Section 1.1 Solving Linear Equations and Inequalities a + 4b c
|
|
- Mitchell Owens
- 5 years ago
- Views:
Transcription
1 Section 1 Solving Linear Equations and Inequalities A. Evaluating Expressions Examples Evaluate the following if a = 7, b =, and c = ( a + c ) + b. a + b c B. The Distributive Property Try the Following Simplify each expression. (x y) 8( x + y). (x y) 6( x y) C. Solving Equations Try the Following Solve for x. (x + ) ( x 1) = x =. 8x 9 + = D. Solving Formulas Try the Following Solve for the variable specified 1 Mm d = at ; a. F = G ; m r E. Inequalities Try the following Solve and graph the inequalities y x x. 1 >. 1 x 7. y + 9 or 18 > y 10 Precalculus Chapter 1 Page 1
2 D. Absolute Value Equations Try the following Solve for x. 8x = 1. x + 7 = E. Absolute Value Inequalities Try the following solve and graph. x 7. x 1 F. x + 0 HW Worksheet Precalculus Chapter 1 Page
3 Section Linear Relations and Functions I. Relations and Functions A. Definitions Relation. Domain. Range. Function B. Examples Determine whether each relation is a function. a) Mappings: b) Tables: x -7 - y c) Ordered Pairs: {(,),(,),(0,7),(0,9) }. Graphs: 1) ) ) Note: Vertical Line Test Precalculus Chapter 1 Page
4 C. Function Values and Notation Function Notation a) y = x 8 vs. f ( x) = x 8 b) Function notation has the advantage of clearly identifying the dependent variable f ( x ), formerly known as y, while at the same time telling you x is the independent variable and that the function itself is called f. c) Function notation allows you to be less wordy. Instead of asking What is the value of y that corresponds to x =? you can ask What is f ( )? :. Examples a) If f ( x) = x, find f (). b) If h( x) = 0.x x.7, find h (6). c) If f x =, find ( ) ( ) x f t. d) Extra: If g a ( ) a 6 =, find g( b + ). II. Linear Equations A. Forms... B. Slope and intercepts Slope. x-intercept. y-intercept Precalculus Chapter 1 Page
5 C. Examples Find the intercepts and slope of the following: a) x y = 16 b) 1 x y = c) y = x. Find the equation of a line with the following description: a) Slope of and goes through the point of (-1,6). b) Goes through the points (,-1) and (,-8). c) Goes through the points (,-1) and (8,-1). II. Parallel and Perpendicular A. Parallel B. Perpendicular C. Examples: Find an equation of a line that is parallel to x y = 7 and goes through the point (-,).. Find an equation of a line that is perpendicular to y = x + and goes through the point (,1). Precalculus Chapter 1 Page
6 III. Modeling Linear Functions A. The table below shows the approximate percent of students who sent applications to two colleges in various years since 198. Draw a scatter plot, best fit line, and find an equation that would predict the approximate percent of students who sent applications to two colleges in various years since 198. What percent of students sent applications in 199? What type of correlation does this data have? Years since Percent IV. Special Functions A. Direct Variation B. Constant Function C. Identity Function D. Absolute Value Function E. Piecewise Function F. Step Function (Greatest Integer Function) G. Examples Graph y = x +. Graph x 1, if x f ( x) = 1, if x > Homework: Worksheets. Graph y = x Precalculus Chapter 1 Page 6
7 Section Systems of Linear Equations and Inequalities Solving systems Graphically Types and and Examples x + y = x y = 0 y = x +. 9x + y = 1 Algebraically Elimination x + y = x y = x y = 17 x + y = Substitution y = x + 9x + y = 1. x + y = x y = 0 Technology x + y = x y = 0. y = x + 9x + y = 1 Precalculus Chapter 1 Page 7
8 Solving Systems Equations in Three Variables There are 9,000 seats in a sports stadium. Tickets for the seats in the upper level sell for $, the ones in the middle level cost $0, and the ones in the bottom level are $ each. The number of seats in the middle and bottom levels together equals the number of seats in the upper level. When all of the seats are sold for an event, the total revenue is $1,19,00. How many seats are there in each level? Inequalities x + y x y x + y 6. x y x + y y < x + 9x + y > Precalculus Chapter 1 Page 8
9 Linear Programming Graph the following constraints. Then find the maximum and minimum values of the function f ( x, y) = x y. x y x + y A landscaping company has crews who rake leaves and mulch. The company schedules hours for mulching jobs and hours for raking jobs. Each crew is scheduled for no more than raking jobs per day. Each crew s schedule is set up for a maximum of 8 hours per day. On the average, the charge for raking a lawn is $0 and the charge for mulching is $0. Find a combination of raking leaves and mulching that will maximize the income the company receives per day from one of its crews. 6 Profit Function: Constraints: a. b. c. d. 6 8 Homework Worksheet Precalculus Chapter 1 Page 9
Chapter 2 Linear Relations and Functions
Chapter Linear Relations and Functions I. Relations and Functions A. Definitions 1. Relation. Domain the variable ( ) 3. Range the variable ( ). Function a) A relationship between ( ) and ( ). b) The output
More informationExample #1: Write an Equation Given Slope and a Point Write an equation in slope-intercept form for the line that has a slope of through (5, - 2).
