Section 1.3: Graphing Equations
|
|
|
- Tyrone Bruce
- 7 years ago
- Views:
Transcription
1 SECTION 1.3 Graphing Equations Section 1.3: Graphing Equations Graphs Intercepts of Graphs Symmetry Circles Graphs Make a table of values and then graph the points from the table. MATH 1310 College Algebra 55
2 CHAPTER 1 An Introduction to Graphs and Lines Make a table of values and then graph the points from the table. Make a table of values and then graph the points from the table. 56 University of Houston Department of Mathematics
3 SECTION 1.3 Graphing Equations Additional Example 1: MATH 1310 College Algebra 57
4 CHAPTER 1 An Introduction to Graphs and Lines Additional Example : 58 University of Houston Department of Mathematics
5 SECTION 1.3 Graphing Equations Additional Example 3: MATH 1310 College Algebra 59
6 CHAPTER 1 An Introduction to Graphs and Lines Additional Example 4: 60 University of Houston Department of Mathematics
7 SECTION 1.3 Graphing Equations Intercepts of Graphs MATH 1310 College Algebra 61
8 CHAPTER 1 An Introduction to Graphs and Lines Additional Example 1: 6 University of Houston Department of Mathematics
9 SECTION 1.3 Graphing Equations Additional Example : MATH 1310 College Algebra 63
10 CHAPTER 1 An Introduction to Graphs and Lines Additional Example 3: 64 University of Houston Department of Mathematics
11 SECTION 1.3 Graphing Equations Symmetry MATH 1310 College Algebra 65
12 CHAPTER 1 An Introduction to Graphs and Lines 66 University of Houston Department of Mathematics
13 SECTION 1.3 Graphing Equations Example Problem: MATH 1310 College Algebra 67
14 CHAPTER 1 An Introduction to Graphs and Lines Additional Example 1: 68 University of Houston Department of Mathematics
15 SECTION 1.3 Graphing Equations Additional Example : Additional Example 3: MATH 1310 College Algebra 69
16 CHAPTER 1 An Introduction to Graphs and Lines 70 University of Houston Department of Mathematics
17 SECTION 1.3 Graphing Equations Additional Example 4: MATH 1310 College Algebra 71
18 CHAPTER 1 An Introduction to Graphs and Lines Circles 7 University of Houston Department of Mathematics
19 SECTION 1.3 Graphing Equations MATH 1310 College Algebra 73
20 CHAPTER 1 An Introduction to Graphs and Lines Additional Example 1: Additional Example : 74 University of Houston Department of Mathematics
21 SECTION 1.3 Graphing Equations Additional Example 3: MATH 1310 College Algebra 75
22 CHAPTER 1 An Introduction to Graphs and Lines 76 University of Houston Department of Mathematics
23 SECTION 1.3 Graphing Equations Additional Example 4: MATH 1310 College Algebra 77
24 Exercise Set 1.3: Graphing Equations Determine which of the following points are on the graph of the given equation x + y = 5; (1, 4), (3, - 7), (, ) 5. x y = 7; (0, -5), (-3, -13), (, - ) 3. xy x + 3 y = 7; (, -5), (-1, 3), ( 6, ) 4. x y = x + y; (3, ), (5, 4), (-7, - 6) 5. x y(3 + xy) = x + 5; (1,1), (-, 3), (-5,0) 6. y ( x xy) = 40; (4, -1), (-3, - ), ( 3, -5) Sketch the graphs of the following equations by plotting points. 7. y = x 5 8. y = 3 x y = x y = x y = x 1. y = x y = 3 x 3 y = x 1 y = x 8 y = x Find the x- and y-intercepts of the graph of each of the following equations. 17. y = 4x y = 3x x + y = x 4y = 4 1. y = x 16. x = 5 y y = x 4. xy = 6 5. y = x y = x x + y = x y = 9 9. x + xy + 3y = x 5xy + 3y = 36 In the following questions, only part of the graph is given. Complete each graph using the given symmetry. 31. x-axis 3. y-axis 33. origin 34. x-axis University of Houston Department of Mathematics y y y y x x x x
