Compound Inequalities. Section 3-6
|
|
- Samuel Fletcher
- 7 years ago
- Views:
Transcription
1 Compound Inequalities Section 3-6
2 Goals Goal To solve and graph inequalities containing the word and. To solve and graph inequalities containing the word or.
3 Vocabulary Compound Inequality Interval Notation
4 Definition The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality. Compound Inequality the result of combining two inequalities. The words and and or are used to describe how the two parts are related.
5 Venn Diagram and Compound Inequalities In this diagram, set A represents some integer solutions of x < 10, and set B represents some integer solutions of x > 0. The overlapping region represents numbers that belong in set A and set B. Those numbers are solutions of both x < 10 and x > 0 (can be written 0 < x < 10).
6 Number Line and Compound Inequalities You can graph the solutions of a compound inequality involving AND by using the idea of an overlapping region. The overlapping region is called the intersection and shows the numbers that are solutions of both inequalities.
7 Venn Diagram and Compound Inequalities In this diagram, set A represents some integer solutions of x < 0, and set B represents some integer solutions of x > 10. The combined shaded regions represent numbers that are solutions of either x < 0 or x >10 (or both).
8 Number Line and Compound Inequalities You can graph the solutions of a compound inequality involving OR by using the idea of combining regions. The combined regions are called the union and show the numbers that are solutions of either inequality. >
9 Compound Inequalities
10 Example: Write a compound inequality for each statement. A. A number x is both less than 4 and greater than or equal to x < 4 B. A number t is either greater than 1 or less than or equal to 7. t > 1 or t 7
11 Your Turn: Write a compound inequality for each statement. A. A number t is both greater than 9 and less than or equal to < t 18.5 B. A number y is either greater than 5 or less than or equal to 1. y > 5 or y 1
12 Writing Math The and compound inequality y < 2 and y < 4 can be written as 2 < y < 4. The or compound inequality y < 1 or y > 9 must be written with the word or.
13 Example: Writing Compound Inequalities Write the compound inequality shown by the graph. The shaded portion of the graph is not between two values, so the compound inequality involves OR. On the left, the graph shows an arrow pointing left, so use either < or. The solid circle at 8 means 8 is a solution so use. x 8 On the right, the graph shows an arrow pointing right, so use either > or. The empty circle at 0 means that 0 is not a solution, so use >. x > 0 The compound inequality is x 8 OR x > 0.
14 Example: Writing Compound Inequalities Write the compound inequality shown by the graph. The shaded portion of the graph is between the values 2 and 5, so the compound inequality involves AND. The shaded values are on the right of 2, so use > or. The empty circle at 2 means 2 is not a solution, so use >. m > 2 The shaded values are to the left of 5, so use < or. The empty circle at 5 means that 5 is not a solution so use <. m < 5 The compound inequality is m > 2 AND m < 5 (or 2 < m < 5).
15 Your Turn: Write the compound inequality shown by the graph. The shaded portion of the graph is between the values 9 and 2, so the compound inequality involves AND. The shaded values are on the right of 9, so use > or. The empty circle at 9 means 9 is not a solution, so use >. x > 9 The shaded values are to the left of 2, so use < or. The empty circle at 2 means that 2 is not a solution so use <. x < 2 The compound inequality is 9 < x AND x < 2 (or 9 < x < 2).
16 Your Turn: Write the compound inequality shown by the graph. The shaded portion of the graph is not between two values, so the compound inequality involves OR. On the left, the graph shows an arrow pointing left, so use either < or. The solid circle at 3 means 3 is a solution, so use. x 3 On the right, the graph shows an arrow pointing right, so use either > or. The solid circle at 2 means that 2 is a solution, so use. x 2 The compound inequality is x 3 OR x 2.
