Chapter 1: Equations and Inequalities Section 1.1: Graphs and Graphing Utilities The Rectangular Coordinate System and Graphs
|
|
- Harold Fox
- 6 years ago
- Views:
Transcription
1 Chapter 1: Equations and Inequalities Section 1.1: Graphs and Graphing Utilities The Rectangular Coordinate System and Graphs Coordinate Geometry y II I P(a, b) (a, b) = (x, y) O x III IV A relationship between two quantities can be expressed as an equation in two variables; y = 4 x 2 An equation is a statement that two algebraic expressions are equal. A solution to an equation in two variables is an ordered pair (x, y) when substituted and evaluated yields a true numerical statement. A graph of an equation consists of the set of ordered pairs that are solutions to the equation. The graph of an equation in two variables is the visual representation of the solution set. From J. P. Wood, Spring
2 Graph the equation: y = 4 x 2 (1) pick values of x (2) evaluate y values x y (3) plot ordered pairs (4) smoothly connect dots Now use TI-83 to graph To find intercepts: x-intercept : set y = 0 and solve for x y-intercept : set x = 0 and solve for y From J. P. Wood, Spring
3 Section 1.2 Linear Equations and Rational Equations Definition of a Linear Equation: A linear equation in one variable x is an equation that can be written in the standard form: ax + b = 0 a,b are reals, a 0 A solution to a linear equation is a value of the variable when substituted and evaluated yields a true numerical statement. Solving equations centers around generating equivalent equations (rules on p 102) Solve the following: 3x 5 = 7 2(x 3) 17 = 13 3(x + 2) Use the TI-83 to verify the solution Linear Equations with Fractions: From J. P. Wood, Spring
4 Rational Equations: A Rational Equation contains one or more rational expressions Solving a Rational Equation Solving a Rational Equation to determine when two equations are equal: Types of Equations: An equation that is true for all values in the domain of the variable is an identity: x 2 9 = (x + 3)(x 3) A conditional equation is one that is true for some but not all permissible values of the variable: 2x + 3 = 17 An inconsistent equation is one that is not true for any permissible value of the variable: x = x + 7 Determine the category (type) of the following equation: 2(x + 1) = 2x + 3 From J. P. Wood, Spring
5 Modeling with Linear Equations Section 1.3: Mathematical Modeling: The process of translating phrases or sentences into algebraic expressions or equations. Strategy for Solving Word Problems: 1. Read problem carefully and then state in own words what the problem is looking for. Let x represent an unknown quantity. 2. If necessary write any other unknowns in terms of x. 3. Write an equation in x that models the verbal problem 4. Solve equation to answer the problem 5. Check solution in original wording of problem Example: You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $20 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $5 with a charge of $0.10 per minute for all long-distance calls. For how many minutes will the costs for the two plans be the same? Example: Your grandmother has $50,000 to invest and needs your help. Part of this money is to be invested in noninsured bonds paying 15% annual interest and the rest of the money is to be invested in a government insured CD paying 7% annual interest. She wants $6000 per year total interest earned from both of these investments. How much money should she invest in each? From J. P. Wood, Spring
6 Example: A rectangular family room is three times as long as it is wide, and its perimeter is 60 ft. Find its dimensions. Common Formulas (p.123) For a circular cylinder, write the formula in terms of height. From J. P. Wood, Spring
7 Section 1.4 Complex Numbers Let s solve: x = 0 For the real numbers a and b, the number a + bi is a complex number a + bi = c + di if and only if a = c and b = d Operations with Complex Numbers Addition and Subtraction: Multiplication: Division using Complex Conjugates The Complex Conjugate of a + bi is a bi From J. P. Wood, Spring
8 Roots of Negative Numbers Principal Square Root of a Negative Number b = i b Operations Involving Square Roots of Negative Numbers From J. P. Wood, Spring
