Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = 7 + m = m 15 = m = 7 + m 8 = = 8


 Anne Arnold
 2 years ago
 Views:
Transcription
1
2 Bell Ringer Solve each equation. Show you work. the solution = 7 + m 8 = 7 + m = m 15 = m 8 = 7 + m 8 = = 8
3 Answers to Homework Worksheet 21
4 Today s Objectives Solving Two Step Equations
5 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Our first two step equation We don t see a multiplication sign so we assume it is multiplication 2x + 5 = x + 0 = 10 2x = 10 2 x = 5 2 2x + 5 = 15 2(5) + 5 = = = 15 The process is basically the same as a one step Identify the variable, it is x Notice the operation of addition, so we do the opposite to both sides Now subtract from both sides The 5 s cancel each other out, by adding/subtracting to 0 (zero) 15 minus 5 is 10 Notice the operation of multiplication, so we do the opposite to both sides Now divide from both sides The 2 s cancel each other out, by dividing to 1 10 divided by 2 is 5 The solution is x = 5 the solution
6 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation We don t see a multiplication sign so we assume it is multiplication 3x  1 = x + 0 = 21 3x = 21 3 x = 7 3 3x  1 = 20 3(7)  1 = = = 20 Identify the variable, it is x Notice the operation of subtraction, so we do the opposite to both sides Now add to both sides The 1 s cancel each other out, by adding/subtracting to 0 (zero) 20 plus 1 is 21 Notice the operation of multiplication, so we do the opposite to both sides Now divide from both sides The 3 s cancel each other out, by dividing to 1 21 divided by 3 is 7 The solution is x = 7 the solution
7 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation We don t see a multiplication sign so we assume it is multiplication 3b  5 = b + 0 = 183b = b = 63b  5 = 133(6)  5 = = = 13 Identify the variable, it is b Notice the operation of subtraction, so we do the opposite to both sides Now add to both sides The 5 s cancel each other out, by adding/subtracting to 0 (zero) 13 plus 5 is 18 Notice the operation of multiplication, so we do the opposite to both sides Now divide from both sides The 3 s cancel each other out, by dividing to 1 18 divided by 3 is 6 The solution is b = 6 the solution
8 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation, but with division n  3 = n  3 = = 7 2 n + 0 = 10 2 (2) n = 10 (2) = 7 7 = 7 n = 20 Identify the variable, it is n Notice the operation of subtraction, so we do the opposite to both sides Now add to both sides The 3 s cancel each other out, by adding/subtracting to 0 (zero) 7 plus 3 is 10 Notice the operation of division, so we do the opposite to both sides Now multiply both sides The 2 s cancel each other out, by multiplying to 1 10 multiplied by 2 is 20 The solution is n = 20 the solution
9 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation, but with division x + 9 = x + 0 = 4 7 (7) x = 4 (7) 7 x = 28 x + 9 = = = = 13 Identify the variable, it is x Notice the operation of addition, so we do the opposite to both sides Now subtract from both sides The 9 s cancel each other out, by adding/subtracting to 0 (zero) 13 minus 9 is 4 Notice the operation of division, so we do the opposite to both sides Now multiply both sides The 7 s cancel each other out, by multiplying to 1 4 multiplied by 7 is 28 The solution is x = 28 the solution
10 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation, but with division x + 3 = x + 0 = 84 (4) x = 8 (4) 4 x + 3 = = = 55 = 5 x = 32 Identify the variable, it is x Notice the operation of addition, so we do the opposite to both sides Now subtract from both sides The 3 s cancel each other out, by adding/subtracting to 0 (zero) 5 minus 3 is 8 Notice the operation of division, so we do the opposite to both sides Now multiply both sides The 4 s cancel each other out, by multiplying to 18 multiplied by 7 is 32 The solution is x = 32 the solution