17 Example: Application The ph level of a popular shampoo is between 6.0 and 6.5 inclusive. Write a compound inequality to show the ph levels of this shampoo. Graph the solutions. Let p be the ph level of the shampoo. 6.0 is less than or equal to ph level is less than or equal to 6.0 p p
18 The free chlorine in a pool should be between 1.0 and 3.0 parts per million inclusive. Write a compound inequality to show the levels that are within this range. Graph the solutions. Let c be the chlorine level of the pool. 1.0 is less than or equal to Your Turn: chlorine is less than or equal to 1.0 c c
19 Example: Solving and Compound Inequalities Solve the compound inequality and graph the solutions. 5 < x + 1 < 2 5 < x + 1 AND x + 1 < < x AND x < 1-6 < x < 1 Since 1 is added to x, subtract 1 from each part of the inequality. The solution set is {x: 6 < x AND x < 1}. Graph -6 < x <
20 Example: Solving and Compound Inequalities Solve the compound inequality and graph the solutions. 8 < 3x < 3x < 3x 12 3 < x 4 Since 1 is subtracted from 3x, add 1 to each part of the inequality. Since x is multiplied by 3, divide each part of the inequality by 3 to undo the multiplication. The solution set is {x:3 < x 4}
21 Your Turn: Solve the compound inequality and graph the solutions. 9 < x 10 < 5 9 < x 10 < < x < 5 Since 10 is subtracted from x, add 10 to each part of the inequality. The solution set is {x:1 < x < 5}. 1 < x < 5 Graph 1 < x <
22 Your Turn: Solve the compound inequality and graph the solutions. 4 3n + 5 < n + 5 < n < 6 3 n < 2 Since 5 is added to 3n, subtract 5 from each part of the inequality. Since n is multiplied by 3, divide each part of the inequality by 3 to undo the multiplication. The solution set is {n: 3 n < 2}. Graph -3 x <
23 Example: Solving or Compound Inequalities Solve the compound inequality and graph the solutions. 8 + t 7 OR 8 + t < t 7 OR 8 + t < t 1 OR t < 6 t < -6 or t -1 Solve each simple inequality. The solution set is {t: t 1 OR t < 6}. Graph t < -6 or t
24 Example: Solving or Compound Inequalities Solve the compound inequality and graph the solutions. 4x 20 OR 3x > 21 4x 20 OR 3x > 21 Solve each simple inequality. The solution set is {x:x 5 OR x > 7 }. x 5 OR x > 7 Graph x 5 or x >
25 Your Turn: Solve the compound inequality and graph the solutions. 2 +r < 12 OR r + 5 > r < 12 OR r + 5 > r < 10 OR r > 14 Solve each simple inequality. The solution set is {r:r < 10 OR r > 14}. r < 10 or r > 14 Graph the union by combining the regions
26 Your Turn: Solve the compound inequality and graph the solutions. 7x 21 OR 2x < 2 7x 21 OR 2x < 2 x 3 OR x < 1 x < -1 or x 3 Solve each simple inequality. The solution set is {x:x 3 OR x < 1}. Graph x < -1 or x
27 Interval Notation Interval Notation: Describes an interval on the number line. Interval Notation includes the use of three special symbols: ( ) [ ]
28 Interval Notation Parentheses ( ) are used when a < or > symbol indicates that the interval s endpoint is NOT included.
29 Interval Notation Brackets [ ] are used when a or symbol indicates that the interval s endpoint IS included.
30 Infinity is used when the interval continues forever in a positive direction and is used when the interval continues forever in a negative direction.
31 What is the graph of [-4, 6)? How do you write [-4, 6) as an inequality? SOLUTION This inequality is also written as -4 < x < 6.
32 Interval Notation What is the graph of x < -1 or x > 2? How do you write this in interval notation? SOLUTION In interval notation, this is written as (, 1] or (2, ).
33 Joke Time What is Beethoven doing in his grave? De-composing What do you call an arrogant household bug? A cocky roach. What's orange and sounds like a parrot? A carrot!
