Solving Linear & Graphing Inequalities
|
|
|
- Evelyn Miles
- 6 years ago
- Views:
Transcription
1 Solving Linear & Graphing Inequalities Sep 7 11:06 PM 1
2 Open circle on the graph means that the inequality will be greater than or less than. > or < Closed circle on the graph means that the inequality will be greater than or equal to OR less equal than or equal. Sep 13 1:02 PM 2
3 If the direction of the GRAPH is pointed to the LEFT, then inequality is "less than" or "less than or equal to" If the direction of the GRAPH is pointed to the RIGHT, then inequality is "greater than" or "greater than or equal to" Sep 13 1:08 PM 3
4 greater than side of any inequality > OR less than side of any inequality less than side of any inequality > greater than side of any inequality Oct 21 11:03 AM 4
5 EXAMPLE 1 Given the graph, below : a) Write a statement in words to express the graph on the number. b) Write an inequality to express the graph on the number line, use x as your variable SOLUTION a) All numbers less than 2. b) or Sep 13 12:58 PM 5
6 EXAMPLE 2 Given the graph, below : a) Write a statement in words to express the graph on the number. b) Write an inequality to express the graph on the number line, use x as your variable SOLUTION a) All numbers greater than or equal to 5. b) or Sep 13 1:23 PM 6
7 EXAMPLE 3 Solve the inequality, then graph the solution set on a number line. SOLUTION Oct 21 11:13 AM 7
8 x 3 x is greater than or equal to Oct 21 11:20 AM 8
9 EXAMPLE 4 Solve the inequality, then graph the solution set on a number line. SOLUTION 23 < 7 5x Oct 21 11:25 AM 9
10 23 < 7 5x < 5x 30 < 5x 5 5 Whenever, you multiply or divide by a NEGATIVE number change the direction of the inequality symbol. 6 > x x is less than than Oct 21 11:30 AM 10
11 EXAMPLE 5 Solve the inequality, then graph the solution set on a number line. SOLUTION Eliminate the fractions by multiplying the entire equation by the least common denominator. Least common denominator of 4, 14, and 7 is ( ) Oct 21 11:37 AM 11
12 28( ) Oct 21 11:41 AM 12
13 +4x + 4x Oct 21 12:01 PM 13
14 Keep the direction of the inequality symbol the same, we divided by a positive number. It does matter that the solution is negative number Oct 21 12:03 PM 14
15 EXAMPLE 6 Solve the inequality, then graph the solution set on a number line. SOLUTION 1 + x + x Oct 21 1:28 PM 15
16 The inequality is TRUE. ALL REAL NUMBERS Sep 7 10:14 PM 16
17 EXAMPLE 7 Solve the inequality, then graph the solution set on a number line. SOLUTION 6x 6x Oct 21 1:35 PM 17
18 The inequality is FALSE. NO SOLUTION Oct 21 1:39 PM 18
19 COMPOUND INEQUALITIES Sep 13 12:44 PM 19
20 EXAMPLE 8 Solve the inequality, then graph the solution set on a number line. SOLUTION Oct 21 1:42 PM 20
21 Oct 21 1:44 PM 21
22 How to graph a compound inequality? Rewrite as 2 separate inequalities. AND Sep 7 10:33 PM 22
23 Graph each inequality separately Oct 21 1:40 PM 23
24 When graphing compound inequalities with an AND, we will take the INTERSECTION of the graphs Sep 13 2:08 PM 24
25 EXAMPLE 9 Solve the inequality, then graph the solution set on a number line. 4x + 3 6x >11 OR 4 (3x 5) 12 SOLUTION 4x + 3 6x >11OR 4 1(3x 5) 12 2x + 3< x < 8 OR 4 1(3x 5) x OR 9 3x 12 Oct 21 2:18 PM 25
26 2x 8 2 > OR 9 3x x 3 2 x < 4 x is less than 4 3x x 1 x is greather than or equal to Oct 21 1:55 PM 26
27 Attachments notebook.galleryitem
constant EXAMPLE #4:
Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value
Part Mark Answer Further Information. Part Mark Answer Further Information Award 1 mark for 20, 15, 35 or. Part Mark Answer Further Information
Cambridge International Examinations Cambridge Checkpoint MATHEMATICS 1112/01 Paper 1 For Examination from 2014 SPECIMEN MARK SCHEME MAXIMUM MARK: 50 This document consists of 11 printed pages and 1 blank
y-intercept remains constant?