9 Section 1.5 Quadratic Equations A quadratic equation is an equation that can be written in the general form: ax 2 + bx + c = 0 Solving Quadratics by Factoring (rules on p.137) Remember the Zero Product Principle: x 2 7x +10 = 0 If ab = 0, then a=0 or b = 0 Solving Quadratics by the Square Root Property Extracting Square Roots: Let u 2 = d If u 2 = d then u =± d Solving Quadratics by Completing the Square: From J. P. Wood, Spring
10 Solving Quadratics by using the Quadratic Formula For any ax 2 + bx + c = 0 x = 2 b b 4ac ± 2a The radicand of the Quadratic equation is called the discriminant ( Look at Table 1.2 on p.146) b 2 4ac If the discriminant is a perfect square, the quadratic is factorable 12x 2 10x 12 4 ways to solve a quadratic: 1. Factor (if factorable) 2. Extract the Root (if in u 2 = d format) 3. Complete the Square (always) 4. Quadratic Equation (always) Pythagorean Theorem a 2 + b 2 = c 2 c a b From J. P. Wood, Spring
11 Section 1.6 Polynomial Equations Radical Equations Equations with Rational Exponents Solving form: If m is even m n x = k If m is odd Equations that are in Quadratic Form Equations Involving Absolute Value Absolute Value: If u = c then u = c or u = -c From J. P. Wood, Spring
12 Section 1.7 Linear Inequalities and Absolute Value Inequalities Interval Notation: Open Interval (a, b) = {x a < x < b} Closed Interval [a, b] = {x a x b} Infinite Interval (a, ) = {x x > a} Infinite Interval (-, b] = {x x b} (More interval notations shown on p.174) Intersections and Unions of Intervals Find (1, 4) [2, 8] and (1, 4) U [2, 8] Solving Linear Inequalities in One Variable (Properties of Inequalities p 177) Addition Property of Inequality Positive Multiplication Property of Inequality From J. P. Wood, Spring
13 Negative Multiplication Property of Inequality Solving a Linear Inequality Containing Fractions Inequalities with Unusual Solution Sets Solving Compound Inequalities Solving Inequalities with Absolute Value u < c iff -c < u < c u > c iff u < -c or u > c From J. P. Wood, Spring
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
More informationCourse Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates
Course Name: MAT 135 Spring 2017 Master Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 01/15/2017 End: 05/31/2017 Course Content: 279 Topics (207
More informationEquations and Inequalities. College Algebra
Equations and Inequalities College Algebra Radical Equations Radical Equations: are equations that contain variables in the radicand How to Solve a Radical Equation: 1. Isolate the radical expression on
More informationSand Springs Public Schools Algebra I Local Objectives
1st Six Weeks Plan for Problem Solving Real Number Operations with Integers Adding and Subtracting Rational Numbers Multiplying and Dividing Rational Numbers The Percent Proportion Simple Probability and
More informationPrep for College Algebra
Prep for College Algebra This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (219 topics + 85 additional topics)
More informationPrep for College Algebra with Trigonometry
Prep for 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 (246 topics +
More informationEvaluate algebraic expressions for given values of the variables.
Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,
More informationQuantile Textbook Report
Quantile Textbook Report Algebra 1 Author Charles, Randall I., et al StateEdition West Virginia Grade Algebra 1 1 Foundations for Algebra 1.1 Variables and Expressions 750Q 1.2 Order of Operations and
More informationCheck 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
More informationChapter R - Review of Basic Algebraic Concepts (26 topics, no due date)
Course Name: Math 00023 Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 245 topics Textbook: Miller/O'Neill/Hyde:
More informationA Correlation of. Pearson. Mathematical Ideas. to the. TSI Topics
A Correlation of Pearson 2016 to the A Correlation of 2016 Table of Contents Module M1. Linear Equations, Inequalities, and Systems... 1 Module M2. Algebraic Expressions and Equations (Other Than Linear)...