7. Solving Linear Inequalities and Compound Inequalities
7. Solving Linear Inequalities and Compound Inequalities Steps for solving linear inequalities are very similar to the steps for solving linear equations. The big differences are multiplying and dividing
More informationCompound Inequalities. AND/OR Problems
Compound Inequalities AND/OR Problems There are two types of compound inequalities. They are conjunction problems and disjunction problems. These compound inequalities will sometimes appear as two simple
More informationChapter 1 Section 4: Compound Linear Inequalities
Chapter 1 Section 4: Compound Linear Inequalities Introduction Compound linear inequalities involve finding the union or intersection of solution sets of two or more linear inequalities. You ve already
More informationAbsolute Value Equations and Inequalities
Key Concepts: Compound Inequalities Absolute Value Equations and Inequalities Intersections and unions Suppose that A and B are two sets of numbers. The intersection of A and B is the set of all numbers
More informationMethod To Solve Linear, Polynomial, or Absolute Value Inequalities:
Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with
More informationInequalities - Absolute Value Inequalities
3.3 Inequalities - Absolute Value Inequalities Objective: Solve, graph and give interval notation for the solution to inequalities with absolute values. When an inequality has an absolute value we will
More information1.4 Compound Inequalities
Section 1.4 Compound Inequalities 53 1.4 Compound Inequalities This section discusses a technique that is used to solve compound inequalities, which is a phrase that usually refers to a pair of inequalities
More informationAlgebra 2 Notes AII.7 Functions: Review, Domain/Range. Function: Domain: Range:
Name: Date: Block: Functions: Review What is a.? Relation: Function: Domain: Range: Draw a graph of a : a) relation that is a function b) relation that is NOT a function Function Notation f(x): Names the
More informationSection 1.1 Real Numbers
. Natural numbers (N):. Integer numbers (Z): Section. Real Numbers Types of Real Numbers,, 3, 4,,... 0, ±, ±, ±3, ±4, ±,... REMARK: Any natural number is an integer number, but not any integer number is
More information2.5 Creating and Solving Compound Inequalities
Name Class Date 2.5 Creating and Solving Compound Inequalities Essential uestion: How can you solve a compound inequality and graph the solution set? Resource Locker Explore Truth Tables and Compound Statements
More informationLinear Equations and Inequalities
Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................
More informationCheck Skills You ll Need. New Vocabulary union intersection disjoint sets. Union of Sets
NY-4 nion and Intersection of Sets Learning Standards for Mathematics..31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets). Check Skills You ll Need
More informationSection 1. Inequalities -5-4 -3-2 -1 0 1 2 3 4 5
Worksheet 2.4 Introduction to Inequalities Section 1 Inequalities The sign < stands for less than. It was introduced so that we could write in shorthand things like 3 is less than 5. This becomes 3 < 5.
More informationInequalities - Solve and Graph Inequalities
3.1 Inequalities - Solve and Graph Inequalities Objective: Solve, graph, and give interval notation for the solution to linear inequalities. When we have an equation such as x = 4 we have a specific value
More informationAnchorage School District/Alaska Sr. High Math Performance Standards Algebra
Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationSet operations and Venn Diagrams. COPYRIGHT 2006 by LAVON B. PAGE
Set operations and Venn Diagrams Set operations and Venn diagrams! = { x x " and x " } This is the intersection of and. # = { x x " or x " } This is the union of and. n element of! belongs to both and,
More informationChapter 2: Linear Equations and Inequalities Lecture notes Math 1010
Section 2.1: Linear Equations Definition of equation An equation is a statement that equates two algebraic expressions. Solving an equation involving a variable means finding all values of the variable
More informationAbsolute Value Equations and Inequalities
. Absolute Value Equations and Inequalities. OBJECTIVES 1. Solve an absolute value equation in one variable. Solve an absolute value inequality in one variable NOTE Technically we mean the distance between
More informationCONTENTS. Please note:
CONTENTS Introduction...iv. Number Systems... 2. Algebraic Expressions.... Factorising...24 4. Solving Linear Equations...8. Solving Quadratic Equations...0 6. Simultaneous Equations.... Long Division
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationReview of Basic Algebraic Concepts
Section. Sets of Numbers and Interval Notation Review of Basic Algebraic Concepts. Sets of Numbers and Interval Notation. Operations on Real Numbers. Simplifying Expressions. Linear Equations in One Variable.
