Solutions Manual

Solutions Manual

Teacher's Materials Project Editor: Joan Lewis Project Editors: Christian Aviles-Scott, Heather Dever Project Administrator: Erin Gray Editorial Assistant: Eric Martin Writers: Ellen Bracken, Kendra Eyer Accuracy Checker: Dudley Brooks Production Editor: Angela Chen Copyeditor: Margaret Moore Editorial Production Manager: Deborah Cogan Production Director: Diana Jean Ray Production Coordinator: Ann Rothenbuhler Text Designer: Jenny Somerville Art Editor: Jason Luz Composition, Technical Art: Interactive Composition Corporation Art and Design Coordinator: Marilyn Perry Cover Designer: Jill Kongabel Printer: Alonzo Printing

Executive Editor: Casey FitzSimons Publisher: Steven Rasmussen

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Key Curriculum Press 1150 65th Street Emeryville, CA 94608 (510) 595-7000 editorial@

Printed in the United States of America

10 9 8 7 6 5 4 3

09 08 07 06

ISBN-13: 978-1-55953-608-0 ISBN-10: 1-55953-608-X

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Chapter 0

Lesson 0.1: Pictures, Graphs, and Diagrams 1 . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 0.2: Symbolic Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Lesson 0.3: Organizing Information 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 0 Review 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Lesson 1.1: Recursively Defined Sequences 13 . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 1.2: Modeling Growth and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Lesson 1.3: A First Look at Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Lesson 1.4: Graphing Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Exploration: Recursion in Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Lesson 1.5: Loans and Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Exploration: Refining the Growth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Chapter 1 Review 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 2 Lesson 2.1: Measures of Central Tendency and Box Plots . . . . . . . . . . . . . 24 Lesson 2.2: Measures of Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Lesson 2.3: Histograms and Percentile Ranks . . . . . . . . . . . . . . . . . . . . . . . . 28 Exploration: Census Microdata 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 2 Review 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3 Lesson 3.1: Linear Equations and Arithmetic Sequences . . . . . . . . . . . . . . 32 Lesson 3.2: Revisiting Slope 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 3.3: Fitting a Line to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Lesson 3.4: The Median-Median Line 37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 3.5: Residuals 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exploration: Residual Plots and Least Squares . . . . . . . . . . . . . . . . . . . . . . . 43 Lesson 3.6: Linear Systems 43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 3.7: Substitution and Elimination 46 . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3 Review 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4 Lesson 4.1: Interpreting Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Lesson 4.2: Function Notation 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 4.3: Lines in Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Lesson 4.4: Translations and the Quadratic Family . . . . . . . . . . . . . . . . . . . 61 Lesson 4.5: Reflections and the Square Root Family . . . . . . . . . . . . . . . . . . 64 Exploration: Rotation as a Composition of Transformations . . . . . . . . . . . 68 Lesson 4.6: Stretches and Shrinks and the Absolute-Value Family . . . . . 68 Lesson 4.7: Transformations and the Circle Family . . . . . . . . . . . . . . . . . . . 72 Lesson 4.8: Compositions of Functions 76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 4 Review 80 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5 Lesson 5.1: Exponential Functions 84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 5.2: Properties of Exponents and Power Functions . . . . . . . . . . . . 88 Lesson 5.3: Rational Exponents and Roots 91 . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 5.4: Applications of Exponential and Power Equations . . . . . . . . . 93 Lesson 5.5: Building Inverses of Functions 96 . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 5.6: Logarithmic Functions 99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 5.7: Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Lesson 5.8: Applications of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Exploration: The Number e 109 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 5 Review 109 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 6 Lesson 6.1: Matrix Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Lesson 6.2: Matrix Operations 115 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 6.3: Row Reduction Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Lesson 6.4: Solving Systems with Inverse Matrices . . . . . . . . . . . . . . . . . . 125 Lesson 6.5: Systems of Linear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 133 Lesson 6.6: Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Chapter 6 Review 141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 7 Lesson 7.1: Polynomial Degree and Finite Differences . . . . . . . . . . . . . . . 149 Lesson 7.2: Equivalent Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Lesson 7.3: Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Lesson 7.4: The Quadratic Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Lesson 7.5: Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Lesson 7.6: Factoring Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Lesson 7.7: Higher-Degree Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Lesson 7.8: More About Finding Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 169 Chapter 7 Review 174 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 8 Lesson 8.1: Graphing Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . 179 Lesson 8.2: Converting from Parametric to Nonparametric Equations . 183 Lesson 8.3: Right Triangle Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Exploration: Parametric Equations for a Circle . . . . . . . . . . . . . . . . . . . . . . 189 Lesson 8.4: Using Trigonometry to Set a Course . . . . . . . . . . . . . . . . . . . . 189 Lesson 8.5: Projectile Motion 192 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 8.6: The Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Lesson 8.7: The Law of Cosines 199 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 8 Review 202 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 9 Lesson 9.1: Using the Distance Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 Lesson 9.2: Circles and Ellipses 209 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 9.3: Parabolas 212 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 9.4: Hyperbolas 215 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exploration: Constructing the Conic Sections . . . . . . . . . . . . . . . . . . . . . . 219 Lesson 9.5: The General Quadratic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Exploration: The Rotation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Lesson 9.6: Introduction to Rational Functions . . . . . . . . . . . . . . . . . . . . . 224 Lesson 9.7: Graphs of Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Lesson 9.8: Operations with Rational Expressions . . . . . . . . . . . . . . . . . . . 230 Chapter 9 Review 232 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 10 Lesson 10.1: Defining the Circular Functions . . . . . . . . . . . . . . . . . . . . . . . 237 Lesson 10.2: Radian Measure and Arc Length . . . . . . . . . . . . . . . . . . . . . . 240 Lesson 10.3: Graphing Trigonometric Functions . . . . . . . . . . . . . . . . . . . . 243 Lesson 10.4: Inverses of Trigonometric Functions . . . . . . . . . . . . . . . . . . . 246 Lesson 10.5: Modeling with Trigonometric Equations . . . . . . . . . . . . . . . 248 Lesson 10.6: Fundamental Trigonometric Identities . . . . . . . . . . . . . . . . . 252 Lesson 10.7: Combining Trigonometric Functions . . . . . . . . . . . . . . . . . . 255 Exploration: Polar Coordinates 258 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 10 Review 259 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 11 Lesson 11.1: Arithmetic Series 262 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 11.2: Infinite Geometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Lesson 11.3: Partial Sums of Geometric Series . . . . . . . . . . . . . . . . . . . . . . 268 Exploration: Seeing the Sum of a Series . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Chapter 11 Review 272 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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