Chapter 6 Class Notes 6-1 Solving Inequalities Using Addition and Subtraction p n 1

Size: px
Start display at page:

Download "Chapter 6 Class Notes 6-1 Solving Inequalities Using Addition and Subtraction p n 1"

Transcription

1 Chapter Class Notes Alg. CP - Solving Inequalities Using Addition and Subtraction p.. t. a. n. r r - Solving Inequalities Using Multiplication and Division p. 0-0 A) n B) n A) B) p When ou multipl or divide b a number, ou must the inequalit sign! A) r B) g 0 C) k D) t Points: at least E: I have at least $0 in m wallet. at most E: I can fit people at most in m car. Ch. Notes CP

2 - Solving Multi-Step Inequalities p. 0- ) A) w B) ) A) z z B) h h If solving an inequalit results in a statement, the solution is. If solving an inequalit results in a statement, the solution is. A) c c B) m m Ch. Notes CP

3 -A Solving Compound Inequalities Involving And p. - compound inequalit: inequalities b the word or the word. And tpe: graph is the of the graphs of the inequalities; can be found b graphing each and determining where the A) a and a 0 B) p and p (Rewrite each of the compound inequalities with the variable between the smbols.) Check our Understanding p. #- ) a and a ) and ) w and w Ch. Notes CP

4 -B Solving Compound Inequalities Involving Or p. - Or tpe: graph is the of the graphs of the inequalities its solution is a solution of inequalit can be found b each A) a or a B) or (If necessar, rewrite each of the compound inequalities in numerical order.) Check our Understanding p. #- ) n or n- ) z or z ) ) Ch. Notes CP

5 -A Solving Absolute Value Equations p. - Absolute-value: distance from Smbol: Absolute-value equation: the is within the absolute value bars; form: Solving an absolute-value equation: o For c 0, is a solution of a b c if is a solution of: or o For c < 0, the absolute-value equation a b c has, since absolute value alwas indicates a number that is not. A) B) n Do p. #- ) r ) ) n

6 Alwas Isolate the Absolute Value term first!!!!!! E. C) D) Check: Check:

7 -B Graphing Absolute Value Functions p.. Find the of the verte. Ask, What makes the epression within the (absolute value bars) equal? E: f f f. Make a. Put the -coordinate of the in the center. Choose some values of to the and.. Complete the -values.. Plot the points. It will make a graph. A) f Domain: Range:

8 B) f Domain: Range: C) f Domain: Range: Minimum and Maimum Values:

9 Stud Guide for Absolute Value Equations Chapter Alg. CP Tpe of Problem How to Solve Write equations; No solution can t have a answer unless there is a neg. sign in front of the Solve Write equations and ; the ab. value term (subtract ); Then write equations and solve; Graph. Find the of the verte; (makes the epression within the equal 0).. Make a of values (verte in center; values less and greater).. each value into equation to determine values.. Graph is.

10 - Graphing Linear Inequalities in Two Variables p. - Linear inequalit: can be written as: Graphing a linear inequalit: Graph. Use a for > or <. Use a for or. Test an in one of the half-planes. Shade the containing the solution. A) B) C) D)

11 E) F) p. # Will the coach be able to bu pizzas and pitchers of drinks?

12 - Graphing Sstems of Inequalities p. - Sstem of inequalities: inequalities with the same ; solved together Solution of a sstem: a region of a that shows the or of the graphs of the inequalities. A) B) C) D)

13 p. #- Use a sstem to solve: variables and inequalities. Name possible solutions:

Ch 3 Alg 2 Note Sheet.doc 3.1 Graphing Systems of Equations

Ch 3 Alg 2 Note Sheet.doc 3.1 Graphing Systems of Equations Ch 3 Alg Note Sheet.doc 3.1 Graphing Sstems of Equations Sstems of Linear Equations A sstem of equations is a set of two or more equations that use the same variables. If the graph of each equation =.4

More information

N x. You should know how to decompose a rational function into partial fractions.

