viii Precalculus with Trigonometry Course Sampler

Comprehensive support for your teaching

and a diverse array of electronic and online resources.

Instructor’s Resources at Key Online

Student Resources at Key Math

Precalculus with Trigonometry

Printed ResourcesTeacher’s EditionBrowse the front matter of the Teacher’s Edition to learn how it can help you plan your year, reach all students, and integrate technology into your teaching.

Solutions ManualComplementing the answers provided in the Teacher’s Edition, Solutions Manual

Assessment ResourcesTo assist you in evaluating your students’ understanding, Assessment Resources includes two forms of all section, chapter, and cumulative tests; solutions for all assessment materials; and formative and summative assessment suggestions from Paul Foerster.

Instructor’s Resource BookEnrichment materials developed specifically for the text include Paul Foerster’s popular Explorations; and Technology Activities using The Geometer’s Sketchpad®, Fathom Dynamic Data® software, and The Geometer’s Sketchpad®, Fathom Dynamic Data® software, and The Geometer’s Sketchpad®, Fathom Dynamic Data®

Comprehensive support for your teachingPrecalculus with Trigonometry comes with comprehensive resources to support Precalculus with Trigonometry comes with comprehensive resources to support Precalculus with Trigonometryyou in all areas of your teaching, including planning tools, teaching strategies, technology integration, supplemental enrichment materials, assessment tools, and a diverse array of electronic and online resources.

Precalculus with TrigonometryResources for Teaching and Learning

Printed Resources Online Resources

Precalculus with Trigonometry Course Sampler ix

Comprehensive support for your teaching

Instructor’s Resources at Key Online

Blackline Masters, and Technology Activities for Sketchpad, Sketchpad, Sketchpad Fathom, and CAS

Sketchpad® Presentation Sketches

Microsoft® Excel, and Fathom® formats

English Language Learners, with space to define mathematical terms in the student’s primary language

Student Resources at Key Math

templates.

Learn more at www.keymath.com/precalc.

Student EditionThe online version of the Student Edition contains all the content of the printed Student Edition with additional features to enrich students’ learning experience.

Learn more at www.keypress.com/keyonline.

Precalculus with Trigonometry

Printed Resources

Instructor’s Resources at Key OnlineAccess the electronic version of the Student Edition and download your teaching resources for Precalculus.

Teacher’s Edition (PDF)

Instructor’s Resource Book (PDF), including Instructor’s Resource Book (PDF), including Instructor’s Resource Book Foerster’s popular Explorations, Blackline Masters, and Technology Activities

Solutions Manual (PDF)Solutions Manual (PDF)Solutions Manual

Assessment Resources (Microsoft Word & PDF)Assessment Resources (Microsoft Word & PDF)Assessment Resources (

English Language Learners, with space to

Printed Resources Online Resources

x Precalculus with Trigonometry Course Sampler

Flexible in content and approach, Precalculus accommodates your school’s curriculum and standards, and it supports your teaching style so you can meet the needs of all your students.

Explorations

teaching notes clear examples

journal prompts, structured reviews, projects, computer-based activities, web-based Dynamic Precalculus Explorations.

Design your Precalculus course exactly the way you want it!

Flexible Content Flexible Approach

Customize the curriculum to match your course.Course Timelines on pages xviii-xix give you options for di�erent courses that you can teach with this text—including Math Analysis, Precalculus, Trigonometry, and more.

Using This Unit and Using This Chapter give you tips on which sections can be abbreviated or omitted.

Precalculus with Trigonometry Course Sampler xi

Selected Explorations are incorporated into the Student Edition; many others are provided in the Instructor’s Resource Book. Students work in cooperative groups or independently to solve problems, explore patterns, and make conjectures about mathematical properties. Explorations also provide rich discussion opportunities for whole-class participation.

Detailed teaching notes and clear examples support a lecture-based approach.

This curriculum also includes journal prompts, structured reviews, projects, computer-based activities, and web-based Dynamic Precalculus Explorations.

