans
wer
usi
ng (1
993,
257
.7) a
nd (1
997,
267
.7):
y
�2.
5x�
4724
.8
c.P
red
icti
on:
300.
2; t
he p
red
icti
on
is r
elia
ble
bec
ause
th
e lin
e p
asse
s th
roug
h m
ost
of
the
po
ints
.
1-6 U
. S. L
ife E
xpec
tanc
y
Bir
th
Num
ber
of
Year
Year
s
1990
75.4
1991
75.5
1992
75.8
1993
75.5
1994
75.7
1995
75.8
2015
?S
our
ce:N
atio
nal C
ente
rfo
r H
ealth
Sta
tistic
s
Po
pul
atio
n G
row
th
Year
Po
pul
atio
n (m
illio
ns)
1991
252.
1
1992
255.
0
1993
257.
7
1994
260.
3
1995
262.
8
1996
265.
2
1997
267.
7
1998
270.
3
1999
272.
9
2010
?S
our
ce:U
.S. C
ensu
s B
urea
u
Answers (Lesson 1-7)
© Glencoe/McGraw-Hill A9 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill21
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-7
Mo
du
s P
on
en
sA
syll
ogis
m is
a d
edu
ctiv
e ar
gum
ent
in w
hic
h a
con
clu
sion
isin
ferr
ed f
rom
tw
o pr
emis
es. W
het
her
a s
yllo
gist
ic a
rgu
men
t is
val
idor
inva
lid
is d
eter
min
ed b
y it
s fo
rm. C
onsi
der
the
foll
owin
g sy
llog
ism
.
Pre
mis
e 1:
If a
lin
e is
per
pen
dicu
lar
to li
ne
m, t
hen
th
e sl
ope
of t
hat
lin
e is
��3 5� .
Pre
mis
e 2:
Lin
e�
is p
erpe
ndi
cula
r to
lin
e m
.C
oncl
usi
on:
� T
he
slop
e of
lin
e�
is �
�3 5� .
An
y st
atem
ent
of t
he
form
, “if
p, t
hen
q,”
su
ch a
s th
e st
atem
ent
inpr
emis
e 1,
can
be
wri
tten
sym
boli
call
y as
p→
q. W
e re
ad t
his
“p
impl
ies
q.”
Th
e sy
llog
ism
abo
ve is
val
id b
ecau
se t
he
argu
men
t fo
rm,
Pre
mis
e 1:
p→
q(T
his
arg
um
ent
says
th
at if
p __im
p__
___l
ies
q__
___
Pre
mis
e 2:
p ____
___
is t
rue
and
p _is
tru
e, t
hen
q _m
ust
Con
clu
sion
:�
qbe
tru
e.)
is a
val
id a
rgu
men
t fo
rm.
Th
e ar
gum
ent
form
abo
ve h
as t
he
Lat
in n
ame
mod
us
pon
ens,
wh
ich
mea
ns
“a m
ann
er o
f af
firm
ing.
” A
ny
mod
us
pon
ens
argu
men
tis
a v
alid
arg
um
ent.
Dec
ide
wh
eth
er e
ach
arg
um
ent
is a
mod
us
pon
ens
arg
um
ent.
1.If
th
e gr
aph
of
a re
lati
on p
asse
s th
e ve
rtic
al li
ne
test
, th
en t
he
rela
tion
is a
fu
nct
ion
. Th
e gr
aph
of
the
rela
tion
f(x
) do
es n
ot p
ass
the
vert
ical
lin
e te
st. T
her
efor
e, f
(x)
is n
ot a
fu
nct
ion
.no
2.If
you
kn
ow t
he
Pyt
hag
orea
n T
heo
rem
, you
wil
l app
reci
ate
Sh
akes
pear
e.
You
do
know
th
e P
yth
agor
ean
Th
eore
m. T
her
efor
e, y
ou w
ill a
ppre
ciat
eS
hak
espe
are.
yes
3.If
th
e ba
se a
ngl
es o
f a
tria
ngl
e ar
e co
ngr
uen
t, t
hen
th
e tr
ian
gle
is
isos
cele
s. T
he
base
an
gles
of
tria
ngl
e A
BC
are
con
gru
ent.