Algebra II: 2-4 Writing Linear Equations Date: Forms of Equations Consider the following graph. The line passes through and. Notice that is the y-intercept of. You can use these two points to find the
More informationBOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 051 Midterm Examination Review
BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 051 Midterm Examination Review Do ONLY 4 CHAPTERS. Your instructor will tell you which 4 chapters to complete. Everyone is required
More informationName Date College Prep Mid-Term Review
Name Date Chapter 4 College Prep Mid-Term Review Define the following terms, and provide an example: Domain: Range: Slope Intercept form: Point Slope Form: Standard Form of a linear equation: Function:
More informationName Class Date. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Travels in Air. Distance (miles) Time (seconds)
Practice - Rate of Change and Slope Find the slope of each line.... O O O Find the slope of the line that passes through each pair of points.. (, ), (7, 5) 5. (8, ), (, ). (, 5), (, 7) 7. (-, 7), (, -)
More informationMAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.
MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the
More informationAlgebra II. Note workbook. Chapter 2. Name
Algebra II Note workbook Chapter 2 Name Algebra II: 2-1 Relations and Functions The table shows the average lifetime and maximum lifetime for some animals. This data can be written as. The ordered pairs
More informationPractice Questions for Math 131 Exam # 1
Practice Questions for Math 131 Exam # 1 1) A company produces a product for which the variable cost per unit is $3.50 and fixed cost 1) is $20,000 per year. Next year, the company wants the total cost
More informationCollege Algebra Unit 1 Standard 2
Name: College Algebra Unit 1 Standard 2 Day Learning Target Assignment Identify parts of coordinate plane and find 1 slope. Worksheet #1 Write linear equations using point slope form. 2 Worksheet #2 Write
More informationCheckpoint 1 Simplifying Like Terms and Distributive Property
Checkpoint 1 Simplifying Like Terms and Distributive Property Simplify the following expressions completely. 1. 3 2 2. 3 ( 2) 3. 2 5 4. 7 3 2 3 2 5. 1 6 6. (8x 5) + (4x 6) 7. (6t + 1)(t 2) 8. (2k + 11)
More informationGUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE
GUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE LEARNING OBJECTIVES In this section, you will: Solve equations in one variable algebraically. Solve a rational equation. Find a linear equation. Given
More informationHow can you use linear functions of two independent variables to represent problem situations?
Problems that occur in business situations often require expressing income as a linear function of one variable like time worked or number of sales. For example, if an employee earns $7.25 per hour, then
More informationd. Predict the number of photos this photographer will keep if she takes 200 photos.
1 Solve. Regression Practice Curve Fitting with Linear Models 1. Vern created a website about his school s sports teams. He has a hit counter on his site that lets him know how many people have visited
More informationChapter 3: Systems of Linear Equations and Inequalities. Chapter 3.1: Solving Linear Systems by Graphing. System of Two Linear Equations: Solution:
Chapter 3: Systems of Linear Equations and Inequalities Chapter 3.1: Solving Linear Systems by Graphing System of Two Linear Equations: Solution: x 3y = 5 Example: Check whether the ordered pair on solution
More informationPRACTICE EXAM UNIT #6: SYSTEMS OF LINEAR INEQUALITIES
_ School: Date: /45 SCAN OR FAX TO: Ms. Stamm (Central Collegiate) stamm.shelly@prairiesouth.ca FAX: (306) 692-6965 PH: (306) 693-4691 PRACTICE EXAM UNIT #6: SYSTEMS OF LINEAR INEQUALITIES Multiple Choice
More informationDefine the word inequality
Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two
More informationMA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.
Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic
More informationCumulative Test 1. Evaluate the expression Answers [32 (17 12) 2 ] [(5 + 3)2 31]
Name Date Cumulative Test 1 Evaluate the expression. 1. 7 + 6 3. 4 5 18 3. 4[3 (17 1) ] 4. 3 [(5 + 3) 31] 5. 3(5m 4) when m = 6. 9x 4 when x = 3 Write an algebraic expression, an equation, or an inequality.
More informationLesson 28: Another Computational Method of Solving a Linear System
Lesson 28: Another Computational Method of Solving a Linear System Student Outcomes Students learn the elimination method for solving a system of linear equations. Students use properties of rational numbers
More informationAlgebra 2 Chapter 2 Page 1
Mileage (MPGs) Section. Relations and Functions. To graph a relation, state the domain and range, and determine if the relation is a function.. To find the values of a function for the given element of
More informationENDURING UNDERSTANDINGS:
Daily Learning Plan: Algebra I Part 2 Unit 6: Systems of Equations and Inequalities Day: Date: Topic: ENDURING UNDERSTANDINGS: 1. Recognizing and analyzing simultaneous relationships between two variables
More informationMourning Sr. High. Algebra II Summer Assignment. 3. If you need help, there are links provided on each page with extra help resources.
Mourning Sr. High Algebra II Summer Assignment Pre AP Algebra students and Honors Algebra students must complete the entire assignment. Regular Algebra students complete the following: Fractions # s 3
More informationEquations With Two or More Variables
! Equations With Two or More Variables You have done a lot of work with relationships involving two related variables. However, many real-world relationships involve three or more variables. For example,
More informationALGEBRA 2 HONORS MIDTERM EXAM
Name: ALGEBRA 2 HONORS MIDTERM EXAM 2011-2012 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Evaluate the given expression if w = 41, x = 5, y = 15, and
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
ALGEBRA 1 Standard 1 Operations with Real Numbers Students simplify and compare expressions. They use rational exponents, and simplify square roots. A1.1.1 A1.1.2 A1.1.3 A1.1.4 A1.1.5 Compare real number
More informationMath 3 Variable Manipulation Part 7 Absolute Value & Inequalities
Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,
More informationSECTION 5.1: Polynomials
1 SECTION 5.1: Polynomials Functions Definitions: Function, Independent Variable, Dependent Variable, Domain, and Range A function is a rule that assigns to each input value x exactly output value y =
More informationChapter 1-2 Add and Subtract Integers
Chapter 1-2 Add and Subtract Integers Absolute Value of a number is its distance from zero on the number line. 5 = 5 and 5 = 5 Adding Numbers with the Same Sign: Add the absolute values and use the sign
More informationBig Idea(s) Essential Question(s)
Middletown Public Schools Mathematics Unit Planning Organizer Subject Math Grade/Course Algebra I Unit 4 Linear Functions Duration 20 instructional days + 4 days reteaching/enrichment Big Idea(s) Essential
More informationChapter Four: Linear Expressions, Equations, and Inequalities
Chapter Four: Linear Expressions, Equations, and Inequalities Index: A: Intro to Inequalities (U2L8) B: Solving Linear Inequalities (U2L9) C: Compound Inequalities (And) (U2L10/11) D: Compound Inequalities
More information1.) Suppose the graph of f(x) looks like this (each tick mark denotes 1 unit). x y
College Algebra Summer 2014 Exam File Exam #1 1.) Suppose the graph of f(x) looks like this (each tick mark denotes 1 unit). Graph g(x) = -0.5 f(x + 1) - 3 2.) Consider the following table of values. x
More informationAlgebra 2 Summer Work Packet
Algebra Summer Work Packet Covering Prerequisite Concepts for Incoming Algebra 1 Students This workbook contains problems designed to ensure the student's readiness for Algebra. The nine topics covered
