Core-Plus Mathematics - Contemporary Mathematics In Context, Course 3

656 Pages·2008·19.64 MB·English

by  McGraw-Hill

i s e
nteractive tudent dition
2nd Edition
James T. Fey • Christian R. Hirsch • Eric W. Hart
Harold L. Schoen • Ann E. Watkins
with
Beth E. Ritsema • Rebecca K. Walker • Sabrina Keller
Robin Marcus • Arthur F. Coxford • Gail Burrill
This material is based upon work supported, in part, by the
National Science Foundation under grant no. ESI 0137718.
Opinions expressed are those of the authors and not
necessarily those of the Foundation.
Copyright © 2009 by the McGraw-Hill Companies, Inc. All rights reserved. Except as
permitted under the United States Copyright Act, no part of this publication may be
reproduced or distributed in any form or by any means, or stored in a database or
retrieval system, without prior permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 978-0-07-877261-0 (Student Edition) Core-Plus Mathematics
MHID: 0-07-877261-3 (Student Edition) Contemporary Mathematics in Context
Course 3 Student Edition
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 071/043 17 16 15 14 13 12 11 10 09 08
Core-Plus Mathematics 2
Development Team
Senior Curriculum Developers Advisory Board Collaborating Teachers
James T. Fey Diane Briars Mary Jo Messenger
University of Maryland Pittsburgh Public Schools Howard County Public Schools,
Maryland
Christian R. Hirsch (Director) Jeremy Kilpatrick
Western Michigan University University of Georgia Jacqueline Stewart
Okemos, Michigan
Eric W. Hart Robert E. Megginson
Maharishi University of University of Michigan
Management Graduate Assistants
Kenneth Ruthven
Allison BrckaLorenz
Harold L. Schoen University of Cambridge
Christopher Hlas
University of Iowa
David A. Smith University of Iowa
Ann E. Watkins Duke University
Madeline Ahearn
California State University,
Northridge Geoffrey Birky
Mathematical Consultants
Kyle Cochran
Deborah Hughes-Hallett
Contributing Curriculum Michael Conklin
University of Arizona / Harvard
Developers University Brandon Cunningham
Beth E. Ritsema Tim Fukawa-Connelly
Stephen B. Maurer
Western Michigan University University of Maryland
Swarthmore College
Rebecca K. Walker Dana Cox
William McCallum
Grand Valley State University Dana Grosser
University of Arizona
Sabrina Keller Anna Kruizenga
Doris Schattschneider
Michigan State University Nicole Lanie
Moravian College
Diane Moore
Robin Marcus
Richard Scheaffer Western Michigan University
University of Maryland
University of Florida
Arthur F. Coxford (deceased)
Undergraduate Assistants
University of Michigan
Evaluation Consultant
Cassie Durgin
Gail Burrill Norman L. Webb University of Maryland
Michigan State University University of Wisconsin-Madison
Rachael Kaluzny
(First edition only)
Jessica Tucker
Technical Coordinator
Western Michigan University
Principal Evaluator
James Laser
Steven W. Ziebarth Western Michigan University
Western Michigan University
iii
Core-Plus Mathematics 2
Field-Test Sites
Core-Plus Mathematics 2 builds on the strengths of the 1st edition, which was shaped by multi-year
field tests in 36 high schools in Alaska, California, Colorado, Georgia, Idaho, Iowa, Kentucky, Michigan,
Ohio, South Carolina, and Texas. Each revised text is the product of a three-year cycle of research and
development, pilot testing and refinement, and field testing and further refinement. Special thanks are
extended to the following teachers and their students who participated in the testing and evaluation of
2nd Edition Course 3.
Hickman High School Riverside University
Columbia, Missouri High School
Sandra Baker Milwaukee, Wisconsin
Lindsay Carlson Cheryl Brenner
Melissa Hundley Scott Hanson
Stephanie Krawczyk Alice Lanphier
Tiffany McCracken
Rock Bridge High School
Dana Meyer
Ryan Pingrey Columbia, Missouri
Cynthia Francisco
Holland Christian Donna Lillard
High School Linda Shumate
Holland, Michigan
Sauk Prairie High School
Brian Lemmen
Prairie du Sac, Wisconsin
Mike Verkaik
Joan Quenan
Malcolm Price Lab School Mary Walz
Cedar Falls, Iowa
Washington High School
Megan Balong
Milwaukee, Wisconsin
James Maltas
Anthony Amoroso
iv
Overview of Course 3
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1 R P
EASONING AND ROOF
Reasoning and Proof develops student understanding of Lesson 1 Reasoning Strategies
formal reasoning in geometric, algebraic, and statistical Lesson 2 Geometric Reasoning
contexts and of basic principles that underlie those
and Proof
reasoning strategies.
