PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to:


 George Holland
 11 months ago
 Views:
Transcription
1 PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGrawHill 8787 Orion Place Columbus, Ohio 43240
2
3 Click the mouse button or press the Space Bar to display the answers.
4 Lesson 131 Lesson 132 Lesson 133 Lesson 134 Lesson 135 Lesson 136 Polynomials Adding Polynomials Subtracting Polynomials Multiplying a Polynomial by a Monomial Linear and Nonlinear Functions Graphing Quadratic and Cubic Functions
5 Example 1 Classify Polynomials Example 2 Degree of a Monomial Example 3 Degree of a Polynomial Example 4 Degree of a RealWorld Polynomial
6 Determine whether is a polynomial. If it is, classify it as a monomial, binomial, or trinomial. Answer: The expression is not a polynomial because has a variable in the denominator.
7 Determine whether is a polynomial. If it is, classify it as a monomial, binomial, or trinomial. Answer: This is a polynomial because it is the difference of two monomials. There are two terms, so it is a binomial.
8 Determine whether each expression is a polynomial. If it is, classify it as a monomial, binomial, or trinomial. a. Answer: yes; trinomial b. Answer: not a polynomial
9 Find the degree of. Answer: The variable w has degree 4, so the degree of 10w 4 is 4.
10 Find the degree of. has degree 3, has degree 7, and z has degree 1. Answer: The degree of
11 Find the degree of each monomial. a. Answer: 3 b. Answer: 8
12 Find the degree of. term 4 degree 7 0 Answer: The greatest degree is 7. So, the degree of the polynomial is 7.
13 Find the degree of. term degree 4 7 Answer: The greatest degree is 7. So, the degree of the polynomial is 7.
14 Find the degree of each polynomial. a. Answer: 6 b. Answer: 5
15 Area The formula for the surface area (A) of a cube is, where s is the side length. Find the degree of the polynomial. Answer:
16 Area The formula for the surface area S of a cylinder with height h and radius r is. Find the degree of the polynomial. Answer: 2
17
18 Click the mouse button or press the Space Bar to display the answers.
19 Example 1 Add Polynomials Example 2 Use Polynomials to Solve a Problem
20 Find. Method 1 Add vertically. Align like terms. Add. Method 2 Add horizontally. Associative and Commutative Properties Answer: The sum is 10w + 1.
21 Find. Method 1 Add vertically. Align like terms. Add. Method 2 Add horizontally. Write the expression. Group like terms. Simplify. Answer: The sum is
22 Find. Write the expression. Simplify. Answer: The sum is
23 Find. Leave a space because there is no other term like xy. Answer: The sum is.
24 Find each sum. a. Answer: b. Answer: c. Answer: d. Answer:
25 Geometry The length of a rectangle is units and the width is 8x 1 units. Find the perimeter. Answer: The perimeter is Formula for the perimeter of a rectangle Replace with and w with Distributive Property Group like terms. Simplify.
26 Find the length of the rectangle if Write the expression. Replace x with 3. Simplify. Answer: The length of the rectangle is 16 units.
27 Geometry The length of a rectangle is units and the width is 6w 3 units. a. Find the perimeter. Answer: b. Find the length if Answer: 39 units
28
29 Click the mouse button or press the Space Bar to display the answers.
30 Example 1 Subtract Polynomials Example 2 Subtract Using the Additive Inverse Example 3 Subtract Polynomials to Solve a Problem
31 Find. Align like terms. Subtract. Answer: The difference is.
32 Find. Align like terms. Subtract. Answer: The difference is.
33 Find each difference. a. Answer: b. Answer:
34 Find. Answer: The difference is x 17. To subtract (3x + 9), add ( 3x 9). Group the like terms. Simplify.
35 Find. The additive inverse of Align the like terms and add the additive inverse. Answer:
36 Find each difference. a. Answer: 10c 7. b. Answer:
37 Geometry The length of a rectangle is units. The width is units. How much longer is the length than the width? difference in measurement Substitution Add additive inverse. Group like terms. Answer: The length is than the width. Simplify. units longer
38 Profit The ABC Company s costs are given by where x = the number of items produced. The revenue is given by 5x. Find the profit, which is the difference between the revenue and the cost. Answer:
39
40 Click the mouse button or press the Space Bar to display the answers.
41 Example 1 Products of a Monomial and a Polynomial Example 2 Product of a Monomial and a Polynomial Example 3 Use a Polynomial to Solve a Problem
42 Find. Distributive Property Simplify. Answer: 24x 16
43 Find. Distributive Property Simplify. Answer:
44 Find each product. a. 3( 5m 2) Answer: 15m 6 b. (4p 8)( 3p) Answer:
45 Find Distributive Property Simplify. Answer:
46 Find Answer:
47 Fences The length of a dog run is 4 feet more than three times its width. The perimeter of the dog run is 56 feet. What are the dimensions of the dog run? Explore Plan You know the perimeter of the dog run. You want to find the dimensions of the dog run. Let w represent the width of the dog run. Then 3w + 4 represents the length. Write an equation. Perimeter equals twice the sum of the length and width. P = 2
48 Solve Write the equation. Replace P with 56 and Combine like terms. Distributive Property Subtract 8 from each side. Divide each side by 8. Answer: The width of the dog run is 6 feet, and the length is
49 Examine Check the reasonableness of the results. The answer checks.
50 Garden The length of a garden is four more than twice its width. The perimeter of the garden is 44 feet. What are the dimensions of the garden? Answer: 6 feet by 16 feet
51
52 Click the mouse button or press the Space Bar to display the answers.
53 Example 1 Identify Functions Using Graphs Example 2 Identify Functions Using Equations Example 3 Identify Functions Using Tables Example 4 Describe a Linear Function
54 Determine whether the graph represents a linear or nonlinear function. Answer: The graph is a straight line, so it represents a linear function.
55 Determine whether the graph represents a linear or nonlinear function. Answer: The graph is a curve, not a straight line, so it represents a nonlinear function.
56 Determine whether each graph represents a linear or nonlinear function. a. b. Answer: nonlinear Answer: linear
57 Determine whether nonlinear function. represents a linear or Answer: This equation represents a linear function because it is written in the form
58 Determine whether nonlinear function. represents a linear or Answer: This equation is nonlinear because x is raised to the second power and the equation cannot be written in the form
59 Determine whether each equation represents a linear or nonlinear function. a. Answer: nonlinear b. Answer: linear
60 Determine whether the table represents a linear or nonlinear function x y As x increases by 2, y decreases by 8. So, this is a linear function. Answer: linear
61 Determine whether the table represents a linear or nonlinear function x y As x increases by 3, y increases by a greater amount each time. So, this is a nonlinear function. Answer: nonlinear
62 Determine whether each table represents a linear or nonlinear function. a. b. x y x y Answer: nonlinear Answer: linear
63 MultipleChoice Test Item Which rule describes a linear function? A B C D Read the Test Item A rule describes a relationship between variables. A rule that can be written in the form describes a relationship that is linear.
64 Solve the Test Item This is a nonlinear function because x is in the denominator and the equation cannot be written in the form quadratic equation You can eliminate choices A and D. Answer: The answer is B. This is a quadratic equation. Eliminate choice C.
65 Check This equation is in the form
66 MultipleChoice Test Item Which rule describes a linear function? A B C D Answer: C
67
68 Click the mouse button or press the Space Bar to display the answers.
69 Example 1 Graph Quadratic Functions Example 2 Use a Function to Solve a Problem Example 3 Graph Cubic Functions
70 Graph. Make a table of values, plot the ordered pairs, and connect the points with a curve. Answer: x (x, y) ( 1.5, 4.5) ( 1, 2) ( 0.5, 0.5) (0.5, 0.5) (0, 0) (1, 2) (1.5, 4.5)
71 Graph. x 2 (x, y) ( 2, 3) Answer: 1 ( 1, 1.5) 0 (0, 1) 1 (1, 1.5) 2 (2, 3)
72 Graph. x 2 1 (x, y) ( 2, 7) ( 1, 4) Answer: 0 (0, 3) 1 (1, 4) 2 (2, 7)
73 Graph each function. a. Answer:
74 Graph each function. b. Answer:
75 Graph each function. c. Answer:
76 Geometry The height of a triangle is 4 times its base. Write a formula for the area and graph it. Find the area of the triangle whose base is 3 units. Words The area of a triangle is equal to onehalf the product of its base and height. Variables. Equations Area is equal to onehalf the product of its base and height A =
77 The equation is. Since the variable b has an exponent of 2, this function is nonlinear. Now graph. Since the base cannot be negative, use only positive values of b. b (b, A) (0, 0) (0.5, 0.5) (1, 2) (1.5, 4.5) (2, 8) (2.5, 12.5)