1. The graph of a line that contains the points ( 1, 5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? F) G) H) J) 2. The graph
You found trigonometric values using the unit circle. (Lesson 4-3)
You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify
Sect Linear Equations in Two Variables
99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite
Ideas beyond Number. Activity worksheets
Ideas beyond Number Activity sheet 1 Task 1 Some students started to solve this equation in different ways: For each statement tick True or False: = = = = Task 2: Counter-examples The exception disproves
Section 2.3 Task List
Summer 2017 Math 108 Section 2.3 67 Section 2.3 Task List Work through each of the following tasks, carefully filling in the following pages in your notebook. Section 2.3 Function Notation and Applications
Learn to solve multistep equations.
Learn to solve multistep equations. Levi has half as many comic books as Jamal has. If you add 6 to the number of comic books Jamal has and then divide by 7, you get the number of comic books Brooke has.
Course Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
Part I: Bell Work When solving an inequality, when would you flip the inequality sign?
Algebra 135 Seminar Lesson 55 Part I: Bell Work When solving an inequality, when would you flip the inequality sign? Part II: Mini-Lesson Review for Ch 6 Test Give a review lesson for the Chapter 6 test.
Graphs, Linear Equations and Functions
Graphs, Linear Equations and Functions There are several ways to graph a linear equation: Make a table of values Use slope and y-intercept Use x and y intercepts Oct 5 9:37 PM Oct 5 9:38 PM Example: Make
Solving Inequalities with Variables on Both Sides 2-5. Warm Up. Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 2x = 7x + 15 x = 3 2. 3y 21 = 4 2y y = 5 3. 2(3z + 1) = 2(z + 3) z = 1 4. 3(p 1) = 3p + 2 no solution
2.3 BUILDING THE PERFECT SQUARE
16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized
CK-12 Algebra II with Trigonometry Concepts 1
1.1 Subsets of Real Numbers 1. Rational Number. Irrational Number. Rational Number 4. Whole Number 5. Integer 6. Irrational Number 7. Real, Rational, Integer, Whole, and Natural Number 8. Real and Rational
Outcome 9 Review Foundations and Pre-Calculus 10
Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line
Radical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:
Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical
,,, A. 1 2 D. 2 E D C B. 1. Which fraction is another name for.02? 2. Which number is the lowest? A. -23 B. -33 C. -43 D.
6 th Grade Math End of the Year Review Directions: Solve each problem below. Show all your work to each question on a separate sheet of paper. You have learned each of these concepts, think hard and do
E. Slope-Intercept Form and Direct Variation (pp )
and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the
Minute Simplify: 12( ) = 3. Circle all of the following equal to : % Cross out the three-dimensional shape.
Minute 1 1. Simplify: 1( + 7 + 1) =. 7 = 10 10. Circle all of the following equal to : 0. 0% 5 100. 10 = 5 5. Cross out the three-dimensional shape. 6. Each side of the regular pentagon is 5 centimeters.
Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3
Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3 Rewrite the equation in standard form. The equation is now in standard form
Solving Equations and Graphing
Solving Equations and Graphing Question 1: How do you solve a linear equation? Answer 1: 1. Remove any parentheses or other grouping symbols (if necessary). 2. If the equation contains a fraction, multiply
Chapter 7 Math Guide
I can write fractions as a sum Write as unit fractions This means the fractions are broken into each individual unit/1 single piece. The fraction is /6. The model shows that pieces are shaded in. If you
171S5.4p Properties of Logarithmic Functions. November 20, CHAPTER 5: Exponential and Logarithmic Functions. Examples. Express as a product.