11 Quick Review x + 6 = x + 0 = 22 (2) x = 2 (2) 2 x = 4 x + 6 = = = 4 4 = 4 14j  7 = j + 0 = 91 14j = j = 7 14j  7 = 91 14(7)  7 = = = a  3 = a + 0 = 8 240a = a = a  3 = = = 5 5 = 5
12 x + 7 = x + 0 = 44 (4) x = 4 (4) 4 x = 16 x + 7 = = = = 11 Quick Review Show your work as you solve the following equations. Then check each. 1. x + 7 = b  50 = h  8 = b  50 = b = b = 22 3b  50 = 16 3(22)  50 = = = 16 7h  8 = h = h = 5 7h  8 = 27 7(5)  8 = = = 27
13 z  5 = (3) z = 2 (3) 3 z = 6 z  5 = = = 33 = 3 Quick Review Show your work as you solve the following equations. Then check each. 4. z  5 = m  13 = k + 12 = m  13 = m = m = 9 6m  13 = 41 6(9)  13 = = = 414k + 12 = k = k = 54k + 12 = 204(5) + 12 = = = 20
14 v  12 = (9) v = 21 (9) 9 v = 189 v  12 = = = 9 9 = 9 Quick Review Show your work as you solve the following equations. Then check each. 7. v  12 = s  7 = p + 7 = s  7 = s = s = 22 2s  7 = 37 2(22)  7 = = = 379p + 7 = p = p = 119p + 7 = 1069(11) + 7 = = = 106
15 Quick Review Show your work as you solve the following equations. Then check each. 10. g + 9 = 203 g + 9 = (3) g = 11 (3) 3 g = 33 g + 9 = = = = 20
16 SHOWING YOUR WORK 10. g + 9 = 203 g + 9 = (3) g = 11 (3) 3 g = 33 g + 9 = = = = 20
17 Assignment Worksheet 73 A
18 Answers to Homework Worksheet 73 A
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 5 Subtracting Integers
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 5 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More informationOrder of Operations  PEMDAS. Rules for Multiplying or Dividing Positive/Negative Numbers
Order of Operations  PEMDAS *When evaluating an expression, follow this order to complete the simplification: Parenthesis ( ) EX. (52)+3=6 (5 minus 2 must be done before adding 3 because it is in parenthesis.)
More information63 Solving Systems by Elimination
Warm Up Simplify each expression. 1. 2y 4x 2(4y 2x) 2. 5(x y) + 2x + 5y Write the least common multiple. 3. 3 and 6 4. 4 and 10 5. 6 and 8 Objectives Solve systems of linear equations in two variables
More informationFractions, Ratios, and Proportions Work Sheets. Contents
Fractions, Ratios, and Proportions Work Sheets The work sheets are grouped according to math skill. Each skill is then arranged in a sequence of work sheets that build from simple to complex. Choose the
More informationMEP Y9 Practice Book A
1 Base Arithmetic 1.1 Binary Numbers We normally work with numbers in base 10. In this section we consider numbers in base 2, often called binary numbers. In base 10 we use the digits 0, 1, 2, 3, 4, 5,
More informationFRACTIONS COMMON MISTAKES
FRACTIONS COMMON MISTAKES 0/0/009 Fractions Changing Fractions to Decimals How to Change Fractions to Decimals To change fractions to decimals, you need to divide the numerator (top number) by the denominator
More information(2 4 + 9)+( 7 4) + 4 + 2
5.2 Polynomial Operations At times we ll need to perform operations with polynomials. At this level we ll just be adding, subtracting, or multiplying polynomials. Dividing polynomials will happen in future
More informationSolving systems by elimination
December 1, 2008 Solving systems by elimination page 1 Solving systems by elimination Here is another method for solving a system of two equations. Sometimes this method is easier than either the graphing
More informationChapter 5: The normal approximation for data
Chapter 5: The normal approximation for data Context................................................................... 2 Normal curve 3 Normal curve.............................................................