More informationSet Theory: Shading Venn Diagrams
Set Theory: Shading Venn Diagrams Venn diagrams are representations of sets that use pictures. We will work with Venn diagrams involving two sets (two-circle diagrams) and three sets (three-circle diagrams).
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationhttps://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...
of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach Bell-Ringer Activity Students
More informationExtra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.
Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson
More informationSection 1: How will you be tested? This section will give you information about the different types of examination papers that are available.
REVISION CHECKLIST for IGCSE Mathematics 0580 A guide for students How to use this guide This guide describes what topics and skills you need to know for your IGCSE Mathematics examination. It will help
More informationHow To Understand And Solve A Linear Programming Problem
At the end of the lesson, you should be able to: Chapter 2: Systems of Linear Equations and Matrices: 2.1: Solutions of Linear Systems by the Echelon Method Define linear systems, unique solution, inconsistent,
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationTHE LANGUAGE OF SETS AND SET NOTATION
THE LNGGE OF SETS ND SET NOTTION Mathematics is often referred to as a language with its own vocabulary and rules of grammar; one of the basic building blocks of the language of mathematics is the language
More informationPrentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)
New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct
More informationis the degree of the polynomial and is the leading coefficient.
Property: T. Hrubik-Vulanovic e-mail: thrubik@kent.edu Content (in order sections were covered from the book): Chapter 6 Higher-Degree Polynomial Functions... 1 Section 6.1 Higher-Degree Polynomial Functions...
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1-100 Overview: This unit models real-world situations by using one- and two-variable linear equations. This unit will further expand upon pervious
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More information1. Graphing Linear Inequalities
Notation. CHAPTER 4 Linear Programming 1. Graphing Linear Inequalities x apple y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationLicensed to: Printed in the United States of America 1 2 3 4 5 6 7 15 14 13 12 11
Licensed to: CengageBrain User This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any
More informationSolving Quadratic & Higher Degree Inequalities
Ch. 8 Solving Quadratic & Higher Degree Inequalities We solve quadratic and higher degree inequalities very much like we solve quadratic and higher degree equations. One method we often use to solve quadratic
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationFlorida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District
Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationAlgebra Cheat Sheets
Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts
More informationSolve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers
More information3.1 Solving Systems Using Tables and Graphs
Algebra 2 Chapter 3 3.1 Solve Systems Using Tables & Graphs 3.1 Solving Systems Using Tables and Graphs A solution to a system of linear equations is an that makes all of the equations. To solve a system
More informationMATH 90 CHAPTER 1 Name:.
MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.
More informationf(x) = g(x), if x A h(x), if x B.
1. Piecewise Functions By Bryan Carrillo, University of California, Riverside We can create more complicated functions by considering Piece-wise functions. Definition: Piecewise-function. A piecewise-function
More information7 Relations and Functions
7 Relations and Functions In this section, we introduce the concept of relations and functions. Relations A relation R from a set A to a set B is a set of ordered pairs (a, b), where a is a member of A,
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationLevel 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3
Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels
More informationMATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationCOMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS
COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving
More informationFlorida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower
Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including
More information1 The Concept of a Mapping
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan 1 The Concept of a Mapping The concept of a mapping (aka function) is important throughout mathematics. We have been dealing
More information1.6. Solve Linear Inequalities E XAMPLE 1 E XAMPLE 2. Graph simple inequalities. Graph compound inequalities
.6 Solve Linear Inequalities Before You solved linear equations. Now You will solve linear inequalities. Why? So you can describe temperature ranges, as in Ex. 54. Key Vocabulary linear inequality compound
More informationAll of mathematics can be described with sets. This becomes more and
CHAPTER 1 Sets All of mathematics can be described with sets. This becomes more and more apparent the deeper into mathematics you go. It will be apparent in most of your upper level courses, and certainly
More information7 Literal Equations and
CHAPTER 7 Literal Equations and Inequalities Chapter Outline 7.1 LITERAL EQUATIONS 7.2 INEQUALITIES 7.3 INEQUALITIES USING MULTIPLICATION AND DIVISION 7.4 MULTI-STEP INEQUALITIES 113 7.1. Literal Equations
More informationNo Solution Equations Let s look at the following equation: 2 +3=2 +7
5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are
More informationAlgebra 1: Basic Skills Packet Page 1 Name: Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14
Algebra 1: Basic Skills Packet Page 1 Name: Number Sense: Add, Subtract, Multiply or Divide without a Calculator Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14 Decimals 7. 43.21
More informationLecture 1. Basic Concepts of Set Theory, Functions and Relations
September 7, 2005 p. 1 Lecture 1. Basic Concepts of Set Theory, Functions and Relations 0. Preliminaries...1 1. Basic Concepts of Set Theory...1 1.1. Sets and elements...1 1.2. Specification of sets...2
More informationAlgebra I Module 1 Lessons 1 28
Eureka Math 2015 2016 Algebra I Module 1 Lessons 1 28 Eureka Math, Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, distributed, modified, sold,
More informationKey Topics What will ALL students learn? What will the most able students learn?