N x. You should know how to decompose a rational function into partial fractions. Section 7. Partial Fractions 0. 0 7 0 0 0 0 Solution:, 0 Equation Equation Eq. Eq. 07. nswers will var. Section 7. Partial Fractions N You should know how to decompose a rational function into partial

More information

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte

More information

Classwork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations

Classwork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations Classwork #0: Final Review: Solving Equations, Word Problems, Linear Equations, Sstems of Linear Equations Solving Equations: Isolate the variable! Things to watch for: when ou have parentheses the inequalit

More information

Intermediate Math Circles Wednesday November Inequalities and Linear Optimization

Intermediate Math Circles Wednesday November Inequalities and Linear Optimization WWW.CEMC.UWATERLOO.CA The CENTRE for EDUCATION in MATHEMATICS and COMPUTING Intermediate Math Circles Wednesda November 21 2012 Inequalities and Linear Optimization Review: Our goal is to solve sstems

More information

CHAPTER 6: LINEAR SYSTEMS AND THEIR GRAPHS

CHAPTER 6: LINEAR SYSTEMS AND THEIR GRAPHS Name: Date: Period: CHAPTER : LINEAR SYSTEMS AND THEIR GRAPHS Notes #: Section.: Solving Linear Sstems b Substitution The solution to a sstem of equations represents the where the. It would be great if

More information

For questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)

For questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each) Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, 1 0 0 c. 0, 1 0 d. 0, 1 0 For questions -, insert , or = to make the sentence true. (1pt each) A. 5

More information

Linear Programming. Maximize the function. P = Ax + By + C. subject to the constraints. a 1 x + b 1 y < c 1 a 2 x + b 2 y < c 2

Linear Programming. Maximize the function. P = Ax + By + C. subject to the constraints. a 1 x + b 1 y < c 1 a 2 x + b 2 y < c 2 Linear Programming Man real world problems require the optimization of some function subject to a collection of constraints. Note: Think of optimizing as maimizing or minimizing for MATH1010. For eample,

More information

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED FOM 11 T GRAPHING LINEAR INEQUALITIES & SET NOTATION - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) INEQUALITY = a mathematical statement that contains one of these four inequalit signs: ,.

More information

Northwest High School s Algebra 2/Honors Algebra 2

Northwest High School s Algebra 2/Honors Algebra 2 Northwest High School s Algebra /Honors Algebra Summer Review Packet 0 DUE Frida, September, 0 Student Name This packet has been designed to help ou review various mathematical topics that will be necessar

More information

8.4. If we let x denote the number of gallons pumped, then the price y in dollars can $ $1.70 $ $1.70 $ $1.70 $ $1.

8.4. If we let x denote the number of gallons pumped, then the price y in dollars can $ $1.70 $ $1.70 $ $1.70 $ $1. 8.4 An Introduction to Functions: Linear Functions, Applications, and Models We often describe one quantit in terms of another; for eample, the growth of a plant is related to the amount of light it receives,

More information

Unit 2 Notes Packet on Quadratic Functions and Factoring

Unit 2 Notes Packet on Quadratic Functions and Factoring Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a

More information

+ = + + = x = + = + = 36x

+ = + + = x = + = + = 36x Ch 5 Alg L Homework Worksheets Computation Worksheet #1: You should be able to do these without a calculator! A) Addition (Subtraction = add the opposite of) B) Multiplication (Division = multipl b the

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 5 Maintaining Mathematical Proficienc Graph the equation. 1. + =. = 3 3. 5 + = 10. 3 = 5. 3 = 6. 3 + = 1 Solve the inequalit. Graph the solution. 7. a 3 > 8. c 9. d 5 < 3 10. 8 3r 5 r

