Unit 3 Day 4. Solving Equations with Rational Exponents and Radicals
|
|
- Edgar Williams
- 5 years ago
- Views:
Transcription
1 Unit Day 4 Solving Equations with Rational Exponents and Radicals
2 Day 4 Warm Up You know a lot about inverses in mathematics we use them every time we solve equations. Write down the inverse operation for each of the following (there could be more than one correct answer) and then give a definition for inverse in your own words. If you get stuck, it may be helpful for you to write the expression out and think what you would do to solve an equation that had that expression on one side of the equation. Use the information from the table above to solve the following equations. Express your answers in simplified radical form. a. 5 b. x 64 4 An inverse is 2 ( y ) 6
3 Day 4 Warm Up ANSWERS Modeling with Exponential Functions: Solving Equations with Rational Exponents and Radicals An inverse is x 7 adding 7 to a number x * /2 multiply by 2 x * 2/5 multiply by 5/2 x/ multiply by x 2 x x 5 5 x 2 x 5 take square root squaring a number raising to the /5 power raising to the 5 th power raising to the 5/2 power
4 Day 4 Warm Up ANSWERS Use the information from the table above to solve the following equations. Express your answers in simplified radical form. a. b. 5 x 64 5 x 64 x x x x x ( y ) ( y ) ( 6) y y y y y
5 Day 4 Warm Up ANSWERS An Inverse is??? 5
6 Homework Answers ~ Packet Page 5-6 Evens OR OR ( ) OR
7 Homework Answers ~ Packet Page 5-6 Evens Continued x (6p) 2 _OR_6 2 2 p a _ OR _ a a a (6x) _OR_ x 0. n 2 7
8 You Try! Notes p a 2 b 6 b a a a 5. 64x 52x 9 x x x 5x x 9 x 8 9. xy 4
9 Notes p. 9 Mixed Review: Simplify each expression.. 75y 2 27 y 45y. 2 8a b 6 b 2 2 y 5y 6ab 6b 2. 08yz 98yz 2 55yz z y 2z 2 y 2z 55y 9 4. x y 2 8x y 6x 4 6
10 Tonight s Homework: Packet pg. 7 0
11 Notes p. 0 Express final answers as radicals! Before partner work, let s do two together! = leave as a decimal HINT: We ll use the Inverses we discussed during today s warm-up! Do st Together Do st Together
12 Notes p. 0 Express final answers as radicals! = leave as a Work with a partner decimal Decide who will be Partner A and who will be Partner B ,500,000 2,500,
13 Yesterday s problems only had one step. However, today there are multiple steps, meaning that one cannot just simplify the radical or rational exponent until it is isolated on one side of the equation. Inverse You can isolate the radical using. There are also some problems below in which the rational exponent or radical is applied to the entire side of the equation. Only in these situations will you undo the rational exponents or radicals first. Before solving the entire problem, make sure you know what the first step will be
14 Steps To Solving Equations With Rational Exponents AND Radicals Radical. We ll do one of these in a minute! Rational Exponent Isolate the Term with the Rational Exponent (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the reciprocal power) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? 4
15 Solving with Rational Exponents and Radicals Lesson Isolate the Term with the Rational Exponent (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the reciprocal power) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? 4. x 2 We ll try a couple together! x 6 2 x = 625 x = 5
16 You Try! Finish these on Notes pg x 5207 x = x x x = x 5 5 = leave as a decimal 7.8 x = x 5 0 x = (2x 7) x = 6
17 Steps To Solving Equations With Rational Exponents AND Radicals Radical Isolate the Term with the Radical (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the Index) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? 7
18 Solving with Rational Exponents and Radicals Lesson Isolate the Term with the Radical (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the Index) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? We ll try a couple together! We ll do the bottom two!. 2x x 5 0 x = 4 8 x = 208
19 One more example A tougher one! Solve x 0 x x = 0 9
20 You Try! Finish Notes pg. = leave as a decimal._ x - 2 = 4 2._ x +2-2 =2 x = 66 x = 94 20
21 Whiteboard Practice! Send a partner to pick up the following each person needs of these: whiteboard marker eraser 2
22 . Solve for x. x 2 4 x 66 22
23 2. Solve for a. a x 94 2
24 . Solve for x. x 2 x 24 24
25 4. Solve for x. x 5 5 x 0 25
26 5. Solve for x. x 7 9 No solution! Always check your answers! 26
27 6. Solve for x. 6 x 2 2 x 27
28 7. Solve for x. 0 x x 2 x 2 28
29 8. Solve for y. 2 y x 9 29
30 9. Solve for b. 5 4b 2 0 x 4 0
31 Homework: Packet pg. 7
Lesson 2. When the exponent is a positive integer, exponential notation is a concise way of writing the product of repeated factors.
