Direct Variation. COMPUTERS Use the graph at the right that shows the output of a color printer.
|
|
- Joshua Lucas
- 7 years ago
- Views:
Transcription
1 9-5 Direct Variation MAIN IDEA Use direct variation to solve problems. New Vocabular direct variation constant of variation Math nline glencoe.com Etra Eamples Personal Tutor Self-Check Quiz CMPUTERS Use the graph at the right that shows the output of a color printer.. What is the constant rate of change, or slope, of the line?. Is the total number of pages printed alwas proportional to the printing time? If so, what is the constant ratio? 3. Compare the constant rate of change to the constant ratio. Pages 8 8 Time (minutes) In the eample above, the number of minutes and the number of pages printed both var, while the ratio of pages printed to minutes,.5 pages per minute, remains constant. When the ratio of two variable quantities is constant, their relationship is called a direct variation. The constant ratio is called the constant of variation. Find a Constant Ratio FUNDRAISER The amount of mone Robin has raised for a bike-a-thon is shown in the graph at the right. Determine the amount that Robin raises for each mile she rides. Since the graph of the data forms a line, the rate of change is constant. Use the graph to find the constant ratio. Amount Raised ($) 3 8 Distance (miles) amount raised distance _ _ Robin raises $7.5 for each mile she rides. _ _ a. SKYDIVING Two minutes after a skdiver opens his parachute, he has descended,9 feet. After 5 minutes, he has descended,75 feet. If the distance varies directl as the time, at what rate is the skdiver descending? Lesson 9-5 Direct Variation 87
2 In a direct variation equation, the constant rate of change, or slope, is assigned a special variable, k. Direct Variation Ke Concept Words Smbols Eample A direct variation is a relationship in which the ratio of to is a constant, k. We sa varies directl with. k = _ or = k, where k = 3 Model = 3 Solve a Direct Variation Real-World Link Most pets age at a different rate than their human companions. For eample, a 3-earold dog is often considered to be in human ears. PETS Refer to the information at the left. Assume that the age of a dog varies directl as its equivalent age in human ears. What is the human-ear age of a dog that is ears old? Write an equation of direct variation. Let represent the dog s actual age and let represent the human-equivalent age. = k Direct variation = k(3) =, = 3 7 = k Simplif. = 7 Substitute for k = 7. Use the equation to find when =. = 7 = 7() = = Multipl. Proportions In Eample, ou can also use a proportion to solve direct variation problems. Write ratios comparing the human equivalent age to the actual age. 3 = = 3 = A dog that is ears old is ears old in human-equivalent ears. b. SHPPING A grocer store sells oranges for $. How much would it cost to bu oranges? Round to the nearest cent if necessar. In a direct variation, the constant of variation k is a constant rate of change. When the -value changes b an amount a, then the -value will change b the corresponding amount ka. In the previous eample, when changed b a factor of, changed b 7() or. 88 Chapter 9 Algebra: Linear Functions
3 Look Back To review proportional relationships, see Lessons - and -5. Not all relationships with a constant rate of change are proportional. Likewise, not all linear functions are direct variations. Identif Direct Variation Determine whether each linear function is a direct variation. If so, state the constant of variation. 3 Miles, Gallons, 3 gallons _ miles _ 5 _ 5 5 Compare the ratios to check for a common ratio. 3_ 75 5 _ 5 Since the ratios are the same, the function is a direct variation. The constant of variation is _ 5. Hours, 8 Earnings, earnings _ hours 3_ or _ 8.33 _ The ratios are not the same, so the function is not a direct variation. c. Das, 5 5 Height, d. Time, 8 Distance, Proportional Linear Function Concept Summar Direct Variations Notice that the graph of a direct variation, which is a proportional linear relationship, is a line that passes through the origin. Table Graph Equation _ = Nonproportional Linear Function Table Graph Equation - - = _ 5_ 3 3_ Lesson 9-5 Direct Variation 89