More information

Algebra 2 Semester Exam Review

Algebra 2 Semester Exam Review Algebra Semester Eam Review 7 Graph the numbers,,,, and 0 on a number line Identif the propert shown rs rs r when r and s Evaluate What is the value of k k when k? Simplif the epression 7 7 Solve the equation

More information

CHAPTER 6: LINEAR SYSTEMS AND THEIR GRAPHS

CHAPTER 6: LINEAR SYSTEMS AND THEIR GRAPHS Name: Date: Period: CHAPTER : LINEAR SYSTEMS AND THEIR GRAPHS Notes #: Section.: Solving Linear Sstems b Substitution The solution to a sstem of equations represents the where the. It would be great if

More information

(2.5) 1. Solve the following compound inequality and graph the solution set.

(2.5) 1. Solve the following compound inequality and graph the solution set. Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. -) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities.

More information

Solve each system by graphing. Check your solution. y =-3x x + y = 5 y =-7

Solve each system by graphing. Check your solution. y =-3x x + y = 5 y =-7 Practice Solving Sstems b Graphing Solve each sstem b graphing. Check our solution. 1. =- + 3 = - (1, ). = 1 - (, 1) =-3 + 5 3. = 3 + + = 1 (, 3). =-5 = - 7. = 3-5 3 - = 0 (1, 5) 5. -3 + = 5 =-7 (, 7).

More information

Instructor: KATHRYN SCHRADER Course: A Kathryn Elizabeth Schrader - Alg 1 Hon (2018 / DARNELL COOKMAN-INTEGRATED)

Instructor: KATHRYN SCHRADER Course: A Kathryn Elizabeth Schrader - Alg 1 Hon (2018 / DARNELL COOKMAN-INTEGRATED) Student: Date: Instructor: KATHRYN SCHRADER Course: 3 3 - A - 37 - Kathrn Elizabeth Schrader - Alg Hon (28 / DARNELL COOKMAN-INTEGRATED) Assignment: Chapter Review. What are the variables of the graph

More information

Chapter 9 Notes Alg. 1H 9-A1 (Lesson 9-3) Solving Quadratic Equations by Finding the Square Root and Completing the Square

Chapter 9 Notes Alg. 1H 9-A1 (Lesson 9-3) Solving Quadratic Equations by Finding the Square Root and Completing the Square Chapter Notes Alg. H -A (Lesson -) Solving Quadratic Equations b Finding the Square Root and Completing the Square p. *Calculator Find the Square Root: take the square root of. E: Solve b finding square

More information

Solving Systems Using Tables and Graphs

Solving Systems Using Tables and Graphs 3-1 Solving Sstems Using Tables and Graphs Vocabular Review 1. Cross out the equation that is NOT in slope-intercept form. 1 5 7 r 5 s a 5!3b 1 5 3 1 7 5 13 Vocabular Builder linear sstem (noun) LIN ee

More information

1.3. Absolute Value and Piecewise-Defined Functions Absolutely Piece-ful. My Notes ACTIVITY

1.3. Absolute Value and Piecewise-Defined Functions Absolutely Piece-ful. My Notes ACTIVITY Absolute Value and Piecewise-Defined Functions Absolutel Piece-ful SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Create Representations, Quickwrite. Graph both = - for < 3 and = - + 7 for

More information

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology. Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the U-shaped graph

More information

Reteaching (continued)

Reteaching (continued) Quadratic Functions and Transformations If a, the graph is a stretch or compression of the parent function b a factor of 0 a 0. 0 0 0 0 0 a a 7 The graph is a vertical The graph is a vertical compression

More information

Topic 1: Writing and Solving Equations and Inequalities

Topic 1: Writing and Solving Equations and Inequalities Topic 1: Writing and Solving Equations and Inequalities In #1 3, solve each equation. Use inverse operations. 1. 8 21 5 = 15 2. 3 10 = 2(4 5) 3. 2( + 2) = 2 + 1 4. The rectangle and square have equivalent

More information

Algebra 2 Honors Summer Packet 2018

Algebra 2 Honors Summer Packet 2018 Algebra Honors Summer Packet 018 Solving Linear Equations with Fractional Coefficients For these problems, ou should be able to: A) determine the LCD when given two or more fractions B) solve a linear

More information

Math 100 Final Exam Review

Math 100 Final Exam Review Math 0 Final Eam Review Name The problems included in this review involve the important concepts covered this semester. Work in groups of 4. If our group gets stuck on a problem, let our instructor know.

