( yields. Combining the terms in the numerator you arrive at the answer:


 Osborne Blake
 2 years ago
 Views:
Transcription
1 Algebra Skillbuilder Solutions: 1. Starting with, you ll need to find a common denominator to add/subtract the fractions. If you choose the common denominator 15, you can multiply each fraction by one accordingly to achieve that denominator: ( yields. Combining the terms in the numerator you arrive at the answer: 2. Beginning with, factor out the 4s on the left hand side of the equation to get alone: Then divide both sides by 4 and you ll have the answer: 3. Starting with remember Order of Operations and deal with the parentheses first. Multply the exponent 2 across the parentheses to yield: Then you can combine the m terms, adding the exponents because you re multiplying their bases: 4. Beginning with:, your job is to combine like terms to solve for a. It s likely easiest to begin by combining on each side of the equals sign: 5a 5a = 3a 0 = 3a So a must equal As you start with, your immediate goal should be to get rid of denominators to have a straight linear equation to work with. In order to do that, multiply both sides of the equation by 5: Then distribute that multiplication across the parentheses: 4c + 10 = 5c 10
2 Then subtract 4c from both sides: 10 = c 10 Then add 10 to both sides: 20 = c 6. Here it s important to keep your goal in mind, which isn t to solve for any one variable but rather for the combination. You start with two equations: So your goal should first be to get rid of the denominator in the first equation by multiplying both sides by y: x + y = 3y Then, as your goal is to solve for a combination of x and z, you ll want to y in terms of x so as to eliminate the y variable. Subtract y from both sides: x = 2y Then divide both sides by 2 and you ll have solved for y: This means that in the other equation, you can plug in instead of y: Then subtract from each side to get the x term alone: z = ½ (x) And then divide both sides by x to get the fraction to match the question, and you ll find that. 7. You begin this problem with two equations: And your goal is to solve for b. Your first goal should be to reduce the number of variables, and the second equation affords you a quick opportunity to do so. Since it tells you that b = 2a, you can plug 2a in for b in the first equation: 4a 2a = 6
3 Meaning that 2a = 6 and a = 3. Since b = 2a, then b = 2(3), so b = This problem tests your familiarity with exponent rules, a very important concept on the GMAT. As you start with, you should recognize that a negative exponent like is the same thing as  essentially you can take the negative exponent, flip it over the fraction bar, and make it positive. So what you really have here is. And with that in mind, you know that if you re multiplying together the same base (in this case 5) to two different exponents, you add the exponents, giving you. 9. The answer here is 0. Remember, = 1, so even though 7 is not a factor of 31, because 1 is a factor of 31 you can still make satisfy the equation. Accordingly, the correct answer is Beginning with, look for squares within the numbers underneath the radical and you ll see that what you really have is:, which means that the answer is. 11. With root problems that involve addition or subtraction, you ll typically want to factor out the roots to eliminate squares within them. As you have, look for ways to pull out actual squares:. This allows you to take the square root of the 3 2 terms, leaving:. Combine the like terms and you ll find the answer: With this problem you should recognize that you can quickly calculate the square root portion, as you know that. That means that is really just, which you know is Remember that with inequalities, you can add and subtract values from either side the same exact way you can with equations (the only time things get tricky is when you multiply or divide by a negative, or a variable). So as you start with:, you can subtract 3a from each side to get:, then to get a alone subtract 6 from both sides, and you ll see that: 14. means that either:, or
4 Solving for each, if 2x + 3 = 5, then subtract 3 from each side to get: 2x = 2, and then divide both sides by 2 to get: x = 1 Or, if 2x + 3 = 5, then subtract three from each side to get: 2x = 8, then divide both sides by 2 to get: x = 4 Looking at the answer choices, you ll only find 4, so 4 is correct. 15. In a quadratic like, you want to factor out the numeric term (in this case 12, but don t forget that it s negative). 12 could be: 1 and 12 2 and 6 3 and 4 Then look for a combination that adds/subtracts to the middle number (4a). Since you need one factor to be negative and one to be positive, the combination that works to add to 4 is (a + 6)(a 2) = 0. But remember you still have to solve the equation. If a = 6 or if a = 2, the equation stands, so the solutions are 2 and You can split into two inequalities to help keep your algebraic manipulation clean. You know that: 3y + 3 > 6, which allows you to subtract 3 from both sides to get: 3y > 9, and then you can divide both sides by 3 to get: y > 3 So that s one part of the solution, and now you can attack the other half. Knowing that: 3y + 3 < 12 allows you to again subtract 3 from both sides to get: 3y < 9, whereby you can again divide by 3 to get: y < 3 Combining what you know, you know that 3 < y < When you re given two inequalities like x + y > 8 and x y < 4, if you can get the signs going in the same direction you can add the inequalities together to eliminate a variable, essentially using the Elimination Method for multiple equations and multiple variables. And since the question asks you about y, your goal should be to eliminate x. You can do that by taking the second inequality:
5 x y < 4, and multiplying everything by 1 to flip the sign: x + y > 4. Pair that with the other inequality: x + y > 8, and add them together 2y > 4 So y > You should recognize the opportunity to use the Difference of Squares rule here, as the given equation fits the form x 2 y 2 = 0: 4x 2 9 = 0 can be written as (2x) = 0 This allows you to transform this into: (2x + 3)(2x 3) = 0, matching answer choice B. 19. This is a great question for using the answer choices as guides, since the question asks for what could be the value of x + y and not what is the value of x + y, the algebra won t necessarily lead to a specific value. You re looking for a number that equals its own square root, and since  1 and 2 don t qualify, the answer must be Solving for c given the equation, you ll first want to create a quadratic by adding 27 to both sides to form:. Then you can divide all terms by 3: for squares:, and now you can either factor or recognize the common algebraic equation, so c must be 3.
Practice Math Placement Exam
Practice Math Placement Exam The following are problems like those on the Mansfield University Math Placement Exam. You must pass this test or take MA 0090 before taking any mathematics courses. 1. What
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 informationChapter 15 Radical Expressions and Equations Notes
Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify
More informationThis is a square root. The number under the radical is 9. (An asterisk * means multiply.)
Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize
More informationEquations and Inequalities
Rational Equations Overview of Objectives, students should be able to: 1. Solve rational equations with variables in the denominators.. Recognize identities, conditional equations, and inconsistent equations.
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 informationCOLLEGE ALGEBRA. Paul Dawkins
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5
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 information1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationCAHSEE on Target UC Davis, School and University Partnerships
UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,
More information2. Simplify. College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses
College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2
More informationIntegration Unit 5 Quadratic Toolbox 1: Working with Square Roots. Using your examples above, answer the following:
Integration Unit 5 Quadratic Toolbox 1: Working with Square Roots Name Period Objective 1: Understanding Square roots Defining a SQUARE ROOT: Square roots are like a division problem but both factors must
More informationNotes for EER #4 Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions.
Notes for EER #4 Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions. Basic Functions In several sections you will be applying shifts
More informationBasic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.
Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:
More informationMathematics Higher Tier, Algebraic Fractions
These solutions are for your personal use only. DO NOT photocopy or pass on to third parties. If you are a school or an organisation and would like to purchase these solutions please contact Chatterton
More informationSTUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS
STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS The intermediate algebra skills illustrated here will be used extensively and regularly throughout the semester Thus, mastering these skills is an
More informationPartial Fractions. Combining fractions over a common denominator is a familiar operation from algebra:
Partial Fractions Combining fractions over a common denominator is a familiar operation from algebra: From the standpoint of integration, the left side of Equation 1 would be much easier to work with than
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationChapter 9: Quadratic Functions 9.3 SIMPLIFYING RADICAL EXPRESSIONS
Chapter 9: Quadratic Functions 9.3 SIMPLIFYING RADICAL EXPRESSIONS Vertex formula f(x)=ax 2 +Bx+C standard d form X coordinate of vertex is Use this value in equation to find y coordinate of vertex form
More information0.8 Rational Expressions and Equations
96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions  that is, algebraic fractions  and equations which contain them. The reader is encouraged to
More informationEAP/GWL Rev. 1/2011 Page 1 of 5. Factoring a polynomial is the process of writing it as the product of two or more polynomial factors.
