Natural Numbers: Also called the counting numbers The set of natural numbers is represented by the symbol,.
|
|
- Erin Powell
- 5 years ago
- Views:
Transcription
1 Name Period Date: Topic: Real Numbers and Their Graphs Standard: 9-12.A.1.3 Objective: Essential Question: What is the significance of a point on a number line? Determine the relative position on the number line and the relative magnitude of integers, decimals, rationals, irrationals, and numbers in scientific notation. The student will learn to graph real numbers on a number line, to compare numbers, and to find their absolute values. Natural Numbers: {1, 2, 3, } Also called the counting numbers The set of natural numbers is represented by the symbol,. Whole Numbers: {0, 1, 2, 3, } The set of whole numbers is the union of the set of natural numbers and the set containing only zero: * +. Integers: {,-3, -2, -1, 0, 1, 2, 3, } The set of integers is represented by the symbol. Summary
2 Rational Numbers: { } e.g. 1,, 0.5,, 0 The set of rational numbers is represented by the symbol, (for quotient). Irrational Numbers:.{ } e.g.,, Real Numbers: The set of real numbers is the union of the set of rational numbers and the set of irrational numbers. The set of real numbers is represented by the symbol,. Value of Real Numbers: The value, or magnitude, of a real number can be represented by placing a dot on a number line. Number Line: A number line is a horizontal line divided into equal segments by short, vertical lines. Each vertical line represents a real value. We usually represent integral values by the vertical lines. We usually indicate the position of zero by a larger line, and we call that location the origin. 2
3 Graphing Real Numbers: Each point on a number line is paired with exactly one real number. That number is called the coordinate of the point. The dots on the number line below have coordinates, 3.1,, 1, and. Each real number is paired with exactly one point on the number line. That point is called the graph of the point. The dots on the number line below are the graphs of the real numbers, 3.1,, 1, and. origin Exercise: Graph the following points on the number line below:,,,. 3
4 Exercise: What are the coordinates of points A, B, and C on the number line below? C B A A: B: C: 4
5 Distance between points on a number line: The distance between two points on a number line is the algebraic difference between their coordinates. What is the coordinate of a point that is of the way from point C, below, to point D? C P D Coordinate of point D: 2 Coordinate of point C: 3 Distance between D and C: ( ) Two fifths of distance Coordinate of point is, ( ) This point is indicated by point P above. 5
6 Exercise: What is the coordinate of a point that is of the way from point C, below, to point D? C D Graph the point. What is the coordinate of a point that is of the way from point C, below, to point D? C D Graph the point. 6
7 Order on a Number Line: On a number line, the larger a number is, the farther to the right its graph is. C D The number line clearly shows that negative three is smaller than two. Moreover, two is larger than negative three. The order of two numbers, as seen on a number line, can be expressed as an inequality. Inequalities: In the above example, we can write, This is read, Negative three is less than two. Moreover, the relationship between these two numbers can also be written as, These two inequalities are equivalent... 7
8 Exercise: Use the number line to fill in the blank in the expressions below with the correct inequality symbol
9 Opposite of a Real Number: Every real number has an opposite. Opposite real numbers lie equidistant from and on opposite sides of the origin. 2 2 The opposite of two is negative two. ( ) The opposite of negative two is two. ( ) Exercise: On the number line below, graph and label the following points: The opposite of one ( ) The opposite of two ( ) The opposite of negative three ( ) The opposite of zero ( ) Zero is its own opposite: ( ) 9
10 Absolute Value of a Real Number: The absolute value of a real number is the distance between the graph of that number and the origin. 2 3 The absolute value of three is three, because the distance between the origin and three is three. The absolute value of negative two is two, because the distance between the origin and negative two is two. Symbolically, absolute value is written using two vertical lines: Definition of Absolute Value: x x x x x x x x x 10
11 Exercise: On the number line below, graph and label the following points: Class work: Page 3 Oral Exercises 1-19 Homework: Page 4 Written Exercises 1-39 odd Page 5 Mixed Review
MA 180 Lecture. Chapter 0. College Algebra and Calculus by Larson/Hodgkins. Fundamental Concepts of Algebra
0.) Real Numbers: Order and Absolute Value Definitions: Set: is a collection of objections in mathematics Real Numbers: set of numbers used in arithmetic MA 80 Lecture Chapter 0 College Algebra and Calculus
More information1)Write the integer that represents the opposite of each real-world. situation. In words, write the meaning of the opposite.