More information

Dœs Chase count when determining the weight and the cost?

Dœs Chase count when determining the weight and the cost? PROBLEM 1 Whitewater Rafting Chase is an eperienced whitewater rafter who guides groups of adults and children out on the water for amazing adventures. The super-raft he uses can hold 00 pounds of weight.

More information

Chapter 6: Systems of Equations and Inequalities

Chapter 6: Systems of Equations and Inequalities Chapter 6: Sstems of Equations and Inequalities 6-1: Solving Sstems b Graphing Objectives: Identif solutions of sstems of linear equation in two variables. Solve sstems of linear equation in two variables

More information

c. x x < 60 d. x x =9. What are the first four terms of the sequence? a. 12, 21, 30, 39 b.

c. x x < 60 d. x x =9. What are the first four terms of the sequence? a. 12, 21, 30, 39 b. Algebra I Unit Reasoning with Linear Equations and Inequalities Post Test... A famil s cell phone plan costs $ per month for, minutes and cents per minute over the limit. This month, the famil paid $..

More information

Summer MA Lesson 14 Section 1.7 (part 2) and Sections 1.1 & 2.8

Summer MA Lesson 14 Section 1.7 (part 2) and Sections 1.1 & 2.8 Summer MA 1500 Lesson 14 Section 1.7 (part ) and Sections 1.1 &.8 I Solving Absolute Value Inequalities Absolute Value Inequalities: u < c or u c, if c 0 The inequalit u < cindicates all values less than

More information

PreCalculus. Ocean Township High School Mathematics Department

PreCalculus. Ocean Township High School Mathematics Department PreCalculus Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from previous courses that ou must be comfortable doing before ou can be successful

More information

Unit 12 Study Notes 1 Systems of Equations

Unit 12 Study Notes 1 Systems of Equations You should learn to: Unit Stud Notes Sstems of Equations. Solve sstems of equations b substitution.. Solve sstems of equations b graphing (calculator). 3. Solve sstems of equations b elimination. 4. Solve

More information

Section 3.1 Solving Linear Systems by Graphing

Section 3.1 Solving Linear Systems by Graphing Section 3.1 Solving Linear Sstems b Graphing Name: Period: Objective(s): Solve a sstem of linear equations in two variables using graphing. Essential Question: Eplain how to tell from a graph of a sstem

More information

Math 154A Elementary Algebra Fall 2014 Final Exam Study Guide

Math 154A Elementary Algebra Fall 2014 Final Exam Study Guide Math A Elementar Algebra Fall 0 Final Eam Stud Guide The eam is on Tuesda, December 6 th from 6:00pm 8:0pm. You are allowed a scientific calculator and a " b 6" inde card for notes. On our inde card be

More information

First Semester Final Review NON-Graphing Calculator

First Semester Final Review NON-Graphing Calculator Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Stud Guide for Test II Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the linear inequalit. 1) 3 + -6 1) - - - - A) B) - - - - - - - -

More information

Ready To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities

Ready To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear

More information

F6 Solving Inequalities

F6 Solving Inequalities UNIT F6 Solving Inequalities: Tet F6 Solving Inequalities F6. Inequalities on a Number Line An inequalit involves one of the four smbols >,, < or The following statements illustrate the meaning of each

More information

Math Intermediate Algebra

Math Intermediate Algebra Math 095 - Intermediate Algebra Final Eam Review Objective 1: Determine whether a relation is a function. Given a graphical, tabular, or algebraic representation for a function, evaluate the function and

More information

Math 100 Final Exam Review

Math 100 Final Exam Review Math 0 Final Eam Review Name The problems included in this review involve the important concepts covered this semester. Work in groups of 4. If our group gets stuck on a problem, let our instructor know.