4 Eample (p. 87) Eample (p. 88). MANUFACTURING The number of computers built varies directl as the number of hours the production line operates. What is the ratio of computers built to hours of production?. TRANSPRTATIN A charter bus travels miles in 3 _ hours. Assuming that the distance traveled is directl proportional to the time traveled, how far will the bus travel in hours? Computers Hours Eamples 3, (p. 89) 3. Determine whether the linear function Hours, 3 5 is a direct variation. If so, state the Miles, constant of variation. For Eercises See Eamples 5 5 3, HELP HMEWRK HELP. GARDENING Janelle planted ornamental grass seeds. After the grass breaks the soil surface, its height varies directl with the number of das. What is the rate of growth? Height (in.) 3 5. JBS The amount Dust earns is directl proportional to the number of newspapers he delivers. How much does Dust earn for each newspaper deliver? Earnings ($) Das 8 Newspapers. SUBMARINES Ten minutes after a submarine is launched from a research ship, it is 5 meters below the surface. After 3 minutes, the submarine has descended 75 meters. At what rate is the submarine diving? 7. MVIES The Stratton famil rented 3 DVDs for $.7. The net weekend, the rented 5 DVDs for $7.5. What is the rental fee for a DVD? 8. MEASUREMENT Morgan used 3 gallons of paint to cover,5 square feet and 5 gallons to paint an additional,75 square feet. How man gallons of paint would she need to cover,8 square feet? 9. MEASUREMENT The weight of an object on Mars varies directl with its weight on Earth. An object that weighs 7 pounds on Mars weighs pounds on Earth. If an object weighs pounds on Earth, how much would it weigh on Mars? 9 Chapter 9 Algebra: Linear Functions
5 . ELECTRNICS The height of a wide-screen television screen is directl proportional to its width. A manufacturer makes a television screen that is centimeters wide and centimeters high. Find the height of a television screen that is 9 centimeters wide. Real-World Link The aspect ratio of a television screen describes the ratio of the width of the screen to the height. Standard screens have an aspect ratio of :3 while wide-screen televisions have an aspect ratio of :9.. BAKING A cake recipe requires _ 3 cups of flour for servings. How much flour is required to make a cake that serves 3? Determine whether each linear function is a direct variation. If so, state the constant of variation... Pictures, Profit, 8 3 Age, 3 Grade, Minutes, 8 Cost, Price, 5 5 Ta, ALGEBRA If varies directl with, write an equation for the direct variation. Then find each value.. If = - when = 9, find when = Find when = if = 8 when =. 8. If = - when = -, what is the value of when = -? 9. Find when = 5, if = 7 when = 8.. Find when = 5, if =. when =.. MEASUREMENT The number of centimeters in a measure varies directl as the number of inches. Find the measure of an object in centimeters if it is 5 inches long. Inches, 9 5 Centimeters, PRACTICE EXTRA PRACTICE See pages 9, 78.. MEASUREMENT The length of the rectangle shown varies directl as its width. What is the perimeter of a rectangle that is meters long? w =. m l = m H..T. Problems 3. PEN ENDED Identif values for and in a direct variation relationship where = 9 when =.. CHALLENGE The amount of stain needed to cover a wood surface is directl proportional to the area of the surface. If 3 pints are required to cover a square deck with a side of 7 feet, how man pints of stain are needed to paint a square deck with a side of feet inches? WRITING IN 5. MATH Write a direct variation equation. Then triple the -value and eplain how to find the corresponding change in the -value. Lesson 9-5 Direct Variation 9
6 . Students in a science class recorded lengths of a stretched spring, as shown in the table below. Length of Stretched Spring Distance Stretched, (centimeters) Mass, (grams) Which equation best represents the relationship between the distance stretched and the mass of an object on the spring? A =- B = C =- _ D = _ 7. SHRT RESPNSE Nicole read pages during a 3-minute independent reading period. How man pages would she read in 5 minutes? 8. To make fruit punch, Kelli must add 8 ounces of pineapple juice for ever ounces of orange juice. If she uses 3 ounces of orange juice, which proportion can she use to find, the number of ounces of pineapple juice she should add to make the punch? F 8_ = _ 3 H 8_ = _ 3 G _ 8 = _ 3 J _ = _ 8 3 Find the slope of each line. (Lesson 9-) JBS The function p = 7.5h describes the relationship between the number of hours h Callie works and the amount she is paid p. Graph the function. Then use our graph to determine how much Callie can epect to earn if she works hours. (Lesson 9-3) 33. HEALTH Man health authorities recommend that a health diet contains no more than 3% of its Calories from fat. If Jennie consumes,5 Calories each da, what is the maimum number of Calories she should consume from fat? (Lesson 5-3) PREREQUISITE SKILL Solve each equation. (Lesson -9) a = = d = n t - = -3 9 Chapter 9 Algebra: Linear Functions
Solving Special Systems of Linear Equations
5. Solving Special Sstems of Linear Equations Essential Question Can a sstem of linear equations have no solution or infinitel man solutions? Using a Table to Solve a Sstem Work with a partner. You invest