2013 2014 Scheme of Work Subject MATHS Year 9 Course/ Year Term 1 Key Topics What will ALL students learn? What will the most able students learn? Number Written methods of calculations Decimals Rounding
More informationFinance Notes ANNUITIES
Annuities Page 1 of 8 ANNUITIES Objectives: After completing this section, you should be able to do the following: Calculate the future value of an ordinary annuity. Calculate the amount of interest earned
More informationMath 166 - Week in Review #4. A proposition, or statement, is a declarative sentence that can be classified as either true or false, but not both.
Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Week in Review #4 Sections A.1 and A.2 - Propositions, Connectives, and Truth Tables A proposition, or statement, is a declarative sentence that
More informationStudents will be able to simplify and evaluate numerical and variable expressions using appropriate properties and order of operations.
Outcome 1: (Introduction to Algebra) Skills/Content 1. Simplify numerical expressions: a). Use order of operations b). Use exponents Students will be able to simplify and evaluate numerical and variable
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationChapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter B. Middle School
Middle School 111.B. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter B. Middle School Statutory Authority: The provisions of this Subchapter B issued under the Texas Education
More informationUseful Mathematical Symbols
32 Useful Mathematical Symbols Symbol What it is How it is read How it is used Sample expression + * ddition sign OR Multiplication sign ND plus or times and x Multiplication sign times Sum of a few disjunction
More informationList the elements of the given set that are natural numbers, integers, rational numbers, and irrational numbers. (Enter your answers as commaseparated
MATH 142 Review #1 (4717995) Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Description This is the review for Exam #1. Please work as many problems as possible
More informationGRADES 7, 8, AND 9 BIG IDEAS
Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for
More informationAlgebra EOC Practice Test #2
Class: Date: Algebra EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following lines is perpendicular to the line y =
More informationF.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions
F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions Analyze functions using different representations. 7. Graph functions expressed
More informationFlorida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper
Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic
More informationSECTION 1.6 Other Types of Equations
BLITMC1B.111599_11-174 12//2 1:58 AM Page 11 Section 1.6 Other Types of Equations 11 12. A person throws a rock upward from the edge of an 8-foot cliff. The height, h, in feet, of the rock above the water
More informationMathematics Curriculum Guide Precalculus 2015-16. Page 1 of 12
Mathematics Curriculum Guide Precalculus 2015-16 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing
More informationGrade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills
Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate
More informationOpen-Ended Problem-Solving Projections
MATHEMATICS Open-Ended Problem-Solving Projections Organized by TEKS Categories TEKSING TOWARD STAAR 2014 GRADE 7 PROJECTION MASTERS for PROBLEM-SOLVING OVERVIEW The Projection Masters for Problem-Solving
More informationr the COR Common Core State Standards Learning Pathways
BUI LT fo COM r the MON COR E 2015 2016 Common Core State Standards Learning Pathways Table of Contents Grade 3...3 Grade 4...8 Grade 5... 13 Grade 6... 18 Grade 7...26 Grade 8...32 Algebra Readiness...36
More information4.9 Graph and Solve Quadratic
4.9 Graph and Solve Quadratic Inequalities Goal p Graph and solve quadratic inequalities. Your Notes VOCABULARY Quadratic inequalit in two variables Quadratic inequalit in one variable GRAPHING A QUADRATIC
More informationMathematical Conventions Large Print (18 point) Edition
GRADUATE RECORD EXAMINATIONS Mathematical Conventions Large Print (18 point) Edition Copyright 2010 by Educational Testing Service. All rights reserved. ETS, the ETS logo, GRADUATE RECORD EXAMINATIONS,
More informationBEST METHODS FOR SOLVING QUADRATIC INEQUALITIES.