Review of Exponential Notation: Lesson 2 - read to the power of, where is the base and is the exponent - if no exponent is denoted, it is understood to be a power of 1 - if no coefficient is denoted, it
More informationAlgebra 2 and Trigonometry
Algebra 2 and Trigonometry Chapter 7: Exponential Functions Name: Teacher: Pd: 1 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs.
More informationNever leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!
1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a
More informationChapter 4: Radicals and Complex Numbers
Section 4.1: A Review of the Properties of Exponents #1-42: Simplify the expression. 1) x 2 x 3 2) z 4 z 2 3) a 3 a 4) b 2 b 5) 2 3 2 2 6) 3 2 3 7) x 2 x 3 x 8) y 4 y 2 y 9) 10) 11) 12) 13) 14) 15) 16)
More informationUnit 3 Day 13 Review 1
Unit 3 Day 13 Review 1 Warm-up! Graph the following functions, with at least 4 points. Find the domain and range. Then, tell how they are changed from their parent graph. (Hint: Remember that the order
More informationChapter 4: Radicals and Complex Numbers
Chapter : Radicals and Complex Numbers Section.1: A Review of the Properties of Exponents #1-: Simplify the expression. 1) x x ) z z ) a a ) b b ) 6) 7) x x x 8) y y y 9) x x y 10) y 8 b 11) b 7 y 1) y
More informationTeacher Road Map for Lesson 23: Solving Complicated Radical Equations
eacher Road Map for Solving Complicated Radical Equations Objective in Student Friendly Language: oday I am: comparing two methods for solving complicated radical equations So that I can: determine the
More informationLESSON 9.1 ROOTS AND RADICALS
LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical
More informationLESSON 6.1 EXPONENTS LESSON 6.1 EXPONENTS 253
LESSON 6.1 EXPONENTS LESSON 6.1 EXPONENTS 5 OVERVIEW Here's what you'll learn in this lesson: Properties of Exponents Definition of exponent, power, and base b. Multiplication Property c. Division Property
More informationCLICKERS!!!!! Multiply.
CLICKERS!!!!! Multiply. 1. 95 x 10 6 2. 8.23 x 10 5 3. 864 x 10-5 4. 7.8 x 10-3 5. 5 x 10 8 6. 1.5 x 10 9 7. 54 x 10-3 8. 6.7 x 10-4 CLICKERS!!!!! Multiply. 1. 95 x 10 6 2. 8.23 x 10 5 3. 864 x 10-5 4.