25 Exercise Set 1.3: Graphing Equations Test the following equations for symmetry with respect to the x-axis, the y-axis, and the origin. Identify the center and radius, and then sketch the graph of the equation y = x + x x = y + y 3 y = 5x x + y = x + y = ( x ) + ( y + 3) = y = x 4 5x + x y = y x y = xy 41. y = 3x + 5x 4. x + y = 5y 43. x + 3 y = x 7 y = 4 For each of the following equations: (a) Test the equation for symmetry. (b) Find and plot the intercepts. (c) Plot a few intermediate points in order to complete the graph. (Keep symmetry in mind to minimize the length of this step.) 45. y = x ( x + ) + ( y 4) = 4 Write an equation of the circle that satisfies the given conditions. 59. Center (-4, -3); radius Center (7, 0); radius Center (-, 5); radius 7 6. Center at the origin; radius Endpoints of a diameter are (-3, 6) and (5, ) 64. Endpoints of a diameter are (5, -3) and (-9, 11) 65. Center (, 5); passes through (-6, 4) 66. Center (-3, 1); passes through (5, -) 67. Center (-,4); tangent to the x-axis. 68. Center (3, -1); tangent to the y-axis. Write an equation for each of the following circles y = 5 x y = y = 9 x 5 x y x y = x 4x 50. y = x + 3 The following equations represent circles. Identify the center and radius of each circle. 51. ( x 3) + ( y + 5) = ( x + 7) + ( y 1) = x + ( y 6) = ( x + 8) + y = y x MATH 1310 College Algebra 79
26 Exercise Set 1.3: Graphing Equations Show that the following equations represent circles by writing them in standard form: ( x h) + ( y k) = r Then identify the center and radius of the circle. 71. x + y + 4x 1y 9 = 0 7. x + y x + 8y 0 = x + y 10y + 1 = x + y 14x + 39 = x + y + x 6y + 7 = x + y x + y = 0 80 University of Houston Department of Mathematics
1.2 GRAPHS OF EQUATIONS. Copyright Cengage Learning. All rights reserved.
1.2 GRAPHS OF EQUATIONS Copyright Cengage Learning. All rights reserved. What You Should Learn Sketch graphs of equations. Find x- and y-intercepts of graphs of equations. Use symmetry to sketch graphs
Circle Name: Radius: Diameter: Chord: Secant:
12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
Contents. 2 Lines and Circles 3 2.1 Cartesian Coordinates... 3 2.2 Distance and Midpoint Formulas... 3 2.3 Lines... 3 2.4 Circles...
Contents Lines and Circles 3.1 Cartesian Coordinates.......................... 3. Distance and Midpoint Formulas.................... 3.3 Lines.................................. 3.4 Circles..................................
Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
Student Activity: To investigate an ESB bill
Student Activity: To investigate an ESB bill Use in connection with the interactive file, ESB Bill, on the Student s CD. 1. What are the 2 main costs that contribute to your ESB bill? 2. a. Complete the
Algebra and Geometry Review (61 topics, no due date)
Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties
ax 2 by 2 cxy dx ey f 0 The Distance Formula The distance d between two points (x 1, y 1 ) and (x 2, y 2 ) is given by d (x 2 x 1 )
SECTION 1. The Circle 1. OBJECTIVES The second conic section we look at is the circle. The circle can be described b using the standard form for a conic section, 1. Identif the graph of an equation as
Clovis Community College Core Competencies Assessment 2014 2015 Area II: Mathematics Algebra
Core Assessment 2014 2015 Area II: Mathematics Algebra Class: Math 110 College Algebra Faculty: Erin Akhtar (Learning Outcomes Being Measured) 1. Students will construct and analyze graphs and/or data
Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
The Distance Formula and the Circle
10.2 The Distance Formula and the Circle 10.2 OBJECTIVES 1. Given a center and radius, find the equation of a circle 2. Given an equation for a circle, find the center and radius 3. Given an equation,
5 Systems of Equations
Systems of Equations Concepts: Solutions to Systems of Equations-Graphically and Algebraically Solving Systems - Substitution Method Solving Systems - Elimination Method Using -Dimensional Graphs to Approximate
For each learner you will need: mini-whiteboard. For each small group of learners you will need: Card set A Factors; Card set B True/false.