1) Write the integer that represents the opposite of each real-world situation. In words, write the meaning of the opposite. a. Example: An atom s positive charge of 7 Opposite: An atom s negative charge
More informationCircles & Interval & Set Notation.notebook. November 16, 2009 CIRCLES. OBJECTIVE Graph a Circle given the equation in standard form.
OBJECTIVE Graph a Circle given the equation in standard form. Write the equation of a circle in standard form given a graph or two points (one being the center). Students will be able to write the domain
More informationClassify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.
Real Numbers and The Number Line Properties of Real Numbers Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers. Square root, radicand,
More informationAlgebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )
Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationALGEBRA I FORM I. Textbook: Algebra, Second Edition;Prentice Hall,2002
ALGEBRA I FORM I Textbook: Algebra, Second Edition;Prentice Hall,00 Prerequisites: Students are expected to have a knowledge of Pre Algebra and proficiency of basic math skills including: positive and
More informationALGEBRA. COPYRIGHT 1996 Mark Twain Media, Inc. ISBN Printing No EB
ALGEBRA By Don Blattner and Myrl Shireman COPYRIGHT 1996 Mark Twain Media, Inc. ISBN 978-1-58037-826-0 Printing No. 1874-EB Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing Company,
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 information+ 37,500. Discuss with your group how do you THINK you would represent 40 degrees below 0 as an integer?
6.1 Integers *I can use positive and negative numbers to show amounts in real-world situations and explain what the number 0 means in those situations. *I can recognize opposite signs of numbers as indicating
More information10.1 Radical Expressions and Functions Math 51 Professor Busken
0. Radical Expressions and Functions Math 5 Professor Busken Objectives Find square roots without a calculator Simplify expressions of the form n a n Evaluate radical functions and find the domain of radical
More information1-1. Expressions and Formulas. Lesson 1-1. What You ll Learn. Active Vocabulary
1-1 Expressions and Formulas What You ll Learn Skim the lesson. Write two things you already know about expressions and formulas. 1. Active Vocabulary 2. Review Vocabulary Identify the four grouping symbols
More informationP.1. Real Numbers. Copyright 2011 Pearson, Inc.
P.1 Real Numbers Copyright 2011 Pearson, Inc. What you ll learn about Representing Real Numbers Order and Interval Notation Basic Properties of Algebra Integer Exponents Scientific Notation and why These
More informationZEROS OF POLYNOMIAL FUNCTIONS ALL I HAVE TO KNOW ABOUT POLYNOMIAL FUNCTIONS
ZEROS OF POLYNOMIAL FUNCTIONS ALL I HAVE TO KNOW ABOUT POLYNOMIAL FUNCTIONS TOOLS IN FINDING ZEROS OF POLYNOMIAL FUNCTIONS Synthetic Division and Remainder Theorem (Compressed Synthetic Division) Fundamental
More informationMath 110 (S & E) Textbook: Calculus Early Transcendentals by James Stewart, 7 th Edition
Math 110 (S & E) Textbook: Calculus Early Transcendentals by James Stewart, 7 th Edition 1 Appendix A : Numbers, Inequalities, and Absolute Values Sets A set is a collection of objects with an important
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 informationLesson 3-7: Absolute Value Equations Name:
Lesson 3-7: Absolute Value Equations Name: In this activity, we will learn to solve absolute value equations. An absolute value equation is any equation that contains an absolute value symbol. To start,
More informationPre-Calculus Midterm Practice Test (Units 1 through 3)
Name: Date: Period: Pre-Calculus Midterm Practice Test (Units 1 through 3) Learning Target 1A I can describe a set of numbers in a variety of ways. 1. Write the following inequalities in interval notation.