More informationUnit 9 Study Sheet Rational Expressions and Types of Equations
Algebraic Fractions: Unit 9 Study Sheet Rational Expressions and Types of Equations Simplifying Algebraic Fractions: To simplify an algebraic fraction means to reduce it to lowest terms. This is done by
More informationUnit 4 Day 4 & 5. Piecewise Functions
Unit 4 Day 4 & 5 Piecewise Functions Warm Up 1. Why does the inverse variation have a vertical asymptote? 2. Graph. Find the asymptotes. Write the domain and range using interval notation. a. b. f(x)=
More informationLESSON 13.1 NONLINEAR EQUATIONS
LESSON. NONLINEAR EQUATIONS LESSON. NONLINEAR EQUATIONS 58 OVERVIEW Here's what you'll learn in this lesson: Solving Equations a. Solving polynomial equations by factoring b. Solving quadratic type equations
More informationPowers, Roots and Radicals. (11) Page #23 47 Column, #51, 54, #57 73 Column, #77, 80
Algebra 2/Trig Unit Notes Packet Name: Period: # Powers, Roots and Radicals () Homework Packet (2) Homework Packet () Homework Packet () Page 277 # 0 () Page 277 278 #7 6 Odd (6) Page 277 278 #8 60 Even
More informationSection 3.7: Solving Radical Equations
Objective: Solve equations with radicals and check for extraneous solutions. In this section, we solve equations that have roots in the problem. As you might expect, to clear a root we can raise both sides
More informationAt the end of this section, you should be able to solve equations that are convertible to equations in linear or quadratic forms:
Equations in Linear and Quadratic Forms At the end of this section, you should be able to solve equations that are convertible to equations in linear or quadratic forms: Equations involving rational expressions
More informationUnit 4 Advanced Functions Review Day
Unit 4 Advanced Functions Review Day Warm-up! Find the domain and range of the following functions. Then, tell how they are changed from their parent graph. (Hint: Remember that the order of transformations
More informationSolving Equations with Variables on Both Sides
2-4 Warm Up Lesson Presentation Lesson Quiz Bell Quiz 2-4 2 pts Simplify. 1. 4x 10x 2 pts 2. -7(x 3) 3 pts 3. 15 (x 2) 10 pts possible 3 pts Solve the equation. 4. 3x + 2 = 8 Questions on 2-3 Objective
More informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra 1 Unit 1: Vocabulary 1) Natural Numbers 2) Whole Numbers 3) Integers 4) Rational Numbers 5) Irrational Numbers 6) Real Numbers 7) Terminating Decimal 8) Repeating Decimal
More informationAlgebra 1B notes and problems March 12, 2009 Factoring page 1
March 12, 2009 Factoring page 1 Factoring Last class, you worked on a set of problems where you had to do multiplication table calculations in reverse. For example, given the answer x 2 + 4x + 2x + 8,
More informationHonors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice
Honors Math 2 Unit 5 Exponential Functions Notes and Activities Name: Date: Pd: Unit Objectives: Objectives: N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
More informationDistributive property and its connection to areas
February 27, 2009 Distributive property and its connection to areas page 1 Distributive property and its connection to areas Recap: distributive property The distributive property says that when you multiply
More informationAlgebra 1 Unit 6 Notes
Algebra 1 Unit 6 Notes Name: Day Date Assignment (Due the next class meeting) Monday Tuesday Wednesday Thursday Friday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday
More informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra 1 Unit 1: Vocabulary 1) Natural Numbers 2) Whole Numbers 3) Integers 4) Rational Numbers 5) Irrational Numbers 6) Real Numbers 7) Terminating Decimal 8) Repeating Decimal
More informationWarm Up Lesson Presentation Lesson Quiz. Holt Algebra 2 2
8-8 Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Simplify each expression. Assume all variables are positive. 1. 2. 3. 4. Write each expression in radical form. 5. 6. Objective Solve radical equations
More informationChapter Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook
Bellwork: Write as a fraction and reduce if you can: 1) 2.7 2) 0.325 Homework Questions??? Write each as a decimal, use repeating decimals when necessary: 3) 5/2 4) 6/8 Evaluate: 5) 2x + y; x = 4, y =
More informationUNIT 14 Exponents. Scientific Notation
Unit 14 CCM6+/7+ Page 1 UNIT 14 Exponents and Scientific Notation CCM6+/7+ Name Math Teacher Projected Test Date Main Ideas Page(s) Unit 14 Vocabulary 2 Exponent Basics, Zero & Negative Exponents 3 6 Multiplying,
More informationChapter 3: Factors, Roots, and Powers
Chapter 3: Factors, Roots, and Powers Section 3.1 Chapter 3: Factors, Roots, and Powers Section 3.1: Factors and Multiples of Whole Numbers Terminology: Prime Numbers: Any natural number that has exactly
More informationChapter 7: Exponents
Chapter 7: Exponents Algebra 1 Chapter 7 Notes Name: Algebra Homework: Chapter 7 (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework Section 7.:
More informationThe trick is to multiply the numerator and denominator of the big fraction by the least common denominator of every little fraction.