EAP/GWL Rev. 1/2011 Page 1 of 5 Factoring a polynomial is the process of writing it as the product of two or more polynomial factors. Example: Set the factors of a polynomial equation (as opposed to an
More information5.1 Radical Notation and Rational Exponents
Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots
More informationIntegrals of Rational Functions
Integrals of Rational Functions Scott R. Fulton Overview A rational function has the form where p and q are polynomials. For example, r(x) = p(x) q(x) f(x) = x2 3 x 4 + 3, g(t) = t6 + 4t 2 3, 7t 5 + 3t
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationAlgebra 1: Topic 1 Notes
Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating
More informationLearning new things and building basic skills
Math Review TABE Answer Key 2 Learning new things and building basic skills may be challenging for you, but they also can be very exciting. When you follow the guidelines for learning basic skills, you
More informationMethod 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
More informationSimplifying Radical Expressions
In order to simplifying radical expression, it s important to understand a few essential properties. Product Property of Like Bases a a = a Multiplication of like bases is equal to the base raised to the
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 informationLINEAR INEQUALITIES. less than, < 2x + 5 x 3 less than or equal to, greater than, > 3x 2 x 6 greater than or equal to,
LINEAR INEQUALITIES When we use the equal sign in an equation we are stating that both sides of the equation are equal to each other. In an inequality, we are stating that both sides of the equation are
More informationAlgebra 1A and 1B Summer Packet
Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationTranslating Mathematical Formulas Into Excel s Language
Translating Mathematical Formulas Into Excel s Language Introduction Microsoft Excel is a very powerful calculator; you can use it to compute a wide variety of mathematical expressions. Before exploring
More informationPreAlgebra  Order of Operations
0.3 PreAlgebra  Order of Operations Objective: Evaluate expressions using the order of operations, including the use of absolute value. When simplifying expressions it is important that we simplify them
More informationRadicals  Rational Exponents
8. Radicals  Rational Exponents Objective: Convert between radical notation and exponential notation and simplify expressions with rational exponents using the properties of exponents. When we simplify
More informationRoots and Powers. Written by: Bette Kreuz Edited by: Science Learning Center Staff
Roots and Powers Written by: Bette Kreuz Edited by: Science Learning Center Staff The objectives for this module are to: 1. Raise exponential numbers to a power. 2. Extract the root of an exponential number.
More informationGRE MATH REVIEW #5. 1. Variable: A letter that represents an unknown number.
GRE MATH REVIEW #5 Eponents and Radicals Many numbers can be epressed as the product of a number multiplied by itself a number of times. For eample, 16 can be epressed as. Another way to write this is
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationExponents, Radicals, and Scientific Notation
General Exponent Rules: Exponents, Radicals, and Scientific Notation x m x n = x m+n Example 1: x 5 x = x 5+ = x 7 (x m ) n = x mn Example : (x 5 ) = x 5 = x 10 (x m y n ) p = x mp y np Example : (x) =
More information6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms
AAU  Business Mathematics I Lecture #6, March 16, 2009 6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms 6.1 Rational Inequalities: x + 1 x 3 > 1, x + 1 x 2 3x + 5
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 informationZeros of a Polynomial Function
Zeros of a Polynomial Function An important consequence of the Factor Theorem is that finding the zeros of a polynomial is really the same thing as factoring it into linear factors. In this section we
More informationSolving Linear Equations  General Equations
1.3 Solving Linear Equations  General Equations Objective: Solve general linear equations with variables on both sides. Often as we are solving linear equations we will need to do some work to set them
More informationOrder of Operations More Essential Practice
Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure
More informationCONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME!
CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! You may have come across the terms powers, indices, exponents and logarithms. But what do they mean? The terms power(s),
More informationGMAT Math: Exponents and Roots (Excerpt)
GMAT Math: Exponents and Roots (Excerpt) Jeff Sackmann / GMAT HACKS January 201 Contents 1 Introduction 2 2 Difficulty Levels Problem Solving 4 4 Data Sufficiency 5 5 Answer Key 6 6 Explanations 7 1 1
More information3.5. Solving Inequalities. Introduction. Prerequisites. Learning Outcomes
Solving Inequalities 3.5 Introduction An inequality is an expression involving one of the symbols,, > or
More informationSection P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities
Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.
More informationName Date Block. Algebra 1 Laws of Exponents/Polynomials Test STUDY GUIDE
Name Date Block Know how to Algebra 1 Laws of Eponents/Polynomials Test STUDY GUIDE Evaluate epressions with eponents using the laws of eponents: o a m a n = a m+n : Add eponents when multiplying powers
More informationDirections Please read carefully!