More informationMini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models
Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic expressions.. Translate English phrases into algebraic expressions.. Determine whether a number is a solution
More informationSection 1.1 Notes. Real Numbers
Section 1.1 Notes Real Numbers 1 Types of Real Numbers The Natural Numbers 1,,, 4, 5, 6,... These are also sometimes called counting numbers. Denoted by the symbol N Integers..., 6, 5, 4,,, 1, 0, 1,,,
More informationbc7f2306 Page 1 Name:
Name: Questions 1 through 4 refer to the following: Solve the given inequality and represent the solution set using set notation: 1) 3x 1 < 2(x + 4) or 7x 3 2(x + 1) Questions 5 and 6 refer to the following:
More informationPENNSYLVANIA. There are laws for performing mathematical operations to ensure that the values obtained will be consistent. Absolute value.
Topic: 1. Real Numbers Days: 15 Know: Understand: Do: Absolute value Number Sets Vocabulary: integers rational numbers irrational numbers simplify evaluate There are laws for performing mathematical operations
More informationName Period. Date: Topic: 9-2 Circles. Standard: G-GPE.1. Objective:
Name Period Date: Topic: 9-2 Circles Essential Question: If the coefficients of the x 2 and y 2 terms in the equation for a circle were different, how would that change the shape of the graph of the equation?
More informationOhio s Learning Standards-Extended. Mathematics. The Real Number System Complexity a Complexity b Complexity c
Ohio s Learning Standards-Extended Mathematics The Real Number System Complexity a Complexity b Complexity c Extend the properties of exponents to rational exponents N.RN.1 Explain how the definition of
More informationcorrelated to the Utah 2007 Secondary Math Core Curriculum Algebra 1
correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 McDougal Littell Algebra 1 2007 correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 The main goal of Algebra is to
More informationSection 1: Sets and Interval Notation
PART 1 From Sets to Functions Section 1: Sets and Interval Notation Introduction Set concepts offer the means for understanding many different aspects of mathematics and its applications to other branches
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 informationCOURSE 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
More informationA video College Algebra course & 6 Enrichment videos
A video College Algebra course & 6 Enrichment videos Recorded at the University of Missouri Kansas City in 1998. All times are approximate. About 43 hours total. Available on YouTube at http://www.youtube.com/user/umkc
More informationSail into Summer with Math!
Sail into Summer with Math! For Students Entering Algebra 1 This summer math booklet was developed to provide students in kindergarten through the eighth grade an opportunity to review grade level math
More informationChapter 1 Review Exercises
Chapter 1 Review Exercises Fill in each blank with the word or phrase that correctly completes the sentence. 1. 0 (zero) is the additive. (1.1) 2. Whole numbers and their opposites make up the set of.
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 informationMATHia Unit MATHia Workspace Overview TEKS
1 Linear Equations Solving Linear Equations Exploring Two-Step Equations Solving Multi-Step Equations Students use a balance tool to explore two-step equations. They use a general strategy to solve any
More informationStudents will be able to simplify numerical expressions and evaluate algebraic expressions. (M)
Morgan County School District Re-3 August What is algebra? This chapter develops some of the basic symbolism and terminology that students may have seen before but still need to master. The concepts of
More information3.9 My Irrational and Imaginary Friends A Solidify Understanding Task
3.9 My Irrational and Imaginary Friends A Solidify Understanding Task Part 1: Irrational numbers Find the perimeter of each of the following figures. Express your answer as simply as possible. 2013 www.flickr.com/photos/lel4nd
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 informationMath 120, Sample Final Fall 2015
Math 10, Sample Final Fall 015 Disclaimer: This sample final is intended to help students prepare for the final exam The final exam will be similar in structure and type of problems, however the actual
More informationMATH 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 informationNumerical Methods. Exponential and Logarithmic functions. Jaesung Lee
Numerical Methods Exponential and Logarithmic functions Jaesung Lee Exponential Function Exponential Function Introduction We consider how the expression is defined when is a positive number and is irrational.