78 By looking at the graph, we find that for a base of 3 units, the area of the triangle is 18 square units.
79 Geometry The length of a rectangle is 3 times its width. Write a formula for the area and graph it. Find the area of the rectangle whose width is 3.5 inches. Answer:
80 Graph. Answer: x 2 1 (x, y) ( 2, 4) ( 1, ) 0 (0, 0) 1 (1, ) 2 (2, 4)
81 Graph. x (x, y) ( 1.5, 4.75) ( 1, 0) (0, 2) (1, 4) (1.5, 8.75) Answer:
82 Graph each function. a. Answer:
83 Graph each function. b. Answer:
84
85 Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the PreAlgebra Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to
86 End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to autoadvance to end custom shows and return to the main presentation.
87
PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to:
PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGrawHill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button
More informationPreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to:
PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGrawHill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button
More informationPreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to:
PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGrawHill 8787 Orion Place Columbus, Ohio 43240 Lesson 51 Lesson 52
More informationAlum Rock Elementary Union School District Algebra I Study Guide for Benchmark III
Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial
More information81 Adding and Subtracting Polynomials
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1. 7ab + 6b 2 2a 3 yes; 3; trinomial 2. 2y 5 +
More information78 Multiplying Polynomials
78 Multiplying Polynomials California Standards 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
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 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 information83 Multiplying Polynomials. Find each product. 1. (x + 5)(x + 2) SOLUTION: 2. (y 2)(y + 4) SOLUTION: 3. (b 7)(b + 3) SOLUTION:
Find each product. 1. (x + 5)(x + ). (y )(y + 4) 3. (b 7)(b + 3) 4. (4n + 3)(n + 9) 5. (8h 1)(h 3) 6. (a + 9)(5a 6) 7. FRAME Hugo is designing a frame as shown. The frame has a width of x inches all the
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers
More informationAlgebra II A Final Exam
Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.
More informationMyMathLab ecourse for Developmental Mathematics
MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationMonomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial
9.1 Add and Subtract Polynomials Before You added and subtracted integers. Now You will add and subtract polynomials. Why? So you can model trends in recreation, as in Ex. 37. Key Vocabulary monomial degree
More informationMathematics Online Instructional Materials Correlation to the 2009 Algebra I Standards of Learning and Curriculum Framework
Provider York County School Division Course Syllabus URL http://yorkcountyschools.org/virtuallearning/coursecatalog.aspx Course Title Algebra I AB Last Updated 2010  A.1 The student will represent verbal
More informationUnit 3 Polynomials Study Guide
Unit Polynomials Study Guide 75 Polynomials Part 1: Classifying Polynomials by Terms Some polynomials have specific names based upon the number of terms they have: # of Terms Name 1 Monomial Binomial
More informationPortable Assisted Study Sequence ALGEBRA IIA
SCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The first half of
More informationSOL WarmUp Graphing Calculator Active
A.2a (a) Using laws of exponents to simplify monomial expressions and ratios of monomial expressions 1. Which expression is equivalent to (5x 2 )(4x 5 )? A 9x 7 B 9x 10 C 20x 7 D 20x 10 2. Which expression
More informationMATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring noncourse based remediation in developmental mathematics. This structure will
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 informationREVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95
REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course. The sheets
More information6.1 Add & Subtract Polynomial Expression & Functions
6.1 Add & Subtract Polynomial Expression & Functions Objectives 1. Know the meaning of the words term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial funciton, quardrtic
More informationCAHSEE on Target UC Davis, School and University Partnerships
UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,
More informationAlgebra. Indiana Standards 1 ST 6 WEEKS
Chapter 1 Lessons Indiana Standards  11 Variables and Expressions  12 Order of Operations and Evaluating Expressions  13 Real Numbers and the Number Line  14 Properties of Real Numbers  15 Adding
More informationVeterans Upward Bound Algebra I Concepts  Honors
Veterans Upward Bound Algebra I Concepts  Honors Brenda Meery Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org Chapter 6. Factoring CHAPTER
More informationUnit 1: Polynomials. Expressions:  mathematical sentences with no equal sign. Example: 3x + 2
Pure Math 0 Notes Unit : Polynomials Unit : Polynomials : Reviewing Polynomials Epressions:  mathematical sentences with no equal sign. Eample: Equations:  mathematical sentences that are equated with
More informationIdentify examples of field properties: commutative, associative, identity, inverse, and distributive.