Complex Fractions A complex fraction is an expression that features fractions within fractions. To simplify complex fractions, we only need to master one very simple method. Simplify 7 6 +3 8 4 3 4 The
More informationCommon Core Algebra 2. Chapter 5: Rational Exponents & Radical Functions
Common Core Algebra 2 Chapter 5: Rational Exponents & Radical Functions 1 Chapter Summary This first part of this chapter introduces radicals and nth roots and how these may be written as rational exponents.
More informationUnit 3 NOTES Honors Common Core Math 2 1. Day 1: Properties of Exponents
Unit NOTES Honors Common Core Math Da : Properties of Eponents Warm-Up: Before we begin toda s lesson, how much do ou remember about eponents? Use epanded form to write the rules for the eponents. OBJECTIVE
More information3.4 Exponential and Logarithmic Equations
3.4 Exponential and Logarithmic Equations Pre-Calculus Mr. Niedert Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 1 / 18 3.4 Exponential and Logarithmic Equations 1 Solving Simple Equations
More informationIn a previous lesson, we solved certain quadratic equations by taking the square root of both sides of the equation.
In a previous lesson, we solved certain quadratic equations by taking the square root of both sides of the equation. x = 36 (x 3) = 8 x = ± 36 x 3 = ± 8 x = ±6 x = 3 ± Taking the square root of both sides
More informationWarm Up. Fourth Grade Released Test Question: 1) Which of the following has the greatest value? 2) Write the following numbers in expanded form: 25:
Warm Up Fourth Grade Released Test Question: 1) Which of the following has the greatest value? A 12.1 B 0.97 C 4.23 D 5.08 Challenge: Plot these numbers on an open number line. 2) Write the following numbers
More informationPositive exponents indicate a repeated product 25n Negative exponents indicate a division by a repeated product
Lesson.x Understanding Rational Exponents Sample Lesson, Algebraic Literacy Earlier, we used integer exponents for a number or variable base, like these: x n Positive exponents indicate a repeated product
More informationWE SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest form, when the radicand has no square factors.
SIMPLIFYING RADICALS: 12 th Grade Math & Science Summer Packet WE SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest form, when the radicand has no square factors. A radical is also in simplest
More informationAlgebra 2 Honors: Final Exam Review
Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt
More informationManipulating Radicals
Lesson 40 Mathematics Assessment Project Formative Assessment Lesson Materials Manipulating Radicals MARS Shell Center University of Nottingham & UC Berkeley Alpha Version Please Note: These materials
More informationSolving Equations with Variables on Both Sides
2-4 Warm Up Lesson Presentation Lesson Quiz Bell Quiz 2-4 1 pt Simplify. 1. 4x 10x 4 pts Solve the equation. 2. 3x + 2 = 8 5 pts possible Questions on 2-3 Objective Solve equations in one variable that
More informationLesson 29: Solving Radical Equations
Lesson 29: Solving Radical Equations Student Outcomes Students develop facility in solving radical equations. Lesson Notes In the previous lesson, students were introduced to the notion of solving radical
More informationHerndon High School Geometry Honors Summer Assignment
Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in
More informationScientific Notation. exploration. 1. Complete the table of values for the powers of ten M8N1.j. 110 Holt Mathematics
exploration Georgia Performance Standards M8N1.j 1. Complete the table of values for the powers of ten. Exponent 6 10 6 5 10 5 4 10 4 Power 3 10 3 2 10 2 1 1 0 2 1 0.01 10 10 1 10 1 1 1 0 1 1 0.1 10 0
More informationLesson 28: A Focus on Square Roots
now Lesson 28: A Focus on Square Roots Student Outcomes Students solve simple radical equations and understand the possibility of extraneous solutions. They understand that care must be taken with the
More informationSummer Packet for Students Taking Introduction to Calculus in the Fall
Summer Packet for Students Taking Introduction to Calculus in the Fall Algebra 2 Topics Needed for Introduction to Calculus Need to know: à Solve Equations Linear Quadratic Absolute Value Polynomial Rational
More informationMathematics GRADE 8 Teacher Packet
COMMON CORE Standards Plus Mathematics GRADE 8 Teacher Packet Copyright 01 Learning Plus Associates All Rights Reserved; International Copyright Secured. Permission is hereby granted to teachers to reprint
More informationUnit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions
CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.