More informationQuadratics  Build Quadratics From Roots
9.5 Quadratics  Build Quadratics From Roots Objective: Find a quadratic equation that has given roots using reverse factoring and reverse completing the square. Up to this point we have found the solutions
More information25 Integers: Addition and Subtraction
25 Integers: Addition and Subtraction Whole numbers and their operations were developed as a direct result of people s need to count. But nowadays many quantitative needs aside from counting require numbers
More informationSometimes it is easier to leave a number written as an exponent. For example, it is much easier to write
4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall
More informationMath Common Core Sampler Test
High School Algebra Core Curriculum Math Test Math Common Core Sampler Test Our High School Algebra sampler covers the twenty most common questions that we see targeted for this level. For complete tests
More informationTons of Free Math Worksheets at:
Topic : Equations of Circles  Worksheet 1 form which has a center at (6, 4) and a radius of 5. x 28x+y 28y12=0 circle with a center at (4,4) and passes through the point (7, 3). center located at
More informationFractions to decimals
Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of
More informationUsing Algebra Tiles for Adding/Subtracting Integers and to Solve 2step Equations Grade 7 By Rich Butera
Using Algebra Tiles for Adding/Subtracting Integers and to Solve 2step Equations Grade 7 By Rich Butera 1 Overall Unit Objective I am currently student teaching Seventh grade at Springville Griffith Middle
More informationFree PreAlgebra Lesson 55! page 1
Free PreAlgebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can
More informationRules of Signs for Decimals
CHAPTER 6 C Rules of Signs for Decimals c GOAL Apply the rules of signs for calculating with decimals. You will need number lines a calculator with a sign change key Learn about the Math Positive and negative
More informationCostVolumeProfit Analysis
CostVolumeProfit Analysis Costvolumeprofit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. In performing this analysis, there
More informationHFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES
HFCC Math Lab Beginning Algebra 1 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES Before being able to solve word problems in algebra, you must be able to change words, phrases, and sentences
More informationAdding and Subtracting Fractions. 1. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.
Tallahassee Community College Adding and Subtracting Fractions Important Ideas:. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.. The numerator
More informationStep 1: Set the equation equal to zero if the function lacks. Step 2: Subtract the constant term from both sides:
In most situations the quadratic equations such as: x 2 + 8x + 5, can be solved (factored) through the quadratic formula if factoring it out seems too hard. However, some of these problems may be solved
More informationSupplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 9 Order of Operations
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More informationNow that we have a handle on the integers, we will turn our attention to other types of numbers.
1.2 Rational Numbers Now that we have a handle on the integers, we will turn our attention to other types of numbers. We start with the following definitions. Definition: Rational Number any number that
More informationMAT 080Algebra II Applications of Quadratic Equations
MAT 080Algebra II Applications of Quadratic Equations Objectives a Applications involving rectangles b Applications involving right triangles a Applications involving rectangles One of the common applications
More informationAnswers to Basic Algebra Review
Answers to Basic Algebra Review 1. 1.1 Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract
More information2.3. Finding polynomial functions. An Introduction:
2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned
More informationAddition and Subtraction of Integers
Addition and Subtraction of Integers Integers are the negative numbers, zero, and positive numbers Addition of integers An integer can be represented or graphed on a number line by an arrow. An arrow pointing
More information1.2 Linear Equations and Rational Equations
Linear Equations and Rational Equations Section Notes Page In this section, you will learn how to solve various linear and rational equations A linear equation will have an variable raised to a power of
More informationSection 1. Inequalities 54 32 1 0 1 2 3 4 5
Worksheet 2.4 Introduction to Inequalities Section 1 Inequalities The sign < stands for less than. It was introduced so that we could write in shorthand things like 3 is less than 5. This becomes 3 < 5.
More informationBig Science Idea. Forces. Name. When you ride a bike, your foot pushes against the pedal. The push makes the wheels of the bike move.
Forces Worksheet 1 Name Forces When you ride a bike, your foot pushes against the pedal. The push makes the wheels of the bike move. When you drop something, it is pulled to the ground by gravity. A PUSH
More informationDirect Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.
Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating
More informationFractions and Linear Equations
Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps
More informationSolving Linear Equations in One Variable. Worked Examples
Solving Linear Equations in One Variable Worked Examples Solve the equation 30 x 1 22x Solve the equation 30 x 1 22x Our goal is to isolate the x on one side. We ll do that by adding (or subtracting) quantities
More informationFactor Diamond Practice Problems
Factor Diamond Practice Problems 1. x 2 + 5x + 6 2. x 2 +7x + 12 3. x 2 + 9x + 8 4. x 2 + 9x +14 5. 2x 2 7x 4 6. 3x 2 x 4 7. 5x 2 + x 18 8. 2y 2 x 1 9. 613x + 6x 2 10. 15 + x 2x 2 Factor Diamond Practice
More informationThe Properties of Signed Numbers Section 1.2 The Commutative Properties If a and b are any numbers,
1 Summary DEFINITION/PROCEDURE EXAMPLE REFERENCE From Arithmetic to Algebra Section 1.1 Addition x y means the sum of x and y or x plus y. Some other words The sum of x and 5 is x 5. indicating addition
More informationNo Solution Equations Let s look at the following equation: 2 +3=2 +7
5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are
More informationVariable. 1.1 Order of Operations. August 17, evaluating expressions ink.notebook. Standards. letter or symbol used to represent a number
1.1 evaluating expressions ink.notebook page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 Square Cube Variable Variable Expression Exponent page 10 page 11 1 Lesson Objectives
More informationSolving Inequalities Examples
Solving Inequalities Examples 1. Joe and Katie are dancers. Suppose you compare their weights. You can make only one of the following statements. Joe s weight is less than Kate s weight. Joe s weight is
More informationBasic numerical skills: EQUATIONS AND HOW TO SOLVE THEM. x + 5 = 7 2 + 52 = 72 5 + (22) = 72 5 = 5. x + 55 = 75. x + 0 = 20.
Basic numerical skills: EQUATIONS AND HOW TO SOLVE THEM 1. Introduction (really easy) An equation represents the equivalence between two quantities. The two sides of the equation are in balance, and solving
More informationCHAPTER 10 MAKING CAPITAL INVESTMENT DECISIONS
CHAPTER 10 MAKING CAPITAL INVESTMENT DECISIONS Answers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will
More informationPREPARATION FOR MATH TESTING at CityLab Academy
PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRETEST
More informationUnit 3: Algebra. Date Topic Page (s) Algebra Terminology 2. Variables and Algebra Tiles 3 5. Like Terms 6 8. Adding/Subtracting Polynomials 9 12
Unit 3: Algebra Date Topic Page (s) Algebra Terminology Variables and Algebra Tiles 3 5 Like Terms 6 8 Adding/Subtracting Polynomials 9 1 Expanding Polynomials 13 15 Introduction to Equations 16 17 One
More information2.6 Exponents and Order of Operations
2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated
More informationPricing Your Work (Overhead Recovery Review)
Pricing Your Work (Overhead Recovery Review) To accurately price your work, you need to be aware of three main factors: 1. The Estimate these costs are the direct costs of labor, equipment, materials,
More informationASA Angle Side Angle SAA Side Angle Angle SSA Side Side Angle. B a C
8.2 The Law of Sines Section 8.2 Notes Page 1 The law of sines is used to solve for missing sides or angles of triangles when we have the following three cases: S ngle Side ngle S Side ngle ngle SS Side
More informationPreAlgebra  Integers
0.1 PreAlgebra  Integers Objective: Add, Subtract, Multiply and Divide Positive and Negative Numbers. The ability to work comfortably with negative numbers is essential to success in algebra. For this
More informationPart 1 Expressions, Equations, and Inequalities: Simplifying and Solving
Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words
More informationParamedic Program PreAdmission Mathematics Test Study Guide
Paramedic Program PreAdmission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page
More informationGrade 6 Math Circles. Exponents
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles November 4/5, 2014 Exponents Quick Warmup Evaluate the following: 1. 4 + 4 + 4 +
More informationSummer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students
Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Studies show that most students lose about two months of math abilities over the summer when they do not engage in
More informationPreCalculus II Factoring and Operations on Polynomials
Factoring... 1 Polynomials...1 Addition of Polynomials... 1 Subtraction of Polynomials...1 Multiplication of Polynomials... Multiplying a monomial by a monomial... Multiplying a monomial by a polynomial...