Topic: Expressions and Operations ALGEBRA II  STANDARD AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationThe graphs coincide. Therefore, the trinomial has been factored correctly. The factors are (x + 2)(x + 12).
86 Solving x^ + bx + c = 0 Factor each polynomial. Confirm your answers using a graphing calculator. 1. x + 14x + 4 In this trinomial, b = 14 and c = 4, so m + p is positive and mp is positive. Therefore,
More informationMATH 100 PRACTICE FINAL EXAM
MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationFactor Polynomials Completely
9.8 Factor Polynomials Completely Before You factored polynomials. Now You will factor polynomials completely. Why? So you can model the height of a projectile, as in Ex. 71. Key Vocabulary factor by grouping
More informationMth 95 Module 2 Spring 2014
Mth 95 Module Spring 014 Section 5.3 Polynomials and Polynomial Functions Vocabulary of Polynomials A term is a number, a variable, or a product of numbers and variables raised to powers. Terms in an expression
More informationALGEBRA I A PLUS COURSE OUTLINE
ALGEBRA I A PLUS COURSE OUTLINE 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 of Best
More informationACTIVITY: Multiplying Binomials Using Algebra Tiles. Work with a partner. Six different algebra tiles are shown below.
7.3 Multiplying Polynomials How can you multiply two binomials? 1 ACTIVITY: Multiplying Binomials Using Algebra Tiles Work with a partner. Six different algebra tiles are shown below. 1 1 x x x x Write
More informationCOGNITIVE TUTOR ALGEBRA
COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,
More informationThis is Solving Quadratic Equations and Graphing Parabolas, chapter 9 from the book Beginning Algebra (index.html) (v. 1.0).
This is Solving Quadratic Equations and Graphing Parabolas, chapter 9 from the book Beginning Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationUtah Core Curriculum for Mathematics
Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions
More information10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED
CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations
More informationAlgebra Success. [OBJECTIVE] The student will learn how to multiply monomials and polynomials.
Algebra Success T697 [OBJECTIVE] The student will learn how to multiply monomials and polynomials. [MATERIALS] Student pages S269 S278 Transparencies T704, T705, T707, T709, T711, T713, T715 Red and yellow
More information5.3 Multiplying Polynomials: Special Products. Copyright Cengage Learning. All rights reserved.
5.3 Multiplying Polynomials: Special Products Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Find products with monomial multipliers Multiplying binomials using the Distributive
More informationStudy Guide and Review  Chapter 8
Study Guide Review  Chapter 8 Solve each equation. Check your solutions. 41. 6x 2 = 12x Factor the trinomial using the Zero Product Property. 43. 3x 2 = 5x Factor the trinomial using the Zero Product
More informationAlgebra 1 Course Objectives
Course Objectives The Duke TIP course corresponds to a high school course and is designed for gifted students in grades seven through nine who want to build their algebra skills before taking algebra in
More information3. Power of a Product: Separate letters, distribute to the exponents and the bases
Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same
More informationFlorida Math 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 Content
20122013 Math Content PATHWAY TO ALGEBRA I Unit Lesson Section Number and Operations in Base Ten Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Regrouping Concepts
More informationFactoring and Applications
Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationLESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6.2 POLYNOMIAL OPERATIONS I Overview In business, people use algebra everyday to find unknown quantities. For example, a manufacturer may use algebra to determine a product s selling price in order
More informationAlgebra II Pacing Guide First Nine Weeks
First Nine Weeks SOL Topic Blocks.4 Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole and natural. 7. Recognize that the
More informationMath 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4)
Chapter 2: Functions and Linear Functions 1. Know the definition of a relation. Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) 2. Know the definition of a function. 3. What
More informationCHAPTER 3: GRAPHS OF QUADRATIC RELATIONS
CHAPTER 3: GRAPHS OF QUADRATIC RELATIONS Specific Expectations Addressed in the Chapter Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology
More informationDMA 060 Polynomials and Quadratic Applications
DMA 060 Polynomials and Quadratic Applications Brief Description This course provides a conceptual study of problems involving graphic and algebraic representations of quadratics. Topics include basic
More informationPark Forest Math Team. Meet #5. Algebra. Selfstudy Packet
Park Forest Math Team Meet #5 Selfstudy Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number
More informationWhole Numbers and Integers (44 topics, no due date)
Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKUKPMR9 ALEKS Course: PreAlgebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole
More informationP.E.R.T. Math Study Guide
A guide to help you prepare for the Math subtest of Florida s Postsecondary Education Readiness Test or P.E.R.T. P.E.R.T. Math Study Guide www.perttest.com PERT  A Math Study Guide 1. Linear Equations
More informationUnderstand the difference between linear equations and quadratic equations Multiply polynomials Factor quadratic equations
LESSON 26: Quadratic Equations part 1 Weekly Focus: quadratic equations Weekly Skill: factoring Lesson Summary: For the warmup, students will solve a problem about oil usage. Activity 1 is an introduction
More information( ) FACTORING. x In this polynomial the only variable in common to all is x.