Level A11 of challenge: D A11 Mathematical goals Starting points Materials required Time needed Factorising cubics To enable learners to: associate x-intercepts with finding values of x such that f (x)
Graphing - Slope-Intercept Form
2.3 Graphing - Slope-Intercept Form Objective: Give the equation of a line with a known slope and y-intercept. When graphing a line we found one method we could use is to make a table of values. However,
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Thursday, January 29, 2004 9:15 a.m. to 12:15 p.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, January 9, 004 9:15 a.m. to 1:15 p.m., only Print Your Name: Print Your School s Name: Print your name and
MATH 110 College Algebra Online Families of Functions Transformations
MATH 110 College Algebra Online Families of Functions Transformations Functions are important in mathematics. Being able to tell what family a function comes from, its domain and range and finding a function
The Geometry of a Circle Geometry (Grades 10 or 11)
The Geometry of a Circle Geometry (Grades 10 or 11) A 5 day Unit Plan using Geometers Sketchpad, graphing calculators, and various manipulatives (string, cardboard circles, Mira s, etc.). Dennis Kapatos
Graphs of Polar Equations
Graphs of Polar Equations In the last section, we learned how to graph a point with polar coordinates (r, θ). We will now look at graphing polar equations. Just as a quick review, the polar coordinate
Aim: How do we find the slope of a line? Warm Up: Go over test. A. Slope -
Aim: How do we find the slope of a line? Warm Up: Go over test A. Slope - Plot the points and draw a line through the given points. Find the slope of the line.. A(-5,4) and B(4,-3) 2. A(4,3) and B(4,-6)
CIRCLE COORDINATE GEOMETRY
CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle
GRAPHING IN POLAR COORDINATES SYMMETRY
GRAPHING IN POLAR COORDINATES SYMMETRY Recall from Algebra and Calculus I that the concept of symmetry was discussed using Cartesian equations. Also remember that there are three types of symmetry - y-axis,
Mohr s Circle. Academic Resource Center
Mohr s Circle Academic Resource Center Introduction The transformation equations for plane stress can be represented in graphical form by a plot known as Mohr s Circle. This graphical representation is
Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
Grade level: secondary Subject: mathematics Time required: 45 to 90 minutes
TI-Nspire Activity: Paint Can Dimensions By: Patsy Fagan and Angela Halsted Activity Overview Problem 1 explores the relationship between height and volume of a right cylinder, the height and surface area,
How to Graph Trigonometric Functions
How to Graph Trigonometric Functions This handout includes instructions for graphing processes of basic, amplitude shifts, horizontal shifts, and vertical shifts of trigonometric functions. The Unit Circle
Dear Accelerated Pre-Calculus Student:
Dear Accelerated Pre-Calculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, college-preparatory mathematics course that will also
High School Functions Interpreting Functions Understand the concept of a function and use function notation.
Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.
MATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
4.4 Transforming Circles
Specific Curriculum Outcomes. Transforming Circles E13 E1 E11 E3 E1 E E15 analyze and translate between symbolic, graphic, and written representation of circles and ellipses translate between different
What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra - Linear Equations & Inequalities T-37/H-37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.
Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that
CHAPTER 1 Linear Equations
CHAPTER 1 Linear Equations 1.1. Lines The rectangular coordinate system is also called the Cartesian plane. It is formed by two real number lines, the horizontal axis or x-axis, and the vertical axis or
Method To Solve Linear, Polynomial, or Absolute Value Inequalities:
Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with
Designing and Drawing a Sprocket Visualizing ideas through the creation of CAD solid models is a key engineering skill.