More informationAdding and Subtracting Integers. Objective: 1a. The student will add and subtract integers with the aid of colored disks.
Algebra/Geometry Institute Summer 2006 Monica Reece Grenada Middle School, Grenada, MS Grade 6 Adding and Subtracting Integers Objective: 1a. The student will add and subtract integers with the aid of
More informationProperties of Real Numbers
16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should
More information1.4 Compound Inequalities
Section 1.4 Compound Inequalities 53 1.4 Compound Inequalities This section discusses a technique that is used to solve compound inequalities, which is a phrase that usually refers to a pair of inequalities
More informationSolving Logarithmic Equations
Solving Logarithmic Equations Deciding How to Solve Logarithmic Equation When asked to solve a logarithmic equation such as log (x + 7) = or log (7x + ) = log (x + 9), the first thing we need to decide
More informationFactoring 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
More informationAlgebra Tiles Activity 1: Adding Integers
Algebra Tiles Activity 1: Adding Integers NY Standards: 7/8.PS.6,7; 7/8.CN.1; 7/8.R.1; 7.N.13 We are going to use positive (yellow) and negative (red) tiles to discover the rules for adding and subtracting
More informationMANCHESTER COLLEGE Department of Education. Length: 25 minutes Grade Intended: PreAlgebra (7 th )
LESSON PLAN by: Kyler Kearby Lesson: Multiplying and dividing integers MANCHESTER COLLEGE Department of Education Length: 25 minutes Grade Intended: PreAlgebra (7 th ) Academic Standard: 7.2.1: Solve
More informationPositive and Negative Integers
0.4 Positive and Negative Integers 0.4 OBJECTIVES 1. Represent integers on a number line 2. Order signed numbers 3. Evaluate numerical expressions involving absolute value When numbers are used to represent
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationFactoring 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
More informationProperty: Rule: Example:
Math 1 Unit 2, Lesson 4: Properties of Exponents Property: Rule: Example: Zero as an Exponent: a 0 = 1, this says that anything raised to the zero power is 1. Negative Exponent: Multiplying Powers with
More informationAlgebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials
Algebra Unit 6 Syllabus revised /7/13 1 Objective: Multiply monomials. Simplify expressions involving powers of monomials. Preassessment: Exponents, Fractions, and Polynomial Expressions Lesson: Pages
More informationMATH0910 Review Concepts (Haugen)
Unit 1 Whole Numbers and Fractions MATH0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,
More informationSimple Examples. This is the information that we are given. To find the answer we are to solve an equation in one variable, x.
Worksheet. Solving Equations in One Variable Section 1 Simple Examples You are on your way to Brisbane from Sydney, and you know that the trip is 1100 km. You pass a sign that says that Brisbane is now
More informationA vector is a directed line segment used to represent a vector quantity.
Chapters and 6 Introduction to Vectors A vector quantity has direction and magnitude. There are many examples of vector quantities in the natural world, such as force, velocity, and acceleration. A vector
More informationMultiple Representations of Equations & What We Know. Note that the worked out our turn and your turn charts can also be used as a matching activity.
Multiple Representations of s & What We California State Standards: 7 AF., 7 AF 3.3, 7 AF 3.4, Alg. 6., Alg. 7., Alg. 8. CCSS: 8.EE.6, 8.F., 8.F., 8.F.4 The idea of this lesson is to have students make
More informationThe Relocation Property
Charles Ledger and Kim Langen, Spirit of Math Schools Introduction The Relocation Property When working in the intermediate level classroom in the North York School Board it became critically clear that
More informationIdentify how changes in volume affect costs
Chapter 18 Identify how changes in volume affect Total variable change in direct proportion to changes in the volume of activity Unit variable cost remains constant Units produced 3 5 Total direct materials
More information2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.
Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard
More informationAP Physics Energy and Springs
AP Physics Energy and Springs Another major potential energy area that AP Physics is enamored of is the spring (the wire coil deals, not the ones that produce water for thirsty humanoids). Now you ve seen
More informationGrade 4 Mathematics Patterns, Relations, and Functions: Lesson 3
Grade 4 Mathematics Patterns, Relations, and Functions: Lesson 3 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes
More informationSOLVING EQUATIONS BY COMPLETING THE SQUARE
SOLVING EQUATIONS BY COMPLETING THE SQUARE s There are several ways to solve an equation by completing the square. Two methods begin by dividing the equation by a number that will change the "lead coefficient"
More informationAccuplacer Elementary Algebra Study Guide for Screen Readers
Accuplacer Elementary Algebra Study Guide for Screen Readers The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra test. Reviewing these
More informationExponents and Radicals
Exponents and Radicals (a + b) 10 Exponents are a very important part of algebra. An exponent is just a convenient way of writing repeated multiplications of the same number. Radicals involve the use of
More informationFY201314 SUMMARY BUDGETFINAL BUDGET COLLEGE VIEW MS
COLLEGE VIEW Budgeted Pupil Count 303.0 BEGINNING FUND BALANCE (Includes ALL Reserves) REVENUES Object/ Source 108,472.00 108,472.00 Local Sources 10001999 537,914.00 537,914.00 Intermediate Sources 20002999
More informationMultiplying and Dividing Listen & Learn PRESENTED BY MATHMANIAC Mathematics, Grade 8
Number Sense and Numeration Integers Multiplying and Dividing PRESENTED BY MATHMANIAC Mathematics, Grade 8 Integers Multiplying and Dividing Introduction Welcome to today s topic Parts of Presentation,
More informationName Date Class Period. How can you use the box method to factor a quadratic trinomial?
Name Date Class Period Activity 9.6 Factoring Using the Box Method MATERIALS QUESTION EXPLORE 1 activity worksheet How can you use the box method to factor a quadratic trinomial? Factor 3x 2 + 16x + 5
More informationSolving a System of Equations
11 Solving a System of Equations 111 Introduction The previous chapter has shown how to solve an algebraic equation with one variable. However, sometimes there is more than one unknown that must be determined
More informationGrade 3 Level. Math Common Core Sampler Test
Grade 3 Level Math Common Core Sampler Test This test sampler covers most of the standards seen at the Common Core Third Grade Level. This portion of curriculum is heavily focused on algebra, fractions,
More informationGrade 4 Level. Math Common Core Sampler Test
Grade 4 Level Math Common Core Sampler Test This test sample is made to be used give students and teachers a basic overview of key Grade 4 Common Core grade level work. All questions are aligned to the
More informationAPTITUDE FOR PROGRAMMING PRACTICE
APTITUDE FOR PROGRAMMING PRACTICE APTITUDE FOR PROGRAMMING PRACTISE EXAMPLES INSTRUCTIONS The following practise examples have been provided for you as reasonable example of what to expect on attending
More informationBasic numerical skills: POWERS AND LOGARITHMS
1. Introduction (easy) Basic numerical skills: POWERS AND LOGARITHMS Powers and logarithms provide a powerful way of representing large and small quantities, and performing complex calculations. Understanding
More informationBasic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics. Indian Institute of Technology, Delhi
Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics. Indian Institute of Technology, Delhi Module No. # 02 Simple Solutions of the 1 Dimensional Schrodinger Equation Lecture No. # 7. The Free
More information47 Numerator Denominator
JH WEEKLIES ISSUE #22 20122013 Mathematics Fractions Mathematicians often have to deal with numbers that are not whole numbers (1, 2, 3 etc.). The preferred way to represent these partial numbers (rational
