# xvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7

Size: px
Start display at page:

Download "xvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7"

## Transcription

1 About the Author v Preface to the Instructor xvi WileyPLUS xxii Acknowledgments xxiii Preface to the Student xxvi 1 The Real Numbers The Real Line 2 Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7 Commutativity and Associativity 7 The Order of Algebraic Operations 8 The Distributive Property 10 Additive Inverses and Subtraction 11 Multiplicative Inverses and the Algebra of Fractions 13 Symbolic Calculators 16 Exercises, Problems, and Worked-out Solutions Inequalities, Intervals, and Absolute Value 24 Positive and Negative Numbers 24 Lesser and Greater 25 Intervals 27 Absolute Value 30 Exercises, Problems, and Worked-out Solutions 33 Chapter Summary and Chapter Review Questions 40 vi

2 vii 2 Combining Algebra and Geometry The Coordinate Plane 42 Coordinates 42 Graphs of Equations 44 Distance Between Two Points 46 Length, Perimeter, and Circumference 48 Exercises, Problems, and Worked-out Solutions Lines 57 Slope 57 The Equation of a Line 58 Parallel Lines 61 Perpendicular Lines 62 Midpoints 64 Exercises, Problems, and Worked-out Solutions Quadratic Expressions and Conic Sections 75 Completing the Square 75 The Quadratic Formula 77 Circles 79 Ellipses 81 Parabolas 83 Hyperbolas 85 Exercises, Problems, and Worked-out Solutions Area 98 Squares, Rectangles, and Parallelograms 98 Triangles and Trapezoids 99 Stretching 101 Circles and Ellipses 102 Exercises, Problems, and Worked-out Solutions 105 Chapter Summary and Chapter Review Questions Functions and Their Graphs Functions 118 Definition and Examples 118 The Graph of a Function 121 The Domain of a Function 124 The Range of a Function 126

3 viii Contents Functions via Tables 128 Exercises, Problems, and Worked-out Solutions Function Transformations and Graphs 142 Vertical Transformations: Shifting, Stretching, and Flipping 142 Horizontal Transformations: Shifting, Stretching, Flipping 145 Combinations of Vertical Function Transformations 149 Even Functions 152 Odd Functions 153 Exercises, Problems, and Worked-out Solutions Composition of Functions 165 Combining Two Functions 165 Definition of Composition 166 Order Matters in Composition 169 Decomposing Functions 170 Composing More than Two Functions 171 Function Transformations as Compositions 172 Exercises, Problems, and Worked-out Solutions Inverse Functions 180 The Inverse Problem 180 One-to-one Functions 181 The Definition of an Inverse Function 182 The Domain and Range of an Inverse Function 184 The Composition of a Function and Its Inverse 185 Comments About Notation 187 Exercises, Problems, and Worked-out Solutions A Graphical Approach to Inverse Functions 197 The Graph of an Inverse Function 197 Graphical Interpretation of One-to-One 199 Increasing and Decreasing Functions 200 Inverse Functions via Tables 203 Exercises, Problems, and Worked-out Solutions 204 Chapter Summary and Chapter Review Questions Polynomial and Rational Functions Integer Exponents 214 Positive Integer Exponents 214

4 ix Properties of Exponents 215 Defining x Negative Integer Exponents 218 Manipulations with Exponents 219 Exercises, Problems, and Worked-out Solutions Polynomials 227 The Degree of a Polynomial 227 The Algebra of Polynomials 228 Zeros and Factorization of Polynomials 230 The Behavior of a Polynomial Near ± 234 Graphs of Polynomials 237 Exercises, Problems, and Worked-out Solutions Rational Functions 245 Ratios of Polynomials 245 The Algebra of Rational Functions 246 Division of Polynomials 247 The Behavior of a Rational Function Near ± 250 Graphs of Rational Functions 253 Exercises, Problems, and Worked-out Solutions Complex Numbers 262 The Complex Number System 262 Arithmetic with Complex Numbers 263 Complex Conjugates and Division of Complex Numbers 264 Zeros and Factorization of Polynomials, Revisited 268 Exercises, Problems, and Worked-out Solutions 271 Chapter Summary and Chapter Review Questions Exponents and Logarithms Exponents and Exponential Functions 280 Roots 280 Rational Exponents 284 Real Exponents 285 Exponential Functions 286 Exercises, Problems, and Worked-out Solutions Logarithms as Inverses of Exponential Functions 293 Logarithms Base 2 293