Choose the teaching approach that supports your style.

Flexible Content Flexible Approach

Course Timelines

Using This Unit Using This Chapter

xii Precalculus with Trigonometry Course Sampler

Precalculus helps you evaluate your students’ learning comprehension with a range of formative and summative assessment tools, including reading analysis, quick review, self-assessment, and section and chapter tests.

Evaluate your students’ progress and understanding.

Assessment Assessment

Reading Analysis allows you to quickly determine if students understand the content of the lesson and can verbally express that understanding. Journal entries provide additional insight into student understanding. Additional reading and re�ecting strategiesalso help your students develop into independent learners, preparing them for college and more advanced math courses.

Self-assessment

Tests

Formative assessment Section Notes

On-page answers in the Teacher’s EditionQuick Review builds e�ciency and increases retention of required skills. You can assess students’ retention of prerequisite concepts, and your students will build �uency in solving routine problems quickly, a skill they will use when taking standardized tests.

Precalculus with Trigonometry Course Sampler xiii

Assessment Assessment

Reading Analysis

Journal entriesreading and re�ecting strategies

Self-assessment is encouraged throughout Precalculus. Students can demonstrate mastery with Quick Review and Reading Analysis problems, Chapter Review sections, practice Chapter Tests with calculator and no-calculator portions, and Cumulative Review sections.

Tests in Assessment Resources are o�ered in Forms A and B, with calculator and no-calculator portions.

Formative assessment is supported by Section Notes in the Teacher’s Edition.On-page answers in the Teacher’s Edition allow you to quickly check correctness of answers.

Quick Review

xiv Precalculus with Trigonometry Course Sampler

The accessibility of the mathematics in Precalculus is central to its design. Precalculus combines varied forms of pedagogy and instructional strategies to engage, challenge, and motivate all learners—struggling students, English Language Learners, and advanced learners alike.

Support strong conceptual development for ALL your students.

Differentiated Instruction Differentiated Instruction

Reading Analysis

Journal

Each concept is clearly developed through graphical, algebraic, numerical, and verbal representations. This approach helps you reach more learners and better prepares students for AP® Calculus.

An investigative approach is supported with Explorationsin the Student Edition and in the Instructor’s Resource Book.

Sketchpad® Presentation Sketches, Dynamic Precalculus Explorations, and other technology activities allow for multiple approaches to understanding a topic.

Multiple representations make the mathematics accessible to more learners.

Notes for di�erentiating instruction

pre-reading

Bilingual dictionary templates,

Precalculus with Trigonometry Course Sampler xv

Differentiated Instruction Differentiated Instruction

Reading Analysis questions help students develop the literacy skills they need to succeed in high school, college, and beyond.

Journal prompts ask students to note their questions and observations about the topics they have been studying. By keeping a journal and sharing entries in class, students improve their ability to express themselves mathematically, in class, students improve their ability to express themselves mathematically, both orally and in writing.

Literacy strategies and notes for differentiating instruction are integrated throughout this curriculum.

graphical, algebraic, numerical, and verbal representations.

Explorations

Notes for di�erentiating instructionprovide insight into areas where students might struggle with concepts or language and suggest pre-reading and other strategies to help them succeed.

Bilingual dictionary templates, found at www.keypress.com/keyonline (for teachers) and www.keymath.com/precalc (for students), help ELL students acquire the mathematical vocabulary they need.

xvi Precalculus with Trigonometry Course Sampler

SketchDrag the sliders to change the values of the parameters A, B, C, and D in the function d(t) = C + A cos B(t − D).

Investigate 1. The waterwheel rotates at 6 revolutions per minute (rpm). Two seconds after you start a stopwatch, point P on the rim of the wheel is at its greatest height, d = 13 ft, above the surface of the water. The center of the waterwheel is 6 ft above the surface. Based on this information, write an equation expressing the height of point P as a function of time.

2. Drag the sliders for A, B, C, and D so that the function d matches the one you wrote in question 1. Press Show Graph of d, and then press Rotate Wheel to see if your solution matches the motion of the waterwheel. If not, readjust the sliders to obtain a function that matches.