More informationClass 8: Numbers Exercise 3B
Class : Numbers Exercise B 1. Compare the following pairs of rational numbers: 1 1 i First take the LCM of. LCM = 96 Therefore: 1 = 96 Hence we see that < 6 96 96 1 1 1 1 = 6 96 1 or we can say that
More informationUnit 1: Equations & Inequalities in One Variable
Date Period Unit 1: Equations & Inequalities in One Variable Day Topic 1 Properties of Real Numbers Algebraic Expressions Solving Equations 3 Solving Inequalities 4 QUIZ 5 Absolute Value Equations 6 Double
More informationNumber Sets 1,0,1,2,3,... } 3. Rational Numbers ( Q) 1. Natural Numbers ( N) A number is a rational number if. it can be written as where a and
Number Sets 1. Natural Numbers ( N) N { 0,1,,,... } This set is often referred to as the counting numbers that include zero.. Integers ( Z) Z {...,,, 1,0,1,,,... }. Rational Numbers ( Q) A number is a
More informationChapter 2. Real Numbers and Monomials. 8/2016 LSowatsky 1
Chapter 2 Real Numbers and Monomials 8/2016 LSowatsky 1 2.1.A Powers and Exponents Main Idea: Use powers and exponents to write large and small numbers. LSowatsky 2 LSowatsky 3 Example: Write each expression
More informationSkills Practice Skills Practice for Lesson 10.1
Skills Practice Skills Practice for Lesson.1 Name Date Higher Order Polynomials and Factoring Roots of Polynomial Equations Problem Set Solve each polynomial equation using factoring. Then check your solution(s).
More informationMathematics Pacing. Instruction: 9/7/17 10/31/17 Assessment: 11/1/17 11/8/17. # STUDENT LEARNING OBJECTIVES NJSLS Resources
# STUDENT LEARNING OBJECTIVES NJSLS Resources 1 Describe real-world situations in which (positive and negative) rational numbers are combined, emphasizing rational numbers that combine to make 0. Represent
More informationChapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers
Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,
More informationGeometry A & Geometry B & Honors Geometry Summer Packet
Geometry A & Geometry B & Honors Geometry Summer Packet RADICALS Radical expressions contain numbers and/or variables under a radical sign,. A radical sign tells you to take the square root of the value
More information8-5. A rational inequality is an inequality that contains one or more rational expressions. x x 6. 3 by using a graph and a table.
A rational inequality is an inequality that contains one or more rational expressions. x x 3 by using a graph and a table. Use a graph. On a graphing calculator, Y1 = x and Y = 3. x The graph of Y1 is
More informationAlgebra SUMMER PACKET Ms. Bank
2016-17 SUMMER PACKET Ms. Bank Just so you know what to expect next year We will use the same text that was used this past year: published by McDougall Littell ISBN-13:978-0-6185-9402-3. Summer Packet
More informationMIDTERM REVIEW. Write an algebraic expression to represent the following verbal expressions. 1) Double the difference of a number and 7.
NAME MIDTERM REVIEW DATE Write an algebraic epression to represent the following verbal epressions. 1) Double the difference of a number and 7. ) Find the value of the epression 0. Solve each equation.
More informationx y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational
More informationName Period. Date: have an. Essential Question: Does the function ( ) inverse function? Explain your answer.
Name Period Date: Topic: 10-3 Composition and Inverses of Functions Essential Question: Does the function inverse function? Explain your answer. have an Standard: F-BF.1c Objective: Compose functions.
More informationNatural Numbers Positive Integers. Rational Numbers
Chapter A - - Real Numbers Types of Real Numbers, 2,, 4, Name(s) for the set Natural Numbers Positive Integers Symbol(s) for the set, -, - 2, - Negative integers 0,, 2,, 4, Non- negative integers, -, -
More informationN= {1,2,3,4,5,6,7,8,9,10,11,...}
1.1: Integers and Order of Operations 1. Define the integers 2. Graph integers on a number line. 3. Using inequality symbols < and > 4. Find the absolute value of an integer 5. Perform operations with
More informationTopics Covered in Math 115
Topics Covered in Math 115 Basic Concepts Integer Exponents Use bases and exponents. Evaluate exponential expressions. Apply the product, quotient, and power rules. Polynomial Expressions Perform addition
More informationReading Mathematical Expressions & Arithmetic Operations Expression Reads Note
Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ
More informationPre-Algebra Unit 2. Rational & Irrational Numbers. Name
Pre-Algebra Unit 2 Rational & Irrational Numbers Name Core Table 2 Pre-Algebra Name: Unit 2 Rational & Irrational Numbers Core: Table: 2.1.1 Define Rational Numbers Vocabulary: Real Numbers the set of
More informationNote: Square Roots: include perfect squares and non-perfect squares in comparing objective and perfect square in order of operations.