5 x Contents Logarithms with Any Base 295 Common Logarithms and the Number of Digits 297 Logarithm of a Power 297 Radioactive Decay and Half-Life 299 Exercises, Problems, and Worked-out Solutions Applications of Logarithms 310 Logarithm of a Product 310 Logarithm of a Quotient 311 Earthquakes and the Richter Scale 312 Sound Intensity and Decibels 313 Star Brightness and Apparent Magnitude 315 Change of Base 316 Exercises, Problems, and Worked-out Solutions Exponential Growth 328 Functions with Exponential Growth 329 Population Growth 333 Compound Interest 335 Exercises, Problems, and Worked-out Solutions 340 Chapter Summary and Chapter Review Questions e and the Natural Logarithm Defining e and ln 350 Estimating Area Using Rectangles 350 Defining e 352 Defining the Natural Logarithm 355 Properties of the Exponential Function and ln 356 Exercises, Problems, and Worked-out Solutions Approximations and area with e and ln 366 Approximation of the Natural Logarithm 366 Approximations with the Exponential Function 368 An Area Formula 369 Exercises, Problems, and Worked-out Solutions Exponential Growth Revisited 376 Continuously Compounded Interest 376 Continuous Growth Rates 377 Doubling Your Money 378

6 xi Exercises, Problems, and Worked-out Solutions 380 Chapter Summary and Chapter Review Questions Systems of Equations Equations and Systems of Equations 388 Solving an Equation 388 Solving a System of Equations Graphically 391 Solving a System of Equations by Substitution 392 Exercises, Problems, and Worked-out Solutions Solving Systems of Linear Equations 399 Linear Equations: How Many Solutions? 399 Systems of Linear Equations 402 Gaussian Elimination 404 Exercises, Problems, and Worked-out Solutions Solving Systems of Linear Equations Using Matrices 411 Representing Systems of Linear Equations by Matrices 411 Gaussian Elimination with Matrices 413 Systems of Linear Equations with No Solutions 415 Systems of Linear Equations with Infinitely Many Solutions 416 How Many Solutions, Revisited 418 Exercises, Problems, and Worked-out Solutions Matrix Algebra 424 Matrix Size 424 Adding and Subtracting Matrices 426 Multiplying a Matrix by a Number 427 Multiplying Matrices 428 The Inverse of a Matrix 433 Exercises, Problems, and Worked-out Solutions 440 Chapter Summary and Chapter Review Questions Sequences, Series, and Limits Sequences 448 Introduction to Sequences 448 Arithmetic Sequences 450 Geometric Sequences 451 Recursively Defined Sequences 454

7 xii Contents Exercises, Problems, and Worked-out Solutions Series 463 Sums of Sequences 463 Arithmetic Series 463 Geometric Series 466 Summation Notation 468 The Binomial Theorem 470 Exercises, Problems, and Worked-out Solutions Limits 483 Introduction to Limits 483 Infinite Series 487 Decimals as Infinite Series 489 Special Infinite Series 491 Exercises, Problems, and Worked-out Solutions 493 Chapter Summary and Chapter Review Questions Trigonometric Functions The Unit Circle 498 The Equation of the Unit Circle 498 Angles in the Unit Circle 499 Negative Angles 501 Angles Greater Than Length of a Circular Arc 503 Special Points on the Unit Circle 504 Exercises, Problems, and Worked-out Solutions Radians 514 A Natural Unit of Measurement for Angles 514 The Radius Corresponding to an Angle 517 Length of a Circular Arc 520 Area of a Slice 521 Special Points on the Unit Circle 522 Exercises, Problems, and Worked-out Solutions Cosine and Sine 529 Definition of Cosine and Sine 529 The Signs of Cosine and Sine 532 The Key Equation Connecting Cosine and Sine 534