More informationDirect Variation. 1. Write an equation for a direct variation relationship 2. Graph the equation of a direct variation relationship
6.5 Direct Variation 6.5 OBJECTIVES 1. Write an equation for a direct variation relationship 2. Graph the equation of a direct variation relationship Pedro makes $25 an hour as an electrician. If he works
More informationMATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60
MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets
More informationMAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 18 units.
1-9 Algebra: Area Formulas MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 1. Find the areas of rectangles and squares. New Vocabulary
More informationNAME DATE PERIOD. 11. Is the relation (year, percent of women) a function? Explain. Yes; each year is
- NAME DATE PERID Functions Determine whether each relation is a function. Eplain.. {(, ), (0, 9), (, 0), (7, 0)} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (, )}. No; in the
More informationThe Slope-Intercept Form
7.1 The Slope-Intercept Form 7.1 OBJECTIVES 1. Find the slope and intercept from the equation of a line. Given the slope and intercept, write the equation of a line. Use the slope and intercept to graph
More informationName Class Date. Additional Vocabulary Support
- Additional Vocabular Support Rate of Change and Slope Concept List negative slope positive slope rate of change rise run slope slope formula slope of horizontal line slope of vertical line Choose the
More informationMATH 185 CHAPTER 2 REVIEW
NAME MATH 18 CHAPTER REVIEW Use the slope and -intercept to graph the linear function. 1. F() = 4 - - Objective: (.1) Graph a Linear Function Determine whether the given function is linear or nonlinear..
More information5 LESSON 5.1. Writing Linear Equations. Writing Linear Equations from Situations and Graphs ESSENTIAL QUESTION
Writing Linear Equations? MDULE 5 LESSN 5.1 ESSENTIAL QUESTIN Writing Linear Equations from Situations and Graphs How can ou use linear equations to solve real-world problems? 8.F.4 LESSN 5.2 Writing Linear
More informationLesson 18 Pythagorean Triples & Special Right Triangles
Student Name: Date: Contact Person Name: Phone Number: Teas Assessment of Knowledge and Skills Eit Level Math Review Lesson 18 Pythagorean Triples & Special Right Triangles TAKS Objective 6 Demonstrate
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabular Define each term in our own words.. function A function is a relation that maps each value of
More informationWhy should we learn this? One real-world connection is to find the rate of change in an airplane s altitude. The Slope of a Line VOCABULARY
Wh should we learn this? The Slope of a Line Objectives: To find slope of a line given two points, and to graph a line using the slope and the -intercept. One real-world connection is to find the rate
More informationSolving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form
SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving
More informationMeasurement/Volume and Surface Area Long-Term Memory Review Grade 7, Standard 3.0 Review 1
Review 1 1. Explain how to convert from a larger unit of measurement to a smaller unit of measurement. Include what operation(s) would be used to make the conversion. 2. What basic metric unit would be
More informationAssessment For The California Mathematics Standards Grade 3
Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,
More informationALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The
More informationAmerican Diploma Project
Student Name: American Diploma Project ALGEBRA l End-of-Course Eam PRACTICE TEST General Directions Today you will be taking an ADP Algebra I End-of-Course Practice Test. To complete this test, you will
More informationRELEASED. North Carolina READY End-of-Grade Assessment Mathematics. Grade 8. Student Booklet
REVISED 7/4/205 Released Form North Carolina READY End-of-Grade Assessment Mathematics Grade 8 Student Booklet Academic Services and Instructional Support Division of Accountabilit Services Copright 203
More information7 Literal Equations and
CHAPTER 7 Literal Equations and Inequalities Chapter Outline 7.1 LITERAL EQUATIONS 7.2 INEQUALITIES 7.3 INEQUALITIES USING MULTIPLICATION AND DIVISION 7.4 MULTI-STEP INEQUALITIES 113 7.1. Literal Equations
More informationINVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4. Example 1
Chapter 1 INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4 This opening section introduces the students to man of the big ideas of Algebra 2, as well as different was of thinking and various problem solving strategies.