Helpful online resources for both teachers and students include supplementary problems, calculator programs, and an enhanced online textbook—accessible whenever you need them.

Enhance your teaching with online resources.

Online Resources Online Resources

Key Math

online textbook.

Dynamic Precalculus Explorations.

calculator programs

data sets

At Key Online you’ll �nd extensive resources you’ll �nd extensive resources to support your teaching and your students’ learning.

Key Online: Resources for Teachers

teaching resources, including assessment materials and PDFs of the Teacher’s Edition.

supplementary problems and solutions.

presentations and activities using The Geometer’s Sketchpad®.

Learn more at www. keypress.com/keyonline.

Learn more at www.keymath.com/precalc.

SketchThe following sketch shows a unit circle in the uv-coordinate system with angles of measure x and 2x radians. The uv-coordinate system is superimposed on an xy-coordinate system with sinusoids y = sin x in red and y = sin 2x in blue.

Investigate 1. Drag the black point to change the value of x. What length on the unit circle does x correspond to? What length does 2x correspond to?

2. How do the (u, v) coordinates of each point correspond to the (x, y) coordinates of points on the sinusoids?

3. Press the Show Lines button. Explain why the red and blue horizontal lines intersect the sinusoids where they do. Does this confirm or change your answer to question 2?

4. Do the moving points on the sinusoids have the same value of x?

Precalculus with Trigonometry Course Sampler xvii

SketchDrag the sliders to change the values of the parameters A, B, C, and D in the function d(t) = C + A cos B(t − D).

Investigate 1. The waterwheel rotates at 6 revolutions per minute (rpm). Two seconds after you start a stopwatch, point P on the rim of the wheel is at its greatest height, d = 13 ft, above the surface of the water. The center of the waterwheel is 6 ft above the surface. Based on this information, write an equation expressing the height of point P as a function of time.

2. Drag the sliders for A, B, C, and D so that the function d matches the one you wrote in question 1. Press Show Graph of d, and then press Rotate Wheel to see if your solution matches the motion of the waterwheel. If not, readjust the sliders to obtain a function that matches.

Online Resources Online Resources

At Key Math students will �nd engaging activities and resources.

online textbook.

Dynamic Precalculus Explorations.

calculator programs

data sets graphing calculators, Excel, and Fathom®.

Key Math: Resources for Students

Key Online

teaching resources, assessment materials

Teacher’s Edition.

supplementary problems

presentations activities

www. keypress.com/keyonline.

Learn more at www.keymath.com/precalc.

SketchThe following sketch shows a unit circle in the uv-coordinate system with angles of measure x and 2x radians. The uv-coordinate system is superimposed on an xy-coordinate system with sinusoids y = sin x in red and y = sin 2x in blue.

Investigate 1. Drag the black point to change the value of x. What length on the unit circle does x correspond to? What length does 2x correspond to?

2. How do the (u, v) coordinates of each point correspond to the (x, y) coordinates of points on the sinusoids?

3. Press the Show Lines button. Explain why the red and blue horizontal lines intersect the sinusoids where they do. Does this confirm or change your answer to question 2?

4. Do the moving points on the sinusoids have the same value of x?

xviii Precalculus with Trigonometry Course Sampler

Precalculus fully integrates technology to help you illustrate difficult concepts and to give students the opportunity to explore ideas, draw mathematical conclusions, and test hypotheses. With this curriculum you can bring everyday relevance to abstract concepts, spark mathematical thinking, and prepare students for AP® Calculus.

Spark mathematical thinking with technology.

Technology Technology

Students use graphing calculatorsevery day to visually explore functions and other topics, investigate real-world applications, and prepare for AP Calculus.

Optional CAS Suggestions in the Teacher’s Edition help you integrate the use of CAS technology.

Additional CAS Problems enhance the problem set for students using a CAS, while CAS Activities provide more in-depth exploration of concepts.