Algebra I Trimester Curriculum Revised 9/4/15 Algebra IA 60 days (36 intructional : 7 review : 7 assessment) (3 days missed) (2 days final assessment) (5 days: Aleks : CDT) Unit 1 - Operations with Real
More informationGCSE AQA Mathematics. Numbers
GCSE Mathematics Numbers Md Marufur Rahman Msc Sustainable Energy Systems Beng (Hons) Mechanical Engineering Bsc (Hons) Computer science & engineering GCSE AQA Mathematics 215/16 Table of Contents Introduction:...
More informationExpressions, Equations and Inequalities Guided Notes
Expressions, Equations and Inequalities Guided Notes Standards: Alg1.M.A.SSE.A.01a - The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression.
More informationMATCHING. Match the correct vocabulary word with its definition
Name Algebra I Block UNIT 2 STUDY GUIDE Ms. Metzger MATCHING. Match the correct vocabulary word with its definition 1. Whole Numbers 2. Integers A. A value for a variable that makes an equation true B.
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 informationA.REI.B.3: Solve Linear Equations and Inequalities in One Variable.
A.REI.B.3: Solve Linear Equations and Inequalities in One Variable. EQUATIONS AND INEQUALITIES A.REI.B.3: Solving Linear Equations and Inequalities in One Variable B. Solve equations and inequalities in
More informationSolutions to Chapter Review Questions, Chapter 0
Instructor s Solutions Manual, Chapter 0 Review Question 1 Solutions to Chapter Review Questions, Chapter 0 1. Explain how the points on the real line correspond to the set of real numbers. solution Start
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 informationStandards of Learning Content Review Notes. Grade 8 Mathematics 1 st Nine Weeks,
Standards of Learning Content Review Notes Grade 8 Mathematics 1 st Nine Weeks, 2016-2017 Revised September 2015 2 Mathematics Content Review Notes Grade 8 Mathematics: First Nine Weeks 2015-2016 -This
More informationUNIT 4 NOTES: PROPERTIES & EXPRESSIONS
UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics
More informationChapter 1. Functions 1.1. Functions and Their Graphs
1.1 Functions and Their Graphs 1 Chapter 1. Functions 1.1. Functions and Their Graphs Note. We start by assuming that you are familiar with the idea of a set and the set theoretic symbol ( an element of
More informationAlgebra 2/Trig H
Welcome to Algebra 2/Trig H 2018-2019 Welcome to Algebra 2/Trigonometry Honors! We are excited that you will be embarking on a journey to expand your understanding of mathematics and its concepts, tools,
More informationStandards Based Map 6 th Grade Math
Standards Based Map 6 th Grade Math Timeline NxG Standard(s) Student I Can Statement(s) / Learning Target(s) M.6.NS.2. Fluently Divide multi-digit numbers using the standard algorithm M.6.NS.3 fluently
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 informationTopic: Solving systems of equations with linear and quadratic inequalities
Subject & Grade: Mathematics, 9 th Grade Topic: Solving systems of equations with linear and quadratic inequalities Aim: How would you find the solution set of a linear and quadratic inequality? Materials:.
More informationEQ: What are limits, and how do we find them? Finite limits as x ± Horizontal Asymptote. Example Horizontal Asymptote
Finite limits as x ± The symbol for infinity ( ) does not represent a real number. We use to describe the behavior of a function when the values in its domain or range outgrow all finite bounds. For example,
More informationGraphing Radicals Business 7
Graphing Radicals Business 7 Radical functions have the form: The most frequently used radical is the square root; since it is the most frequently used we assume the number 2 is used and the square root
More information1.2 Algebraic Expressions and Sets of Numbers
Section. Algebraic Expressions and Sets of Numbers 7. Algebraic Expressions and Sets of Numbers S Identify and Evaluate Algebraic Expressions. Identify Natural Numbers, Whole Numbers, Integers, and Rational
More informationdownload from
Table of Contents Chapter 1 Basic Concepts Pretests... 1 Mini-Lectures... Additional Exercises... 1 Chapter Tests... 19 Chapter Equations and Inequalities Pretests... 7 Mini-Lectures... 1 Additional Exercises...