BEST METHODS FOR SOLVING QUADRATIC INEQUALITIES. I. GENERALITIES There are 3 common methods to solve quadratic inequalities. Therefore, students sometimes are confused to select the fastest and the best
More informationMathematical Conventions. for the Quantitative Reasoning Measure of the GRE revised General Test
Mathematical Conventions for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview The mathematical symbols and terminology used in the Quantitative Reasoning measure
More informationDeterminants can be used to solve a linear system of equations using Cramer s Rule.
2.6.2 Cramer s Rule Determinants can be used to solve a linear system of equations using Cramer s Rule. Cramer s Rule for Two Equations in Two Variables Given the system This system has the unique solution
More informationPre-Calculus Graphing Calculator Handbook
Pre-Calculus Graphing Calculator Handbook I. Graphing Functions A. Button for Functions This button is used to enter any function to be graphed. You can enter up to 10 different functions at a time. Use
More informationGreatest Common Factors and Least Common Multiples with Venn Diagrams
Greatest Common Factors and Least Common Multiples with Venn Diagrams Stephanie Kolitsch and Louis Kolitsch The University of Tennessee at Martin Martin, TN 38238 Abstract: In this article the authors
More informationSummer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students
Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Studies show that most students lose about two months of math abilities over the summer when they do not engage in
More informationExamples of Tasks from CCSS Edition Course 3, Unit 5
Examples of Tasks from CCSS Edition Course 3, Unit 5 Getting Started The tasks below are selected with the intent of presenting key ideas and skills. Not every answer is complete, so that teachers can
More informationAlgebra I Teacher Notes Expressions, Equations, and Formulas Review
Big Ideas Write and evaluate algebraic expressions Use expressions to write equations and inequalities Solve equations Represent functions as verbal rules, equations, tables and graphs Review these concepts
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationNational 5 Mathematics Course Assessment Specification (C747 75)
National 5 Mathematics Course Assessment Specification (C747 75) Valid from August 013 First edition: April 01 Revised: June 013, version 1.1 This specification may be reproduced in whole or in part for
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.1-2 Grade 6 Math : Sub-Claim A The student solves problems involving the Major Content for grade/course with
More informationof surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationGreatest Common Factor (GCF) Factoring
Section 4 4: Greatest Common Factor (GCF) Factoring The last chapter introduced the distributive process. The distributive process takes a product of a monomial and a polynomial and changes the multiplication
More informationAccentuate the Negative: Homework Examples from ACE
Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),
More informationUnit 1: Integers and Fractions
Unit 1: Integers and Fractions No Calculators!!! Order Pages (All in CC7 Vol. 1) 3-1 Integers & Absolute Value 191-194, 203-206, 195-198, 207-210 3-2 Add Integers 3-3 Subtract Integers 215-222 3-4 Multiply
More informationScientific Notation. Section 7-1 Part 2
Scientific Notation Section 7-1 Part 2 Goals Goal To write numbers in scientific notation and standard form. To compare and order numbers using scientific notation. Vocabulary Scientific Notation Powers
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationCOLLEGE ALGEBRA 10 TH EDITION LIAL HORNSBY SCHNEIDER 1.1-1
10 TH EDITION COLLEGE ALGEBRA LIAL HORNSBY SCHNEIDER 1.1-1 1.1 Linear Equations Basic Terminology of Equations Solving Linear Equations Identities 1.1-2 Equations An equation is a statement that two expressions
More information