Th
eref
ore,
tr
ian
gle
AB
Cis
isos
cele
s.ye
s4.
Wh
en x
�– 3
, x2
�9.
Th
eref
ore,
if t
�– 3
, it
foll
ows
that
t2
�9.
yes
5.S
ince
x >
10,
x >
0. I
t is
tru
e th
at x
> 0
. Th
eref
ore,
x >
10.
no
© G
lenc
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cGra
w-H
ill20
Ad
vanc
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athe
mat
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Con
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Pie
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un
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ph
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un
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th
e ta
x ra
tes
for
the
diff
eren
t in
com
es b
y u
sin
g a
step
fu
nct
ion
.
�2
if x
�
11
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if�
1
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21
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if x
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x�
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1
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eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
1-7
Inco
me
Tax
Rat
es f
or
a C
oup
le F
iling
Jo
intl
y
Lim
its
of
Taxa
ble
Tax
Inco
me
Rat
e
$0to
$41,
200
15%
$41,
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to $
99,6
0028
%
$99,
601
to $
151,
750
31%
$151
,751
to
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36%
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and
up
39.6
%
So
urce
:Inf
orm
atio
n P
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e A
lman
ac
© Glencoe/McGraw-Hill A10 Advanced Mathematical Concepts
Answers (Lesson 1-6)
© G
lenc
oe/M
cGra
w-H
ill24
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
1-8
Lin
e D
esi
gn
s: A
rt a
nd
Ge
om
etr
yIt
erat
ion
pat
hs
that
spi
ral i
n t
owar
d an
att
ract
or o
r sp
iral
ou
t fr
oma
repe
ller
cre
ate
inte
rest
ing
desi
gns.
By
insc
ribi
ng
poly
gon
s w
ith
inpo
lygo
ns
and
usi
ng
the
tech
niq
ues
of
lin
e de
sign
, you
can
cre
ate
you
r ow
n in
tere
stin
g sp
iral
des
ign
s th
at c
reat
e an
illu
sion
of
curv
es.
1.M
ark
off
equ
al u
nit
s on
2.C
onn
ect
two
poin
ts t
hat
3.D
raw
th
e se
con
dth
e si
des
of a
squ
are.
are
equ
al d
ista
nce
s fr
om(a
djac
ent)
sid
e of
th
ead
jace
nt
vert
ices
.in
scri
bed
squ
are.
4.D
raw
th
e ot
her
tw
o si
des
5.R
epea
t S
tep
1 fo
r th
e6.
Rep
eat
Ste
ps 2
, 3,
of t
he
insc
ribe
d sq
uar
ein
scri
bed
squ
are.
(U
se t
he
and
4 fo
r th
e sa
me
nu
mbe
r of
divi
sion
s).
insc
ribe
d sq
uar
e.
7.R
epea
t S
tep
1 fo
r th
e8.
Rep
eat
Ste
ps 2
, 3, a
nd
4,9.
Rep
eatt
he
proc
edu
ren
ew s
quar
e.fo
r th
e th
ird
insc
ribe
das
oft
en a
syo
u w
ish
.sq
uar
e.
10.S
upp
ose
you
r fi
rst
insc
ribe
d sq
uar
e is
a c
lock
wis
e ro
tati
onli
ke t
he
one
at t
he
righ
t. H
ow w
ill t
he
desi
gn y
ou c
reat
eco
mpa
re t
o th
e de
sign
cre
ated
abo
ve, w
hic
h u
sed
a co
un
terc
lock
wis
e ro
tati
on? O
ne d
esig
n is
the
m
irro
r re
flect
ion
of
the
oth
er.
11.C
reat
e ot
her
spi
ral d
esig
ns
by in
scri
bin
g tr
ian
gles
wit
hin
tria
ngl
es a
nd
pen
tago
ns
wit
hin
pen
tago
ns.
S
ee s
tud
ents
’ wo
rk.