Math Xa Algebra Practice Problems (Solutions) Fall 2008 Directions Please read carefully! You will not be allowed to use a calculator or any other aids on the Algebra PreTest or PostTest. Be sure to
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationSummer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2
Summer Math Packet Student Name: Say Hello to Algebra 2 For Students Entering Algebra 2 This summer math booklet was developed to provide students in middle school an opportunity to review grade level
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 information1.3 Order of Operations
1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit
More informationCore Maths C1. Revision Notes
Core Maths C Revision Notes November 0 Core Maths C Algebra... Indices... Rules of indices... Surds... 4 Simplifying surds... 4 Rationalising the denominator... 4 Quadratic functions... 4 Completing the
More informationIndices and Surds. The Laws on Indices. 1. Multiplication: Mgr. ubomíra Tomková
Indices and Surds The term indices refers to the power to which a number is raised. Thus x is a number with an index of. People prefer the phrase "x to the power of ". Term surds is not often used, instead
More informationSolution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2
5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square
More information1.1 Solving a Linear Equation ax + b = 0
1.1 Solving a Linear Equation ax + b = 0 To solve an equation ax + b = 0 : (i) move b to the other side (subtract b from both sides) (ii) divide both sides by a Example: Solve x = 0 (i) x = 0 x = (ii)
More informationPilot Flyskole AS Hangarveien 13 N3241 Sandefjord Tlf Epost Preparatory Course.
Pilot Flyskole AS Hangarveien 13 N3241 Sandefjord Tlf +47 9705 6840 Epost post@pilot.no www.pilot.no Preparatory Course Mathematics Pilot Flight School 2014 Order of operations Operations means things
More information7. Solving Linear Inequalities and Compound Inequalities
7. Solving Linear Inequalities and Compound Inequalities Steps for solving linear inequalities are very similar to the steps for solving linear equations. The big differences are multiplying and dividing
More informationAlgebra I Pacing Guide Days Units Notes 9 Chapter 1 ( , )
Algebra I Pacing Guide Days Units Notes 9 Chapter 1 (1.11.4, 1.61.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationFlorida Department of Education/Office of Assessment January 2012. Algebra 1 EndofCourse Assessment Achievement Level Descriptions
Florida Department of Education/Office of Assessment January 2012 Algebra 1 EndofCourse Assessment Achievement Level Descriptions Algebra 1 EOC Assessment Reporting Category Functions, Linear Equations,
More informationAdditional Examples of using the Elimination Method to Solve Systems of Equations
Additional Examples of using the Elimination Method to Solve Systems of Equations. Adjusting Coecients and Avoiding Fractions To use one equation to eliminate a variable, you multiply both sides of that
More informationA. Factoring Method  Some, but not all quadratic equations can be solved by factoring.
DETAILED SOLUTIONS AND CONCEPTS  QUADRATIC EQUATIONS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! PLEASE NOTE
More information3. Power of a Product: Separate letters, distribute to the exponents and the bases
Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same
More informationQuadratic Functions. Copyright Cengage Learning. All rights reserved.
Quadratic Functions 4 Copyright Cengage Learning. All rights reserved. Solving by the Quadratic Formula 2 Example 1 Using the quadratic formula Solve the following quadratic equations. Round your answers
More informationBalancing Chemical Equations
Balancing Chemical Equations A mathematical equation is simply a sentence that states that two expressions are equal. One or both of the expressions will contain a variable whose value must be determined
More informationLecture 7 : Inequalities 2.5
3 Lecture 7 : Inequalities.5 Sometimes a problem may require us to find all numbers which satisfy an inequality. An inequality is written like an equation, except the equals sign is replaced by one of
More informationPolynomial and Rational Functions
Polynomial and Rational Functions Quadratic Functions Overview of Objectives, students should be able to: 1. Recognize the characteristics of parabolas. 2. Find the intercepts a. x intercepts by solving
More informationQuadratics  Quadratic Formula
9.4 Quadratics  Quadratic Formula Objective: Solve quadratic equations by using the quadratic formula. The general from of a quadratic is ax + bx + c = 0. We will now solve this formula for x by completing
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 informationEXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS
To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires
More informationAlgebra. Indiana Standards 1 ST 6 WEEKS
Chapter 1 Lessons Indiana Standards  11 Variables and Expressions  12 Order of Operations and Evaluating Expressions  13 Real Numbers and the Number Line  14 Properties of Real Numbers  15 Adding
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 informationWest WindsorPlainsboro Regional School District Algebra I Part 2 Grades 912
West WindsorPlainsboro Regional School District Algebra I Part 2 Grades 912 Unit 1: Polynomials and Factoring Course & Grade Level: Algebra I Part 2, 9 12 This unit involves knowledge and skills relative
More informationEquations, Lenses and Fractions
46 Equations, Lenses and Fractions The study of lenses offers a good real world example of a relation with fractions we just can t avoid! Different uses of a simple lens that you may be familiar with are
More informationCOLLEGE ALGEBRA 10 TH EDITION LIAL HORNSBY SCHNEIDER 1.11
10 TH EDITION COLLEGE ALGEBRA LIAL HORNSBY SCHNEIDER 1.11 1.1 Linear Equations Basic Terminology of Equations Solving Linear Equations Identities 1.12 Equations An equation is a statement that two expressions
More informationSimplifying Exponential Expressions
Simplifying Eponential Epressions Eponential Notation Base Eponent Base raised to an eponent Eample: What is the base and eponent of the following epression? 7 is the base 7 is the eponent Goal To write
More informationeday Lessons Mathematics Grade 8 Student Name:
eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times
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 informationYear 9 set 1 Mathematics notes, to accompany the 9H book.