More informationGraphing Linear Equations
6.3 Graphing Linear Equations 6.3 OBJECTIVES 1. Graph a linear equation b plotting points 2. Graph a linear equation b the intercept method 3. Graph a linear equation b solving the equation for We are
More informationAlgebra II Notes Piecewise Functions Unit 1.5. Piecewise linear functions. Math Background
Piecewise linear functions Math Background Previousl, ou Related a table of values to its graph. Graphed linear functions given a table or an equation. In this unit ou will Determine when a situation requiring
More informationFCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby
More informationAlgebra EOC Practice Test #4
Class: Date: Algebra EOC Practice Test #4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. For f(x) = 3x + 4, find f(2) and find x such that f(x) = 17.
More informationFlorida Algebra I EOC Online Practice Test
Florida Algebra I EOC Online Practice Test Directions: This practice test contains 65 multiple-choice questions. Choose the best answer for each question. Detailed answer eplanations appear at the end
More informationFor 14 15, use the coordinate plane shown. represents 1 kilometer. 10. Write the ordered pairs that represent the location of Sam and the theater.
Name Class Date 12.1 Independent Practice CMMN CRE 6.NS.6, 6.NS.6b, 6.NS.6c, 6.NS.8 m.hrw.com Personal Math Trainer nline Assessment and Intervention For 10 13, use the coordinate plane shown. Each unit
More informationSummer Math Exercises. For students who are entering. Pre-Calculus
Summer Math Eercises For students who are entering Pre-Calculus 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 informationMath Questions & Answers
What five coins add up to a nickel? five pennies (1 + 1 + 1 + 1 + 1 = 5) Which is longest: a foot, a yard or an inch? a yard (3 feet = 1 yard; 12 inches = 1 foot) What do you call the answer to a multiplication
More informationSystems of Linear Equations: Solving by Substitution
8.3 Sstems of Linear Equations: Solving b Substitution 8.3 OBJECTIVES 1. Solve sstems using the substitution method 2. Solve applications of sstems of equations In Sections 8.1 and 8.2, we looked at graphing
More informationNorth Carolina Community College System Diagnostic and Placement Test Sample Questions
North Carolina Communit College Sstem Diagnostic and Placement Test Sample Questions 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationALGEBRA 1 SKILL BUILDERS
ALGEBRA 1 SKILL BUILDERS (Etra Practice) Introduction to Students and Their Teachers Learning is an individual endeavor. Some ideas come easil; others take time--sometimes lots of time- -to grasp. In addition,
More informationFINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) -
More informationALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The
More information6. The given function is only drawn for x > 0. Complete the function for x < 0 with the following conditions:
Precalculus Worksheet 1. Da 1 1. The relation described b the set of points {(-, 5 ),( 0, 5 ),(,8 ),(, 9) } is NOT a function. Eplain wh. For questions - 4, use the graph at the right.. Eplain wh the graph
More informationFSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers
FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward
More information10-3 Area of Parallelograms
0-3 Area of Parallelograms MAIN IDEA Find the areas of parallelograms. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest,
More informationTo Multiply Decimals
4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 24, 2012 9:15 a.m. to 12:15 p.m.