More informationWORKSHEET FOR PROCESSING TD BENEFIT CLAIM (not applicable to employees on 56hour workweek) A: FIRST CLAIM IN CALENDAR YEAR
HRD (TDI)3 Rev. 2/00 Dept: Payroll #: WORKSHEET FOR PROCESSING TD BENEFIT CLAIM (not applicable to employees on 56hour workweek) Claimant s Name: Class Title: BU Code: SR / WB: SSN: A: FIRST CLAIM IN
More informationCofactor Expansion: Cramer s Rule
Cofactor Expansion: Cramer s Rule MATH 322, Linear Algebra I J. Robert Buchanan Department of Mathematics Spring 2015 Introduction Today we will focus on developing: an efficient method for calculating
More informationAlgebra Practice Problems for Precalculus and Calculus
Algebra Practice Problems for Precalculus and Calculus Solve the following equations for the unknown x: 1. 5 = 7x 16 2. 2x 3 = 5 x 3. 4. 1 2 (x 3) + x = 17 + 3(4 x) 5 x = 2 x 3 Multiply the indicated polynomials
More informationUnit 7 Polynomials. 7 1 Naming Polynomials. 7 2 Adding/Subtracting Polynomials. 7 3 Multiplying Monomials. 7 4 Dividing Monomials
Unit 7 Polnomials 7 1 Naming Polnomials 7 Adding/Subtracting Polnomials 7 Multipling Monomials 7 Dividing Monomials 7 Multipling (Monomial b Pol) 7 6 Multipling Polnomials 7 7 Special Products 0 Section
More information2x + y = 3. Since the second equation is precisely the same as the first equation, it is enough to find x and y satisfying the system
1. Systems of linear equations We are interested in the solutions to systems of linear equations. A linear equation is of the form 3x 5y + 2z + w = 3. The key thing is that we don t multiply the variables
More informationAlgebraic Expressions and Equations: Applications I: Translating Words to Mathematical Symbols
OpenStaCNX module: m35046 1 Algebraic Epressions and Equations: Applications I: Translating Words to Mathematical Symbols Wade Ellis Denny Burzynski This work is produced by OpenStaCNX and licensed under
More informationFY201516 SUMMARY BUDGET COLLEGE VIEW MS
Charter Fund Budgeted Pupil Count 443.0 BEGINNING FUND BALANCE (Includes ALL Reserves) REVENUES Object/ Source $276,255 276,255.00 Local Sources 10001999 $3,898,269 3,898,269.00 Intermediate Sources 20002999
More information5.7 Literal Equations
5.7 Literal Equations Now that we have learned to solve a variety of different equations (linear equations in chapter 2, polynomial equations in chapter 4, and rational equations in the last section) we
More informationReconciliation Form: Additional Instructions for Construction
Reconciliation Form: Additional Instructions for Construction In light of recent changes to mandatory coverage in the construction industry, we recognize that many of you are new to the Reconciliation
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationMatrices Worksheet. Adding the results together, using the matrices, gives
Matrices Worksheet This worksheet is designed to help you increase your confidence in handling MATRICES. This worksheet contains both theory and exercises which cover. Introduction. Order, Addition and
More informationFactoring Trinomials using Algebra Tiles Student Activity
Factoring Trinomials using Algebra Tiles Student Activity Materials: Algebra Tiles (student set) Worksheet: Factoring Trinomials using Algebra Tiles Algebra Tiles: Each algebra tile kits should contain
More informationIntroduction to Macroeconomics TOPIC 2: The Goods Market
TOPIC 2: The Goods Market Annaïg Morin CBS  Department of Economics August 2013 Goods market Road map: 1. Demand for goods 1.1. Components 1.1.1. Consumption 1.1.2. Investment 1.1.3. Government spending
More informationNotes from February 11
Notes from February 11 Math 130 Course web site: www.courses.fas.harvard.edu/5811 Two lemmas Before proving the theorem which was stated at the end of class on February 8, we begin with two lemmas. The
More information