05 Webster St. Hanover Massachusetts 0339 Tel. 78 878 5 Fax 78 878 6708 Designing and Drawing a Sprocket Visualizing ideas through the creation of CAD solid models is a key engineering skill. The following
Sample Problems. Practice Problems
Lecture Notes Circles - Part page Sample Problems. Find an equation for the circle centered at (; ) with radius r = units.. Graph the equation + + = ( ).. Consider the circle ( ) + ( + ) =. Find all points
Mathematics on the Soccer Field
Mathematics on the Soccer Field Katie Purdy Abstract: This paper takes the everyday activity of soccer and uncovers the mathematics that can be used to help optimize goal scoring. The four situations that
7.4A/7.4B STUDENT ACTIVITY #1
7.4A/7.4B STUDENT ACTIVITY #1 Write a formula that could be used to find the radius of a circle, r, given the circumference of the circle, C. The formula in the Grade 7 Mathematics Chart that relates the
Equations. #1-10 Solve for the variable. Inequalities. 1. Solve the inequality: 2 5 7. 2. Solve the inequality: 4 0
College Algebra Review Problems for Final Exam Equations #1-10 Solve for the variable 1. 2 1 4 = 0 6. 2 8 7 2. 2 5 3 7. = 3. 3 9 4 21 8. 3 6 9 18 4. 6 27 0 9. 1 + log 3 4 5. 10. 19 0 Inequalities 1. Solve
Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan
Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan I. Topic: Slope-Intercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.
Florida Department of Education/Office of Assessment January 2012. Grade 6 FCAT 2.0 Mathematics Achievement Level Descriptions
Florida Department of Education/Office of Assessment January 2012 Grade 6 FCAT 2.0 Mathematics Achievement Level Descriptions Grade 6 FCAT 2.0 Mathematics Reporting Category Fractions, Ratios, Proportional
Graphing Linear Equations
Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope
3.3. Solving Polynomial Equations. Introduction. Prerequisites. Learning Outcomes
Solving Polynomial Equations 3.3 Introduction Linear and quadratic equations, dealt within Sections 3.1 and 3.2, are members of a class of equations, called polynomial equations. These have the general
High School Geometry Test Sampler Math Common Core Sampler Test
High School Geometry Test Sampler Math Common Core Sampler Test Our High School Geometry sampler covers the twenty most common questions that we see targeted for this level. For complete tests and break
Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in
Gouvernement du Québec Ministère de l Éducation, 2004 04-00910 ISBN 2-550-43701-2
Gouvernement du Québec Ministère de l Éducation, 2004 04-00910 ISBN 2-550-43701-2 Legal deposit Bibliothèque nationale du Québec, 2004 1. INTRODUCTION This Definition of the Domain for Summative Evaluation
Number Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
AP Physics 1 Summer Assignment
AP Physics 1 Summer Assignment AP Physics 1 Summer Assignment Welcome to AP Physics 1. This course and the AP exam will be challenging. AP classes are taught as college courses not just college-level courses,
x 2 + y 2 = 1 y 1 = x 2 + 2x y = x 2 + 2x + 1
Implicit Functions Defining Implicit Functions Up until now in this course, we have only talked about functions, which assign to every real number x in their domain exactly one real number f(x). The graphs
Trigonometric Functions: The Unit Circle
Trigonometric Functions: The Unit Circle This chapter deals with the subject of trigonometry, which likely had its origins in the study of distances and angles by the ancient Greeks. The word trigonometry
Name Date Class. Lines and Segments That Intersect Circles. AB and CD are chords. Tangent Circles. Theorem Hypothesis Conclusion
Section. Lines That Intersect Circles Lines and Segments That Intersect Circles A chord is a segment whose endpoints lie on a circle. A secant is a line that intersects a circle at two points. A tangent
Circles - Past Edexcel Exam Questions
ircles - Past Edecel Eam Questions 1. The points A and B have coordinates (5,-1) and (13,11) respectivel. (a) find the coordinates of the mid-point of AB. [2] Given that AB is a diameter of the circle,
BEST METHODS FOR SOLVING QUADRATIC INEQUALITIES.