More informationAlgebra 2 Summer Review Packet
Algebra Summer Review Packet Welcome to Algebra! Attached you will find the learning targets your teacher thinks you should know BEFORE you come to class in the fall and problems to help you practice these
More informationTopics Covered in Math 115
Topics Covered in Math 115 Basic Concepts Integer Exponents Use bases and exponents. Evaluate exponential expressions. Apply the product, quotient, and power rules. Polynomial Expressions Perform addition
More informationUNIT 5: Systems of Equations
Algebra 2 Trig UNIT 5: Systems of Equations Name: Teacher: Pd: 1 Table of Contents Day 1: Review Solving Linear Systems SWBAT: Solve linear systems algebraically and graphically. Homework: Page 7 Day 2:
More informationChetek-Weyerhaeuser High School
Chetek-Weyerhaeuser High School Unit 1 Variables and Expressions Math RtI Units and s Math RtI A s 1. I can use mathematical properties to evaluate expressions. I can use mathematical properties to evaluate
More informationElementary Algebra SAMPLE Final Examination Fall 2017
Elementary Algebra NAME: SAMPLE Final Examination Fall 2017 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full
More informationAdvAlg5.3SolvingSystemsBySubstitution.notebook February 26, 2018
Oct 14 4:53 PM 1 Why do we need algebraic techniques to solve systems? To find exact solutions The substitution method for solving systems of equations uses what property of equality? Substitution property
More informationFLC Ch 1-3 (except 1.4, 3.1, 3.2) Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry
Math 370 Precalculus [Note to Student: Read/Review Sec 1.1: The Distance and Midpoint Formulas] Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry Defns A graph is said to be symmetric
More informationUnit 12: Systems of Equations
Section 12.1: Systems of Linear Equations Section 12.2: The Substitution Method Section 12.3: The Addition (Elimination) Method Section 12.4: Applications KEY TERMS AND CONCEPTS Look for the following
More information2) (9, 1), (3, 9) 2) A) C) 5 6. Use the vertical line test to determine whether the graph is the graph of a function. 4) 4)
Test 2 Name (please print) Find the slope of the line that goes through the given points. 1) (-4, 2), (-3, 2) 1) A) 4 B) - 4 7 C) 0 D) undefined 2) (9, 1), (3, 9) 2) A) - 4 3 B) 4 3 C) 5 6 D) - 3 4 Determine
More informationTopic: Solving systems of equations with linear and quadratic inequalities
Subject & Grade: Mathematics, 9 th Grade Topic: Solving systems of equations with linear and quadratic inequalities Aim: How would you find the solution set of a linear and quadratic inequality? Materials:.
More informationSection 7.1 Objective 1: Solve Quadratic Equations Using the Square Root Property Video Length 12:12
Section 7.1 Video Guide Solving Quadratic Equations by Completing the Square Objectives: 1. Solve Quadratic Equations Using the Square Root Property. Complete the Square in One Variable 3. Solve Quadratic
More informationA) (-1, -1, -2) B) No solution C) Infinite solutions D) (1, 1, 2) A) (6, 5, -3) B) No solution C) Infinite solutions D) (1, -3, -7)
Algebra st Semester Final Exam Review Multiple Choice. Write an equation that models the data displayed in the Interest-Free Loan graph that is provided. y = x + 80 y = -0x + 800 C) y = 0x 00 y = 0x +
More informationAbsolute Value Functions
Absolute Value Functions Absolute Value Functions The Absolute Value Function is a piecewise-defined function made up of two linear functions. In its basic form f ( x) x it is one of our toolkit functions.
More informationPage Points Score Total: 100
Math 1130 Spring 2019 Sample Exam 1c 1/31/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 8 pages (including this cover page) and 7 problems. Check to see if any pages
More informationANSWER KEY. Checklist Do I understand? Test Date: A-Day 2/7. Algebra 1 Benchmark Review study guide is due on test day!