More information

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The

More information

4-9. Solving Absolute Value Equations and Inequalities. Solving x = a. Lesson

4-9. Solving Absolute Value Equations and Inequalities. Solving x = a. Lesson Chapter Lesson -9 Solving Absolute Value Equations and Inequalities BIG IDEA Inequalities with a + b on one side and a positive number c on the other side can be solved b using the fact that a + b must

More information

Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression

Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important

More information

Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE

Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE The SAT Subject Tests Answer Eplanations TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE Mathematics Level & Visit sat.org/stpractice to get more practice and stud tips for the Subject Test

More information

Systems of Linear Inequalities

Systems of Linear Inequalities . Sstems of Linear Inequalities sstem of linear inequalities? How can ou sketch the graph of a ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. + Inequalit

More information

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences Lesson 7.1 Polnomial Degree and Finite Differences 1. Identif the degree of each polnomial. a. 1 b. 0. 1. 3. 3 c. 0 16 0. Determine which of the epressions are polnomials. For each polnomial, state its

More information

Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!

Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit! Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).

More information

Algebra 2 Summer Recommendations

Algebra 2 Summer Recommendations Algebra Summer Recommendations Book section 0.1 Representing Functions Terminolog Quadrants, Relations, Functions, Domain, Range, Mapping 1. State the domain and range of each relation in set notation.

More information

MATH 60 Review Problems for Final Exam

MATH 60 Review Problems for Final Exam MATH 60 Review Problems for Final Eam Scientific Calculators Onl - Graphing Calculators Not Allowed NO CLASS NOTES PERMITTED Evaluate the epression for the given values. m 1) m + 3 for m = 3 2) m 2 - n2

More information

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1 Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab

More information

3.1 Graph Quadratic Functions

3.1 Graph Quadratic Functions 3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your

More information

NAME DATE PERIOD. Study Guide and Intervention

NAME DATE PERIOD. Study Guide and Intervention NAME DATE PERID Stud Guide and Intervention Graph To graph a quadratic inequalit in two variables, use the following steps: 1. Graph the related quadratic equation, = a 2 + b + c. Use a dashed line for

More information

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) A SYSTEM OF LINEAR INEQUALITIES = a problem where or more inequalities are graphed on the same grid, the solution

More information

Ready To Go On? Skills Intervention 10-1 Introduction to Conic Sections

Ready To Go On? Skills Intervention 10-1 Introduction to Conic Sections Find this vocabular word in Lesson 10-1 and the Multilingual Glossar. Graphing Parabolas and Hperbolas on a Calculator A is a single curve, whereas a has two congruent branches. Identif and describe each

More information

Algebra I Chapter 6: Solving and Graphing Linear Inequalities

Algebra I Chapter 6: Solving and Graphing Linear Inequalities Algebra I Chapter 6: Solving and Graphing Linear Inequalities Jun 10 9:21 AM Chapter 6 Lesson 1 Solve Inequalities Using Addition and Subtraction Vocabulary Words to Review: Inequality Solution of an Inequality

More information

Writing Quadratic Functions in Standard Form

Writing Quadratic Functions in Standard Form Chapter Summar Ke Terms standard form (general form) of a quadratic function (.1) parabola (.1) leading coefficient (.) second differences (.) vertical motion model (.3) zeros (.3) interval (.3) open interval

More information

Name Class Date. t = = 10m. n + 19 = = 2f + 9

Name Class Date. t = = 10m. n + 19 = = 2f + 9 1-4 Reteaching Solving Equations To solve an equation that contains a variable, find all of the values of the variable that make the equation true. Use the equality properties of real numbers and inverse

More information

Summer Math Packet (revised 2017)

Summer Math Packet (revised 2017) Summer Math Packet (revised 07) In preparation for Honors Math III, we have prepared a packet of concepts that students should know how to do as these concepts have been taught in previous math classes.