More informationEquations. Rational Equations. Example. 2 x. a b c 2a. Examine each denominator to find values that would cause the denominator to equal zero
Solving Other Types of Equations Rational Equations Examine each denominator to find values that would cause the denominator to equal zero Multiply each term by the LCD or If two terms cross-multiply Solve,
More informationB. Complex number have a Real part and an Imaginary part. 1. written as a + bi some Examples: 2+3i; 7+0i; 0+5i
Section 11.8 Complex Numbers I. The Complex Number system A. The number i = -1 1. 9 and 24 B. Complex number have a Real part and an Imaginary part II. Powers of i 1. written as a + bi some Examples: 2+3i;
More informationStudy Guide for Math 095
Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.
More informationCheck boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and
Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication
More informationNEW YORK ALGEBRA TABLE OF CONTENTS
NEW YORK ALGEBRA TABLE OF CONTENTS CHAPTER 1 NUMBER SENSE & OPERATIONS TOPIC A: Number Theory: Properties of Real Numbers {A.N.1} PART 1: Closure...1 PART 2: Commutative Property...2 PART 3: Associative
More informationMinnesota State Colleges and Universities Intermediate Algebra Sample Questions
Minnesota State Colleges and Universities Intermediate Algebra Sample Questions 013 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College
More informationVOYAGER INSIDE ALGEBRA CORRELATED TO THE NEW JERSEY STUDENT LEARNING OBJECTIVES AND CCSS.
We NJ Can STUDENT Early Learning LEARNING Curriculum OBJECTIVES PreK Grades 8 12 VOYAGER INSIDE ALGEBRA CORRELATED TO THE NEW JERSEY STUDENT LEARNING OBJECTIVES AND CCSS www.voyagersopris.com/insidealgebra
More informationCenterville Jr. High School Curriculum Mapping Honors Algebra 1 st Nine Weeks Kristen Soots
Centerville Jr. High School Curriculum Mapping 1 st Nine Weeks Kristen Soots 1.0.2 RNE.1 & RNE.2 1.2.1 L.1 & L.2 How do you classify and use real numbers? How do you translate a verbal sentence into an
More informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More information8th Grade Math Definitions
8th Grade Math Definitions Absolute Value: 1. A number s distance from zero. 2. For any x, is defined as follows: x = x, if x < 0; x, if x 0. Acute Angle: An angle whose measure is greater than 0 and less
More informationGlossary. Glossary 981. Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle
More informationAdvanced Algebra Scope and Sequence First Semester. Second Semester
Last update: April 03 Advanced Algebra Scope and Sequence 03-4 First Semester Unit Name Unit : Review of Basic Concepts and Polynomials Unit : Rational and Radical Epressions Sections in Book 0308 SLOs
More informationA is any of ordered pairs. The set of all. components of the pairs is called the of the
Section 8.1: INTRODUCTION TO FUNCTIONS When you are done with your homework you should be able to Find the domain and range of a relation Determine whether a relation is a function Evaluate a function
More informationBeginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More informationSolving Quadratic Equations by Formula
Algebra Unit: 05 Lesson: 0 Complex Numbers All the quadratic equations solved to this point have had two real solutions or roots. In some cases, solutions involved a double root, but there were always
More informationMA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.
Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic
More informationAlgebra 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
More information3. If a coordinate is zero the point must be on an axis. If the x-coordinate is zero, where will the point be?
Chapter 2: Equations and Inequalities Section 1: The Rectangular Coordinate Systems and Graphs 1. Cartesian Coordinate System. 2. Plot the points ( 3, 5), (4, 3), (3, 4), ( 3, 0) 3. If a coordinate is
More informationAlgebra 2. Curriculum (524 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.
More informationCheck 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
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationFlorida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper
Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper Whole Numbers MDECL1: Perform operations on whole numbers (with applications,
More informationMATH 8. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability
MATH 8 Unit 1: Rational and Irrational Numbers (Term 1) 1. I CAN write an algebraic expression for a given phrase. 2. I CAN define a variable and write an equation given a relationship. 3. I CAN use order
More informationPreCalculus. 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.
More informationCHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic
CHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic equations. They can be solved using a graph, a perfect square,
More informationReview 1. 1 Relations and Functions. Review Problems
Review 1 1 Relations and Functions Objectives Relations; represent a relation by coordinate pairs, mappings and equations; functions; evaluate a function; domain and range; operations of functions. Skills
More informationFlorida Math Curriculum (433 topics)
Florida Math 0028 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
More informationIntermediate Algebra with Applications
Lakeshore Technical College 10-804-118 Intermediate Algebra with Applications Course Outcome Summary Course Information Alternate Title Description Total Credits 4 Total Hours 72 Pre/Corequisites Prerequisite
More informationAlgebra 1 Duxbury Middle School > > Grade 8 > Mathematics > Algebra 1 > Iacadoro, Stephanie Tuesday, February 28, 2017, 11:58AM
Algebra 1 Duxbury Middle School > 2016-2017 > Grade 8 > Mathematics > Algebra 1 > Iacadoro, Stephanie Tuesday, February 28, 2017, 11:58AM Unit Unit 0: Preparing for Algebra * for 282 only (Week 1, 9 Skills
More informationIndex. Index. Index A53
A Addition of integers, 1 linear equations, 4 linear inequalities, 54 of polynomials, 337, 340 341, 396 Property of Equality, 4 of Inequality, 54 of radicals and square roots, 465, 470 in units of measure,
More informationALGEBRA I CURRICULUM GUIDE Overview and Scope & Sequence
ALGEBRA I CURRICULUM GUIDE Overview and Scope & Sequence Loudoun County Public Schools 2013-2014 (Additional curriculum information and resources for teachers can be accessed through CMS) Algebra I Nine
More informationAlgebra 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.
More informationAccessible Topic - Topics accessible to visually impaired students using a screen reader.
Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334
More informationArea Formulas. Linear
Math Vocabulary and Formulas Approximate Area Arithmetic Sequences Average Rate of Change Axis of Symmetry Base Behavior of the Graph Bell Curve Bi-annually(with Compound Interest) Binomials Boundary Lines
More informationAlgebra I. CORE TOPICS (Key Concepts & Real World Context) UNIT TITLE
CHAPTER 1 Using variables Exponents and Order of Operations Exploring real numbers Adding real numbers Subtracting real numbers Multiplying and dividing real numbers The Distributive Property Properties
More informationGrade 8 Math Curriculum Map Erin Murphy
Topic 1 Variables and Expressions 2 Weeks Summative Topic Test: Students will be able to (SWBAT) use symbols o represent quantities that are unknown or that vary; demonstrate mathematical phrases and real-world
More informationMATH 7 HONORS. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability
MATH 7 HONORS Unit 1: Rational and Irrational Numbers (Term 1) 1. I CAN write an algebraic expression for a given phrase. 2. I CAN define a variable and write an equation given a relationship. 3. I CAN
More informationSOLUTIONS FOR PROBLEMS 1-30
. Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).