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3 Logarithmic Functions
CH4-1 Inequalities and Their Graphs
Fall, 2011-2012 Mrs. Kummer Background: Many times we don t know the answer but we certainly know what rangewe need or want. For example, nurses want to see body temperatures of what? Nurses might look
Additional Practice. Name Date Class. 1. Estimate the numbers represented by points A E. 2. Graph the following numbers on the number line below.
Additional Practice Investigation 1 1. Estimate the numbers represented by points A E. A B C D E 6 4 2 0 2 4 6 2. Graph the following numbers on the number line below. 1 4 a. - 2 b. 4 c. - 5.5 d. 2 7 2
Fractions Presentation Part 1
New Jersey Center for Teaching and Learning Slide / Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and
2-3. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra McDougal 1 Algebra 1
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 5a = 30 6 2. 10 3. 4. Graph each inequality. 5. x 10 6. x < 3 Objectives Solve one-step inequalities
Lesson 1 6. Algebra: Variables and Expression. Students will be able to evaluate algebraic expressions.
Lesson 1 6 Algebra: Variables and Expression Students will be able to evaluate algebraic expressions. P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable
COMPETENCY BASED ASSESSMENT TEST SUBJECT: MATHEMATICS TOTAL MARKS: 25. Points to Remember
COMPETENCY BASED ASSESSMENT TEST SUBJECT: MATHEMATICS TOTAL MARKS: 25 CLASS: III Name: School: TIME : 1 HOUR Roll No: Section: Points to Remember 1. First write your name, roll number, section and the
BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals BIG IDEA 1:
BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals Multiplying and Dividing Decimals Explain the difference between an exact answer and an estimated
MCAS/DCCAS Mathematics Correlation Chart Grade 4
MCAS/DCCAS Mathematics Correlation Chart Grade 4 MCAS Finish Line Mathematics Grade 4 MCAS Standard DCCAS Standard DCCAS Standard Description Unit 1: Number Sense Lesson 1: Whole Number Place Value Lesson
MATH Exam 2 Solutions November 16, 2015
MATH 1.54 Exam Solutions November 16, 15 1. Suppose f(x, y) is a differentiable function such that it and its derivatives take on the following values: (x, y) f(x, y) f x (x, y) f y (x, y) f xx (x, y)
Slope. Domain 2 Lesson 11. Getting the Idea
Domain Lesson Slope Common Core Standard: 8.EE. Getting the Idea The graph of a linear equation is a straight line. The steepness of the line is called its slope. The slope shows the rate at which two
Lesson 11: Linear Functions, Part 2
Lesson 11 continues the study of linear functions. In this lesson, we look at how to write linear equations in slope-intercept and general form and applications where these may be used. We also look at
Prolegomena. Chapter Using Interval Notation 1
Chapter 1 Prolegomena 1.1 Using Interval Notation 1 Interval notation is another method for writing domain and range. In set builder notation braces (curly parentheses {} ) and variables are used to express
5-6 Study Guide. Radical Expressions and Rational Exponents. Attendance Problems. Simplify each expression. (No decimal answers!
Page 1 of 12 Radical Expressions and Rational Exponents Attendance Problems. Simplify each expression. (No decimal answers) 11 8 7 7 2 2.. 2. 11 6. I can rewrite radical expressions by using rational exponents.