ANSWER KEY Name: Algebra 1 Benchmark Review study guide is due on test day! Test Date: A-Day 2/7 Checklist Do I understand? Unit 1 Solving Equations and Inequalities Two Step Equations Properties of Real
More informationWarm Up. Unit #1: Basics of Algebra
1) Write an equation of the given points ( 3, 4) & (5, 6) Warm Up 2) Which of the following choices is the Associative Property 1) 4(x + 2) = 4x + 8 2) 4 + 5 = 5 + 4 3) 5 + ( 5) = 0 4) 4 + (3 + 1) = (4
More informationMFM2P Foundations of Mathematics Unit 3 Lesson 11
The Line Lesson MFMP Foundations of Mathematics Unit Lesson Lesson Eleven Concepts Introduction to the line Using standard form of an equation Using y-intercept form of an equation x and y intercept Recognizing
More informationFoundations of Math. Chapter 3 Packet. Table of Contents
Foundations of Math Chapter 3 Packet Name: Table of Contents Notes #43 Solving Systems by Graphing Pg. 1-4 Notes #44 Solving Systems by Substitution Pg. 5-6 Notes #45 Solving by Graphing & Substitution
More informationAn equation is a statement that states that two expressions are equal. For example:
Section 0.1: Linear Equations Solving linear equation in one variable: An equation is a statement that states that two expressions are equal. For example: (1) 513 (2) 16 (3) 4252 (4) 64153 To solve the
More informationAlgebra I. Course Outline
Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative
More informationChapter 6 Outline Systems of Linear Inequalities
SOLVES AN INEQUALITY Chapter 6 Outline Systems of Linear Inequalities FORGETS TO FLIP THE SYMBOL Date Topic Homework Lesson 1: Exploring Linear Inequalities Homework Completion Complete In Progress Not
More informationHomework 1. 3x 12, 61.P (x) = 3t 21 Section 1.2
Section 1.1 Homework 1 (34, 36) Determine whether the equation defines y as a function of x. 34. x + h 2 = 1, 36. y = 3x 1 x + 2. (40, 44) Find the following for each function: (a) f(0) (b) f(1) (c) f(
More informationCarbon Career & Technical Institute
Course: Algebra I Carbon Career & Technical Institute A1.1.1.3.1 - Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Aug. and Sept.
More informationAlgebra 2 Practice Midterm
Name: Algebra 2 Practice Midterm Circle the letter for the correct answer. 1. A study comparing patients who received a new medicine with those who did not is. A. an observational study C. an experiment
More informationNAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve = 6 3v = -3(c + 5)
FINAL EXAM REVIEW, p. 1 NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve. 1. = 6 v. 1 = -(c + 5). 5 (x ) = 6. 7x + = 5x + 8 5. r 1 1 6. x 1 x 5 Write an equation, and then solve. 7. Ben joined The
More informationStudy Guide and Intervention
- Slope Stud Guide and Intervention Slope change in Slope m of a Line For points (, ) and (, ), where, m change in Eample Eample Determine the slope of the line that passes through (, ) and (, ). m Slope
More informationUnit 9: Quadratics Intercept Form
For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic
More informationChapter Two B: Linear Expressions, Equations, and Inequalities
Chapter Two B: Linear Expressions, Equations, and Inequalities Index: A: Intro to Inequalities (U2L8) Page 1 B: Solving Linear Inequalities (U2L9) Page 7 C: Compound Inequalities (And) (U2L10/11) Page
More information5-7 Solving Quadratic Inequalities. Holt Algebra 2
Example 1: Graphing Quadratic Inequalities in Two Variables Graph f(x) x 2 7x + 10. Step 1 Graph the parabola f(x) = x 2 7x + 10 with a solid curve. x f(x) 0 10 1 3 2 0 3-2 3.5-2.25 4-2 5 0 6 4 7 10 Example
More informationMath 1101 Chapter 2 Review Solve the equation. 1) (y - 7) - (y + 2) = 4y A) B) D) C) ) 2 5 x x = 5
Math 1101 Chapter 2 Review Solve the equation. 1) (y - 7) - (y + 2) = 4y A) - 1 2 B) - 9 C) - 9 7 D) - 9 4 2) 2 x - 1 3 x = A) -10 B) 7 C) -7 D) 10 Find the zero of f(x). 3) f(x) = 6x + 12 A) -12 B) -2
More information5. Determine the discriminant for each and describe the nature of the roots.