Technology Notes

Dynamic Precalculus Explorations

Precalculus Presentation Sketches,

Precalculus with Trigonometry Course Sampler xix

fully integrates technology

bring everyday relevance to abstract concepts, spark mathematical thinking, and prepare students for AP® Calculus.

Technology Technology

graphing calculators

CAS Suggestions

CAS Problems

CAS Activities

Technology Notes suggest ways you can enrich your course with the use of Sketchpad® or Fathom®. They also provide guidance for using calculator programs.

Dynamic Precalculus Explorations, available at www.keymath.com/precalc, help students investigate a variety of concepts in the Student Edition.

Precalculus Presentation Sketches,available online, let you present concepts visually and dynamically with Sketchpad.

xx Precalculus with Trigonometry Course Sampler

Precalculus facilitates course planning with �exible timelines, extensive teaching notes, and easy access to teaching and technology resources.

Plan your course with exceptional teaching and technology resources.

Interleaf pages at the beginning of each chapter provide valuable information for planning, including a chapter overview, pacing guides, a list of teaching and technology resources, and a brief description of which sections in the chapter can be skipped if time is limited.

Course Planning Course Planning

Pacing Guides

Section Notes Problem Notes

Important Terms and Concepts

Precalculus with Trigonometry Course Sampler xxi

easy access to teaching and technology resources.

Interleaf pages provide valuable information for planning

Course Planning Course Planning

Pacing Guides at the start of each chapter help you plan.

Section Notes give extensive guidance for teaching each section and Problem Notes give tips and background on the concepts behind many problems.

Important Terms and Concepts are noted at the beginning of each section.

xxii Precalculus with Trigonometry Course Sampler

Students love this textbook because it is written with their interests and needs in mind. Author Paul Foerster draws on 50 years of classroom teaching experience and student feedback to give students exactly what teaching experience and student feedback to give students exactly what they need to succeed in this course and be prepared for AP Calculus.

Engage students, maximize their understanding of Precalculus, and prepare them for AP® Calculus.

AP Calculus Preparation Quick-Reference Icons

multiple representations

Quick Review problems

Exploration

Reading Analysis questions

5minQuick Review problems

Calculator notes

CAS notes and problems

Dynamic Precalculus Explorations

presentation sketches and activities.

Fathom® activities.

Refer to the Internet

Examples of student work

Objectives are stated in every section.

Important properties, definitions, techniques, andprocedures are called out in the text.

Graphing calculator use is modeled in examples.

Chapter Review, Chapter Test, and Concept Problems help students assess their own understanding, prepare for testing, and explore concepts further.

Glossary, Answers to Selected Problems, and a quick reference to important formulas appear in the back of the book, giving students extra support.

Problem Sets, found at the end of each section, include both conceptual problems and problems for drill and practice, to help students prepare for Calculus.

Precalculus with Trigonometry Course Sampler xxiii

AP Calculus Preparation Quick-Reference Icons

Foerster’s top three tips for success:

Use multiple representations to engage all students.

Assign Quick Review problems to refresh skills as needed and give students practice doing routine problems quickly, an important skill for standardized tests.

Start with an Exploration to make learning math fun.

Reading Analysis questions teach students how to read a

mathematics book by asking them to summarize the main ideas of the section in their own words.

5minQuick Review problems get students used to doing

routine things quickly. routine things quickly.

Calculator notes provide tips on using graphing calculators.

CAS notes and problems help you integrate CAS into your curriculum.

Enrich learning with Dynamic Precalculus Explorations atwww.keymath.com/precalc.

Enhance learning with Sketchpad® presentation sketches

and activities.

Dynamically explore data with Fathom® activities.

Refer to the Internet to answer a question, complete an activity,

or look for more information.

Examples of student work model Examples of student work model Examples of student workproblem solutions.

Objectives

Important properties, definitions, techniques,procedures

examples.

Chapter Review, Chapter Test, and Concept Problems

Glossary, Answers to Selected Problemsimportant formulas

Problem Sets