INTEGRATED ALGEBRA The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesda, Januar 4, 01 9:15 a.m. to 1:15 p.m., onl Student Name: School Name: Print our name and
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationRatios (pages 288 291)
A Ratios (pages 2 29) A ratio is a comparison of two numbers by division. Ratio Arithmetic: to : Algebra: a to b a:b a b When you write a ratio as a fraction, write it in simplest form. Two ratios that
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 27, 2015 1:15 to 4:15 p.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesday, January 27, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More informationChapter 6 Quadratic Functions
Chapter 6 Quadratic Functions Determine the characteristics of quadratic functions Sketch Quadratics Solve problems modelled b Quadratics 6.1Quadratic Functions A quadratic function is of the form where
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Wednesday, June 12, 2013 1:15 to 4:15 p.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, June 12, 2013 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More informationALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only Student Name: School Name: The
More informationWe start with the basic operations on polynomials, that is adding, subtracting, and multiplying.
R. Polnomials In this section we want to review all that we know about polnomials. We start with the basic operations on polnomials, that is adding, subtracting, and multipling. Recall, to add subtract
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationQuadratic Equations and Functions
Quadratic Equations and Functions. Square Root Propert and Completing the Square. Quadratic Formula. Equations in Quadratic Form. Graphs of Quadratic Functions. Verte of a Parabola and Applications In
More informationFractional Part of a Set
Addition and Subtraction Basic Facts... Subtraction Basic Facts... Order in Addition...7 Adding Three Numbers...8 Inverses: Addition and Subtraction... Problem Solving: Two-Step Problems... 0 Multiplication
More informationGrade 6 FCAT 2.0 Mathematics Sample Questions
Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become
More informationMath 1 Chapter 3 notes.notebook. October 22, 2012. Examples
Chapter 3 SOLVING LINEAR EQUATIONS!! Lesson 3 1 Solve one step equations Key Vocab: Inverse operations: are two operations that undo each other. Addition and subtraction Multiplication and division equivalent
More informationSECTION 2-2 Straight Lines
- Straight Lines 11 94. Engineering. The cross section of a rivet has a top that is an arc of a circle (see the figure). If the ends of the arc are 1 millimeters apart and the top is 4 millimeters above
More informationChapter 3 & 8.1-8.3. Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3x - 4y = 10 16x + 8y = 10
Chapter 3 & 8.1-8.3 These are meant for practice. The actual test is different. Determine whether the pair of equations represents parallel lines. 1) 9 + 3 = 12 27 + 9 = 39 1) Determine whether the pair
More informationTallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
More informationMEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:
MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding
More informationTHE POWER RULES. Raising an Exponential Expression to a Power
8 (5-) Chapter 5 Eponents and Polnomials 5. THE POWER RULES In this section Raising an Eponential Epression to a Power Raising a Product to a Power Raising a Quotient to a Power Variable Eponents Summar
More information1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model
1. Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described b piecewise functions. LEARN ABOUT the Math A cit parking lot uses
More informationALGEBRA I (Common Core) Monday, January 26, 2015 1:15 to 4:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Monday, January 26, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More information1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =
Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is
More informationMathematical goals. Starting points. Materials required. Time needed
Level A7 of challenge: C A7 Interpreting functions, graphs and tables tables Mathematical goals Starting points Materials required Time needed To enable learners to understand: the relationship between
More information2.3 Quadratic Functions
88 Linear and Quadratic Functions. Quadratic Functions You ma recall studing quadratic equations in Intermediate Algebra. In this section, we review those equations in the contet of our net famil of functions:
More informationLINEAR FUNCTIONS OF 2 VARIABLES
CHAPTER 4: LINEAR FUNCTIONS OF 2 VARIABLES 4.1 RATES OF CHANGES IN DIFFERENT DIRECTIONS From Precalculus, we know that is a linear function if the rate of change of the function is constant. I.e., for
More informationGrade 8 FCAT 2.0 Mathematics Sample Questions
Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become
More informationEQUATIONS OF LINES IN SLOPE- INTERCEPT AND STANDARD FORM
. Equations of Lines in Slope-Intercept and Standard Form ( ) 8 In this Slope-Intercept Form Standard Form section Using Slope-Intercept Form for Graphing Writing the Equation for a Line Applications (0,
More informationHigh Flying Balloons
Second Grade Science Design Brief High Flying Balloons Background: In our study of science we have been investigating the three stages of matter: solids, liquids and gases. You will use your knowledge
More information5.1 Understanding Linear Functions
Name Class Date 5.1 Understanding Linear Functions Essential Question: What is a linear function? Resource Locker Eplore 1 Recognizing Linear Functions A race car can travel up to 210 mph. If the car could
More informationSECTION 2.2. Distance and Midpoint Formulas; Circles
SECTION. Objectives. Find the distance between two points.. Find the midpoint of a line segment.. Write the standard form of a circle s equation.. Give the center and radius of a circle whose equation
More informationIndicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities.