More information

Ch 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.

Ch 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet. Ch Alg L Note Sheet Ke Do Activit 1 on our Ch Activit Sheet. Chapter : Quadratic Equations and Functions.1 Modeling Data With Quadratic Functions You had three forms for linear equations, ou will have

More information

QUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta

QUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta QUADRATIC GRAPHS ALGEBRA 2 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Quadratic Graphs 1/ 16 Adrian Jannetta Objectives Be able to sketch the graph of a quadratic function Recognise the shape

More information

Math 50 - Elementary Algebra Final Exam, Fall 2010

Math 50 - Elementary Algebra Final Exam, Fall 2010 Math - Elementar Algebra Final Eam, Fall Name: Date: Score: / Show the necessar work on the test cop. For an of the graphs use a straightedge to receive full credit. Place our answers in the blanks provided

More information

Graph the linear system and estimate the solution. Then check the solution algebraically.

Graph the linear system and estimate the solution. Then check the solution algebraically. (Chapters and ) A. Linear Sstems (pp. 6 0). Solve a Sstem b Graphing Vocabular Solution For a sstem of linear equations in two variables, an ordered pair (x, ) that satisfies each equation. Consistent

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Eam Review MAC 1 Spring 0 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) {-

More information

Math098 Practice Final Test

Math098 Practice Final Test Math098 Practice Final Test Find an equation of the line that contains the points listed in the table. 1) 0-6 1-2 -4 3-3 4-2 Find an equation of the line. 2) 10-10 - 10 - -10 Solve. 3) 2 = 3 + 4 Find the

More information

Graphing Inequalities

Graphing Inequalities 10 Graphg Inequalities In this chapter, ou will practice graphg equalities that have one or two variables. When there is onl one variable, ou use a number le. When there are two variables, ou use a coordate

More information

APPENDIX D Rotation and the General Second-Degree Equation

APPENDIX D Rotation and the General Second-Degree Equation APPENDIX D Rotation and the General Second-Degree Equation Rotation of Aes Invariants Under Rotation After rotation of the - and -aes counterclockwise through an angle, the rotated aes are denoted as the

More information

Graph Linear Inequalities in Two Variables. You solved linear inequalities in one variable. You will graph linear inequalities in two variables.

Graph Linear Inequalities in Two Variables. You solved linear inequalities in one variable. You will graph linear inequalities in two variables. TEKS.8 a.5 Before Now Graph Linear Inequalities in Two Variables You solved linear inequalities in one variable. You will graph linear inequalities in two variables. Wh? So ou can model data encoding,

More information

FALL 2012 MATH 1324 REVIEW EXAM 2

FALL 2012 MATH 1324 REVIEW EXAM 2 FALL 0 MATH 3 REVIEW EXAM MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the order of the matri product AB and the product BA, whenever the

More information

MEP Pupil Text 16. The following statements illustrate the meaning of each of them.

MEP Pupil Text 16. The following statements illustrate the meaning of each of them. MEP Pupil Tet Inequalities. Inequalities on a Number Line An inequalit involves one of the four smbols >,, < or. The following statements illustrate the meaning of each of them. > : is greater than. :

More information

LESSON 4.3 GRAPHING INEQUALITIES

LESSON 4.3 GRAPHING INEQUALITIES LESSON.3 GRAPHING INEQUALITIES LESSON.3 GRAPHING INEQUALITIES 9 OVERVIEW Here s what ou ll learn in this lesson: Linear Inequalities a. Ordered pairs as solutions of linear inequalities b. Graphing linear