8 xiii The Graphs of Cosine and Sine 535 Exercises, Problems, and Worked-out Solutions More Trigonometric Functions 542 Definition of Tangent 542 The Sign of Tangent 544 Connections Among Cosine, Sine, and Tangent 545 The Graph of Tangent 545 Three More Trigonometric Functions 547 Exercises, Problems, and Worked-out Solutions Trigonometry in Right Triangles 555 Trigonometric Functions via Right Triangles 555 Two Sides of a Right Triangle 557 One Side and One Angle of a Right Triangle 558 Exercises, Problems, and Worked-out Solutions Trigonometric Identities 566 The Relationship Among Cosine, Sine, and Tangent 566 Trigonometric Identities for the Negative of an Angle 568 Trigonometric Identities with π Trigonometric Identities Involving a Multiple of π 572 Exercises, Problems, and Worked-out Solutions 575 Chapter Summary and Chapter Review Questions Trigonometric Algebra and Geometry Inverse Trigonometric Functions 584 The Arccosine Function 584 The Arcsine Function 587 The Arctangent Function 590 Exercises, Problems, and Worked-out Solutions Inverse Trigonometric Identities 599 Composition of Trigonometric Functions and Their Inverses 599 The Arccosine, Arcsine, and Arctangent of t: Graphical Approach 600 The Arccosine, Arcsine, and Arctangent of t: Algebraic Approach 602 Arccosine Plus Arcsine 603 The Arctangent of 1 t 604 More Compositions with Inverse Trigonometric Functions 605

9 xiv Contents Exercises, Problems, and Worked-out Solutions Using Trigonometry to Compute Area 613 The Area of a Triangle via Trigonometry 613 Ambiguous Angles 614 The Area of a Parallelogram via Trigonometry 616 The Area of a Polygon 617 Trigonometric Approximations 619 Exercises, Problems, and Worked-out Solutions The Law of Sines and the Law of Cosines 628 The Law of Sines 628 Using the Law of Sines 629 The Law of Cosines 631 Using the Law of Cosines 632 When to Use Which Law 634 Exercises, Problems, and Worked-out Solutions Double-Angle and Half-Angle Formulas 644 The Cosine of 2θ 644 The Sine of 2θ 645 The Tangent of 2θ 646 The Cosine and Sine of θ The Tangent of θ Exercises, Problems, and Worked-out Solutions Addition and Subtraction Formulas 658 The Cosine of a Sum and Difference 658 The Sine of a Sum and Difference 660 The Tangent of a Sum and Difference 661 Exercises, Problems, and Worked-out Solutions 662 Chapter Summary and Chapter Review Questions Applications of Trigonometry Parametric Curves 672 Curves in the Coordinate Plane 672 Graphing Inverse Functions as Parametric Curves 677 Shifting, Stretching, or Flipping a Parametric Curve 678 Exercises, Problems, and Worked-out Solutions 681

10 xv 11.2 Transformations of Trigonometric Functions 687 Amplitude 687 Period 689 Phase Shift 692 Fitting Transformations of Trigonometric Functions to Data 694 Exercises, Problems, and Worked-out Solutions Polar Coordinates 705 Defining Polar Coordinates 705 Converting from Polar to Rectangular Coordinates 706 Converting from Rectangular to Polar Coordinates 707 Graphs of Polar Equations 711 Exercises, Problems, and Worked-out Solutions Vectors 718 An Algebraic and Geometric Introduction to Vectors 718 Vector Addition 720 Vector Subtraction 723 Scalar Multiplication 725 The Dot Product 726 Exercises, Problems, and Worked-out Solutions The Complex Plane 732 Complex Numbers as Points in the Plane 732 Geometric Interpretation of Complex Multiplication and Division 734 De Moivre s Theorem 737 Finding Complex Roots 738 Exercises, Problems, and Worked-out Solutions 739 Chapter Summary and Chapter Review Questions 741 Photo Credits 743 Index 745

### Contents. About the Author. Preface to the Instructor. xxi. Acknowledgments. xxiii. Preface to the Student

About the Author v Preface to the Instructor v Acknowledgments i Preface to the Student iii Chapter 0 The Real Numbers 1 0.1 The Real Line 2 Construction of the Real Line 2 Is Ever Real Number Rational?

