Precalculus, 7th Edition © 2022
The new edition of Precalculus, published by Pearson, combines updated teaching tools and applications with the fundamentals that have made this a hallmark text in high school math curricula.
- New section-level, enhanced assignments
- New Integrated Review activities
- New Stress Management activities
- Graphing and Functions that model data throughout the sections and exercise sets
Precalculus Program with Digital Integration
Precalculus supports students with flexible materials and tools that build confidence in their ability to learn complex math.
Motivated Learning
Lessons and activities engage students through familiar contexts that demonstrate the power of math. Automatic feedback on their homework encourages them to learn and achieve more.
Ease and Flexibility
Teachers can remove the guesswork for helping students reach grade level with a suite of intuitive analytic tools that show instructional needs and student progress.
Conceptual Understanding
Precalculus forms connections between the ideas in each chapter to develop adaptability in applying previous ideas to new contexts. Students can carry those skills with them to future classes.
Technological Leverage
Online capabilities allow teachers to create blended or 100% digital solutions and take full advantage of the technology they have at their disposal.
Precalculus Teaching Solutions
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Develop Visualization Skills to Strengthen Understanding
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Meet Students’ Varying Skill Levels
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Support the Whole Student in the Effort to Succeed
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Help Students Study Efficiently and Apply Understanding
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Set Up Your Course Quickly and Easily
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GeoGebra ExercisesNew GeoGebra Graphing Exercises help students demonstrate their understanding. They interact directly with the graph similarly to how they would on paper.
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Revised and Expanded LibraryThe revised and expanded library adds many more Interactive Figures to the Video & Resource Library. Interactive Figures bring mathematical concepts to life and help students see the concepts through directed explorations and purposeful manipulation. They encourage active learning, critical thinking, and conceptual understanding.
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Blitzer Bonus VideosBlitzer Bonus Videos provide historical, interdisciplinary, and otherwise interesting connections to the algebra being studied. Students discover how math is a dynamic and fascinating discipline.
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MathTalk VideosFun, application-based MathTalk Videos show students how the math they are learning applies to the real world and why they should care about math. They are accompanied by an Instructor Guide and assessment questions can be assigned through MyMathLab® for School.
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Assignable Videos and ExercisesInstructional videos and an assignable library of algorithmic exercises can accompany each corequisite objective.
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Readiness QuizzesReadiness Quizzes address key arithmetic and introductory algebra topics that can be assigned to target corequisite instruction or simply to make sure students are prepared for their coursework.
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Integrated ReviewAn updated Integrated Review at the chapter level provides a Skills Check assessment to pinpoint which prerequisite topics students need to review. Videos, worksheets, and a Corequisite Support eText provide additional instruction. Instructors who prefer to review at the section level can assign the new Enhanced Assignments instead.
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Guided Practice WorksheetsGuided Practice worksheets accompany each section of the text. They start with a catchy headline and motivating real-world connection followed by numerous “Solved Problems” and “Pencil Problems.”
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Classroom ActivitiesClassroom Activities for selected sections contain recommended group size, material needed, and time to complete.
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Integrated Review WorksheetsIntegrated Review worksheets for every prerequisite objective. These worksheets feature both instruction and practice.
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Integrated Review ActivitiesNew Integrated Review Activities for selected topics provide hands-on work with important prerequisites.
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Coloring PagesColoring Pages from Blitzer’s striking book covers are provided as a fun form of “stress management.”
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Video ProgramA dynamic Video Program includes fresh, interactive objective videos that walk students through the concepts from every objective of the text. Chapter Test prep videos include step-by-step solutions to all the Chapter Test exercises from the textbook.
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Video AssignmentsNew Video Assignments featuring short videos with corresponding MyMathLab for School exercises are available for each section of the text. These editable assignments are especially helpful for online classes or “flipped” classes, where some or all learning takes place independently.
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Personal Inventory Assessments33 new Personal Inventory Assessments in MyMathLab for School are a collection of online activities designed to promote self-reflection and metacognition in students. Topics include Stress Management, Diagnosing Poor Performance, Enhancing Motivation, and Time Management.
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Mindset Videos and ExercisesNew Mindset videos and assignable, open-ended exercises foster a growth mindset in students. This material encourages them to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities.
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Essential Topic Video SeriesThe new College Algebra Essential Topic Video series and worksheets cover what a college algebra student must understand to succeed in the course. Videos can be assigned in MyMathLab for School to remind students of crucial content before they begin their exercises.
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Setup & Solve ExercisesMore and revised Setup & Solve Exercises have been added to the MyMathLab for School course. These require students to first describe how they will set up and approach the problem, reflecting test-taking expectations.
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Voice BalloonsVoice Balloons translate algebraic ideas into everyday English, clarify problem-solving procedures, present alternative ways of understanding concepts, and connect problem solving to concepts students have already learned
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Check Point ExamplesEach Check Point Example is followed by a similarly matched Check Point Problem that gives students a chance to test their understanding of the example.
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Great Question! FeatureGreat Question! feature presents a variety of study tips in the context of students’ questions. Answers to the questions offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions. This feature can also help alleviate student anxiety when asking questions in class.
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Modeling DataGraphing and Functions that model data appear in nearly every section and exercise set. Examples and exercises use graphs of functions to explore relationships between data and to provide ways of visualizing a problem’s solution.