Part 1: Year 9 set 1 Mathematics notes, to accompany the 9H book. equations 1. (p.1), 1.6 (p. 44), 4.6 (p.196) sequences 3. (p.115) Pupils use the Elmwood Press Essential Maths book by David Raymer (9H
More informationInequalities  Solve and Graph Inequalities
3.1 Inequalities  Solve and Graph Inequalities Objective: Solve, graph, and give interval notation for the solution to linear inequalities. When we have an equation such as x = 4 we have a specific value
More informationDecimal and Fraction Review Sheet
Decimal and Fraction Review Sheet Decimals Addition To add 2 decimals, such as 3.25946 and 3.514253 we write them one over the other with the decimal point lined up like this 3.25946 +3.514253 If one
More informationMath 002 Intermediate Algebra
Math 002 Intermediate Algebra Student Notes & Assignments Unit 4 Rational Exponents, Radicals, Complex Numbers and Equation Solving Unit 5 Homework Topic Due Date 7.1 BOOK pg. 491: 62, 64, 66, 72, 78,
More informationSupplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 8 Powers and Exponents
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 8 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More informationChapter 2: Linear Equations and Inequalities Lecture notes Math 1010
Section 2.1: Linear Equations Definition of equation An equation is a statement that equates two algebraic expressions. Solving an equation involving a variable means finding all values of the variable
More informationTips for Solving Mathematical Problems
Tips for Solving Mathematical Problems Don Byrd Revised late April 2011 The tips below are based primarily on my experience teaching precalculus to highschool students, and to a lesser extent on my other
More informationSect Solving Systems of Equations by Addition (Elimination)
Sect 4.3  Solving Systems of Equations by Addition (Elimination) Concept # Solving System of Linear Equations in Two Variables by Addition (Elimination). A variant of the Addition Property of Equality
More informationSECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS
(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic
More informationSolving univariate equations
Click on the links below to jump directly to the relevant section Solving univariate equations Solving for one variable in a multivariate equation Solving systems of multivariate equations Solving univariate
More informationGCSE Revision Notes Mathematics Number s and Algebra
GCSE Revision Notes Mathematics Number s and Algebra irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;
More information1.01 b) Operate with polynomials.
1.01 Write equivalent forms of algebraic expressions to solve problems. a) Apply the laws of exponents. There are a few rules that simplify our dealings with exponents. Given the same base, there are ways
More informationTemperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.
Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is
More informationThis assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the
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 information0.7 Quadratic Equations
0.7 Quadratic Equations 8 0.7 Quadratic Equations In Section 0..1, we reviewed how to solve basic nonlinear equations by factoring. The astute reader should have noticed that all of the equations in that
More informationSimplifying Radical Expressions
9.2 Simplifying Radical Expressions 9.2 OBJECTIVES. Simplify expressions involving numeric radicals 2. Simplify expressions involving algebraic radicals In Section 9., we introduced the radical notation.
More informationSolving Linear Equations  Fractions
1.4 Solving Linear Equations  Fractions Objective: Solve linear equations with rational coefficients by multiplying by the least common denominator to clear the fractions. Often when solving linear equations
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 information