Discovery Activity: Slope
Page 1 of 14 1. Lesson Title: Discovering Slope-Intercept Form 2. Lesson Summary: This lesson is a review of slope and guides the students through discovering slope-intercept form using paper/pencil and
Solving Inequalities with Variables on Both Sides
Warm Up Lesson Presentation Lesson Quiz 1 Section 3-5 1 2 pts Bell Quiz 3-5 Solve each equation. 1. 2x = 7x + 15 3 pts 2. Solve and graph 5(2 b) > 5 2. 5 pts possible Section 3-5 2 Questions on 3-4 Section
Chapter 0 Getting Started on the TI-83 or TI-84 Family of Graphing Calculators
Chapter 0 Getting Started on the TI-83 or TI-84 Family of Graphing Calculators 0.1 Turn the Calculator ON / OFF, Locating the keys Turn your calculator on by using the ON key, located in the lower left
Honors Algebra 2 w/ Trigonometry Chapter 14: Trigonometric Identities & Equations Target Goals
Honors Algebra w/ Trigonometry Chapter 14: Trigonometric Identities & Equations Target Goals By the end of this chapter, you should be able to Identify trigonometric identities. (14.1) Factor trigonometric
Grade 7 Math notes Unit 5 Operations with Fractions
Grade 7 Math notes Unit Operations with Fractions name: Using Models to Add Fractions We can use pattern blocks to model fractions. A hexagon is whole A trapezoid is of the whole. A parallelogram is of
CHAPTER 3 DECIMALS. EXERCISE 8 Page Convert 0.65 to a proper fraction may be written as: 100. i.e = =
CHAPTER 3 DECIMALS EXERCISE 8 Page 21 1. Convert 0.65 to a proper fraction. 0.65 may be written as: 0.65 100 100 i.e. 0.65 65 100 Dividing both numerator and denominator by 5 gives: 65 13 100 20 Hence,
GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: Read (in standard form) whole numbers. whole numbers Equivalent Whole Numbers
CRAWFORDSVILLE COMMUNITY SCHOOL CORPORATION 1 GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: 2019 2020 GRADING PERIOD: QUARTER 1 MASTER COPY 1 20 19 NUMBER SENSE Whole Numbers 4.NS.1: Read and write whole
MATH 021 TEST 2 REVIEW SHEET
TO THE STUDENT: MATH 021 TEST 2 REVIEW SHEET This Review Sheet gives an outline of the topics covered on Test 2 as well as practice problems. Answers for all problems begin on page 8. In several instances,
Algebra 1 Online:
Dear Algebra 2 Students, Within this packet you will find mathematical concepts and skills learned in Algebra 1 that are the foundation from which Algebra 2 is built. These concepts need to be reviewed
Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane
Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant
1.7 Parallel and Perpendicular Lines
Section 1.7 Parallel and Perpendicular Lines 11 Eplaining the Concepts 17. Name the five forms of equations of lines given in this section. 18. What tpe of line has one -intercept, but no -intercept? 19.
2. Questions on Classwork and Homework form yesterday. 4. Completing the square to solve quadratic
1. Warm -up word problem - 2. Questions on Classwork and Homework form yesterday 3. Number Sense. 4. Completing the square to solve quadratic equations 1 2 3 Apr 12 12:35 PM 4 Apr 13 2:12 PM 5 6 7 factors
Block: Date: Name: REVIEW Linear Equations. 7.What is the equation of the line that passes through the point (5, -3) and has a slope of -3?
Name: REVIEW Linear Equations 1. What is the slope of the line y = -2x + 3? 2. Write the equation in slope-intercept form. Block: Date: 7.What is the equation of the line that passes through the point
Outcome 7 Review. *Recall that -1 (-5) means
Outcome 7 Review Level 2 Determine the slope of a line that passes through A(3, -5) and B(-2, -1). Step 1: Remember that ordered pairs are in the form (x, y). Label the points so you can substitute into
Unit 11: Linear Equations and Inequalities
Section 11.1: General Form ax + by = c Section 11.2: Applications General Form Section 11.3: Linear Inequalities in Two Variables Section 11.4: Graphing Linear Inequalities in Two Variables KEY TERMS AND
Perfect Squares that are Written as Fractions or Decimals
Math 9: Unit 1 Lesson 2 Perfect Squares that are Written as Fractions or Decimals Part 1: Fractions There are two ways to determine the square root of a perfect square that is written as a fraction: 1.
Math 154 :: Elementary Algebra
Math :: Elementary Algebra Section 9. Section 9. Section 9. Section 9. Section 9. Section 9.6 Math :: Elementary Algebra Section 9. Introduction to Square Roots. This answer should be in your own words..