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Brief Review BoxesBrief Review Boxes summarize the most critical prerequisite mathematical skills students should know in order to master the chapter’s objectives. This feature appears whenever a particular skill is first needed and eliminates the need for reteaching.
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Concept and Vocabulary ChecksConcept and Vocabulary Checks are short-answer exercises that precede the exercise sets to assess students’ understanding of the definitions and concepts presented in each section.
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Practice PLUS ProblemsMore challenging Practice PLUS problems require students to combine several skills or concepts. With an average of ten Practice PLUS problems per exercise set, instructors have flexibility to create assignments that push students’ thinking.
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Make Sense? Exercises“Make Sense?” classroom discussion exercises ask students to determine whether statements are sensible then explain why or why not. Teachers can use the answers to gauge conceptual understanding.
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Retaining the Concepts ExercisesRetaining the Concepts exercises present an opportunity to keep skills fresh and work towards mastery through review of previously learned materials.
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Preview ExercisesPreview Exercises prepare students for material in the section ahead.
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Achieving Success BoxesAchieving Success boxes at the end of many sections in Chapters 1-5 offer strategies for persistence in college mathematics courses.
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Enhanced AssignmentsNew section-level Enhanced Assignments include just-in-time prerequisite review to help keep skills fresh, reinforce key concepts, and provide opportunities to work selected exercises without learning aids. Teachers gain a truer sense of students’ understanding.
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In-Text Teaching ToolsNew in-text teaching tools are available in every section of the Annotated Instructor’s Edition to include a list of resources that are available in MyMathLab for School to incorporate into teaching or homework assignments.
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Early Alert FeatureThe new Early Alert feature in Performance Analytics use predictive analytics to identify struggling students, even if their assignment scores are not cause for concern. In both Performance Analytics and Early Alerts, instructors can email students individually or by group to provide feedback.
Empower Your Math Students with the MyMathLab® Platform from Pearson
MyMathLab® for School from Pearson provides flexible online resources to ensure students are successful in their course and beyond.
PEARSON, MYLAB, MYMATHLAB, MATHXL, MASTERING, STATCRUNCH, REVEL and the Pearson Logo are trademarks owned and/or registered by Pearson plc and/or its affiliates. All other third party marks associated with these products are the property of their respective owners. Copyright in the works referenced herein is owned by Pearson Education, Inc. Pearson Education has control over the editorial content in these instructional materials.
AP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, these products.
More About Precalculus, 7th Edition
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Bob Blitzer Author BioBob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to College Algebra, Bob has written textbooks covering developmental mathematics, introductory algebra, intermediate algebra, trigonometry, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.
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Table of Contents
- Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Exponents and Scientific Notation
P.3 Radicals and Rational Exponents
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions
P.7 Equations
P.8 Modeling with Equations
P.9 Linear Inequalities and Absolute Value Inequalities
- Functions and Graphs
1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and Their Graphs
1.3 More on Functions and Their Graphs
1.4 Linear Functions and Slope 1.5 More on Slope
1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
1.10 Modeling with Functions
- Polynomial and Rational Functions
2.1 Complex Numbers
2.2 Quadratic Functions
2.3 Polynomial Functions and Their Graphs
2.4 Dividing Polynomials; Remainder and Factor Theorems
2.5 Zeros of Polynomial Functions
2.6 Rational Functions and Their Graphs
2.7 Polynomial and Rational Inequalities
2.8 Modeling Using Variation
- Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Properties of Logarithms 3.4 Exponential and Logarithmic Equations
3.5 Exponential Growth and Decay; Modeling Data
- Trigonometric Functions
4.1 Angles and Radian Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications of Trigonometric Functions
- Analytic Trigonometry
5.1 Verifying Trigonometric Identities
5.2 Sum and Difference Formulas
5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
5.4 Product-to-Sum and Sum-to-Product Formulas
5.5 Trigonometric Equations
- Additional Topics in Trigonometry
6.1 The Law of Sines
6.2 The Law of Cosines
6.3 Polar Coordinates
6.4 Graphs of Polar Equations
6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
6.6 Vectors
6.7 The Dot Product
- Systems of Equations and Inequalities
7.1 Systems of Linear Equations in Two Variables
7.2 Systems of Linear Equations in Three Variables
7.3 Partial Fractions
7.4 Systems of Nonlinear Equations in Two Variables 7.5 Systems of Inequalities
7.6 Linear Programming
- Matrices and Determinants
8.1 Matrix Solutions to Linear Systems
8.2 Inconsistent and Dependent Systems and Their Applications
8.3 Matrix Operations and Their Applications
8.4 Multiplicative Inverses of Matrices and Matrix Equations
8.5 Determinants and
Cramer's Rule
- Conic Sections and Analytic Geometry
9.1 The Ellipse
9.2 The Hyperbola
9.3 The Parabola
9.4 Rotation of Axes
9.5 Parametric Equations
9.6 Conic Sections in Polar Coordinates
- Sequences, Induction, and Probability
10.1 Sequences and Summation Notation
10.2 Arithmetic Sequences 10.3 Geometric Sequences and Series
10.4 Mathematical Induction 10.5 The Binomial Theorem
10.6 Counting Principles, Permutations, and Combinations
10.7 Probability
- Introduction to Calculus
11.1 Finding Limits Using Tables and Graphs
11.2 Finding Limits Using Properties of Limits
11.3 Limits and Continuity
11.4 Introduction to Derivatives
- Prerequisites: Fundamental Concepts of Algebra