### Contents. CHAPTER P Prerequisites 1. CHAPTER 1 Functions and Graphs 69. P.1 Real Numbers 1. P.2 Cartesian Coordinate System 14

CHAPTER P Prerequisites 1 P.1 Real Numbers 1 Representing Real Numbers ~ Order and Interval Notation ~ Basic Properties of Algebra ~ Integer Exponents ~ Scientific Notation P.2 Cartesian Coordinate System

### Pre-Calculus and Trigonometry Capacity Matrix

Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational expressions Solve polynomial equations and equations involving rational expressions Review Chapter 1 and their

### College Algebra and Trigonometry

GLOBAL EDITION College Algebra and Trigonometry THIRD EDITION J. S. Ratti Marcus McWaters College Algebra and Trigonometry, Global Edition Table of Contents Cover Title Page Contents Preface Resources

### Algebra 2. Chapter 4 Exponential and Logarithmic Functions. Chapter 1 Foundations for Functions. Chapter 3 Polynomial Functions

Algebra 2 Chapter 1 Foundations for Chapter 2 Quadratic Chapter 3 Polynomial Chapter 4 Exponential and Logarithmic Chapter 5 Rational and Radical Chapter 6 Properties and Attributes of Chapter 7 Probability

### Tennessee s State Mathematics Standards Precalculus

Tennessee s State Mathematics Standards Precalculus Domain Cluster Standard Number Expressions (N-NE) Represent, interpret, compare, and simplify number expressions 1. Use the laws of exponents and logarithms

### MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators*

Content Standard 1.0 (HS) Patterns, Algebra and Functions Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving functional patterns and relationships.

### Algebra II Learning Targets

Chapter 0 Preparing for Advanced Algebra LT 0.1 Representing Functions Identify the domain and range of functions LT 0.2 FOIL Use the FOIL method to multiply binomials LT 0.3 Factoring Polynomials Use

### Pre-Calculus and Trigonometry Capacity Matrix

Pre-Calculus and Capacity Matri Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational epressions Solve polynomial equations and equations involving rational epressions

### PreCalculus. Curriculum (447 topics additional topics)

PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

### PRECALCULUS BISHOP KELLY HIGH SCHOOL BOISE, IDAHO. Prepared by Kristina L. Gazdik. March 2005

PRECALCULUS BISHOP KELLY HIGH SCHOOL BOISE, IDAHO Prepared by Kristina L. Gazdik March 2005 1 TABLE OF CONTENTS Course Description.3 Scope and Sequence 4 Content Outlines UNIT I: FUNCTIONS AND THEIR GRAPHS

### Curriculum Catalog

2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents PRE-CALCULUS COURSE OVERVIEW...1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT

### Quantile Textbook Report

Quantile Textbook Report Algebra 2 Author Charles, Randall I., et al StateEdition West Virginia Grade Algebra 2 1 Expressions, Equations, and Inequalities 1.1 Patterns and Expressions 930Q 1.2 Properties

### DRAFT. Pre-calculus Curriculum Map Quarter 1 Chapters P 2. Extraneous Critical numbers Test intervals

Quarter 1 Chapters P 2 Plot points in the coordinate plane and use distance and midpoint formulas. Sketch graphs of equations. Find and use slope of a line to write and graph linear equations. Solve equations:

### PreCalculus. Curriculum (637 topics additional topics)

PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

### Unit 1. Revisiting Parent Functions and Graphing

Unit 1 Revisiting Parent Functions and Graphing Precalculus Analysis Pacing Guide First Nine Weeks Understand how the algebraic properties of an equation transform the geometric properties of its graph.