More information

review math0410 (1-174) and math 0320 ( ) aafinm mg

review math0410 (1-174) and math 0320 ( ) aafinm mg Eam Name review math04 (1-174) and math 0320 (17-243) 03201700aafinm0424300 mg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplif. 1) 7 2-3 A)

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Eam Review MAC 1 Fall 011 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) A)

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 100 Eam 3 Review (Chapters 5-6) Name The problems included in this review involve the important concepts covered in chapters 5 and 6. You will comlete this review in two rounds: (1) In the individual

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter

More information

Introduction to Inequalities

Introduction to Inequalities Algebra Module A7 Introduction to Inequalities Copright This publication The Northern Alberta Institute of Technolog 00. All Rights Reserved. LAST REVISED Nov., 007 Introduction to Inequalities Statement

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Stud Guide - Ch 3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The bar graph below shows the number of students b major in the College of

More information

UNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x

UNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x 5A galler of graphs Objectives To recognise the rules of a number of common algebraic relations: = = = (rectangular hperbola) + = (circle). To be able to sketch the graphs of these relations. To be able

More information

College Algebra Final, 7/2/10

College Algebra Final, 7/2/10 NAME College Algebra Final, 7//10 1. Factor the polnomial p() = 3 5 13 4 + 13 3 + 9 16 + 4 completel, then sketch a graph of it. Make sure to plot the - and -intercepts. (10 points) Solution: B the rational

More information

Algebra 2 CPA Summer Assignment 2018

Algebra 2 CPA Summer Assignment 2018 Algebra CPA Summer Assignment 018 This assignment is designed for ou to practice topics learned in Algebra 1 that will be relevant in the Algebra CPA curriculum. This review is especiall important as ou

More information

7.1 Solving Linear Systems by Graphing

7.1 Solving Linear Systems by Graphing 7.1 Solving Linear Sstems b Graphing Objectives: Learn how to solve a sstem of linear equations b graphing Learn how to model a real-life situation using a sstem of linear equations With an equation, an

More information

Decimal Operations No Calculators!!! Directions: Perform the indicated operation. Show all work. Use extra paper if necessary.

Decimal Operations No Calculators!!! Directions: Perform the indicated operation. Show all work. Use extra paper if necessary. Decimal Operations No Calculators!!! Directions: Perform the indicated operation. Show all work. Use etra paper if necessar. Find.8 +.9...09 +. + 0.06 =. 6.08 + 6.8 + 00. =. 8. 6.09 =. 00.908. = Find.

More information

Systems of Linear Equations: Solving by Graphing

Systems of Linear Equations: Solving by Graphing 8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From

More information

Use the slope-intercept form to graph the equation. 8) 6x + y = 0

Use the slope-intercept form to graph the equation. 8) 6x + y = 0 03 Review Solve the inequalit. Graph the solution set and write it in interval notation. 1) -2(4-9) < - + 2 Use the slope-intercept form to graph the equation. 8) 6 + = 0 Objective: (2.8) Solve Linear

More information

Name Date PD. Systems of Equations and Inequalities

Name Date PD. Systems of Equations and Inequalities Name Date PD Sstems of Equations and Inequalities Sstems of Equations Vocabular: A sstem of linear equations is A solution of a sstem of linear equations is Points of Intersection (POI) are the same thing

More information

PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.

PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line. MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for

More information

x. 4. 2x 10 4x. 10 x

x. 4. 2x 10 4x. 10 x CCGPS UNIT Semester 1 COORDINATE ALGEBRA Page 1 of Reasoning with Equations and Quantities Name: Date: Understand solving equations as a process of reasoning and eplain the reasoning MCC9-1.A.REI.1 Eplain

More information

Vertex. March 23, Ch 9 Guided Notes.notebook

Vertex. March 23, Ch 9 Guided Notes.notebook March, 07 9 Quadratic Graphs and Their Properties A quadratic function is a function that can be written in the form: Verte Its graph looks like... which we call a parabola. The simplest quadratic function