More information7.5 Rationalizing Denominators and Numerators of Radical Expressions
440 CHAPTER Rational Exponents, Radicals, and Complex Numbers 86. Find the area and perimeter of the trapezoid. (Hint: The area of a trapezoid is the product of half the height 6 meters and the sum of
More informationLesson 6b Rational Exponents & Radical Functions
Lesson 6b Rational Exponents & Radical Functions In this lesson, we will continue our review of Properties of Exponents and will learn some new properties including those dealing with Rational and Radical
More information9 3 Base. We will apply 1 the properties of exponents. Name:
Learning Objective We will apply the properties of exponents. Name:.2. CFU Activate Prior Knowledge What are we going to do? What does apply mean? Apply means. An exponential expression contains a base
More informationWhat Fun! It's Practice with Scientific Notation!
What Fun! It's Practice with Scientific Notation! Review of Scientific Notation Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000
More informationSolving Equations by Multiplying or Dividing
2-2 Warm Up Lesson Presentation Lesson Quiz Bell Quiz 2-2 3 pts Solve each equation. Check your answer. 1. u -15 = -8 3 pts 3 pts 2. 19 + a = 19 3. -12 + f = 3 10 pts possible 1 pt for putting your name
More informationWe will work with two important rules for radicals. We will write them for square roots but they work for any root (cube root, fourth root, etc.).
College algebra We will review simplifying radicals, exponents and their rules, multiplying polynomials, factoring polynomials, greatest common denominators, and solving rational equations. Pre-requisite
More informationAlgebra Summer Review Packet
Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills
More informationRadical Expressions and Graphs 8.1 Find roots of numbers. squaring square Objectives root cube roots fourth roots
8. Radical Expressions and Graphs Objectives Find roots of numbers. Find roots of numbers. The opposite (or inverse) of squaring a number is taking its square root. Find principal roots. Graph functions
More informationChapter 7: Exponents
Chapter : Exponents Algebra Chapter Notes Name: Algebra Homework: Chapter (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework M / Review of Sections.-.
More informationReteach Simplifying Algebraic Expressions
1-4 Simplifying Algebraic Expressions To evaluate an algebraic expression you substitute numbers for variables. Then follow the order of operations. Here is a sentence that can help you remember the order
More informationMathematics Success Grade 8
T538 Mathematics Success Grade 8 [OBJECTIVE] The student will compare functions represented algebraically, graphically, with verbal descriptions or in tables and identify functions as linear or non-linear.