Lesson 3 Algebraic Reasoning
Topics include inductive and deductive reasoning strategies; and Proof
principles of logical reasoning—Affirming the Hypothesis Lesson 4 Statistical Reasoning
and Chaining Implications; relation among angles formed
Lesson 5 Looking Back
by two intersecting lines or by two parallel lines and a
transversal; rules for transforming algebraic expressions
and equations; design of experiments including the role
of randomization, control groups, and blinding; sampling
distribution, randomization test, and statistical significance.
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2 I L
NEQUALITIES AND INEAR
P
ROGRAMMING
Inequalities and Linear Programming develops student Lesson 1 Inequalities in
ability to reason both algebraically and graphically to solve One Variable
inequalities in one and two variables, introduces systems Lesson 2 Inequalities in
of inequalities in two variables, and develops a strategy
Two Variables
for optimizing a linear function in two variables within
Lesson 3 Looking Back
a system of linear constraints on those variables.
Topics include inequalities in one and two variables,
number line graphs, interval notation, systems of linear
inequalities, and linear programming.
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3 S C
IMILARITY AND ONGRUENCE
Similarity and Congruence extends student understanding of Lesson 1 Reasoning about
similarity and congruence and their ability to use those Similar Triangles
relations to solve problems and to prove geometric assertions Lesson 2 Reasoning about
with and without the use of coordinates.
Congruent Triangles
Topics include connections between Law of Cosines, Lesson 3 Looking Back
Law of Sines, and sufficient conditions for similarity and
congruence of triangles, centers of triangles, applications of
similarity and congruence in real-world contexts, necessary
and sufficient conditions for parallelograms, sufficient
conditions for congruence of parallelograms, and midpoint
connector theorems.
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Overview of Course 3
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4 S V
AMPLES AND ARIATION
Samples and Variation extends student understanding of the Lesson 1 Normal Distributions
measurement of variability, develops student ability to use Lesson 2 Binomial
the normal distribution as a model of variation, introduces
Distributions
students to the binomial distribution and its use in decision
Lesson 3 Statistical Process
making, and introduces students to the probability and
Control
statistical inference involved in control charts used in
industry for statistical process control. Lesson 4 Looking Back
Topics include normal distribution, standardized scores,
binomial distributions (shape, expected value, standard
deviation), normal approximation to a binomial distribution,
odds, statistical process control, control charts, and the
Central Limit Theorem.
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5 P
OLYNOMIAL AND
R F
ATIONAL UNCTIONS
Polynomial and Rational Functions extends student ability Lesson 1 Polynomial
to represent and draw inferences about polynomial and Expressions and
rational functions using symbolic expressions and Functions
manipulations. Lesson 2 Quadratic
Polynomials
Topics include definition and properties of polynomials,
operations on polynomials; completing the square, proof Lesson 3 Rational Expressions
of the quadratic formula, solving quadratic equations and Functions
(including complex number solutions), vertex form of Lesson 4 Looking Back
quadratic functions; definition and properties of rational
functions, operations on rational expressions.
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6 C C F
IRCLES AND IRCULAR UNCTIONS
Circles and Circular Functions develops student Lesson 1 Properties of Circles
understanding of relationships among special lines, Lesson 2 Circular Motion and
segments, and angles in circles and the ability to use
Periodic Functions
properties of circles to solve problems; develops student
Lesson 3 Looking Back
understanding of circular functions and the ability to use
these functions to model periodic change; and extends
student ability to reason deductively in geometric settings.
Topics include properties of chords, tangent lines, and
central and inscribed angles of circles; linear and angular
velocity; radian measure of angles; and circular functions
as models of periodic change.
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Overview of Course 3
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7 R I
ECURSION AND TERATION
Recursion and Iteration extends student ability to represent, Lesson 1 Modeling Sequential
analyze, and solve problems in situations involving Change Using
sequential and recursive change. Recursion and
Iteration
Topics include iteration and recursion as tools to model and
Lesson 2 A Recursive View
analyze sequential change in real-world contexts, including
of Functions
compound interest and population growth; arithmetic,
geometric, and other sequences; arithmetic and geometric Lesson 3 Iterating Functions
series; finite differences; linear and nonlinear recurrence Lesson 4 Looking Back
relations; and function iteration, including graphical iteration
and fixed points.