More informationOnline Courses for High School Students
Online Courses for High School Students 1-888-972-6237 Algebra I Course Description: Students explore the tools of algebra and learn to identify the structure and properties of the real number system;
More informationMath 75 Mini-Mod Due Dates Spring 2016
Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing
More informationGlossary. Glossary Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Acute triangle A triangle in which all three angles are acute Addends The
More informationAlgebra 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
More informationSolving Multi-Step Equations
1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract terms to both sides of the equation to get the
More informationAlgebra 2 & Trigonometry Honors Midterm Review 2016
Algebra & Trigonometry Honors Midterm Review 016 Solving Equations 1) Find all values of x that satisfy the equation, 5x 1 = x + 3 ) Solve the following by completing the square. Express your answer in
More informationAlgebra 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
More informationAlgebra 1 Standards Curriculum Map Bourbon County Schools. Days Unit/Topic Standards Activities Learning Targets ( I Can Statements) 1-19 Unit 1
Algebra 1 Standards Curriculum Map Bourbon County Schools Level: Grade and/or Course: Updated: e.g. = Example only Days Unit/Topic Standards Activities Learning Targets ( I 1-19 Unit 1 A.SSE.1 Interpret
More informationAn equation is a statement that states that two expressions are equal. For example:
Section 0.1: Linear Equations Solving linear equation in one variable: An equation is a statement that states that two expressions are equal. For example: (1) 513 (2) 16 (3) 4252 (4) 64153 To solve the
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationMAT 1033 Final Review for Intermediate Algebra (Revised April 2013)
1 This review corresponds to the Charles McKeague textbook. Answers will be posted separately. Section 2.1: Solve a Linear Equation in One Variable 1. Solve: " = " 2. Solve: "# = " 3. Solve: " " = " Section
More informationALGEBRA 1B GOALS. 1. The student should be able to use mathematical properties to simplify algebraic expressions.
GOALS 1. The student should be able to use mathematical properties to simplify algebraic expressions. 2. The student should be able to add, subtract, multiply, divide, and compare real numbers. 3. The
More informationNorth Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents.
North Seattle Community College Math 084 Chapter 1 Review For the test, be sure to show all work! Turn off cell phones. Perform the operation. Perform the operation. Write the product using exponents.
More informationMATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline
MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 1-75 odd) A. Simplify fractions. B. Change mixed numbers
More informationAlgebra 1 / 8 th Grade Algebra Curriculum
1 st Quarter 9 weeks Write algebraic examples. Evaluate expressions and solve open sentences. Use algebraic properties of identity and equality. Use conditional statements and counterexamples. variable
More informationRecognize the appropriate method for factoring a polynomial Use a general strategy for factoring polynomials
Section 6.5: A GENERAL FACTORING STRATEGY When you are done with your homework you should be able to Recognize the appropriate method for factoring a polynomial Use a general strategy for factoring polynomials
More informationCUNY Elementary Algebra Final Exam (CEAFE) Fall 2012 Item Results and Learning Outcomes Correspondence
1 CUNY Elementary Algebra Final Exam (CEAFE) Fall 2012 Item Results and Learning Outcomes Correspondence Purpose of Exam: Students enrolled in any CUNY Elementary Algebra developmental courses, workshops
More informationAlgebra I. Unit 1 Connections to Algebra
Unit 1 Connections to Algebra Time: 15 days Objectives: 1, 2, 8 and 9 Translate verbal into mathematical Write using exponents Use the order of operations to evaluate Solve open sentences by performing
More information( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2
470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can
More informationAlgebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target
Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target SB Activity Activity 1 Investigating Patterns 1-1 Learning Targets: Identify patterns in data. Use tables, graphs,
More informationA Partial List of Topics: Math Spring 2009
A Partial List of Topics: Math 112 - Spring 2009 This is a partial compilation of a majority of the topics covered this semester and may not include everything which might appear on the exam. The purpose
More informationRon 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
More informationCONTENTS COLLEGE ALGEBRA: DR.YOU
1 CONTENTS CONTENTS Textbook UNIT 1 LECTURE 1-1 REVIEW A. p. LECTURE 1- RADICALS A.10 p.9 LECTURE 1- COMPLEX NUMBERS A.7 p.17 LECTURE 1-4 BASIC FACTORS A. p.4 LECTURE 1-5. SOLVING THE EQUATIONS A.6 p.
More informationAlgebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals
Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive
More informationCopyright 2012 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/6
Course Name: MTH099 Fall 2012 Prov Course Code: ADPNR-EADAW ALEKS Course: Beginning and Intermediate Algebra Combined Instructor: Lynd Course Dates: Begin: 08/23/2012 End: 01/20/2013 Course Content: 210
More information2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
More informationALGEBRA I CURRICULUM OUTLINE
ALGEBRA I CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines
More informationUnits: 10 high school credits UC requirement category: c General Course Description:
Summer 2015 Units: 10 high school credits UC requirement category: c General Course Description: ALGEBRA I Grades 7-12 This first year course is designed in a comprehensive and cohesive manner ensuring
More informationCopyright 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
More informationGraphing Quadratic Functions 9.1
Quadratic Functions - Graphing Quadratic Functions 9.1 f ( x) = a x + b x + c (also called standard form). The graph of quadratic functions is called a parabola. Axis of Symmetry a central line which makes
More informationPre-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
More informationSection 7.4: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH DIFFERENT DENOMINATORS
INTERMEDIATE ALGEBRA WORKBOOK/FOR USE WITH ROBERT BLITZER S TEXTBOOK INTRODUCTORY AND INTERMEDIATE ALGEBRA FOR COLLEGE STUDENTS, 4TH ED. Section 7.4: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH DIFFERENT
More informationChapter 1. Equations and Inequalities. 1.1 Basic Equations
Chapter 1. Equations and Inequalities 1.1 Basic Equations Properties of Equalities (the Cancellation properties): 1. A = B if and only if A + C = B + C 2. A = B if and only if AC = BC ( C 0 ) The values
More informationWest Windsor-Plainsboro Regional School District Algebra Grade 8
West Windsor-Plainsboro Regional School District Algebra Grade 8 Content Area: Mathematics Unit 1: Foundations of Algebra This unit involves the study of real numbers and the language of algebra. Using
More informationCollege 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)
More informationNFC ACADEMY COURSE OVERVIEW
NFC ACADEMY COURSE OVERVIEW Algebra I Fundamentals is a full year, high school credit course that is intended for the student who has successfully mastered the core algebraic concepts covered in the prerequisite
More informationCourse Number 420 Title Algebra I Honors Grade 9 # of Days 60
Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number
More informationMath 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
More informationElementary 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
More informationMath 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
More informationAnswers to Sample Exam Problems
Math Answers to Sample Exam Problems () Find the absolute value, reciprocal, opposite of a if a = 9; a = ; Absolute value: 9 = 9; = ; Reciprocal: 9 ; ; Opposite: 9; () Commutative law; Associative law;
More informationCHAPTER 3: Quadratic Functions and Equations; Inequalities
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 3: Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers 3.2 Quadratic Equations, Functions, Zeros, and
More informationIntegrated Arithmetic and Basic Algebra
211 771 406 III T H I R D E D I T I O N Integrated Arithmetic and Basic Algebra Bill E. Jordan Seminole Community College William P. Palow Miami-Dade College Boston San Francisco New York London Toronto
More information2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY
2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY The following are topics that you will use in Geometry and should be retained throughout the summer. Please use this practice to review the topics you
More informationIntermediate 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
More informationCommon Core State Standards for Mathematics - High School PARRC Model Content Frameworks Mathematics Algebra 2
A Correlation of CME Project Algebra 2 Common Core 2013 to the Common Core State Standards for , Common Core Correlated to the Number and Quantity The Real Number System N RN Extend the properties of exponents
More informationSubtraction Property of Equality terms. x-axis x-coordinate x-intercept y-axis y-coordinate y-intercept
Algebra I Chapter 1 Chapter 2 additive identity range absolute value algebraic expression reciprocal additive inverses Associative Property Reflexive Property of Equality back-to-back stem and leaf bar
More informationTeacher: CORE Algebra Year: Essential Questions Content Skills Vocabulary Assessments
Teacher: CORE Algebra Year: 2010-11 Course: Algebra Month: All Months S e p t e m b e r THE LANGUAGE OF ALGEBRA AND REAL NUMBERS Essential Questions Content Skills Vocabulary Assessments Algebraic Properties
More informationALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices
ALGEBRA 2 Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number
More informationAlg II Syllabus (First Semester)
Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities Lesson 01: Solving linear equations Lesson 02: Solving linear inequalities (See Calculator Appendix A and associated video.)
More information