### 9-12 Mathematics Vertical Alignment ( )

Algebra I Algebra II Geometry Pre- Calculus U1: translate between words and algebra -add and subtract real numbers -multiply and divide real numbers -evaluate containing exponents -evaluate containing

### STEM-Prep Pathway SLOs

STEM-Prep Pathway SLOs Background: The STEM-Prep subgroup of the MMPT adopts a variation of the student learning outcomes for STEM from the courses Reasoning with Functions I and Reasoning with Functions

### Algebra and Trigonometry

Algebra and Trigonometry 978-1-63545-098-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Jay Abramson, Arizona State

### Math Prep for College Physics

Math Prep for College Physics This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (190 topics + 52 additional

### Algebra 2. Curriculum (384 topics additional topics)

Algebra 2 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

### Integrated Math III. IM3.1.2 Use a graph to find the solution set of a pair of linear inequalities in two variables.

Standard 1: Algebra and Functions Students solve inequalities, quadratic equations, and systems of equations. They graph polynomial, rational, algebraic, and piece-wise defined functions. They graph and

### ALGEBRA & TRIGONOMETRY FOR CALCULUS MATH 1340

ALGEBRA & TRIGONOMETRY FOR CALCULUS Course Description: MATH 1340 A combined algebra and trigonometry course for science and engineering students planning to enroll in Calculus I, MATH 1950. Topics include:

### Polynomials and Rational Functions. Quadratic Equations and Inequalities. Remainder and Factor Theorems. Rational Root Theorem

Pre-Calculus Pre-AP Scope and Sequence - Year at a Glance Pre-Calculus Pre-AP - First Semester Pre-calculus with Limits; Larson/Hostetler Three Weeks 1 st 3 weeks 2 nd 3 weeks 3 rd 3 weeks 4 th 3 weeks

### College Algebra & Trig w Apps

WTCS Repository 10-804-197 College Algebra & Trig w Apps Course Outcome Summary Course Information Description Total Credits 5.00 This course covers those skills needed for success in Calculus and many

### Region 16 Board of Education. Precalculus Curriculum

Region 16 Board of Education Precalculus Curriculum 2008 1 Course Description This course offers students an opportunity to explore a variety of concepts designed to prepare them to go on to study calculus.

### Check boxes of Edited Copy of Sp Topics (was 261-pilot)

Check boxes of Edited Copy of 10023 Sp 11 253 Topics (was 261-pilot) Intermediate Algebra (2011), 3rd Ed. [open all close all] R-Review of Basic Algebraic Concepts Section R.2 Ordering integers Plotting

### Instructional Units Plan Algebra II

Instructional Units Plan Algebra II This set of plans presents the topics and selected for ACT s rigorous Algebra II course. The topics and standards are arranged in ten units by suggested instructional

### Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS

Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS (i) Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams;

### Mathematics AKS

Integrated Algebra I A - Process Skills use appropriate technology to solve mathematical problems (GPS) (MAM1_A2009-1) build new mathematical knowledge through problem-solving (GPS) (MAM1_A2009-2) solve

### Precalculus. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th edition, McGraw- Hill, ISBN:

Precalculus Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th edition, McGraw- Hill, 2008. ISBN: 978-0-07-331263-7. Course Description This course provides a working

### Course Catalog. Pre-calculus Glynlyon, Inc.

Course Catalog Pre-calculus 2016 Glynlyon, Inc. Table of Contents COURSE OVERVIEW... 1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT 4: CIRCULAR

### Math Review for AP Calculus

Math Review for AP Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

### Math Prep for Statics

Math Prep for Statics This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

Common Core Edition Table of Contents ALGEBRA 1 Chapter 1 Foundations for Algebra 1-1 Variables and Expressions 1-2 Order of Operations and Evaluating Expressions 1-3 Real Numbers and the Number Line 1-4

### Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10

Prep for Calculus This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (281 topics + 125 additional topics) Real

### MATH Spring 2010 Topics per Section

MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line

### Precalculus. Course Text. Course Description. Course Objectives. StraighterLine MAT201: Precalculus

Precalculus Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th edition, McGraw-Hill, 2008. ISBN: 9780073312637 [This text is available as an etextbook at purchase

### The Research- Driven Solution to Raise the Quality of High School Core Courses. Algebra I I. Instructional Units Plan

The Research- Driven Solution to Raise the Quality of High School Core Courses Algebra I I Instructional Units Plan Instructional Units Plan Algebra II This set of plans presents the topics and selected

### Algebra I. Course Outline

Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative

NFC ACADEMY COURSE OVERVIEW Pre-calculus is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic and conceptual geometric concepts covered

### College Algebra. Third Edition. Concepts Through Functions. Michael Sullivan. Michael Sullivan, III. Chicago State University. Joliet Junior College