4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following
More informationAlgebra. Chapter 6: Systems of Equations and Inequalities. Name: Teacher: Pd:
Algebra Chapter 6: Systems of Equations and Inequalities Name: Teacher: Pd: Table of Contents Chapter 6-1: SWBAT: Identify solutions of systems of linear equations in two variables; Solve systems of linear
More informationChapter 3: Inequalities, Lines and Circles, Introduction to Functions
QUIZ AND TEST INFORMATION: The material in this chapter is on Quiz 3 and Exam 2. You should complete at least one attempt of Quiz 3 before taking Exam 2. This material is also on the final exam and used
More informationGraphical Solutions of Linear Systems
Graphical Solutions of Linear Systems Consistent System (At least one solution) Inconsistent System (No Solution) Independent (One solution) Dependent (Infinite many solutions) Parallel Lines Equations
More informationAlgebra 1. Unit 3: Quadratic Functions. Romeo High School
Algebra 1 Unit 3: Quadratic Functions Romeo High School Contributors: Jennifer Boggio Jennifer Burnham Jim Cali Danielle Hart Robert Leitzel Kelly McNamara Mary Tarnowski Josh Tebeau RHS Mathematics Department
More informationSeymour Public Schools Curriculum
Algebra II continues the study of functions. Students learn operations with functions and graphing of different types of functions. Students solve equations and perform operations with exponents, matrices
More information1 y = Recitation Worksheet 1A. 1. Simplify the following: b. ( ) a. ( x ) Solve for y : 3. Plot these points in the xy plane:
Math 13 Recitation Worksheet 1A 1 Simplify the following: a ( ) 7 b ( ) 3 4 9 3 5 3 c 15 3 d 3 15 Solve for y : 8 y y 5= 6 3 3 Plot these points in the y plane: A ( 0,0 ) B ( 5,0 ) C ( 0, 4) D ( 3,5) 4
More informationAlgebra 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 informationElementary Algebra SAMPLE Final Examination Spring 2015
Elementary Algebra NAME: SAMPLE Final Examination Spring 2015 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full
More information6.3 Standard Form. Comparing Forms of Linear Equations. Explore. The slope is. Circle true or false. You can read the slope from the equation.
Name Class Date 6.3 Standard Form Essential Question: How can you write a linear equation in standard form given properties of the line including its slope and points on the line? Resource Locker Explore
More informationSection 3 Topic 1 Input and Output Values
Section 3: Introduction to Functions Section 3 Topic 1 Input and Output Values A function is a relationship between input and output. Ø Ø Domain is the set of values of x used for the input of the function.
More informationAlgebra 1 CP Semester Exam Review
Name: Hr: Algebra CP Semester Eam Review GET ORGANIZED. Successful studing begins with being organized. Bring this packet with ou to class ever da. DO NOT FALL BEHIND. Do the problems that are assigned
More informationUnit 7: It s in the System
Unit 7: It s in the System Investigation 1: Linear Equations with Two Variables I can convert between standard and slope intercept forms, and graph systems of equations. Solving equations is one of the
More informationPacing Guide Algebra 1
Pacing Guide Algebra Chapter : Equations and Inequalities (one variable) Section Section Title Learning Target(s) I can. Evaluate and Simplify Algebraic Expressions. Evaluate and simplify numeric and algebraic
More informationNON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer x y
NON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer. 1. 2. 3. x -1 0 1 2 3 y 5 7 2-1 -8 4 & 5. Refer to the numbered graphs 4 5 6. x -3 2
More informationInequalities Chapter Test
Inequalities Chapter Test Part 1: For questions 1-9, circle the answer that best answers the question. 1. Which graph best represents the solution of 8 4x < 4 A. B. C. D. 2. Which of the following inequalities
More informationAlgebra Summer Review Packet
Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills
More informationMAFS Algebra 1. Systems of Equations and Inequalities. Day 10 - Student Packet
MAFS Algebra 1 Systems of Equations and Inequalities Day 10 - Student Packet Day 10: Systems of Equations and Inequalities MAFS.912.A-REI.3.5, MAFS.912.A-REI.3.6, MAFS.912.A-REI.4.10 I CAN graph a system
More informationAlgebra 1 Unit 2 Benchmark Exam
Name: Block: Date: Algebra 1 Unit 2 Benchmark Exam Scoring For Teacher Use Only 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Total / 11/27/2013 NJ DOE Unit 2_Algebra 1 Page 1 1. Solve the
More informationOcean Township High School Mathematics Department
Algebra Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from Algebra 1 that you must be comfortable doing before you can be successful in
More information(b) Equation for a parabola: c) Direction of Opening (1) If a is positive, it opens (2) If a is negative, it opens