More informationAnswers to Sample Exam Problems
Math Answers to Sample Exam Problems () Find the absolute value, reciprocal, opposite of a if a = 9; a = ; Absolute value: 9 = 9; = ; Reciprocal: 9 ; ; Opposite: 9; () Commutative law; Associative law;
More informationUnit 2 Day 7. Quadratic Formula & the Discriminant
Unit Day 7 Quadratic Formula & the Discriminant 1 Warm Up Day 7 1. Solve each of the quadratic functions by graphing and algebraic reasoning: a. x 3 = 0 b. x + 5x 8 = 0 c. Explain why having alternative
More informationAlgebra II Chapter 5: Polynomials and Polynomial Functions Part 1
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions
More informationICM ~ Unit 4 ~ Day 3. Horizontal Asymptotes, End Behavior
ICM ~ Unit 4 ~ Day 3 Horizontal Asymptotes, End Behavior Warm Up ~ Day 3 1. Find the domain, then convert to fractional/rational eponent. f ( ) 7. Simplify completely: 3( + 5). 3. Find the domain, & y
More informationChapter 1 Indices & Standard Form
Chapter 1 Indices & Standard Form Section 1.1 Simplifying Only like (same letters go together; same powers and same letter go together) terms can be grouped together. Example: a 2 + 3ab + 4a 2 5ab + 10
More informationCH 73 THE QUADRATIC FORMULA, PART II
1 CH THE QUADRATIC FORMULA, PART II INTRODUCTION W ay back in Chapter 55 we used the Quadratic Formula to solve quadratic equations like 6x + 1x + 0 0, whose solutions are 5 and 8. In fact, all of the
More informationAssignment 2.1. Exponent Properties: The Product Rule
Assignment.1 NAME: Exponent Properties: The Product Rule What is the difference between x and x? Explain in complete sentences and with examples. Product Repeated Multiplication Power of the form a b 5
More informationWarm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2
4-5 Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Solve. 1. log 16 x = 3 2 64 2. log x 1.331 = 3 1.1 3. log10,000 = x 4 Objectives Solve exponential and logarithmic equations and equalities.
More informationLet me just tell you how, then I ll use an example to make it more clear.
CHAPTER 15 Equations with Radicals Sec. 1 Simplifying Radicals From grade school, you can probably remember how to take square roots of numbers like 25, 64, and the 100. The number on the inside of the
More informationFree Pre-Algebra Lesson 16! page 1. Simplify First Algebraic equations may have expressions that can be simplified on either side of the equals sign.
Free Pre-Algebra Lesson 16! page 1 Lesson 16 Solving Equations, Part 2 The equations we ve solved so far have had one operation on the variable. Once we ve undone that one operation, the equation is solved.
More information9.2 Multiplication Properties of Radicals
Section 9.2 Multiplication Properties of Radicals 885 9.2 Multiplication Properties of Radicals Recall that the equation x 2 = a, where a is a positive real number, has two solutions, as indicated in Figure
More informationWorking with Square Roots. Return to Table of Contents
Working with Square Roots Return to Table of Contents 36 Square Roots Recall... * Teacher Notes 37 Square Roots All of these numbers can be written with a square. Since the square is the inverse of the
More informationReview for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.
LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in
More informationExtending the Number System
Analytical Geometry Extending the Number System Extending the Number System Remember how you learned numbers? You probably started counting objects in your house as a toddler. You learned to count to ten
More informationNatural Whole Integer Rational Irrational Real. Sep 8 6:51 AM. Today we are starting our first non review unit REAL NUMBERS
Warm Up: 1. Prove that 0.14 can be written as a fraction 2. Mark a check in each column that idenfies the subset of the Real number system to which the number belongs. Natural Whole Integer Rational Irrational
More informationB.3 Solving Equations Algebraically and Graphically
B.3 Solving Equations Algebraically and Graphically 1 Equations and Solutions of Equations An equation in x is a statement that two algebraic expressions are equal. To solve an equation in x means to find
More information27 = 3 Example: 1 = 1
Radicals: Definition: A number r is a square root of another number a if r = a. is a square root of 9 since = 9 is also a square root of 9, since ) = 9 Notice that each positive number a has two square
More informationLESSON 7.1 FACTORING POLYNOMIALS I
LESSON 7.1 FACTORING POLYNOMIALS I LESSON 7.1 FACTORING POLYNOMIALS I 293 OVERVIEW Here s what you ll learn in this lesson: Greatest Common Factor a. Finding the greatest common factor (GCF) of a set of
More informationGraphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation.
Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation. 1. y = x + 2 2. f(x) = x 1. y = x +. g(x) = 2 x 1. y = x + 2 + 6. h(x)
More informationSOLUTIONS FOR PROBLEMS 1-30
. Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).