© G
lenc
oe/M
cGra
w-H
ill23
Ad
vanc
ed M
athe
mat
ical
Con
cep
ts
Pra
ctic
eN
AM
E__
____
____
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© Glencoe/McGraw-Hill A11 Advanced Mathematical Concepts
Page 25
1. A
2. A
3. C
4. A
5. D
6. A
7. B
8. D
9. C
10. C
11. C
Page 26
12. D
13. D
14. C
15. C
16. A
17. C
18. B
19. C
20. B
Bonus: D
Page 27
1. C
2. B
3. D
4. A
5. D
6. D
7. C
8. B
9. C
10. B
11. D
Page 28
12. A
13. B
14. B
15. C
16. A
17. D
18. D
19. A
20. C
Bonus: D
Chapter 1 Answer KeyForm 1A Form 1B
© Glencoe/McGraw-Hill A12 Advanced Mathematical Concepts
Page 29
1. D
2. C
3. B
4. A
5. D
6. A
7. D
8. C
9. A
10. B
11. D
Page 30
12. D
13. A
14. A
15. B
16. C
17. C
18. B
19. B
20. A
Bonus: C
Page 31
1. D � {�2, �1, 0, 1, 2},R � {�1, 0, 1, 2}; yes
2.
3.
4. �x �
13
�, x � �3
5. �x2 �
16x
�
6. ��61�
7.
8.
9.
10.
Page 32
11. y � �23
�x � �133�
12. x � 3y � 5 � 0
13. coinciding
14. y � �32
�x � 6
15. 2x � y � 2 � 0
16. y � �3x � 50
17.
18.
19.
20.
Chapter 1 Answer KeyForm 1C Form 2A
2x2 � 4xh � 2h2 �
x � h
D � {xx � 1}, R � all reals; no
m � �2100; average annual rate of change in car’s value
© Glencoe/McGraw-Hill A13 Advanced Mathematical Concepts
Page 33
1. D � {�3, �1, 0}, R � {0, 1, 4, 5}; no
2. 3a2 � 12a � 8
3. {(�2, 2), (0, 2),
4. x3 � 2x2 � 4x � 8
5. �x2 �
12
�
6. �12
7.
8.
9.
10.44; average annual rate ofincrease in thebike’s cost
Page 34
11. y � � �12
� x � 3
12. 4x � 3y � 12 � 0
13. perpendicular
14. y � �13
�x � 7
15. x � 2 � 0
16. y � 18x � 10
17.
18.
19.
20.
Bonus: x2 � 3
Page 35
1. D � {�1, 0, 2}; R � {0, 2, 3, 4};no
2. 17
3. {(1, 0), (2, 1),
(2, 2)}; no
4. x2 � x � 3
5. x2 � 3
6. �45�
7.
8.
9.
10.40; average annual rate ofincrease in thecoin’s value
Page 36
11. y � �12
� x � 5
12. 4x � y � 4 � 0
13. parallel
14. y � 3
15. x � 2y � 2 � 0
16. y � �253� x � �
45,5352�
17.
18.
19.
20.
Bonus: 6
Chapter 1 Answer KeyForm 2B Form 2C
(2, 2)}; yes
© Glencoe/McGraw-Hill A14 Advanced Mathematical Concepts
CHAPTER 1 SCORING RUBRIC
Level Specific Criteria
3 Superior • Shows thorough understanding of the concepts equations of parallel and perpendicular lines and adding, subtracting, multiplying, dividing, and composing functions.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Word problem concerning composition of functions is appropriate and makes sense.
• Goes beyond requirements of some or all problems.
2 Satisfactory, • Shows understanding of the concepts equations of parallel with Minor and perpendicular lines and adding, subtracting, multiplying, Flaws dividing, and composing functions.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Word problem concerning composition of functions is appropriate and makes sense.
• Satisfies all requirements of problems.
1 Nearly • Shows understanding of most of the concepts Satisfactory, equations of parallel and perpendicular lines and adding, with Serious subtracting, multiplying, dividing, and composing functions.Flaws • May not use appropriate strategies to solve problems.
• Computations are mostly correct.• Written explanations are satisfactory.• Word problem concerning composition of functions is mostly appropriate and sensible.
• Satisfies most requirements of problems.
0 Unsatisfactory • Shows little or no understanding of the concepts equations of parallel and perpendicular lines and adding, subtracting, multiplying, dividing, and composing functions.
• May not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are not satisfactory.• Word problem concerning composition of functions is not appropriate or sensible.