FACTORING Factoring is similar to breaking up a number into its multiples. For example, 10=5*. The multiples are 5 and. In a polynomial it is the same way, however, the procedure is somewhat more complicated
More information52 Dividing Polynomials. Simplify. 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 SOLUTION: 4. (2a 2 4a 8) (a + 1) SOLUTION: 6. (y 5 3y 2 20) (y 2) SOLUTION:
Simplify. 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 4. (2a 2 4a 8) (a + 1) 6. (y 5 3y 2 20) (y 2) esolutions Manual  Powered by Cognero Page 1 Simplify. 8. (10x 2 + 15x + 20) (5x + 5) 10. 12. Simplify esolutions
More information6.4 Factoring Polynomials
Name Class Date 6.4 Factoring Polynomials Essential Question: What are some ways to factor a polynomial, and how is factoring useful? Resource Locker Explore Analyzing a Visual Model for Polynomial Factorization
More informationALGEBRA 1/ALGEBRA 1 HONORS
ALGEBRA 1/ALGEBRA 1 HONORS CREDIT HOURS: 1.0 COURSE LENGTH: 2 Semesters COURSE DESCRIPTION The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical
More informationFlorida Algebra 1 EndofCourse 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 informationMathematics Placement
Mathematics Placement The ACT COMPASS math test is a selfadaptive test, which potentially tests students within four different levels of math including prealgebra, algebra, college algebra, and trigonometry.
More informationMonomials with the same variables to the same powers are called like terms, If monomials are like terms only their coefficients can differ.
Chapter 7.1 Introduction to Polynomials A monomial is an expression that is a number, a variable or the product of a number and one or more variables with nonnegative exponents. Monomials that are real
More informationcalled and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles?
Factoring Reporting Category Topic Expressions and Operations Factoring polynomials Primary SOL A.2c The student will perform operations on polynomials, including factoring completely first and seconddegree
More informationAlgebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test
Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action
More informationSolving Quadratic Equations by Completing the Square
9. Solving Quadratic Equations by Completing the Square 9. OBJECTIVES 1. Solve a quadratic equation by the square root method. Solve a quadratic equation by completing the square. Solve a geometric application
More informationBasic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.
Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:
More informationexpression is written horizontally. The Last terms ((2)( 4)) because they are the last terms of the two polynomials. This is called the FOIL method.
A polynomial of degree n (in one variable, with real coefficients) is an expression of the form: a n x n + a n 1 x n 1 + a n 2 x n 2 + + a 2 x 2 + a 1 x + a 0 where a n, a n 1, a n 2, a 2, a 1, a 0 are
More information52 Dividing Polynomials. Simplify. SOLUTION: ANSWER: 4y + 2x (3a 2 b 6ab + 5ab 2 )(ab) 1 SOLUTION: ANSWER: 3a + 5b (x 2 6x 20) (x + 2)
1. Simplify. 4. (2a 2 4a 8) (a + 1) 4y + 2x 2 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 3a + 5b 6 5. (3z 4 6z 3 9z 2 + 3z 6) (z + 3) 3. (x 2 6x 20) (x + 2) esolutions Manual  Powered by Cognero Page 1 6. (y 5 3y
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 informationMATH 90 CHAPTER 6 Name:.