More information

Algebra II Practice Semester Exam Specification Sheet

Algebra II Practice Semester Exam Specification Sheet Algebra II Practice Semester Exam Specification Sheet 1. Properties of real numbers. Procedure (write procedure or process) 3. Concept development/linkage. Theorem/factual knowledge (of theorems and rules)

More information

Practice UNIT 2 ACTIVITY 2.2 ACTIVITY 2.1

Practice UNIT 2 ACTIVITY 2.2 ACTIVITY 2.1 ACTIVITY.. Use the regression capabilities of our graphing calculator to create a model to represent the data in the table. - - 0. -. ACTIVITY. Determine the -intercept and end behavior of each function.

More information

Unit 26 Solving Inequalities Inequalities on a Number Line Solution of Linear Inequalities (Inequations)

Unit 26 Solving Inequalities Inequalities on a Number Line Solution of Linear Inequalities (Inequations) UNIT Solving Inequalities: Student Tet Contents STRAND G: Algebra Unit Solving Inequalities Student Tet Contents Section. Inequalities on a Number Line. of Linear Inequalities (Inequations). Inequalities

More information

Honors Algebra

Honors Algebra Honors Algebra 08-09 Honors Algebra is a rigorous course that requires the use of Algebra skills. The summer work is designed to maintain and reinforce these prerequisite skills so as to prepare ou for

More information

Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.

Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots. Name: Quadratic Functions Objective: To be able to graph a quadratic function and identif the verte and the roots. Period: Quadratic Function Function of degree. Usuall in the form: We are now going to

More information

Placement Test. Circle the letter of the correct answer.

Placement Test. Circle the letter of the correct answer. Week Unit 0. What is the place value where the numbers differ?,7,7 A ones tens hundreds thousands. 70 A 6,0 6,0,0,0. 7 A 00 909 999 99. Which of the following is equivalent to the product of? A ( ) (0

More information

Pure Core 1. Revision Notes

Pure Core 1. Revision Notes Pure Core Revision Notes Ma 06 Pure Core Algebra... Indices... Rules of indices... Surds... 4 Simplifing surds... 4 Rationalising the denominator... 4 Quadratic functions... 5 Completing the square....

More information

Mt. Douglas Secondary

Mt. Douglas Secondary Foundations of Math 11 Section.1 Review: Graphing a Linear Equation 57.1 Review: Graphing a Linear Equation A linear equation means the equation of a straight line, and can be written in one of two forms.

More information

Vocabulary. Term Page Definition Clarifying Example degree of a monomial. degree of a polynomial. end behavior. leading coefficient.

Vocabulary. Term Page Definition Clarifying Example degree of a monomial. degree of a polynomial. end behavior. leading coefficient. CHAPTER 6 Vocabular The table contains important vocabular terms from Chapter 6. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. Term Page Definition Clarifing

More information

REVIEW. Topic Essential Question. Vocabulary Review. Use Vocabulary in Writing Describe how to solve 3 7

REVIEW. Topic Essential Question. Vocabulary Review. Use Vocabulary in Writing Describe how to solve 3 7 ? Topic Essential Question What procedures can be used to write and solve equations and inequalities? REVIEW TOPIC 4 Vocabular Review Complete each definition with a vocabular word. Vocabular dependent

More information

Chapter 8 Vocabulary Check

Chapter 8 Vocabulary Check 28 CHAPTER 8 Quadratic Equations and Functions d. What is the level of methane emissions for that ear? (Use our rounded answer from part (c).) (Round this answer to 2 decimals places.) Use a graphing calculator

More information

Algebra 1, Semester 1, District Final REVIEW Solve the equation.

Algebra 1, Semester 1, District Final REVIEW Solve the equation. Algebra, Semester, District Final REVIEW 6-7 Solve the equation... - = 9. 8. The admission fee to an amusement park is $. It costs an additional d dollars to rent a locker to hold our belongings. The total

More information