College Algebra Concepts Through Functions Third Edition Michael Sullivan Chicago State University Michael Sullivan, III Joliet Junior College PEARSON Boston Columbus Indianapolis New York San Francisco

### Secondary Honors Algebra II Objectives

Secondary Honors Algebra II Objectives Chapter 1 Equations and Inequalities Students will learn to evaluate and simplify numerical and algebraic expressions, to solve linear and absolute value equations

### COURSE OF STUDY MATHEMATICS

COURSE OF STUDY MATHEMATICS Name of Course: Pre-Calculus Course Number: 340 Grade Level: 12 Length of Course: 180 Days Type of Offering: Academic/Elective Credit Value: 1 credit Prerequisite/s: Algebra

### Content Guidelines Overview

Content Guidelines Overview The Pearson Video Challenge is open to all students, but all video submissions must relate to set of predetermined curriculum areas and topics. In the following pages the selected

### HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT P r e c a l c u l u s ( A ) KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS and Graphs Polynomial, Power,

### PreCalculus Honors Curriculum Pacing Guide First Half of Semester

Unit 1 Introduction to Trigonometry (9 days) First Half of PC.FT.1 PC.FT.2 PC.FT.2a PC.FT.2b PC.FT.3 PC.FT.4 PC.FT.8 PC.GCI.5 Understand that the radian measure of an angle is the length of the arc on

### Intermediate Algebra

Intermediate Algebra 978-1-63545-084-2 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) Openstax Lyn Marecek, MaryAnne Anthony-Smith

### College Algebra with Corequisite Support: Targeted Review

College Algebra with Corequisite Support: Targeted Review 978-1-63545-056-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable)

### Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.2 Solving Quadratic Equations

Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.1.1 Solve Simple Equations Involving Absolute Value 0.2 Solving Quadratic Equations 0.2.1 Use the

### THE PYTHAGOREAN THEOREM

THE STORY SO FAR THE PYTHAGOREAN THEOREM USES OF THE PYTHAGOREAN THEOREM USES OF THE PYTHAGOREAN THEOREM SOLVE RIGHT TRIANGLE APPLICATIONS USES OF THE PYTHAGOREAN THEOREM SOLVE RIGHT TRIANGLE APPLICATIONS

### Portable Assisted Study Sequence ALGEBRA IIB

SCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The second half of

### Catholic Central High School

Catholic Central High School Course: Basic Algebra 2 Department: Mathematics Length: One year Credit: 1 Prerequisite: Completion of Basic Algebra 1 or Algebra 1, Basic Plane Geometry or Plane Geometry,

### HHS Pre-Calculus Reference Book

HHS Pre-Calculus Reference Book Purpose: To create a reference book to review topics for your final exam and to prepare you for Calculus. Instructions: Students are to compose a reference book containing

### , Precalculus, Quarter 1

2017.18, Precalculus, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency

### Intermediate Level Learning Targets

Learning Target #1: Develop proficiency in analyzing, graphing and solving linear equations and inequalities. F1.1,,, B1. C1. 1.1 Students will be able to identify different types of relations and functions.

NFC ACADEMY COURSE OVERVIEW Algebra II Honors is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic

### MyMathLab for School Precalculus Graphical, Numerical, Algebraic Common Core Edition 2016

A Correlation of MyMathLab for School Precalculus Common Core Edition 2016 to the Tennessee Mathematics Standards Approved July 30, 2010 Bid Category 13-090-10 , Standard 1 Mathematical Processes Course

### Precalculus AB Honors Pacing Guide First Nine Weeks Unit 1. Tennessee State Math Standards

Precalculus AB Honors Pacing Guide First Nine Weeks Unit 1 Revisiting Parent Functions and Graphing P.F.BF.A.1 Understand how the algebraic properties of an equation transform the geometric properties

### hmhco.com Adaptive. Intuitive. Transformative. AGA Scope and Sequence

hmhco.com Adaptive. Intuitive. Transformative. AGA Algebra 1 Geometry Algebra 2 Scope and Sequence Number and Quantity The Real Number System (N-RN) Properties of exponents to rational exponents Properties

### Maths for Map Makers

SUB Gottingen 7 210 050 861 99 A 2003 Maths for Map Makers by Arthur Allan Whittles Publishing Contents /v Chapter 1 Numbers and Calculation 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14

### MILLIS PUBLIC SCHOOLS

MILLIS PUBLIC SCHOOLS Curriculum Guide High School Math The Millis Public Schools Curriculum Guide highlights the Power Standards for each grade level, Grade 9 through Grade 12 for the Math department.