Roots and Radicals Chapter Questions
Roots and Radicals Chapter Questions 1. What are the properties of a square? 2. What does taking the square root have to do with the area of a square? 3. Why is it helpful to memorize perfect squares?
DIVISION BY FRACTIONS
DIVISION BY FRACTIONS 6.. 6.. Division by fractions introduces three methods to help students understand how dividing by fractions works. In general, think of division for a problem like 8 as, In 8, how
Keystone Exams: Algebra I Assessment Anchors and Eligible Content. Pennsylvania Department of Education
Keystone Exams: Algebra I Assessment Anchors and Pennsylvania Department of Education www.education.state.pa.us 2010 PENNSYLVANIA DEPARTMENT OF EDUCATION General Introduction to the Keystone Exam Assessment
Cambridge Secondary 1 Progression Test. Mark scheme. Mathematics. Stage 9
Cambridge Secondary 1 Progression Test Mark scheme Mathematics Stage 9 DC (CW/SW) 9076/8RP These tables give general guidelines on marking answers that involve number and place value, and units of length,
UNC Charlotte 2012 Algebra
March 5, 2012 1. In the English alphabet of capital letters, there are 15 stick letters which contain no curved lines, and 11 round letters which contain at least some curved segment. How many different
x < 7 x > 3 x 9 2x - 6 = x = 4 3x = x = x = -2 x = 7 5x + 8 > 23 2x 4 14 x + 3 < NOTES Solving Multi Step Inequalities
BELLWORK: Solve each equation. A) x 16 = 12 B) 3x + 5 = 1 C) 2(x 3) = 8 +16 +16 x = 4-5 -5 3x = -6 3 3 x = -2 2x - 6 = 8 +6 +6 2x = 14 2 2 x = 7 LESSON 2. 4 - Solving Multi-Step Inequalities Works very
Numbers & Operations Chapter Problems
Numbers & Operations 8 th Grade Chapter Questions 1. What are the properties of a square? 2. What does taking the square root have to do with the area of a square? 3. Why is it helpful to memorize perfect
Summer Assignment Packet 2011
Direction: Multiple Choice -Choose the correct answer by circling the letter. 1. Which number represents four hundred twenty-eight thousand six hundred eight? A 4,268 B 42,868 C 428,608 D 428,680 2. What
Quick Answers - Chapter : Relations and Functions: Check for Understanding
of 38 9/5/2012 8:07 AM Quick Answers - Chapter 1 1-1: Relations and Functions: Check for Understanding 1. 9. 2. 10. 11. 3. 12. 13. 4. 14. 15. of 38 9/5/2012 8:07 AM 5. 16. 6. 7. 8. 1-1: Relations and Functions:
Standardized Tasks. Eighth Grade
Standardized Tasks Eighth Grade Problem 1 (from AIMS: The Pythagorean Relationship) Objective 3.02 Apply geometric properties and relationships, including the Pythagorean theorem to solve problems. Objective
Grade 4 Mathematics Indiana Academic Standards Crosswalk
Grade 4 Mathematics Indiana Academic Standards Crosswalk 2014 2015 The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content and the ways
Wednesday, May 4, Proportions
Proportions Proportions Proportions What are proportions? Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar
CCS Algebra I Assessment Test 1B Name Per
CCS Algebra I Assessment Test 1B Name Per Do this test carefully showing all of your work and, in the case of multiple choice items, filling in the circle of the letter of the correct response. Note which
Review for Mastery. Identifying Linear Functions
Identifying Linear Functions You can determine if a function is linear by its graph, ordered pairs, or equation. Identify whether the graph represents a linear function. Step 1: Determine whether the graph
Use smooth curves to complete the graph between and beyond the vertical asymptotes.
