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Table of Contents v CME Project • Mathematics II v

National Advisory Board The National Advisory Board met early in the project, providing critical feedback on the instructional design and the overall organization. Members include

Richard Askey, University of Wisconsin Edward Barbeau, University of Toronto Hyman Bass, University of MichiganCarol Findell, Boston University Arthur Heinricher, Worcester Polytechnic InstituteRoger Howe, Yale UniversityBarbara Janson, Janson AssociatesKenneth Levasseur, University of Massachusetts, LowellJames Madden, Louisiana State University, Baton RougeJacqueline Miller, Education Development CenterJames Newton, University of MarylandRobert Segall, Greater Hartford Academy of Mathematics and ScienceGlenn Stevens, Boston UniversityHerbert Wilf, University of PennsylvaniaHung-Hsi Wu, University of California, Berkeley

Core Mathematical Consultants Dick Askey, Ed Barbeau, and Roger Howe have been involved in an even more substantial way, reviewing chapters and providing detailed and critical advice on every aspect of the program. Dick and Roger spent many hours reading and criticizing drafts, brainstorming with the writing team, and offering advice on everything from the logical organization to the actual numbers used in problems. We can’t thank them enough.

Teacher Advisory Board The Teacher Advisory Board for the CME Project was essential in help ing us create an effective format for our lessons that embodies the philosophy and goals of the program. Their debates about pedagogi cal issues and how to develop mathematical top ics helped to shape the distinguishing features of the curriculum so that our lessons work effective ly in the classroom. The advisory board includes

Jayne Abbas, Richard Coffey, Charles Garabedian, Dennis Geller, Eileen Herlihy, Doreen Kilday, Gayle Masse, Hugh McLaughlin, Nancy McLaughlin, Allen Olsen, Kimberly Osborne, Brian Shoemaker, and Benjamin Sinwell

Field-Test Teachers Our field-test teachers gave us the benefit of their classroom experi ence by teaching from our draft lessons and giv ing us extensive, critical feedback that shaped the drafts into realistic, teachable lessons. They shared their concerns, questions, challenges, and successes and kept us focused on the real world. Some of them even welcomed us into their classrooms as co-teachers to give us the direct experience with students that we needed to hone our lessons. Working with these expert professionals has been one of the most gratifying parts of the development—they are “highly qualified” in the most profound sense.

California Barney Martinez, Jefferson High School, Daly City; Calvin Baylon and Jaime Lao, Bell Junior High School, San Diego; Colorado Rocky Cundiff, Ignacio High School, Ignacio; Illinois Jeremy Kahan, Tammy Nguyen, and Stephanie Pederson, Ida Crown Jewish Academy, Chicago; Massachusetts Carol Martignette, Chris Martino, and Kent Werst, Arlington High School, Arlington; Larry Davidson, Boston University Academy, Boston; Joe Bishop and Carol Rosen, Lawrence High School, Lawrence; Maureen Mulryan, Lowell High School, Lowell; Felisa Honeyman, Newton South High School, Newton Centre; Jim Barnes and Carol Haney, Revere High School, Revere; New Hampshire Jayne Abbas and Terin Voisine, Cawley Middle School, Hooksett; New Mexico Mary Andrews, Las Cruces High School, Las Cruces; Ohio James Stallworth, Hughes Center, Cincinnati; Texas Arnell Crayton, Bellaire High School, Bellaire; Utah Troy Jones, Waterford School, Sandy; Washington Dale Erz, Kathy Greer, Karena Hanscom, and John Henry, Port Angeles High School, Port Angeles; Wisconsin Annette Roskam, Rice Lake High School, Rice Lake.

Special thanks go to our colleagues at Pearson, most notably Elizabeth Lehnertz, Joe Will, and Stewart Wood. The program benefits from their expertise in every way, from the actual mathematics to the design of the printed page.

Contributors to the CME Project

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A Daily Planner precedes each chapter and gives you lesson-by-lesson suggestions for that chapter.

chapter 1 Functions and Polynomials 13 Days

Lesson TiTLe Lesson TiTLe

1.0 Anatomy of a Polynomial 1.06 The Factor Theorem

1.01 Getting Started 1.07 Getting Started

1.02 Lagrange Interpolation—Fitting Polynomial Functions to Tables 1.08 Quadratics

1.03 Agreeing to Disagree—Finding Functions with Specific Values 1.09 Factoring Cubes

1.04 Getting Started 1.10 Pippins and Cheese—More Factoring Techniques

1.05 Polynomial Division 1.11 Rational Expressions

chapter 2 Sequences and Series 18 Days

Lesson TiTLe Lesson TiTLe

2.0 Two Types of Definitions 2.09 Getting Started

2.01 Getting Started 2.10 Arithmetic Sequences and Series

2.02 Gauss’s Method and Euclid’s Method 2.11 Geometric Sequences and Series

2.03 Ways to Visualize Sums 2.12 Limits

2.04 The g Notation 2.13 Repeating Decimals

2.05 Getting Started 2.14 Getting Started

2.06 Definite and Indefinite Sums 2.15 Pascal’s Triangle

2.07 g Identities 2.16 The Binomial Theorem

2.08 Tables and Figurate Numbers

chapter 3 Statistical Inference 22 Days

Lesson TiTLe Lesson TiTLe

3.01 Getting Started 3.10 Getting Started

3.02 Probability and Pascal’s Triangle 3.11 Experiments and Simulations

3.03 Polynomial Powers 3.12 Bernoulli Trials

3.04 Expected Value 3.13 Surveys, Studies, and Experiments

3.05 Lotteries 3.14 Sampling and Margin of Error

3.06 Getting Started 3.15 Getting Started

3.07 Variance and Standard Deviation 3.16 The Central Limit Theorem

3.08 Adding Variance 3.17 The Normal Distribution

3.09 Repeated Experiments

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chapter 4 Trigonometry 18 Days

Lesson TiTLe Lesson TiTLe

4.0 Right Triangle Trigonometry 4.08 Graphing the Tangent Function

4.01 Getting Started 4.09 The Angle-Sum Identities

4.02 Extending the Domain, Part 1—0° to 360° 4.10 Getting Started

4.03 Extending the Domain, Part 2—All Real Numbers 4.11 The Area of a Triangle

4.04 The Pythagorean Identity 4.12 The Law of Sines

4.05 Solving Trigonometric Equations 4.13 The Law of Cosines

4.06 Getting Started 4.14 Heron’s Formula—Using Side Lengths to Find the Area of a Triangle

4.07 Graphing Cosine and Sine

chapter 5 Analyzing Trigonometric Functions 10 Days

Lesson TiTLe Lesson TiTLe

5.01 Getting Started 5.05 Analyzing Graphs—The Sine and Cosine Functions

5.02 Trigonometry With Radians 5.06 Getting Started

5.03 Graphing Cosine and Sine Functions 5.07 Sinusoidal Functions—Amplitude, Period, Phase Shift

5.04 Solving Cosine and Sine Equations 5.08 Applying Trigonometric Functions

chapter 6 Complex Numbers and Polynomials 11 Days

Lesson TiTLe Lesson TiTLe

6.01 Getting Started 6.06 Powers of Complex Numbers

6.02 The Complex Plane 6.07 Roots of Unity

6.03 Another Form for Complex Numbers— r cis u 6.08 Geometry of Roots of Unity

6.04 The Multiplication Law 6.09 Arithmetic With Roots of Unity—Regular Polygons

6.05 Getting Started

chapter 7 Polynomial and Rational Functions 16 DaysLesson TiTLe Lesson TiTLe

7.01 Getting Started 7.07 Graphing Rational Functions

7.02 Continuity of Polynomial Functions 7.08 Revisiting Secants and Tangents

7.03 Graphs and Secant Lines 7.09 Getting Started

7.04 Polynomials in Powers of x – a 7.10 Monthly Payments

7.05 Secants and Tangents 7.11 The Factorial Function

7.06 Getting Started

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chapter 8 Exponential and Logarithmic Functions 16 Days

lesson title lesson title

8.01 Getting Started 8.09 Graphing Logarithmic Functions

8.02 Graphs of Exponential Functions 8.10 The Logarithmic Scale

8.03 Tables of Exponential Functions 8.11 Getting Started

8.04 Properties of Exponential Functions 8.12 Compound Interest; the Number e

8.05 Exponential Functions, One-to-One 8.13 Another Way to Find e

8.06 Getting Started 8.14 The Natural Logarithm Function

8.07 Defining Logarithms 8.15 Analysis of f(x) = ex and g(x) = ln x

8.08 Laws of Logarithms

chapter 9 Optimization and Geometric Modeling 14 Days

lesson title lesson title

9.0 Equations as Point-Testers 9.07 Areas of Similar Polygons

9.01 Getting Started 9.08 Getting Started

9.02 Finding the Shortest Path 9.09 Slicing Cones

9.03 Reflecting to Find the Shortest Path 9.10 Conics at the Origin

9.04 Getting Started 9.11 Conics Anywhere

9.05 Maximizing Areas, Part 1 9.12 They Are All the Same—A Continuous Family of Curves

9.06 Maximizing Areas, Part 2

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