BEST METHODS FOR SOLVING QUADRATIC INEQUALITIES. I. GENERALITIES There are 3 common methods to solve quadratic inequalities. Therefore, students sometimes are confused to select the fastest and the best
Unit 5: Coordinate Geometry Practice Test
Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this
Geometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
Graphing Linear Equations in Two Variables
Math 123 Section 3.2 - Graphing Linear Equations Using Intercepts - Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the
Factoring Quadratic Trinomials
Factoring Quadratic Trinomials Student Probe Factor x x 3 10. Answer: x 5 x Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials. Part 1 of the lesson consists
The Circumference Function
2 Geometry You have permission to make copies of this document for your classroom use only. You may not distribute, copy or otherwise reproduce any part of this document or the lessons contained herein
Algebra 1 Course Title
Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept
To draw a line. To create a construction line by specifying two points
Drawing Lines, Polygons and Rectangles The line is the basic object in AutoCAD. You can create a variety of lines: single lines, multiple line segments with and without arcs, multiple parallel lines, and
Requisite Approval must be attached
Requisite Approval must be attached CITRUS COMMUNITY COLLEGE DISTRICT DEPARTMENT Mathematics COURSE NUMBER MATH 148 TITLE Intermediate Algebra I THIS COURSE IS CLASSIFIED AS: DEGREE APPLICABLE UNIT VALUE
How To Factor Quadratic Trinomials
Factoring Quadratic Trinomials Student Probe Factor Answer: Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials Part 1 of the lesson consists of circle puzzles
CK-12 Geometry: Parts of Circles and Tangent Lines
CK-12 Geometry: Parts of Circles and Tangent Lines Learning Objectives Define circle, center, radius, diameter, chord, tangent, and secant of a circle. Explore the properties of tangent lines and circles.
Math 1. Month Essential Questions Concepts/Skills/Standards Content Assessment Areas of Interaction
Binghamton High School Rev.9/21/05 Math 1 September What is the unknown? Model relationships by using Fundamental skills of 2005 variables as a shorthand way Algebra Why do we use variables? What is a
To Be or Not To Be a Linear Equation: That Is the Question
To Be or Not To Be a Linear Equation: That Is the Question Linear Equation in Two Variables A linear equation in two variables is an equation that can be written in the form A + B C where A and B are not
Gouvernement du Québec Ministère de l Éducation, 2004 04-00815 ISBN 2-550-43543-5
Gouvernement du Québec Ministère de l Éducation, 004 04-00815 ISBN -550-43543-5 Legal deposit Bibliothèque nationale du Québec, 004 1. INTRODUCTION This Definition of the Domain for Summative Evaluation
Autumn 1 Maths Overview. Year groups Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 1 Number and place value. Counting. 2 Sequences and place value.
Autumn 1 Maths Overview. Year groups Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 1 Number and place Counting. 2 Sequences and place Number facts and counting. Money and time. Length, position and
Linear Approximations ACADEMIC RESOURCE CENTER
Linear Approximations ACADEMIC RESOURCE CENTER Table of Contents Linear Function Linear Function or Not Real World Uses for Linear Equations Why Do We Use Linear Equations? Estimation with Linear Approximations
MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:
MEMORANDUM To: All students taking the CLC Math Placement Eam From: CLC Mathematics Department Subject: What to epect on the Placement Eam Date: April 0 Placement into MTH 45 Solutions This memo is an
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will
MTH 100 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created June 6, 2011
MTH 00 College Algebra Essex County College Division of Mathematics Sample Review Questions Created June 6, 0 Math 00, Introductory College Mathematics, covers the mathematical content listed below. In
Graphs of Proportional Relationships
Graphs of Proportional Relationships Student Probe Susan runs three laps at the track in 12 minutes. A graph of this proportional relationship is shown below. Explain the meaning of points A (0,0), B (1,4),
Students will use various media (computer, graphing calculator, paper and pencil) to graph/sketch linear equations.
Title: Lines, Lines, Everywhere!! A discovery/exploration lesson investigating equations of the form y = mx + b to see how the values of b and m affects the graph. Link to Outcomes: Communication/ Cooperation
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:
Algebra II A Final Exam
Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.