• Does not satisfy requirements of problems.
Chapter 1 Answer Key
© Glencoe/McGraw-Hill A15 Advanced Mathematical Concepts
Open-Ended Assessment
Page 371a. The fourth side must have the same
slope as 2y � x � 11, but it must havea different y-intercept. The slope-intercept form of 2y � x � 11 is y � � �1
2� x � �1
21� .
Let the equation of the fourth side be y � � �1
2�x.
1b. If one angle is a right angle, the parallelogram is a rectangle. The slope-intercept form of y � 2x � 3 isy � 2x � 3. The slopes of y � � �1
2� x and y � 2x � 3 are
negative reciprocals of each other.Hence, the lines are perpendicular,and the parallelogram is a rectangle.
1c.
Yes, the points of intersection arethe vertices of a rectangle.
2a. ƒ (x) � x � 4
2b. ( ƒ � g)(x) � x � 4 � 2x2 � 1� 2x2 � x � 5
(g � ƒ )(x) � 2x2 � 1 � x � 4� 2x2 � x � 5� ( ƒ � g)(x)
2c. ( ƒ � g)(x) � x � 4 � (2x2 � 1)� �2x2 � x � 3
( g � ƒ )(x) � 2x2 � 1 � (x � 4)� 2x2 � x � 3� ( ƒ � g)(x)
2d. ( ƒ � g)(x) � (x� 4)(2x2 � 1)� 2x3 � x � 8x2 � 4� 2x3 � 8x2 � x � 4
( g � ƒ )(x) � ( 2x2 � 1)(x � 4)� 2x3 � 8x2 � x � 4� ( ƒ � g)(x)
2e. ( ƒ � g)(x) � �2xx2
��
41
�
(g � ƒ )(x) � �2xx2
��
41�
� ( ƒ � g)(x)
2f. Addition and multiplication offunctions are commutative, butsubtraction and division are not.
3. Sample answer: Jeanette bought anelectric wok that was originally pricedat $38. The department storeadvertised an immediate rebate of $5as well as a 25% discount on smallappliances. What was the final price ofthe wok? Let x represent the originalprice of the wok, r (x ) represent theprice after the rebate, and d (x ) theprice after the discount. r (d (x )) �$23.50 and d (r (x )) � $24.75. Thedomain of each composition is $38,however, the range of the compositiondiffers with the order of thecomposition.
Chapter 1 Answer Key
© Glencoe/McGraw-Hill A16 Advanced Mathematical Concepts
Mid-Chapter TestPage 38
1. D � {�3, 0, 1}, R � {�2, 0, 1, 3}, no
2. 11
3. 2a2 � 3a � 3
4. 4x3 � 2x2
5. �x12� � 1
6.
7.
8. �25�
9. 3x � 2y � 7 � 0
10. y � �17x � 120
Quiz APage 39
1. D � {2, 3, 4, 5}, R � {�3, �2, 3}; yes
2. {(0, 0), (1,1), (1, �1), (2, 2), (2, �2)}; no
3. 16
4. 8x3 � 12x2
5. 8x2 � 3
Quiz BPage 39
1.
2.
3. x � �23
�
4. y � � �23
�x � 4
5. x � 2y � 2 � 0
Quiz CPage 40
1. parallel
2. none of these
3. 2x � y � 8 � 0
4. y � � �13
� x � 2
5. 10.3%
Quiz DPage 40
1.
2.
3.
4.
Chapter 1 Answer Key
42
�44�4
�6
© Glencoe/McGraw-Hill A17 Advanced Mathematical Concepts
SAT/ACT Practice Cumulative ReviewPage 41
1. D
2. B
3. B
4. D
5. E
6. D
7. E
8. C
9. E
10. D
Page 42
11. D
12. A
13. B
14. B
15. C
16. E
17. A
18. C
19. 13
20. 1.2
Page 43
1. {(�1, 5), (0, 1), (1, �3), (2, �7)}; yes
2. 24
3. �x2 �
12
�
4.
5.
6. x � 2y � 2 � 0
7. y � 3x � 5
8. y � 5x � 9960
9.
10.
Chapter 1 Answer Key
BLANK