### Unit 1 Linear Functions I CAN: A.1.a Solve single-step and multistep equations and inequalities in one variable

CUMBERLAND COUNTY SCHOOL DISTRICT BENCHMARK ASSESSMENT CURRICULUM PACING GUIDE School: CCHS Subject: Precalculus Grade: 12 Benchmark Assessment 1 Instructional Timeline: Units 1, 2, 3 Term 1 Dependent

### CURRICULUM PACING GUIDE GRADE/SUBJECT: Precalculus Vertical Alignment. 1st Nine Weeks 1

1st Nine Weeks 17 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply

### Prentice Hall Geometry (c) 2007 correlated to American Diploma Project, High School Math Benchmarks

I1.1. Add, subtract, multiply and divide integers, fractions and decimals. I1.2. Calculate and apply ratios, proportions, rates and percentages to solve problems. I1.3. Use the correct order of operations

Course Description This course includes an in-depth analysis of algebraic problem solving preparing for College Level Algebra. Topics include: Equations and Inequalities, Linear Relations and Functions,

### Check boxes of Edited Copy of Sp Topics (was 217-pilot)

Check boxes of Edited Copy of 10024 Sp 11 213 Topics (was 217-pilot) College Algebra, 9th Ed. [open all close all] R-Basic Algebra Operations Section R.1 Integers and rational numbers Rational and irrational

### Algebra II. A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.

Standard 1: Relations and Functions Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.

### Curriculum Catalog

2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents ALGEBRA II COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND PROBLEMS... 2 UNIT 3: LINEAR

### Unit 1. Revisiting Parent Functions and Graphing

Unit 1 Revisiting Parent Functions and Graphing Revisiting Statistics (Measures of Center and Spread, Standard Deviation, Normal Distribution, and Z-Scores Graphing abs(f(x)) and f(abs(x)) with the Definition

### Integrated Math 3 Math 3 Course Description:

Course Description: Integrated Math 3 Math 3 Course Description: Integrated strands include algebra, functions, geometry, trigonometry, statistics, probability and discrete math. Scope and sequence includes

### Scope and Sequence: National Curriculum Mathematics from Haese Mathematics (7 10A)

Scope and Sequence: National Curriculum Mathematics from Haese Mathematics (7 10A) Updated 06/05/16 http://www.haesemathematics.com.au/ Note: Exercises in red text indicate material in the 10A textbook

### Ron Paul Curriculum Mathematics 8 Lesson List

Ron Paul Curriculum Mathematics 8 Lesson List 1 Introduction 2 Algebraic Addition 3 Algebraic Subtraction 4 Algebraic Multiplication 5 Week 1 Review 6 Algebraic Division 7 Powers and Exponents 8 Order

### Sophomore Year: Algebra II Textbook: Algebra II, Common Core Edition Larson, Boswell, Kanold, Stiff Holt McDougal 2012

Sophomore Year: Algebra II Tetbook: Algebra II, Common Core Edition Larson, Boswell, Kanold, Stiff Holt McDougal 2012 Course Description: The purpose of this course is to give students a strong foundation

### How well do I know the content? (scale 1 5)

Page 1 I. Number and Quantity, Algebra, Functions, and Calculus (68%) A. Number and Quantity 1. Understand the properties of exponents of s I will a. perform operations involving exponents, including negative

### Binomials defined, 13 division by, FOIL method and, 22 multiplying binomial by trinomial,

5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-1 Index Absolute value defined, 46 functions and, 126 59 Absolute value equations, solutions, 46 49 Absolute value inequalities, solutions, 263 267 Acceleration,

### Algebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards

Algebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards Standard 2 : Number & Operations CLE 3103.2.1: CLE 3103.2.2: CLE 3103.2.3:

### Elementary and Intermediate Algebra

Elementary and Intermediate Algebra 978-1-63545-106-1 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek, Santa

### Curriculum Guide Algebra 2 Advanced

Unit 1: Equations and Inequalities Biblical Worldview Essential Questions: Is your life balanced as a believer? Are you a real Christian? 13 Lessons A2#1, A2#2 1. Use a number line to graph and order real

ALGEBRA II WITH TRIGONOMETRY COURSE OUTLINE SPRING 2009. MR. YATES Vocabulary Unit 1: Polynomials Scientific Notation Exponent Base Polynomial Degree (of a polynomial) Constant Linear Quadratic Cubic Monomial

### College Algebra with Corequisite Support: A Blended Approach

College Algebra with Corequisite Support: A Blended Approach 978-1-63545-058-3 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable)

### Milford Public Schools Curriculum. Department: Mathematics Course Name: Precalculus Level 1

Milford Public Schools Curriculum Department: Mathematics Course Name: Precalculus Level 1 UNIT 1 Unit Description: Students will construct polynomial graphs with zeros and end behavior, and apply limit

### Precalculus P. Precalculus includes the following domains and clusters:

Precalculus P Precalculus is designed to prepare students for college level STEM focused courses. Students extend their knowledge of the complex number system to use complex numbers in polynomial identities

### Prentice Hall Mathematics, Algebra Correlated to: Achieve American Diploma Project Algebra II End-of-Course Exam Content Standards

Core: Operations on Numbers and Expressions Priority: 15% Successful students will be able to perform operations with rational, real, and complex numbers, using both numeric and algebraic expressions,

### College Algebra with Corequisite Support: A Compressed Approach

College Algebra with Corequisite Support: A Compressed Approach 978-1-63545-059-0 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable)

College Algebra 978-1-63545-097-2 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Text Jay Abramson, Arizona State University

### High School Mathematics Honors PreCalculus

High School Mathematics Honors PreCalculus This is an accelerated course designed for the motivated math students with an above average interest in mathematics. It will cover all topics presented in Precalculus.

### Foundations of Mathematics

Foundations of Mathematics 978-1-63545-087-3 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek, Santa Ana College

### TEACHER CERTIFICATION EXAM 1.0 KNOWLEDGE OF ALGEBRA Identify graphs of linear inequalities on a number line...1

TABLE OF CONTENTS COMPETENCY/SKILL PG # 1.0 KNOWLEDGE OF ALGEBRA...1 1.1. Identify graphs of linear inequalities on a number line...1 1.2. Identify graphs of linear equations and inequalities in the coordinate

### Algebra 2 Khan Academy Video Correlations By SpringBoard Activity

SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in

### Algebra 2 Khan Academy Video Correlations By SpringBoard Activity

SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in

### SPECIALIST MATHEMATICS

SPECIALIST MATHEMATICS (Year 11 and 12) UNIT A A1: Combinatorics Permutations: problems involving permutations use the multiplication principle and factorial notation permutations and restrictions with

### T a b l e o f C o n t e n t s

T a b l e o f C o n t e n t s C O M P E T E N C Y 1 KNOWLEDGE OF ALGEBRA... 1 SKILL 1.1: Apply the properties of real numbers: closure, commutative, associative, distributive, transitive, identities, and

### WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ALGEBRA II

UNIT: Review of Basic Algebra Skills as Needed SR1 and any Supplemental Materials UNIT : What skills from Algebra I are used in Algebra II? Review Algebra I Skills as Needed SR1 and any additional resources

### College Algebra with Trigonometry

College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (556 topics + 614 additional

### Mr. Kelly s Algebra II Syllabus

Algebra II Syllabus The following is a general description and an outline of the topics covered in a full year of algebra II. The outline is broken into parts A and B to correspond to our trimesters. It

### Math 4C Fall 2008 Final Exam Study Guide Format 12 questions, some multi-part. Questions will be similar to sample problems in this study guide,

Math 4C Fall 2008 Final Exam Study Guide Format 12 questions, some multi-part. Questions will be similar to sample problems in this study guide, homework problems, lecture examples or examples from the