More informationLesson 3.5 Exercises, pages
Lesson 3.5 Exercises, pages 232 238 A 4. Calculate the value of the discriminant for each quadratic equation. a) 5x 2-9x + 4 = 0 b) 3x 2 + 7x - 2 = 0 In b 2 4ac, substitute: In b 2 4ac, substitute: a 5,
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 informationBUILD YOUR VOCABULARY
C H A P T E R BUILD YOUR VOCABULARY This is an alphabetical list of new vocabulary terms you will learn in Chapter. As you complete the study notes for the chapter, you will see Build Your Vocabulary reminders
More informationth Grade Intermediate Algebra 1Q 1. Standard Sample Problems Resources Mastery Date/Notes
2015-2016 7th Grade Intermediate Algebra 1Q 1 Apply and extend previous understandings of operations with fractions. 7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add
More information2.5 Compound Inequalities
Section.5 Compound Inequalities 89.5 Compound Inequalities S 1 Find the Intersection of Two Sets. Solve Compound Inequalities Containing and. Find the Union of Two Sets. 4 Solve Compound Inequalities Containing
More informationAgile Mind Mathematics 8 Scope and Sequence, Indiana Academic Standards for Mathematics
Prior to Grade 8, students have written and interpreted expressions, solved equations and inequalities, explored quantitative relationships between dependent and independent variables, and solved problems
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 informationSTUDY GUIDE Math 20. To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition
STUDY GUIDE Math 0 To the students: To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition When you study Algebra, the material is presented to you in a logical sequence.
More informationA group of figures, representing a number, is called a numeral. Numbers are divided into the following types.
1. Number System Quantitative Aptitude deals mainly with the different topics in Arithmetic, which is the science which deals with the relations of numbers to one another. It includes all the methods that
More informationOrder of Operations. Real numbers
Order of Operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply and divide from left to right. 4. Add
More informationMATH 1111 Section P.1 Bland. Algebraic Expressions - An algebraic expression is a combination of variables and numbers using operations.
MATH 1111 Section P.1 Bland Variable A letter or symbol used to represent a number. Algebraic Expressions - An algebraic expression is a combination of variables and numbers using operations. Coefficient
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 informationCROSSWalk. for the Co on Core State Standards
Mathematics Grade 8 CROSSWalk for the Co on Core State Standards Table of Contents Common Core State Standards Correlation Chart... 6 Domain 1 The Number System.... Domain 1: Diagnostic Assessment for
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 informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More informationWhat students need to know for... ALGEBRA II
What students need to know for... ALGEBRA II 2017-2018 NAME This is a MANDATORY assignment that will be GRADED. It is due the first day of the course. Your teacher will determine how it will be counted
More informationLiberal High School Lesson Plans
Monday, 5/8/2017 Liberal High School Lesson Plans er:david A. Hoffman Class:Algebra III 5/8/2017 To 5/12/2017 Students will perform math operationsto solve rational expressions and find the domain. How
More informationSHOW ALL YOUR WORK IN A NEAT AND ORGANIZED FASHION
Intermediate Algebra TEST 1 Spring 014 NAME: Score /100 Please print SHOW ALL YOUR WORK IN A NEAT AND ORGANIZED FASHION Course Average No Decimals No mixed numbers No complex fractions No boxed or circled
More informationHigh School Preparation for Algebra 1
High School Preparation for Algebra 1 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
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 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 informationAlgebra 1 First Semester Exam Answer Section
Algebra 1 First Semester Exam Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Level B REF: MALG0086 TOP: Lesson 1.2 Apply Order of Operations KEY: whole variable evaluate substitute rational expression
More information3.3 Real Zeros of Polynomial Functions
71_00.qxp 12/27/06 1:25 PM Page 276 276 Chapter Polynomial and Rational Functions. Real Zeros of Polynomial Functions Long Division of Polynomials Consider the graph of f x 6x 19x 2 16x 4. Notice in Figure.2
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 informationAlgebra 1 Correlation of the ALEKS course Algebra 1 to the Washington Algebra 1 Standards
Algebra 1 Correlation of the ALEKS course Algebra 1 to the Washington Algebra 1 Standards A1.1: Core Content: Solving Problems A1.1.A: Select and justify functions and equations to model and solve problems.
More information