5.3 Graphs of Rational Functions Guidelines for Graphing Rational Functions 1. Find and plot the x-intercepts. (Set numerator = 0 and solve for x) 2. Find and plot the y-intercepts. (Let x = 0 and solve
Introduction to Fractions
Introduction to Fractions A fraction is a quantity defined by a numerator and a denominator. For example, in the fraction ½, the numerator is 1 and the denominator is 2. The denominator designates how
A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
3.2 Proving Identities
3.. Proving Identities www.ck.org 3. Proving Identities Learning Objectives Prove identities using several techniques. Working with Trigonometric Identities During the course, you will see complex trigonometric
TABLE OF CONTENTS. Number and Operations Algebra Geometry Measurement 35, 89, 148, 149, 150, 200, 252, 254, 274, 297
Mathematical Reasoning Level D Table of Contents TABLE OF CONTENTS About the Author...ii About This Book... vii How to Use This Book... vii Teaching Suggestions... vii General Comments... viii Answers...
Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8
Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2007 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
Honors Algebra 2 Assignment Sheet - Chapter 1
Assignment Sheet - Chapter 1 #01: Read the text and the examples in your book for the following sections: 1.1, 1., and 1.4. Be sure you read and understand the handshake problem. Also make sure you copy
4 th Grade Mathematics Learning Targets By Unit
INSTRUCTIONAL UNIT UNIT 1: WORKING WITH WHOLE NUMBERS UNIT 2: ESTIMATION AND NUMBER THEORY PSSA ELIGIBLE CONTENT M04.A-T.1.1.1 Demonstrate an understanding that in a multi-digit whole number (through 1,000,000),
Variables and expressions Block 1 Student Activity Sheet
Block 1 Student Activity Sheet 1. Record your understandings of key vocabulary for this topic. Vocabulary term My understanding of what the term means Examples that show the meaning of the term. a. Variable
NOTES: SIGNED INTEGERS DAY 1
NOTES: SIGNED INTEGERS DAY 1 MULTIPLYING and DIVIDING: Same Signs (POSITIVE) + + = + positive x positive = positive = + negative x negative = positive Different Signs (NEGATIVE) + = positive x negative
Appendix M TERMINOLOGY. Slope of a Line. Slope. Undefined Slope. Slope-Intercept Form
Appendices : Slope of a Line TERMINOLOGY For each of the following terms, provide ) a definition in our own words, 2) the formal definition (as provided b our text or instructor), and ) an example of the
Triangles, Rectangles, Squares, and Circles
Triangles, Rectangles, Squares, and Circles Triangle sides Rectangle 4 sides Lesson 21 21 Square length a rectangle with 4 equal sides width Measures of a circle: Radius = 1 diameter Diameter = 2 radius
Solutions to Problem Set 6 - Fall 2008 Due Tuesday, Oct. 21 at 1:00
18.781 Solutions to Problem Set 6 - Fall 008 Due Tuesday, Oct. 1 at 1:00 1. (Niven.8.7) If p 3 is prime, how many solutions are there to x p 1 1 (mod p)? How many solutions are there to x p 1 (mod p)?
4-2 Using Intercepts. Warm Up Lesson Presentation Lesson Quiz
4-2 Using Intercepts Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 5x + 0 = 10 2 2. 33 = 0 + 3y 11 3. 1 4. 2x + 14 = 3x + 4 2 5. 5y 1 = 7y +
The bottom number in the fraction is called the denominator. The top number is called the numerator.
For Topics 8 and 9, the students should know: Fractions are a part of a whole. The bottom number in the fraction is called the denominator. The top number is called the numerator. Equivalent fractions
Principles of Mathematics 12: Explained!
Principles of Mathematics : Eplained! www.math.com PART I MULTIPLICATION & DIVISION IDENTITLES Algebraic proofs of trigonometric identities In this lesson, we will look at various strategies for proving
1999 Mathcounts National Sprint Round Solutions
999 Mathcounts National Sprint Round Solutions. Solution: 5. A -digit number is divisible by if the sum of its digits is divisible by. The first digit cannot be 0, so we have the following four groups
You MUST know the big 3 formulas!