Section.1 Graphing Quadratics Objectives: 1. Graph Quadratic Functions. Find the ais of symmetry and coordinates of the verte of a parabola.. Model data using a quadratic function. y = 5 I. Think and Discuss
More information[DOC] GRAPHING LINEAR EQUATIONS WORKSHEET ANSWERS EBOOK
05 March, 2018 [DOC] GRAPHING LINEAR EQUATIONS WORKSHEET ANSWERS EBOOK Document Filetype: PDF 335.63 KB 0 [DOC] GRAPHING LINEAR EQUATIONS WORKSHEET ANSWERS EBOOK These function tables give students practice
More informationMath 2 Variable Manipulation Part 7 Absolute Value & Inequalities
Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,
More informationRational Numbers. Integers. Irrational Numbers
EOC Review: Pre-Algebra Unit Rational Numbers Integers Irrational Numbers Ex: Matrices: Ex 1: Ex 2: Ex 3: Unit 1 Equations Equations To solve an equation, use your calculator. STEPS: 1. Menu 2. Algebra
More informationGetting to the Roots of Quadratics
NAME BACKGROUND Graphically: The real roots of a function are the x-coordinates of the points at which the graph of the function intercepts/crosses the x-axis. For a quadratic function, whose graph is
More informationSections 8.1 & 8.2 Systems of Linear Equations in Two Variables
Sections 8.1 & 8.2 Systems of Linear Equations in Two Variables Department of Mathematics Porterville College September 7, 2014 Systems of Linear Equations in Two Variables Learning Objectives: Solve Systems
More informationCartesian Plane. Analytic Geometry. Unit Name
3.1cartesian Unit Name Analytic Geometry Unit Goals 1. Create table of values in order to graph &/or determine if a relation is linear. Determine slope 3. Calculate missing information for linearelationships.
More information6.3 Standard Form. Comparing Forms of Linear Equations. Explore. Circle true or false. The slope is. You can read the slope from the equation.
Name Class Date 6. Standard Form Essential Question: How can you write a linear equation in standard form given properties of the line including its slope and points on the line? Resource Locker Explore
More informationAdlai E. Stevenson High School Course Description
Adlai E. Stevenson High School Course Description Division: Course Number: Course Title: Special Education/Mathematics MTH0N1/MTH0N2 Instructional Algebra Enriched Course Description: Algebra Enriched
More informationAlgebra I Keystone Quiz Linear Inequalities - (A ) Systems Of Inequalities, (A ) Interpret Solutions To Inequality Systems
Algebra I Keystone Quiz Linear Inequalities - (A1.1.3.2.1) Systems Of Inequalities, (A1.1.3.2.2) Interpret Solutions To Inequality Systems 1) Student Name: Teacher Name: Jared George Date: Score: The linear
More informationAlgebra I Block Curriculum Map Key : Glencoe Algebra I; Glencoe Study Guide (SG) Glencoe Handbook (HB) Aleks (A)
Time frame Unit/Concepts PA Eligible Content Standard Assessments Resources Support Materials Period 1 Preparing for Algebra: Problem solving Number systems and operations A1.1.1.4.1 Use estimation to
More information7.1 Solving Systems of Equations
Date: Precalculus Notes: Unit 7 Systems of Equations and Matrices 7.1 Solving Systems of Equations Syllabus Objectives: 8.1 The student will solve a given system of equations or system of inequalities.
More informationAlgebra I Learning Targets Chapter 1: Equations and Inequalities (one variable) Section Section Title Learning Target(s)
Chapter 1: Equations and Inequalities (one variable) Section Learning Target(s) I can 1.2 Evaluate and Simplify Algebraic Expressions 1. Evaluate and simplify numeric and algebraic expressions (order of
More informationMATH 126 TEST 1 SAMPLE
NAME: / 60 = % MATH 16 TEST 1 SAMPLE NOTE: The actual exam will only have 13 questions. The different parts of each question (part A, B, etc.) are variations. Know how to do all the variations on this
More informationMATH 8. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability
MATH 8 Unit 1: Rational and Irrational Numbers (Term 1) 1. I CAN write an algebraic expression for a given phrase. 2. I CAN define a variable and write an equation given a relationship. 3. I CAN use order
More informationPennsylvania Algebra I Assessment Anchors and Eligible Content
A Correlation of Algebra 1, 2018 To the Assessment Anchors and Eligible Content Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved to the MODULE 1 Operations and Linear Equations
More informationLesson 10: Comparing Functions and their features
Lesson 10: Comparing Functions and their features Standards: MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of
More informationNote: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice.
College Algebra - Unit 2 Exam - Practice Test Note: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice. MULTIPLE CHOICE.
More information