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8 I F
NVERSE UNCTIONS
Inverse Functions develops student understanding of Lesson 1 What Is An Inverse
inverses of functions with a focus on logarithmic functions Function?
and their use in modeling and analyzing problem situations Lesson 2 Common Logarithms
and data patterns.
and Their Properties
Topics include inverses of functions; logarithmic functions Lesson 3 Inverse
and their relation to exponential functions, properties of Trigonometric
logarithms, equation solving with logarithms; and inverse Functions
trigonometric functions and their applications to solving Lesson 4 Looking Back
trigonometric equations.
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Contents
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1 R P
EASONING AND ROOF
Lesson 1
Reasoning Strategies. . . . . . . . . . . . . . . . . . . . . . 2
Investigations
1 Reasoned Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Reasoning with If-Then Statements . . . . . . . . . . . . . . . . . . . . . . 10
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Lesson 2
Geometric Reasoning and Proof . . . . . . . . . . . . . . 29
Investigations
1 Reasoning about Intersecting Lines and Angles . . . . . . . . . . . . . . . 30
2 Reasoning about Parallel Lines and Angles . . . . . . . . . . . . . . . . . . 35
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Lesson 3
Algebraic Reasoning and Proof. . . . . . . . . . . . . . . 52
Investigations
1 Reasoning with Algebraic Expressions . . . . . . . . . . . . . . . . . . . . 53
2 Reasoning with Algebraic Equations . . . . . . . . . . . . . . . . . . . . . 58
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Lesson 4
Statistical Reasoning . . . . . . . . . . . . . . . . . . . . . 74
Investigations
1 Design of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2 By Chance or from Cause? . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3 Statistical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Lesson 5
Looking Back . . . . . . . . . . . . . . . . . . . . . . . . 102
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2 I L P
NEQUALITIES AND INEAR ROGRAMMING
Lesson 1
Inequalities in One Variable . . . . . . . . . . . . . . . . 108
Investigations
1 Getting the Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2 Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3 Complex Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Lesson 2
Inequalities in Two Variables. . . . . . . . . . . . . . . 127
Investigations
1 Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2 Linear Programming—A Graphic Approach . . . . . . . . . . . . . . . . . . 132
3 Linear Programming—Algebraic Methods . . . . . . . . . . . . . . . . . . 137
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144
Lesson 3
Looking Back . . . . . . . . . . . . . . . . . . . . . . . . .158
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Contents
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3 S C
IMILARITY AND ONGRUENCE
Lesson 1
Reasoning about Similar Triangles . . . . . . . . . . . . 162
Investigations
1 When Are Two Polygons Similar? . . . . . . . . . . . . . . . . . . . . . . . 164
2 Sufficient Conditions for Similarity of Triangles . . . . . . . . . . . . . . . . 168
3 Reasoning with Similarity Conditions . . . . . . . . . . . . . . . . . . . . . 173
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Lesson 2
Reasoning about Congruent Triangles . . . . . . . . . 195
Investigations
1 Congruence of Triangles Revisited. . . . . . . . . . . . . . . . . . . . . . . 196
2 Congruence in Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . .200
3 Congruence in Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . .204
4 Congruence-Preserving Transformations . . . . . . . . . . . . . . . . . . .208
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Lesson 3
Looking Back. . . . . . . . . . . . . . . . . . . . . . . . . .229
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4 S V
AMPLES AND ARIATION
Lesson 1
Normal Distributions . . . . . . . . . . . . . . . . . . . . 236
Investigations
1 Characteristics of a Normal Distribution. . . . . . . . . . . . . . . . . . . . 237
2 Standardized Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
3 Using Standardized Values to Find Percentiles . . . . . . . . . . . . . . . . 245
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248
Lesson 2
Binomial Distributions . . . . . . . . . . . . . . . . . . . 259
Investigations
1 Shape, Center, and Spread . . . . . . . . . . . . . . . . . . . . . . . . . .260
2 Binomial Distributions and Making Decisions . . . . . . . . . . . . . . . . .266
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Lesson 3
Statistical Process Control . . . . . . . . . . . . . . . . . 283
Investigations
1 Out of Control Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . .285
2 False Alarms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294
3 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 297
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303
Lesson 4
Looking Back. . . . . . . . . . . . . . . . . . . . . . . . . . 316
ix