More informationLesson 26: Solving Rational Equations
Lesson 2: Solving Rational Equations Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to
More informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More informationMath 2 UNIT 3: Radicals
Math 2 UNIT : Radicals 1 Date Lesson Quiz Topic Homework Monday 2/20 Tuesday 2/21 Wednesday 2/22 Simplifying Radicals Solving Radical Equations Solving Radical Equations Thursday 2/2 Exponential Rules
More informationLesson 3-2: Solving Linear Systems Algebraically
Yesterday we took our first look at solving a linear system. We learned that a linear system is two or more linear equations taken at the same time. Their solution is the point that all the lines have
More information4-3 Logarithmic Functions
4-3 Logarithmic Functions Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Use mental math to evaluate.. 4 3 2. 6 4 2 3. 0 5 0.0000 4. 5. A power has a base of 2 and exponent of 4. Write and evaluate
More information5.1. Integer Exponents and Scientific Notation. Objectives. Use the product rule for exponents. Define 0 and negative exponents.
Chapter 5 Section 5. Integer Exponents and Scientific Notation Objectives 2 4 5 6 Use the product rule for exponents. Define 0 and negative exponents. Use the quotient rule for exponents. Use the power
More informationYOU CAN BACK SUBSTITUTE TO ANY OF THE PREVIOUS EQUATIONS
The two methods we will use to solve systems are substitution and elimination. Substitution was covered in the last lesson and elimination is covered in this lesson. Method of Elimination: 1. multiply
More informationSecondary Two Mathematics: An Integrated Approach Module 3 - Part One Imaginary Number, Exponents, and Radicals
Secondary Two Mathematics: An Integrated Approach Module 3 - Part One Imaginary Number, Exponents, and Radicals By The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis
More informationLogarithmic Functions
Warm Up Use mental math to evaluate.. 4 3 2. 6 4 2 3. 0 5 0.0000 4. 5. A power has a base of 2 and exponent of 4. Write and evaluate the power. ( 2) 4 = 6 Write equivalent forms for exponential and logarithmic
More informationAlgebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
More informationPractice Calculus Test without Trig
Practice Calculus Test without Trig The problems here are similar to those on the practice test Slight changes have been made 1 What is the domain of the function f (x) = 3x 1? Express the answer in interval
More informationFundamentals. Copyright Cengage Learning. All rights reserved.
Fundamentals Copyright Cengage Learning. All rights reserved. 1.2 Exponents and Radicals Copyright Cengage Learning. All rights reserved. Objectives Integer Exponents Rules for Working with Exponents Scientific
More information8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors
8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.
More informationLESSON 7.2 FACTORING POLYNOMIALS II
LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +
More informationExponents. Reteach. Write each expression in exponential form (0.4)
9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,
More information22. RADICALS. x add 5. multiply by 7
22. RADICALS doing something, then undoing it The concept of doing something and then undoing it is very important in mathematics. Here are some eamples: Take a number. Add 5 to it. How can you get back
More informationUnit 2: Functions and Patterns
For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 2: Functions and Patterns Note Packet Date Topic/Assignment Page Due Date Score (For Teacher Use Only) Warm-Ups 2-A Intro to Functions 2-B Tile
More informationHow can we see it? Is there another way?
You have solved a variety of equations in this course. In this lesson, by looking at equations in different ways, you will be able to solve even more complicated equations quickly and easily. These new
More informationLesson 3: Polynomials and Exponents, Part 1
Lesson 2: Introduction to Variables Assessment Lesson 3: Polynomials and Exponents, Part 1 When working with algebraic expressions, variables raised to a power play a major role. In this lesson, we look
More informationMath 096--Quadratic Formula page 1
Math 096--Quadratic Formula page 1 A Quadratic Formula. Use the quadratic formula to solve quadratic equations ax + bx + c = 0 when the equations can t be factored. To use the quadratic formula, the equation
More informationName: How Long Does It Take? (Part 1)
Name: How Long Does It Take? (Part 1) Standards Addressed in this Task MGSE9-12.N.RN.1, MGSE9-12.N.RN.2, MGSE9-12.N.RN.3 Before sending astronauts to investigate the new planet of Exponentia, NASA decided
More information2.3 Solving Equations Containing Fractions and Decimals
2. Solving Equations Containing Fractions and Decimals Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Solve equations containing fractions
More information