MATH 90 CHAPTER 6 Name:. 6.1 GCF and Factoring by Groups Need To Know Definitions How to factor by GCF How to factor by groups The Greatest Common Factor Factoring means to write a number as product. a
More informationPolynomials. Key Terms. quadratic equation parabola conjugates trinomial. polynomial coefficient degree monomial binomial GCF
Polynomials 5 5.1 Addition and Subtraction of Polynomials and Polynomial Functions 5.2 Multiplication of Polynomials 5.3 Division of Polynomials Problem Recognition Exercises Operations on Polynomials
More informationMAT 0950 Course Objectives
MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. Identify
More information1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
More informationAlgebra II New Summit School High School Diploma Program
Syllabus Course Description: Algebra II is a two semester course. Students completing this course will earn 1.0 unit upon completion. Required Materials: 1. Student Text Glencoe Algebra 2: Integration,
More informationPOLYNOMIAL FUNCTIONS
POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a
More informationUNIT TWO POLYNOMIALS MATH 421A 22 HOURS. Revised May 2, 00
UNIT TWO POLYNOMIALS MATH 421A 22 HOURS Revised May 2, 00 38 UNIT 2: POLYNOMIALS Previous Knowledge: With the implementation of APEF Mathematics at the intermediate level, students should be able to: 
More informationBig Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
More informationDefinitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder).
Math 50, Chapter 8 (Page 1 of 20) 8.1 Common Factors Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder). Find all the factors of a. 44 b. 32
More informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More information72 Factoring by GCF. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1
72 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify. 1. 2(w + 1) 2. 3x(x 2 4) 2w + 2 3x 3 12x Find the GCF of each pair of monomials. 3. 4h 2 and 6h 2h 4. 13p and 26p
More informationSection 2.4: Applications and Writing Functions
CHAPTER 2 Polynomial and Rational Functions Section 2.4: Applications and Writing Functions Setting up Functions to Solve Applied Problems Maximum or Minimum Value of a Quadratic Function Setting up Functions
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationSTUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS
STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS The intermediate algebra skills illustrated here will be used extensively and regularly throughout the semester Thus, mastering these skills is an
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationPlacement Test Review Materials for
Placement Test Review Materials for 1 To The Student This workbook will provide a review of some of the skills tested on the COMPASS placement test. Skills covered in this workbook will be used on the
More informationIntroduction to the Instructor TERM 1
Introduction to the Instructor TERM 1 This calendar of lessons was prepared as a textbook independent sequence of lessons and the order of topics can be modified based on the textbook selection. The columns
More informationAlgebra II Semester Exam Review Sheet
Name: Class: Date: ID: A Algebra II Semester Exam Review Sheet 1. Translate the point (2, 3) left 2 units and up 3 units. Give the coordinates of the translated point. 2. Use a table to translate the graph
More informationFlorida Department of Education/Office of Assessment January 2012. Algebra 1 EndofCourse Assessment Achievement Level Descriptions
Florida Department of Education/Office of Assessment January 2012 Algebra 1 EndofCourse Assessment Achievement Level Descriptions Algebra 1 EOC Assessment Reporting Category Functions, Linear Equations,
More informationState whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence. 1. x + 5x + 6 is an example of a prime polynomial. The statement is false. A
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 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 informationChapter 8. Quadratic Equations and Functions
Chapter 8. Quadratic Equations and Functions 8.1. Solve Quadratic Equations KYOTE Standards: CR 0; CA 11 In this section, we discuss solving quadratic equations by factoring, by using the square root property
More informationMTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006
MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions Created January 7, 2006 Math 092, Elementary Algebra, covers the mathematical content listed below. In order
More informationMATH Fundamental Mathematics II.
MATH 10032 Fundamental Mathematics II http://www.math.kent.edu/ebooks/10032/funmath2.pdf Department of Mathematical Sciences Kent State University December 29, 2008 2 Contents 1 Fundamental Mathematics
More informationCourse Title: Honors Algebra Course Level: Honors Textbook: Algebra 1 Publisher: McDougall Littell
Course Title: Honors Algebra Course Level: Honors Textbook: Algebra Publisher: McDougall Littell The following is a list of key topics studied in Honors Algebra. Identify and use the properties of operations
More informationAlgebra I Pacing Guide Days Units Notes 9 Chapter 1 ( , )
Algebra I Pacing Guide Days Units Notes 9 Chapter 1 (1.11.4, 1.61.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationSummer Math Exercises. For students who are entering. PreCalculus
Summer Math Eercises For students who are entering PreCalculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn
More information