MA107 Precalculus Algebra Exam 2 Review Solutions
MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write
Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
Picking Distractors for Multiple Choice Questions
Picking Distractors for Multiple Choice Questions Maplesoft, a division of Waterloo Maple Inc., 008 Multiple choice questions are an appealing format for both instructors and students. In fact, some instructors
D.2. The Cartesian Plane. The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles. D10 APPENDIX D Precalculus Review
D0 APPENDIX D Precalculus Review SECTION D. The Cartesian Plane The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles The Cartesian Plane An ordered pair, of real numbers has as its
FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA
FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x
PRACTICE FINAL. Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 10cm.
PRACTICE FINAL Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 1cm. Solution. Let x be the distance between the center of the circle
Curve Fitting in Microsoft Excel By William Lee
Curve Fitting in Microsoft Excel By William Lee This document is here to guide you through the steps needed to do curve fitting in Microsoft Excel using the least-squares method. In mathematical equations
PRACTICE PROBLEMS IN ALGEBRA, TRIGONOMETRY, AND ANALYTIC GEOMETRY
PRACTICE PROLEMS IN ALGERA, TRIGONOMETRY, AND ANALYTIC GEOMETRY The accompanying problems from the subjects covered on the Mathematics Placement Examination can be used by students to identify subject
EXPERIMENT: MOMENT OF INERTIA
OBJECTIVES EXPERIMENT: MOMENT OF INERTIA to familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body as mass plays in
Phase Portraits for u = A u
Phase Portraits for u = A u How to Construct a Phase Portrait Badly Threaded Solution Curves Solution Curve Tangent Matching Phase Portrait Illustration Phase plot by computer Revised Computer Phase plot
How To Pass A M3 Exam
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
Section 6.4. Lecture 23. Section 6.4 The Centroid of a Region; Pappus Theorem on Volumes. Jiwen He. Department of Mathematics, University of Houston
Section 6.4 Lecture 23 Section 6.4 The Centroid of a Region; Pappus Theorem on Volumes Jiwen He Department of Mathematics, University of Houston jiwenhe@math.uh.edu math.uh.edu/ jiwenhe/math1431 Jiwen
Polynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
Graphing Quadratic Functions
Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x- value and L be the y-values for a graph. 1. How are the x and y-values related? What pattern do you see? To enter the
NEOSHO COUNTY COMMUNITY COLLEGE MASTER COURSE SYLLABUS
NEOSHO COUNTY COMMUNITY COLLEGE MASTER COURSE SYLLABUS COURSE IDENTIFICATION Course Code/Number: MATH 113 Course Title: College Algebra Division: Applied Science (AS) Liberal Arts (LA) Workforce Development
Systems of Equations - Addition/Elimination
4.3 Systems of Equations - Addition/Elimination Objective: Solve systems of equations using the addition/elimination method. When solving systems we have found that graphing is very limited when solving
To learn the proper method for conducting and analyzing a laboratory experiment. To determine the value of pi.
Name Date Regents Physics Lab #3R Period Mrs. Nadworny Partners: (1 pt) Circumference vs. Diameter Due Date Purpose To learn the proper method for conducting and analyzing a laboratory experiment. To determine
1.1 Practice Worksheet
Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)
G C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.
THE COMPLEX EXPONENTIAL FUNCTION
Math 307 THE COMPLEX EXPONENTIAL FUNCTION (These notes assume you are already familiar with the basic properties of complex numbers.) We make the following definition e iθ = cos θ + i sin θ. (1) This formula
Additional Topics in Math
Chapter Additional Topics in Math In addition to the questions in Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, the SAT Math Test includes several questions that are
4.9 Graph and Solve Quadratic
4.9 Graph and Solve Quadratic Inequalities Goal p Graph and solve quadratic inequalities. Your Notes VOCABULARY Quadratic inequalit in two variables Quadratic inequalit in one variable GRAPHING A QUADRATIC
Geometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
GeoGebra. 10 lessons. Gerrit Stols
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
Advanced Math Study Guide
Advanced Math Study Guide Topic Finding Triangle Area (Ls. 96) using A=½ bc sin A (uses Law of Sines, Law of Cosines) Law of Cosines, Law of Cosines (Ls. 81, Ls. 72) Finding Area & Perimeters of Regular
CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical