Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Size: px
Start display at page:

Download "Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:"

Transcription

1 Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

2

3 Click the mouse button or press the Space Bar to display the answers.

4 Lesson 13-1 Lesson 13-2 Lesson 13-3 Lesson 13-4 Lesson 13-5 Lesson 13-6 Polynomials Adding Polynomials Subtracting Polynomials Multiplying a Polynomial by a Monomial Linear and Nonlinear Functions Graphing Quadratic and Cubic Functions

5 Example 1 Classify Polynomials Example 2 Degree of a Monomial Example 3 Degree of a Polynomial Example 4 Degree of a Real-World Polynomial

6 Determine whether is a polynomial. If it is, classify it as a monomial, binomial, or trinomial. Answer: The expression is not a polynomial because has a variable in the denominator.

7 Determine whether is a polynomial. If it is, classify it as a monomial, binomial, or trinomial. Answer: This is a polynomial because it is the difference of two monomials. There are two terms, so it is a binomial.

8 Determine whether each expression is a polynomial. If it is, classify it as a monomial, binomial, or trinomial. a. Answer: yes; trinomial b. Answer: not a polynomial

9 Find the degree of. Answer: The variable w has degree 4, so the degree of 10w 4 is 4.

10 Find the degree of. has degree 3, has degree 7, and z has degree 1. Answer: The degree of

11 Find the degree of each monomial. a. Answer: 3 b. Answer: 8

12 Find the degree of. term 4 degree 7 0 Answer: The greatest degree is 7. So, the degree of the polynomial is 7.

13 Find the degree of. term degree 4 7 Answer: The greatest degree is 7. So, the degree of the polynomial is 7.

14 Find the degree of each polynomial. a. Answer: 6 b. Answer: 5

15 Area The formula for the surface area (A) of a cube is, where s is the side length. Find the degree of the polynomial. Answer:

16 Area The formula for the surface area S of a cylinder with height h and radius r is. Find the degree of the polynomial. Answer: 2

17

18 Click the mouse button or press the Space Bar to display the answers.

19 Example 1 Add Polynomials Example 2 Use Polynomials to Solve a Problem

20 Find. Method 1 Add vertically. Align like terms. Add. Method 2 Add horizontally. Associative and Commutative Properties Answer: The sum is 10w + 1.

21 Find. Method 1 Add vertically. Align like terms. Add. Method 2 Add horizontally. Write the expression. Group like terms. Simplify. Answer: The sum is

22 Find. Write the expression. Simplify. Answer: The sum is

23 Find. Leave a space because there is no other term like xy. Answer: The sum is.

24 Find each sum. a. Answer: b. Answer: c. Answer: d. Answer:

25 Geometry The length of a rectangle is units and the width is 8x 1 units. Find the perimeter. Answer: The perimeter is Formula for the perimeter of a rectangle Replace with and w with Distributive Property Group like terms. Simplify.

26 Find the length of the rectangle if Write the expression. Replace x with 3. Simplify. Answer: The length of the rectangle is 16 units.

27 Geometry The length of a rectangle is units and the width is 6w 3 units. a. Find the perimeter. Answer: b. Find the length if Answer: 39 units

28

29 Click the mouse button or press the Space Bar to display the answers.

30 Example 1 Subtract Polynomials Example 2 Subtract Using the Additive Inverse Example 3 Subtract Polynomials to Solve a Problem

31 Find. Align like terms. Subtract. Answer: The difference is.

32 Find. Align like terms. Subtract. Answer: The difference is.

33 Find each difference. a. Answer: b. Answer:

34 Find. Answer: The difference is x 17. To subtract (3x + 9), add ( 3x 9). Group the like terms. Simplify.

35 Find. The additive inverse of Align the like terms and add the additive inverse. Answer:

36 Find each difference. a. Answer: 10c 7. b. Answer:

37 Geometry The length of a rectangle is units. The width is units. How much longer is the length than the width? difference in measurement Substitution Add additive inverse. Group like terms. Answer: The length is than the width. Simplify. units longer

38 Profit The ABC Company s costs are given by where x = the number of items produced. The revenue is given by 5x. Find the profit, which is the difference between the revenue and the cost. Answer:

39

40 Click the mouse button or press the Space Bar to display the answers.

41 Example 1 Products of a Monomial and a Polynomial Example 2 Product of a Monomial and a Polynomial Example 3 Use a Polynomial to Solve a Problem

42 Find. Distributive Property Simplify. Answer: 24x 16

43 Find. Distributive Property Simplify. Answer:

44 Find each product. a. 3( 5m 2) Answer: 15m 6 b. (4p 8)( 3p) Answer:

45 Find Distributive Property Simplify. Answer:

46 Find Answer:

47 Fences The length of a dog run is 4 feet more than three times its width. The perimeter of the dog run is 56 feet. What are the dimensions of the dog run? Explore Plan You know the perimeter of the dog run. You want to find the dimensions of the dog run. Let w represent the width of the dog run. Then 3w + 4 represents the length. Write an equation. Perimeter equals twice the sum of the length and width. P = 2

48 Solve Write the equation. Replace P with 56 and Combine like terms. Distributive Property Subtract 8 from each side. Divide each side by 8. Answer: The width of the dog run is 6 feet, and the length is

49 Examine Check the reasonableness of the results. The answer checks.

50 Garden The length of a garden is four more than twice its width. The perimeter of the garden is 44 feet. What are the dimensions of the garden? Answer: 6 feet by 16 feet

51

52 Click the mouse button or press the Space Bar to display the answers.

53 Example 1 Identify Functions Using Graphs Example 2 Identify Functions Using Equations Example 3 Identify Functions Using Tables Example 4 Describe a Linear Function

54 Determine whether the graph represents a linear or nonlinear function. Answer: The graph is a straight line, so it represents a linear function.

55 Determine whether the graph represents a linear or nonlinear function. Answer: The graph is a curve, not a straight line, so it represents a nonlinear function.

56 Determine whether each graph represents a linear or nonlinear function. a. b. Answer: nonlinear Answer: linear

57 Determine whether nonlinear function. represents a linear or Answer: This equation represents a linear function because it is written in the form

58 Determine whether nonlinear function. represents a linear or Answer: This equation is nonlinear because x is raised to the second power and the equation cannot be written in the form

59 Determine whether each equation represents a linear or nonlinear function. a. Answer: nonlinear b. Answer: linear

60 Determine whether the table represents a linear or nonlinear function x y As x increases by 2, y decreases by 8. So, this is a linear function. Answer: linear

61 Determine whether the table represents a linear or nonlinear function x y As x increases by 3, y increases by a greater amount each time. So, this is a nonlinear function. Answer: nonlinear

62 Determine whether each table represents a linear or nonlinear function. a. b. x y x y Answer: nonlinear Answer: linear

63 Multiple-Choice Test Item Which rule describes a linear function? A B C D Read the Test Item A rule describes a relationship between variables. A rule that can be written in the form describes a relationship that is linear.

64 Solve the Test Item This is a nonlinear function because x is in the denominator and the equation cannot be written in the form quadratic equation You can eliminate choices A and D. Answer: The answer is B. This is a quadratic equation. Eliminate choice C.

65 Check This equation is in the form

66 Multiple-Choice Test Item Which rule describes a linear function? A B C D Answer: C

67

68 Click the mouse button or press the Space Bar to display the answers.

69 Example 1 Graph Quadratic Functions Example 2 Use a Function to Solve a Problem Example 3 Graph Cubic Functions

70 Graph. Make a table of values, plot the ordered pairs, and connect the points with a curve. Answer: x (x, y) ( 1.5, 4.5) ( 1, 2) ( 0.5, 0.5) (0.5, 0.5) (0, 0) (1, 2) (1.5, 4.5)

71 Graph. x 2 (x, y) ( 2, 3) Answer: 1 ( 1, 1.5) 0 (0, 1) 1 (1, 1.5) 2 (2, 3)

72 Graph. x 2 1 (x, y) ( 2, 7) ( 1, 4) Answer: 0 (0, 3) 1 (1, 4) 2 (2, 7)

73 Graph each function. a. Answer:

74 Graph each function. b. Answer:

75 Graph each function. c. Answer:

76 Geometry The height of a triangle is 4 times its base. Write a formula for the area and graph it. Find the area of the triangle whose base is 3 units. Words The area of a triangle is equal to one-half the product of its base and height. Variables. Equations Area is equal to one-half the product of its base and height A =

77 The equation is. Since the variable b has an exponent of 2, this function is nonlinear. Now graph. Since the base cannot be negative, use only positive values of b. b (b, A) (0, 0) (0.5, 0.5) (1, 2) (1.5, 4.5) (2, 8) (2.5, 12.5)

78 By looking at the graph, we find that for a base of 3 units, the area of the triangle is 18 square units.

79 Geometry The length of a rectangle is 3 times its width. Write a formula for the area and graph it. Find the area of the rectangle whose width is 3.5 inches. Answer:

80 Graph. Answer: x 2 1 (x, y) ( 2, 4) ( 1, ) 0 (0, 0) 1 (1, ) 2 (2, 4)

81 Graph. x (x, y) ( 1.5, 4.75) ( 1, 0) (0, 2) (1, 4) (1.5, 8.75) Answer:

82 Graph each function. a. Answer:

83 Graph each function. b. Answer:

84

85 Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Pre-Algebra Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to

86 End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.

87

Mathematics Placement

Mathematics Placement Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

More information

Algebra II New Summit School High School Diploma Program

Algebra II New Summit School High School Diploma Program Syllabus Course Description: Algebra II is a two semester course. Students completing this course will earn 1.0 unit upon completion. Required Materials: 1. Student Text Glencoe Algebra 2: Integration,

More information

MATD 0390 - Intermediate Algebra Review for Pretest

MATD 0390 - Intermediate Algebra Review for Pretest MATD 090 - Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: - - + [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x +

More information

Learning Objectives 9.2. Media Run Times 9.3

Learning Objectives 9.2. Media Run Times 9.3 Unit 9 Table of Contents Unit 9: Factoring Video Overview Learning Objectives 9.2 Media Run Times 9.3 Instructor Notes 9.4 The Mathematics of Factoring Polynomials Teaching Tips: Conceptual Challenges

More information

IOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.

IOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa. IOWA End-of-Course Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of $2,000. She also earns $500 for

More information

Florida Math for College Readiness

Florida Math for College Readiness Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

More information

Algebra II and Trigonometry

Algebra II and Trigonometry Algebra II and Trigonometry Textbooks: Algebra 2: California Publisher: McDougal Li@ell/Houghton Mifflin (2006 EdiHon) ISBN- 13: 978-0618811816 Course descriphon: Algebra II complements and expands the

More information

13. Write the decimal approximation of 9,000,001 9,000,000, rounded to three significant

13. Write the decimal approximation of 9,000,001 9,000,000, rounded to three significant æ If 3 + 4 = x, then x = 2 gold bar is a rectangular solid measuring 2 3 4 It is melted down, and three equal cubes are constructed from this gold What is the length of a side of each cube? 3 What is the

More information

Such As Statements, Kindergarten Grade 8

Such As Statements, Kindergarten Grade 8 Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential

More information

Blue Pelican Alg II First Semester

Blue Pelican Alg II First Semester Blue Pelican Alg II First Semester Teacher Version 1.01 Copyright 2009 by Charles E. Cook; Refugio, Tx (All rights reserved) Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities

More information

FSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers

FSCJ 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 information

Basic Math for the Small Public Water Systems Operator

Basic Math for the Small Public Water Systems Operator Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the

More information

Virginia Placement Test Practice Questions and Answers

Virginia Placement Test Practice Questions and Answers Virginia Placement Test Practice Questions and Answers Table of Contents Practice Problems for UNIT 1 Operations with Positive Fractions... 1 Practice Problems for UNIT Operations with Positive Decimals

More information

MEP Pupil Text 12. A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued.

MEP Pupil Text 12. A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued. MEP Pupil Text Number Patterns. Simple Number Patterns A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued. Worked Example Write down the

More information

8-5 Using the Distributive Property. Use the Distributive Property to factor each polynomial. 1. 21b 15a SOLUTION:

8-5 Using the Distributive Property. Use the Distributive Property to factor each polynomial. 1. 21b 15a SOLUTION: Use the Distributive Property to factor each polynomial. 1. 1b 15a The greatest common factor in each term is 3.. 14c + c The greatest common factor in each term is c. 3. 10g h + 9gh g h The greatest common

More information

Virginia Placement Test Practice Questions and Answers

Virginia Placement Test Practice Questions and Answers Virginia Placement Test Practice Questions and Answers Table of Contents Practice Problems for MTE Operations with Positive Fractions... Practice Problems for MTE Operations with Positive Decimals and

More information

Example 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph

Example 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph The Effect of Taxes on Equilibrium Example 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph Solution to part a: Set the

More information

DOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2

DOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2 DOE-HDBK-1014/2-92 JUNE 1992 DOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2 U.S. Department of Energy Washington, D.C. 20585 FSC-6910 Distribution Statement A. Approved for public release; distribution

More information

College Readiness Math MOOC

College Readiness Math MOOC College Readiness Math MOOC Instructor Information: Dr. Jennifer Kosiak, jkosiak@uwlax.edu General email: mathmooc@uwlax.edu Mathematics Department, University of Wisconsin- La Crosse Description: The

More information

XV. Mathematics, Grade 10

XV. Mathematics, Grade 10 XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 2011 grade 10 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework

More information

(x- 3)3. (x- 3)3 =U. 3. Factor completely the given polynomial. ENHANCED

(x- 3)3. (x- 3)3 =U. 3. Factor completely the given polynomial. ENHANCED Student: Instructor: Vicky Kauffman Assignment: Final problems Date: Course: Kauffman's Math 12 1 1. A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window

More information

Graphing and Solving Nonlinear Inequalities

Graphing and Solving Nonlinear Inequalities APPENDIX LESSON 1 Graphing and Solving Nonlinear Inequalities New Concepts A quadratic inequality in two variables can be written in four different forms y < a + b + c y a + b + c y > a + b + c y a + b

More information

Consultant: Lynn T. Havens. Director of Project CRISS Kalispell, Montana

Consultant: Lynn T. Havens. Director of Project CRISS Kalispell, Montana Teacher Annotated Edition Study Notebook Consultant: Lynn T. Havens SM Director of Project CRISS Kalispell, Montana i_sn_c1fmtwe_893629.indd i 3/16/09 9:17:03 PM Copyright by The McGraw-Hill Companies,

More information

Statistics Revision Sheet Question 6 of Paper 2

Statistics Revision Sheet Question 6 of Paper 2 Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of

More information

12-1 Representations of Three-Dimensional Figures

12-1 Representations of Three-Dimensional Figures Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

More information

Algebra II Unit 1: Foundations of Functions 2014-2015. 27 2.2 Linear Equations Day 1. HW: Linear Equations WS 1. 3 Quiz 2.1, 2.2, and 2.

Algebra II Unit 1: Foundations of Functions 2014-2015. 27 2.2 Linear Equations Day 1. HW: Linear Equations WS 1. 3 Quiz 2.1, 2.2, and 2. Algebra II Unit 1: Foundations of Functions 2014-2015 Aug 25 School Starts Class rules, etc 26 2.1 Relations and Functions HW: Relations and functions WS 27 2.2 Linear Equations Day 1 HW: Linear Equations

More information

Chapter 6 Quadratic Functions

Chapter 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 information

1.3. Maximum or Minimum of a Quadratic Function. Investigate A

1.3. Maximum or Minimum of a Quadratic Function. Investigate A < P1-6 photo of a large arched bridge, similar to the one on page 292 or p 360-361of the fish book> Maximum or Minimum of a Quadratic Function 1.3 Some bridge arches are defined by quadratic functions.

More information

Factoring Methods. Example 1: 2x + 2 2 * x + 2 * 1 2(x + 1)

Factoring Methods. Example 1: 2x + 2 2 * x + 2 * 1 2(x + 1) Factoring Methods When you are trying to factor a polynomial, there are three general steps you want to follow: 1. See if there is a Greatest Common Factor 2. See if you can Factor by Grouping 3. See if

More information

Interpretation of Test Scores for the ACCUPLACER Tests

Interpretation of Test Scores for the ACCUPLACER Tests Interpretation of Test Scores for the ACCUPLACER Tests ACCUPLACER is a trademark owned by the College Entrance Examination Board. Visit The College Board on the Web at: www.collegeboard.com/accuplacer

More information

Diablo Valley College Catalog 2014-2015

Diablo Valley College Catalog 2014-2015 Mathematics MATH Michael Norris, Interim Dean Math and Computer Science Division Math Building, Room 267 Possible career opportunities Mathematicians work in a variety of fields, among them statistics,

More information

9 Areas and Perimeters

9 Areas and Perimeters 9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.

More information

Mathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer

Mathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer MATH Degree: A.S. AS-T for Transfer Division of /Statistics & Engineering Anne E. Licciardi, Dean South Gym 220 916-558-2202 Associate in Science Degree Program Information The mathematics program provides

More information

Using Excel to find Perimeter, Area & Volume

Using Excel to find Perimeter, Area & Volume Using Excel to find Perimeter, Area & Volume Level: LBS 4 V = lwh Goal: To become familiar with Microsoft Excel by entering formulas into a spreadsheet in order to calculate the perimeter, area and volume

More information

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring 4.7 Solving Quadratic Equations by Factoring 4.7 OBJECTIVE 1. Solve quadratic equations by factoring The factoring techniques you have learned provide us with tools for solving equations that can be written

More information

For example, estimate the population of the United States as 3 times 10⁸ and the

For example, estimate the population of the United States as 3 times 10⁸ and the CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number

More information

Just What Do You Mean? Expository Paper Myrna L. Bornemeier

Just What Do You Mean? Expository Paper Myrna L. Bornemeier Just What Do You Mean? Expository Paper Myrna L. Bornemeier In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics

More information

Mathematics as Problem Solving The students will demonstrate the ability to gather information from a graphical representation of an equation.

Mathematics as Problem Solving The students will demonstrate the ability to gather information from a graphical representation of an equation. Title: Another Way of Factoring Brief Overview: Students will find factors for quadratic equations with a leading coefficient of one. The students will then graph these equations using a graphing calculator

More information

If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?

If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question

More information

COMPASS Placement Test Preparation Packet

COMPASS Placement Test Preparation Packet COMPASS Placement Test Preparation Packet For preparing to take the COMPASS Math Placement Test Funded through the Gulf-Coast PASS Grant Table of Contents: 1. The COMPASS Test 1 The COMPASS Test 3 Test

More information

Month Rabbits # Pairs

Month Rabbits # Pairs 1. Fibonacci s Rabbit Problem. Fibonacci rabbits come in pairs. Once a pair is two months old, it bears another pair and from then on bears one pair every month. Starting with a newborn pair at the beginning

More information

Unit 5 Area. What Is Area?

Unit 5 Area. What Is Area? Trainer/Instructor Notes: Area What Is Area? Unit 5 Area What Is Area? Overview: Objective: Participants determine the area of a rectangle by counting the number of square units needed to cover the region.

More information

Intro to Excel spreadsheets

Intro to Excel spreadsheets Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using

More information

Spreadsheet. Parts of a Spreadsheet. Entry Bar

Spreadsheet. Parts of a Spreadsheet. Entry Bar Spreadsheet Parts of a Spreadsheet 1. Open the AppleWorks program. Select spreadsheet. 2. Explore the spreadsheet setup for a while. Active Cell Address Entry Bar Column Headings Row Headings Active Cell

More information

EXCEL SPREADSHEET MANUAL

EXCEL SPREADSHEET MANUAL EXCEL SPREADSHEET MANUAL to accompany CALCULUS FOR THE LIFE SCIENCES GREENWELL RITCHEY LIAL Paula Grafton Young Salem College J. Todd Lee Elon College Boston San Francisco New York London Toronto Sydney

More information

Programming Your Calculator Casio fx-7400g PLUS

Programming Your Calculator Casio fx-7400g PLUS Programming Your Calculator Casio fx-7400g PLUS Barry Kissane Programming Your Calculator: Casio fx-7400g PLUS Published by Shriro Australia Pty Limited 72-74 Gibbes Street, Chatswood NSW 2067, Australia

More information

Find the Relationship: An Exercise in Graphing Analysis

Find the Relationship: An Exercise in Graphing Analysis Find the Relationship: An Eercise in Graphing Analsis Computer 5 In several laborator investigations ou do this ear, a primar purpose will be to find the mathematical relationship between two variables.

More information

Quadratic Equations and Functions

Quadratic 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 information

Primes. Name Period Number Theory

Primes. Name Period Number Theory Primes Name Period A Prime Number is a whole number whose only factors are 1 and itself. To find all of the prime numbers between 1 and 100, complete the following exercise: 1. Cross out 1 by Shading in

More information

Mathematical Practices

Mathematical Practices The New Illinois Learning Standards for Mathematics Incorporating the Common Core Mathematical Practices Grade Strand Standard # Standard K-12 MP 1 CC.K-12.MP.1 Make sense of problems and persevere in

More information

NOT AN OFFICIAL SCORE REPORT. Summary of Results

NOT AN OFFICIAL SCORE REPORT. Summary of Results From SAT TEST MARCH 8, 214 Summary of Results Page 1 of 1 Congratulations on taking the SAT Reasoning Test! You re showing colleges that you are serious about getting an education. The SAT is one indicator

More information

04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators

04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators 04 Mathematics CO-SG-FLD004-03 Program for Licensing Assessments for Colorado Educators Readers should be advised that this study guide, including many of the excerpts used herein, is protected by federal

More information

4.3 Least Squares Approximations

4.3 Least Squares Approximations 18 Chapter. Orthogonality.3 Least Squares Approximations It often happens that Ax D b has no solution. The usual reason is: too many equations. The matrix has more rows than columns. There are more equations

More information

DEFINITION 5.1.1 A complex number is a matrix of the form. x y. , y x

DEFINITION 5.1.1 A complex number is a matrix of the form. x y. , y x Chapter 5 COMPLEX NUMBERS 5.1 Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of matrices. DEFINITION 5.1.1 A complex number is a matrix of

More information

Revised Version of Chapter 23. We learned long ago how to solve linear congruences. ax c (mod m)

Revised Version of Chapter 23. We learned long ago how to solve linear congruences. ax c (mod m) Chapter 23 Squares Modulo p Revised Version of Chapter 23 We learned long ago how to solve linear congruences ax c (mod m) (see Chapter 8). It s now time to take the plunge and move on to quadratic equations.

More information

Custom Question Builder Tutorial

Custom Question Builder Tutorial Custom Question Builder Tutorial Introduction Pearson Education, 2011 (1/21/2011) Page 1 CONTACT INFORMATION General Information MyMathLab: www.mymathlab.com MyStatLab: www.mystatlab.com MathXL: www.mathxl.com

More information

Mathematics Program Description Associate in Arts Degree Program Outcomes Required Courses............................. Units

Mathematics Program Description Associate in Arts Degree Program Outcomes Required Courses............................. Units Program Description Successful completion of this maj will assure competence in mathematics through differential and integral calculus, providing an adequate background f employment in many technological

More information

MINNESOTA DEPARTMENT OF PUBLIC SAFETY State Fire Marshal Division STATEMENT OF POLICY. State Fire Marshal

MINNESOTA DEPARTMENT OF PUBLIC SAFETY State Fire Marshal Division STATEMENT OF POLICY. State Fire Marshal MINNESOTA DEPARTMENT OF PUBLIC SAFETY State Fire Marshal Division STATEMENT OF POLICY Policy #: Subject of Policy: INS-04 (2007) Escape Windows Revised and Approved By: Title: Jerry Rosendahl State Fire

More information

SAN DIEGO COMMUNITY COLLEGE DISTRICT CITY COLLEGE ASSOCIATE DEGREE COURSE OUTLINE

SAN DIEGO COMMUNITY COLLEGE DISTRICT CITY COLLEGE ASSOCIATE DEGREE COURSE OUTLINE MATH 098 CIC Approval: BOT APPROVAL: STATE APPROVAL: EFFECTIVE TERM: SAN DIEGO COMMUNITY COLLEGE DISTRICT CITY COLLEGE ASSOCIATE DEGREE COURSE OUTLINE SECTION I SUBJECT AREA AND COURSE NUMBER: Mathematics

More information

Online Developmental Mathematics Instruction in Colleges and Universities: An Exploratory Investigation

Online Developmental Mathematics Instruction in Colleges and Universities: An Exploratory Investigation Online Developmental Mathematics Instruction in Colleges and Universities: An Exploratory Investigation Taylor Martin Nicole Forsgren Velasquez Jason Maughan ABSTRACT 1 Mathematics proficiency is critical

More information

USING A TI-83 OR TI-84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS

USING A TI-83 OR TI-84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS USING A TI-83 OR TI-84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS W. SCOTT STREET, IV DEPARTMENT OF STATISTICAL SCIENCES & OPERATIONS RESEARCH VIRGINIA COMMONWEALTH UNIVERSITY Table

More information

FRESHMAN SOPHOMORE JUNIOR SENIOR. Algebra 2** (H) Algebra 2 H. Pre-Calculus H Honors Pre-Calculus and/or AP Statistics

FRESHMAN SOPHOMORE JUNIOR SENIOR. Algebra 2** (H) Algebra 2 H. Pre-Calculus H Honors Pre-Calculus and/or AP Statistics MATH DEPARTMENT COURSE DESCRIPTIONS The Mathematics Department provides a challenging curriculum that strives to meet the needs of a diverse student body by: Helping the student realize that the analytical

More information

How to make a line graph using Excel 2007

How to make a line graph using Excel 2007 How to make a line graph using Excel 2007 Format your data sheet Make sure you have a title and each column of data has a title. If you are entering data by hand, use time or the independent variable in

More information

Exploring Relationships between Highest Level of Education and Income using Corel Quattro Pro

Exploring Relationships between Highest Level of Education and Income using Corel Quattro Pro Exploring Relationships between Highest Level of Education and Income using Corel Quattro Pro Created by Michael Lieff (m@lieff.net) Faculty of Education, Queen s University While on practicum at Statistics

More information

How To Use A Spreadsheet Excel for the Mac and PC-Windows by John D. Winter

How To Use A Spreadsheet Excel for the Mac and PC-Windows by John D. Winter How To Use A Spreadsheet Excel for the Mac and PC-Windows by John D. Winter Most good spreadsheets have very similar capabilities, but the syntax of the commands differs slightly. I will use the keyboard

More information

PROOFS BY DESCENT KEITH CONRAD

PROOFS BY DESCENT KEITH CONRAD PROOFS BY DESCENT KEITH CONRAD As ordinary methods, such as are found in the books, are inadequate to proving such difficult propositions, I discovered at last a most singular method... that I called the

More information

Rolle s Theorem. q( x) = 1

Rolle s Theorem. q( x) = 1 Lecture 1 :The Mean Value Theorem We know that constant functions have derivative zero. Is it possible for a more complicated function to have derivative zero? In this section we will answer this question

More information

Mathematics: Content Knowledge

Mathematics: Content Knowledge The Praxis Study Companion Mathematics: Content Knowledge 5161 www.ets.org/praxis Welcome to the Praxis Study Companion Welcome to the Praxis Study Companion Prepare to Show What You Know You have been

More information

Figure 2.1: Center of mass of four points.

Figure 2.1: Center of mass of four points. Chapter 2 Bézier curves are named after their inventor, Dr. Pierre Bézier. Bézier was an engineer with the Renault car company and set out in the early 196 s to develop a curve formulation which would

More information

Mathematics INDIVIDUAL PROGRAM INFORMATION 2014 2015. 866.Macomb1 (866.622.6621) www.macomb.edu

Mathematics INDIVIDUAL PROGRAM INFORMATION 2014 2015. 866.Macomb1 (866.622.6621) www.macomb.edu Mathematics INDIVIDUAL PROGRAM INFORMATION 2014 2015 866.Macomb1 (866.622.6621) www.macomb.edu Mathematics PROGRAM OPTIONS CREDENTIAL TITLE CREDIT HOURS REQUIRED NOTES Associate of Arts Mathematics 62

More information

Topography of an Origin Project and Workspace

Topography of an Origin Project and Workspace Origin Basics Topography of an Origin Project and Workspace When you start Origin, a new project opens displaying a worksheet window in the workspace. The worksheet is one type of window available in Origin.

More information

Estimating the Average Value of a Function

Estimating the Average Value of a Function Estimating the Average Value of a Function Problem: Determine the average value of the function f(x) over the interval [a, b]. Strategy: Choose sample points a = x 0 < x 1 < x 2 < < x n 1 < x n = b and

More information

2 Integrating Both Sides

2 Integrating Both Sides 2 Integrating Both Sides So far, the only general method we have for solving differential equations involves equations of the form y = f(x), where f(x) is any function of x. The solution to such an equation

More information

On using numerical algebraic geometry to find Lyapunov functions of polynomial dynamical systems

On using numerical algebraic geometry to find Lyapunov functions of polynomial dynamical systems Dynamics at the Horsetooth Volume 2, 2010. On using numerical algebraic geometry to find Lyapunov functions of polynomial dynamical systems Eric Hanson Department of Mathematics Colorado State University

More information

PRE-CALCULUS with TRIGONOMETRY MTH 166 Online

PRE-CALCULUS with TRIGONOMETRY MTH 166 Online PRE-CALCULUS with TRIGONOMETRY MTH 166 Online INSTRUCTOR INFORMATION Name: Dr. Pablo Chalmeta Phone: 540-674-3600, ext. 4266 (or 4115) Email: pchalmeta@nr.edu Office: Godbey Hall, Room 48 (or Mall 115A)

More information

Exercise: Building and zone geometry import from SketchUp

Exercise: Building and zone geometry import from SketchUp Exercise: Building and zone geometry import from SketchUp Purpose Learn how to create and import building and zone geometry from SketchUp into IDA ICE. Learn how to work with imported building and zone

More information

Alabama Department of Postsecondary Education. Representing The Alabama Community College System

Alabama Department of Postsecondary Education. Representing The Alabama Community College System Alabama Department of Postsecondary Education Representing The Alabama Community College System Central Alabama Community College MTH 100 Intermediate Algebra Prerequisite: MTH 092 or MTH 098 or appropriate

More information

Example 1: Dear Abby. Stat Camp for the Full-time MBA Program

Example 1: Dear Abby. Stat Camp for the Full-time MBA Program Stat Camp for the Full-time MBA Program Daniel Solow Lecture 4 The Normal Distribution and the Central Limit Theorem 188 Example 1: Dear Abby You wrote that a woman is pregnant for 266 days. Who said so?

More information

7 Enclosed Areas. When you have completed this chapter, you will be able to:

7 Enclosed Areas. When you have completed this chapter, you will be able to: 7 Enclosed Areas Our designs so far have consisted entirely of open linework, except for a brief introduction to Fill Attributes on page 3-15. Closed linework may delineate an Area, such as a section of

More information

M1. (a) (i) 4.5 allow 1 mark for correct substitution i.e. 9 2 2

M1. (a) (i) 4.5 allow 1 mark for correct substitution i.e. 9 2 2 M. (a) (i) 4.5 allow mark for correct substitution i.e. 9 (ii) m/s accept answer given in (a)(i) if not contradicted here (iii) (iv) speed straight line from the origin passing through (s, 9m/s) allow

More information

Lesson 9: Using If-Then Moves in Solving Equations

Lesson 9: Using If-Then Moves in Solving Equations Student Outcomes Students understand and use the addition, subtraction, multiplication, division, and substitution properties of equality to solve word problems leading to equations of the form pppp +

More information

TI-Nspire Technology Version 3.2 Release Notes

TI-Nspire Technology Version 3.2 Release Notes TI-Nspire Technology Version 3.2 Release Notes Release Notes 1 Introduction Thank you for updating your TI Nspire products to Version 3.2. This version of the Release Notes has updates for all of the following

More information

Creating Hyperlinks & Buttons InDesign CS6

Creating Hyperlinks & Buttons InDesign CS6 Creating Hyperlinks & Buttons Adobe DPS, InDesign CS6 1 Creating Hyperlinks & Buttons InDesign CS6 Hyperlinks panel overview You can create hyperlinks so that when you export to Adobe PDF or SWF in InDesign,

More information

Overview... 2. Accounting for Business (MCD1010)... 3. Introductory Mathematics for Business (MCD1550)... 4. Introductory Economics (MCD1690)...

Overview... 2. Accounting for Business (MCD1010)... 3. Introductory Mathematics for Business (MCD1550)... 4. Introductory Economics (MCD1690)... Unit Guide Diploma of Business Contents Overview... 2 Accounting for Business (MCD1010)... 3 Introductory Mathematics for Business (MCD1550)... 4 Introductory Economics (MCD1690)... 5 Introduction to Management

More information

Problem of the Month: Digging Dinosaurs

Problem of the Month: Digging Dinosaurs : The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of

More information

Assumption College Final Examination Content

Assumption College Final Examination Content Final Examination Content EP-M 3/1 Semester 2 Academic Year 2013 Code: MA20212 Subject: Mathematical Skills 6 books / Pages Sum Final Coordinate Geometry 1. - Cartesian Coordinate System - Rectangular

More information

Interactive Voting System. www.ivsystem.nl. IVS-Basic IVS-Professional 4.4

Interactive Voting System. www.ivsystem.nl. IVS-Basic IVS-Professional 4.4 Interactive Voting System www.ivsystem.nl IVS-Basic IVS-Professional 4.4 Manual IVS-Basic 4.4 IVS-Professional 4.4 1213 Interactive Voting System The Interactive Voting System (IVS ) is an interactive

More information

Maple Quick Start. Introduction. Talking to Maple. Using [ENTER] 3 (2.1)

Maple Quick Start. Introduction. Talking to Maple. Using [ENTER] 3 (2.1) Introduction Maple Quick Start In this introductory course, you will become familiar with and comfortable in the Maple environment. You will learn how to use context menus, task assistants, and palettes

More information

The mathematics of RAID-6

The mathematics of RAID-6 The mathematics of RAID-6 H. Peter Anvin 1 December 2004 RAID-6 supports losing any two drives. The way this is done is by computing two syndromes, generally referred P and Q. 1 A quick

More information

how to use dual base log log slide rules

how to use dual base log log slide rules how to use dual base log log slide rules by Professor Maurice L. Hartung The University of Chicago Pickett The World s Most Accurate Slide Rules Pickett, Inc. Pickett Square Santa Barbara, California 93102

More information

Why are Word Problems so Darned Hard? Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.edu

Why are Word Problems so Darned Hard? Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.edu Why are Word Problems so Darned Hard? Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.edu Preface: Why middle school math is important My friend complains to a hospital doctor

More information

(15.) To find the distance from point A to point B across. a river, a base line AC is extablished. AC is 495 meters

(15.) To find the distance from point A to point B across. a river, a base line AC is extablished. AC is 495 meters (15.) To find the distance from point A to point B across a river, a base line AC is extablished. AC is 495 meters long. Angles

More information

Chapter 2. Software: (preview draft) Getting Started with Stella and Vensim

Chapter 2. Software: (preview draft) Getting Started with Stella and Vensim Chapter. Software: (preview draft) Getting Started with Stella and Vensim Stella and Vensim are icon-based programs to support the construction and testing of system dynamics models. I use these programs

More information

NCTM Content Standard/National Science Education Standard

NCTM Content Standard/National Science Education Standard Title: BASE-ic Space Travel Brief Overview: This unit introduces the concepts of bases and exponents (or powers) in order to gain a deeper understanding of place value. Students will assume the role of

More information

Alabama Department of Postsecondary Education

Alabama Department of Postsecondary Education Date Adopted 1998 Dates reviewed 2007, 2011, 2013 Dates revised 2004, 2008, 2011, 2013, 2015 Alabama Department of Postsecondary Education Representing Alabama s Public Two-Year College System Jefferson

More information

RANGER COLLEGE Math 1314 College Algebra - ONLINE

RANGER COLLEGE Math 1314 College Algebra - ONLINE RANGER COLLEGE Math 1314 College Algebra - ONLINE ONLINE Instructor: Kimberly Calton Office Location: Early Campus Office Hours: Otherwise by appointment only Cell Phone: 512-914-8883 E-Mail: kcalton@rangercollege.edu

More information

Chapter 4: The Concept of Area

Chapter 4: The Concept of Area Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding

More information

Beginning PowerPoint: Hands-On Exercise (Windows XP) Regent University

Beginning PowerPoint: Hands-On Exercise (Windows XP) Regent University Beginning PowerPoint: Hands-On Exercise (Windows XP) 10/1/02 (Creation Date) 01/08/2004 Regent University The Center for Teaching & Learning 1 Beginning PowerPoint: Hands-On Exercise (Windows XP) 1. Open

More information

( 1)2 + 2 2 + 2 2 = 9 = 3 We would like to make the length 6. The only vectors in the same direction as v are those

( 1)2 + 2 2 + 2 2 = 9 = 3 We would like to make the length 6. The only vectors in the same direction as v are those 1.(6pts) Which of the following vectors has the same direction as v 1,, but has length 6? (a), 4, 4 (b),, (c) 4,, 4 (d), 4, 4 (e) 0, 6, 0 The length of v is given by ( 1) + + 9 3 We would like to make

More information

Math 046 Online Course Syllabus Elementary Algebra and Geometry

Math 046 Online Course Syllabus Elementary Algebra and Geometry Math 046 Online Course Syllabus Elementary Algebra and Geometry THIS IS AN 8 WEEK CLASS Carol Murphy, Professor CRN # 08391 Online office hours: Tuesdays from 8 9 pm Office Phone: 619-388-7691 Fall Other

More information