3 rd Grade Math Learning Targets Algebra: Indicator 1: Use procedures to transform algebraic expressions. 3.A.1.1. Students are able to explain the relationship between repeated addition and multiplication.
More informationMath 152, Intermediate Algebra Practice Problems #1
Math 152, Intermediate Algebra Practice Problems 1 Instructions: These problems are intended to give ou practice with the tpes Joseph Krause and level of problems that I epect ou to be able to do. Work
More informationFinal Word Problem Practice #1
Final Word Problem Practice #1 Beginning Algebra / Math 100 Fall 2013 506 (Prof. Miller) Student Name/ID: Instructor Note: Assignment: Set up a tutoring appointment with one of the campus tutors or with
More informationKeystone National Middle School Math Level 8 Placement Exam
Keystone National Middle School Math Level 8 Placement Exam 1) A cookie recipe calls for the following ingredients: 2) In the quadrilateral below, find the measurement in degrees for x? 1 ¼ cups flour
More informationSolving Systems Using Tables and Graphs. Use the chart below to review vocabulary. These vocabulary words will help you complete this page.
- ELL Support Solving Sstems Using Tables and Graphs Use the chart below to review vocabular. These vocabular words will help ou complete this page. Word Classif (verb) KLAS uh fah Classified (verb) KLAS
More informationSLOPE OF A LINE 3.2. section. helpful. hint. Slope Using Coordinates to Find 6% GRADE 6 100 SLOW VEHICLES KEEP RIGHT
. Slope of a Line (-) 67. 600 68. 00. SLOPE OF A LINE In this section In Section. we saw some equations whose graphs were straight lines. In this section we look at graphs of straight lines in more detail
More informationFlorida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District
Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve
More informationExample 1: Model A Model B Total Available. Gizmos. Dodads. System:
Lesson : Sstems of Equations and Matrices Outline Objectives: I can solve sstems of three linear equations in three variables. I can solve sstems of linear inequalities I can model and solve real-world
More informationArea is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
More informationPizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
More informationMathematics Common Core Sample Questions
New York State Testing Program Mathematics Common Core Sample Questions Grade The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and
More informationCh.4 Fractions and Mixed Numbers
Ch. Fractions and Mixed Numbers. An Introduction to Fractions. Multiplying Fractions. Dividing Fractions. Adding and Subtracting Fractions. Multiplying and Dividing Mixed Numbers.6 Adding and Subtracting
More information1. Which of the 12 parent functions we know from chapter 1 are power functions? List their equations and names.
Pre Calculus Worksheet. 1. Which of the 1 parent functions we know from chapter 1 are power functions? List their equations and names.. Analyze each power function using the terminology from lesson 1-.
More informationObjective To introduce a formula to calculate the area. Family Letters. Assessment Management
Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationOne basic concept in math is that if we multiply a number by 1, the result is equal to the original number. For example,
MA 35 Lecture - Introduction to Unit Conversions Tuesday, March 24, 205. Objectives: Introduce the concept of doing algebra on units. One basic concept in math is that if we multiply a number by, the result
More informationBuilt-In Workbooks. Skills. Reference. Prerequisite Skills... 600. Extra Practice... 616. Mixed Problem Solving... 648
Built-In Workbooks Prerequisite Skills.......................... 600 Etra Practice............................. 616 Mied Problem Solving.................... 648 Preparing for Standardized Tests............
More informationMEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.
MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units
More information1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model
. Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described b piecewise functions. LEARN ABOUT the Math A cit parking lot uses
More informationFunctions and Graphs CHAPTER INTRODUCTION. The function concept is one of the most important ideas in mathematics. The study
Functions and Graphs CHAPTER 2 INTRODUCTION The function concept is one of the most important ideas in mathematics. The stud 2-1 Functions 2-2 Elementar Functions: Graphs and Transformations 2-3 Quadratic
More information4. What could be the rule for the pattern in the table? n 1 2 3 4 5 Rule 3 5 7 9 11
5 th Grade Practice Test Objective 1.1 1. John has two fewer marbles than Kay. If Kay has marbles, how many marbles does John have? 2 2 2 2 2. What is if + 17 = 26? 43 19 11 9 3. ll the cakes at the bake
More informationLevel D - Form 1 - Applied Mathematics: Measurement
Level D - Form 1 - Applied Mathematics: Measurement Sample Question What time does this clock show? A 1:20 B 1:23 C 2:23 D 2:43 Level D - Form 1 - Applied Mathematics: Measurement 1. A movie begins at
More informationTeacher Resource Sampler. Includes Spanish Resources
Teacher Resource Sampler Includes Spanish Resources -6-5 9 0 0 0 0 online access to 0-13-31859-. S LEARNING Go beyond the tetbook with Pearson Algebra 1 Pearson Algebra 1 Common Core Edition 015 provides
More informationEquation Solving Principles
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Module 7 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. You are given information about a straight line. Use two points to graph the equation.
More informationInterpreting Graphs. Interpreting a Bar Graph
1.1 Interpreting Graphs Before You compared quantities. Now You ll use graphs to analyze data. Why? So you can make conclusions about data, as in Example 1. KEY VOCABULARY bar graph, p. 3 data, p. 3 frequency
More informationMathematics Common Core Sample Questions
New York State Testing Program Mathematics Common Core Sample Questions Grade6 The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and
More information1. a. standard form of a parabola with. 2 b 1 2 horizontal axis of symmetry 2. x 2 y 2 r 2 o. standard form of an ellipse centered
Conic Sections. Distance Formula and Circles. More on the Parabola. The Ellipse and Hperbola. Nonlinear Sstems of Equations in Two Variables. Nonlinear Inequalities and Sstems of Inequalities In Chapter,
More informationPerimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
More information9-Objective 1: The student will describe functional relationships in a variety of ways.
Texas Assessment of Knowledge and Skills Grade: 09 Subject: Mathematics Administration: Spring 2003 NOTE: Measurement questions may have had scale altered in duplication. 9-Objective 1: The student will
More informationSummer Math Packet. For Students Entering Grade 5 $3.98. Student s Name 63 9 = Review and Practice of Fairfield Math Objectives and CMT Objectives
Summer Math Packet 63 9 = Green Yellow Green Orange Orange Yellow $3.98 1 Green A B C D Red 8 1 2 3 4 5 Student s Name June 2013 Review and Practice of Fairfield Math Objectives and CMT Objectives 1 Summer
More informationAcquisition Lesson Plan for the Concept, Topic or Skill---Not for the Day
Acquisition Lesson Plan Concept: Linear Systems Author Name(s): High-School Delaware Math Cadre Committee Grade: Ninth Grade Time Frame: Two 45 minute periods Pre-requisite(s): Write 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 informationLESSON EIII.E EXPONENTS AND LOGARITHMS
LESSON EIII.E EXPONENTS AND LOGARITHMS LESSON EIII.E EXPONENTS AND LOGARITHMS OVERVIEW Here s what ou ll learn in this lesson: Eponential Functions a. Graphing eponential functions b. Applications of eponential
More information