Name 3-13 Review Geometry Period Date Unit 3 Lines and angles Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation Writing the equation of a line given a graph. Graphing
Working with Integer Exponents
4.2 Working with Integer Exponents GOAL Investigate powers that have integer or zero exponents. LEARN ABOUT the Math The metric system of measurement is used in most of the world. A key feature of the
In this section, you will learn the basic trigonometric identities and how to use them to prove other identities.
4.6 Trigonometric Identities Solutions to equations that arise from real-world problems sometimes include trigonometric terms. One example is a trajectory problem. If a volleyball player serves a ball
TABLE OF CONTENTS. NCTM Standards. Number and Operations Algebra Geometry Measurement 25, 38, 41, 101, 119, 219, 227, 230, 244, 252, 269, 273
NCTM Stards Action Skills Addition TABLE OF CONTENTS About the Authors...ii NCTM Stards... iii How to Use This Book... vii Teaching Suggestions... vii Definitions... 85 Answers... 9 Number Operations Algebra
Lesson 7A Slope-Intercept Formula
Lesson 7A Slope-Intercept Formula Terms Two new words that describe what we've been doing in graphing lines are slope and intercept. The slope is referred to as "m" (a mountain has slope and starts with
Sample: Do Not Reproduce RAT3 STUDENT PAGES. RATIONAL NUMBERS Student Pages for Packet 3: Ordering and Equivalence.
Name Period Date RATIONAL NUMBERS Student Pages for Packet : Ordering and Equivalence RAT. RAT.2 Ordering Fractions on a Number Line Use sense-making strategies to compare and order fractions. Identify
Lesson 16: The Computation of the Slope of a Non Vertical Line
++ Lesson 16: The Computation of the Slope of a Non Vertical Line Student Outcomes Students use similar triangles to explain why the slope is the same between any two distinct points on a non vertical
Total Marks : 100 READ THE FOLLOWING DIRECTIONS CAREFULLY:
Mathematics Writing Time : 2 Hours Total Marks : 100 READ THE FOLLOWING DIRECTIONS CAREFULLY: 1. Do not write in the first fifteen minutes. This time is to be spent on reading the questions. After having
Thinking Rationally. Identifying and Ordering Rational Numbers
Thinking Rationally Identifying and Ordering Rational Numbers 1 WARM UP Determine the fraction represented by the shaded part of each grid. If necessary, rewrite in lowest terms. 1. 2. LEARNING GOALS Understand
TONBRIDGE SCHOOL. Year 9 Entrance Examinations for entry in 2016 MATHEMATICS. Saturday, 7th November 2015 Time allowed: 1 hour Total Marks: 100
Name:... School: TONBRIDGE SCHOOL Year 9 Entrance Examinations for entry in 2016 MATHEMATICS Saturday, 7th November 2015 Time allowed: 1 hour Total Marks: 100 Instructions: THIS IS A NON-CALCULATOR PAPER
Investigating Intercepts
Unit: 0 Lesson: 01 1. Can more than one line have the same slope? If more than one line has the same slope, what makes the lines different? a. Graph the following set of equations on the same set of aes.
Factored Form When a = 1
Lesson 4 Hart Interactive Algebra Lesson 4: Factored Form When a = Opening Activity Graph Exchange Your group will need: one quadratic graph. A. For your given graph, circle the graph number on the table
Tennessee Senior Bridge Mathematics
A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10 A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts
4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. ( 2, 8) and (4, 2) 1 3. (3, 3) and (12,
Divide Fractions and Whole Numbers
Lesson 8 Divide Fractions and Whole Numbers You can use a number line to help you divide a whole number by a fraction Divide 6 4 _ 2 Step Draw a number line from 0 to 6 Divide the number line into halves
MATH 074 REVIEW FOR CHAPTER 2 and 3 - Sections , ( Fractions) a) 18: b) 20: c) 48: d) 60: e) 59:
MATH 074 REVIEW FOR CHAPTER 2 and 3 - Sections 2.1-2.4, 3.1-3.5 ( Fractions) A. Can you list all the factors of a given number? 1. List all the factors of each of the following numbers. a) 18: b) 20: c)