Sum or difference of Cubes
|
|
- Veronica Dorsey
- 6 years ago
- Views:
Transcription
1 Sum or difference of Cubes
2 Factoring Cubes 5 practice problems EVERY time you look at a factoring problem, start with the question: Is there a GCF? What s a GCF? It s a number or a variable that all the terms in the problem have in common, that you divide out of all of them before you get started. We ll use it a LOT in section 5., some in 5.4, not much in this part of 5.5. Nevertheless, we ll keep asking ourselves that question. :-D
3 Cubes: a 15 Start this game the same way we ve been playing: Is there a GCF? No, so count the terms. There are, so this is one of those weird ones!!! Since the exponent is a, this must be a cube problem: a SOAP. Now, all changes. One regular set of parenthesis, one larger. Also, write down the cube root of each of those two terms, then cross out the original terms. a 15 a 5 ( )( ) The terms a and 5 are your little building blocks. You ll build your answer from those. First, put them in the first set of parenthesis, along with the original sign in your problem. ( a 5)( ) Fill out the second set of parenthesis on the next page.
4 SOAP Same Opposite Always Positive The second set of parenthesis has terms in it. ( a 5)( ) In the first spot goes the first term times itself. ( a 5)( a ) In the back spot goes the last term times itself. ( a 5)( a 5) And in that middle spot goes the two terms times each other. ( a 5)( a 5a 5) Now put the correct signs in. SOAP this problem! ( a 5)( a 5a 5) ( a 5)( a 5a 5)
5 Cubes: x 8 Start this game the same way we ve been playing: Is there a GCF? No, so count the terms. There are, so this is one of those weird ones!!! Since the exponent is a, this must be a cube problem: a SOAP. Now, all changes. One regular set of parenthesis, one larger. Also, write down the cube root of each of those two terms, then cross out the original terms. x 8 x ( )( ) The terms x and are your little building blocks. You ll build your answer from those. First, put them in the first set of parenthesis, along with the original sign in your problem. ( x )( ) Fill out the second set of parenthesis on the next page.
6 SOAP Same Opposite Always Positive The second set of parenthesis has terms in it. ( x )( ) In the first spot goes the first term times itself. ( x )( x ) In the back spot goes the last term times itself. ( x )( x 4) And in that middle spot goes the two terms times each other. ( x )( x x 4) Now put the correct signs in. SOAP this problem! ( x )( x x 4) ( x )( x x 4)
7 Cubes: x 1 Start this game the same way we ve been playing: Is there a GCF? No, so count the terms. There are, so this is one of those weird ones!!! Since the exponent is a, this must be a cube problem: a SOAP. Now, all changes. One regular set of parenthesis, one larger. Also, write down the cube root of each of those two terms, then cross out the original terms. 7x 1 x 1 ( )( ) The terms x and 1 are your little building blocks. You ll build your answer from those. First, put them in the first set of parenthesis, along with the original sign in your problem. (x 1)( ) Fill out the second set of parenthesis on the next page.
8 SOAP Same Opposite Always Positive The second set of parenthesis has terms in it. (x 1)( ) In the first spot goes the first term times itself. (x 1)(9 x ) In the back spot goes the last term times itself. (x 1)(9 x 1) And in that middle spot goes the two terms times each other. (x 1)(9 x x 1) Now put the correct signs in. SOAP this problem! (x 1)(9 x x 1) (x 1)(9 x x 1)
9 Cubes: a 64 Start this game the same way we ve been playing: Is there a GCF? No, so count the terms. There are, so this is one of those weird ones!!! Since the exponent is a, this must be a cube problem: a SOAP. Now, all changes. One regular set of parenthesis, one larger. Also, write down the cube root of each of those two terms, then cross out the original terms. a 64 a 4 ( )( ) The terms a and 4 are your little building blocks. You ll build your answer from those. First, put them in the first set of parenthesis, along with the original sign in your problem. ( a 4)( ) Fill out the second set of parenthesis on the next page.
10 SOAP Same Opposite Always Positive The second set of parenthesis has terms in it. ( a 4)( ) In the first spot goes the first term times itself. ( a 4)( a ) In the back spot goes the last term times itself. ( a 4)( a 16) And in that middle spot goes the two terms times each other. ( a 4)( a 4a 16) Now put the correct signs in. SOAP this problem! ( a 4)( a 4a 16) ( a 4)( a 4a 16)
11 Cubes: y 8 Start this game the same way we ve been playing: Is there a GCF? No, so count the terms. There are, so this is one of those weird ones!!! Since the exponent is a, this must be a cube problem: a SOAP. Now, all changes. One regular set of parenthesis, one larger. Also, write down the cube root of each of those two terms, then cross out the original terms. 7y 8 y ( )( ) The terms y and are your little building blocks. You ll build your answer from those. First, put them in the first set of parenthesis, along with the original sign in your problem. (y )( ) Fill out the second set of parenthesis on the next page.
12 SOAP Same Opposite Always Positive The second set of parenthesis has terms in it. (y )( ) In the first spot goes the first term times itself. (y )(9 y ) In the back spot goes the last term times itself. (y )(9 y 4) And in that middle spot goes the two terms times each other. (y )(9 y 6y 4) Now put the correct signs in. SOAP this problem! (y )(9 y 6y 4) (y )(9 y 6y 4)
Factoring - Special Products
Factoring - Special Products When factoring there are a few special products that, if we can recognize them, can help us factor polynomials. The first is one we have seen before. When multiplying special
More informationModule 7 Highlights. Mastered Reviewed. Sections ,
Sections 5.3 5.6, 6.1 6.6 Module 7 Highlights Andrea Hendricks Math 0098 Pre-college Algebra Topics Degree & leading coeff. of a univariate polynomial (5.3, Obj. 1) Simplifying a sum/diff. of two univariate
More informationExponents. Common Powers
Exponents An exponent defines the number of times a number is to be multiplied by itself. For example, in a b, where a is the base and b the exponent, a is multiplied by itself btimes. In a numerical example,
More informationThe Absolute Value Symbol
Section 1 3: Absolute Value and Powers The Absolute Value Symbol The symbol for absolute value is a pair of vertical lines. These absolute value brackets act like the parenthesis that we use in order of
More informationPreCalculus 300. Algebra 2 Review
PreCalculus 00 Algebra Review Algebra Review The following topics are a review of some of what you learned last year in Algebra. I will spend some time reviewing them in class. You are responsible for
More informationAlgebra 1 Review. Properties of Real Numbers. Algebraic Expressions
Algebra 1 Review Properties of Real Numbers Algebraic Expressions Real Numbers Natural Numbers: 1, 2, 3, 4,.. Numbers used for counting Whole Numbers: 0, 1, 2, 3, 4,.. Natural Numbers and 0 Integers:,
More informationPrepared by Sa diyya Hendrickson. Package Summary
Introduction Prepared by Sa diyya Hendrickson Name: Date: Package Summary Exponent Form and Basic Properties Order of Operations Using Divisibility Rules Finding Factors and Common Factors Primes, Prime
More informationRev Name Date. . Round-off error is the answer to the question How wrong is the rounded answer?
Name Date TI-84+ GC 7 Avoiding Round-off Error in Multiple Calculations Objectives: Recall the meaning of exact and approximate Observe round-off error and learn to avoid it Perform calculations using
More information( 3) ( 4 ) 1. Exponents and Radicals ( ) ( xy) 1. MATH 102 College Algebra. still holds when m = n, we are led to the result
Exponents and Radicals ZERO & NEGATIVE EXPONENTS If we assume that the relation still holds when m = n, we are led to the result m m a m n 0 a = a = a. Consequently, = 1, a 0 n n a a a 0 = 1, a 0. Then
More informationMore Ways to Solve & Graph Quadratics The Square Root Property If x 2 = a and a R, then x = ± a
More Ways to Solve & Graph Quadratics The Square Root Property If x 2 = a and a R, then x = ± a Example: Solve using the square root property. a) x 2 144 = 0 b) x 2 + 144 = 0 c) (x + 1) 2 = 12 Completing
More informationConverting Between Mixed Numbers & Improper Fractions
01 Converting Between Mixed Numbers & Improper Fractions A mixed number is a whole number and a fraction: 4 1 2 An improper fraction is a fraction with a larger numerator than denominator: 9 2 You can
More informationHi. I m a three. I m always a three. I never ever change. That s why I m a constant.
Lesson 1-1: 1 1: Evaluating Expressions Hi. I m a three. I m always a three. I never ever change. That s why I m a constant. 3 Real life changes, though. So to talk about real life, math needs things that
More informationSection a) f(x-3)+4 = (x 3) the (-3) in the parenthesis moves right 3, the +4 moves up 4
Section 4.3 1a) f(x-3)+4 = (x 3) 2 + 4 the (-3) in the parenthesis moves right 3, the +4 moves up 4 Answer 1a: f(x-3)+4 = (x 3) 2 + 4 The graph has the same shape as f(x) = x 2, except it is shifted right
More informationYou can graph the equation, then have the calculator find the solutions/roots/zeros/x intercepts.
To find zeros, if you have a quadratic, x 2, then you can use the quadratic formula. You can graph the equation, then have the calculator find the solutions/roots/zeros/x intercepts. Apr 22 10:39 AM Graphing
More informationChapter 0: Algebra II Review
Chapter 0: Algebra II Review Topic 1: Simplifying Polynomials & Exponential Expressions p. 2 - Homework: Worksheet Topic 2: Radical Expressions p. 32 - Homework: p. 45 #33-74 Even Topic 3: Factoring All
More informationUnit 3B- Complex Numbers, Factoring, Parabola. Yujia Shen, Jonathan Kurian, Ryan Okushi
Unit 3B- Complex Numbers, Factoring, Parabola Yujia Shen, Jonathan Kurian, Ryan Okushi Complex Numbers i = A complex number is a number that can be expressed in the form a+bi, where a and b are real numbers
More informationSolving Problems with Similar Triangles
Solving Problems with Similar Triangles xample 1: Given that lines and are parallel in the figure to the right, determine the value of x, the distance between points and. Solution: First, we can demonstrate
More information6.1 Evaluate Roots and Rational Exponents
VOCABULARY:. Evaluate Roots and Rational Exponents Radical: We know radicals as square roots. But really, radicals can be used to express any root: 0 8, 8, Index: The index tells us exactly what type of
More informationLesson 1: Arithmetic Review
Lesson 1: Arithmetic Review Topics and Objectives: Order of Operations Fractions o Improper fractions and mixed numbers o Equivalent fractions o Fractions in simplest form o One and zero Operations on
More informationSection 3.7 Notes. Rational Functions. is a rational function. The graph of every rational function is smooth (no sharp corners)
Section.7 Notes Rational Functions Introduction Definition A rational function is fraction of two polynomials. For example, f(x) = x x + x 5 Properties of Rational Graphs is a rational function. The graph
More information1.1 evaluating expressions 2017 ink.notebook. August 18, page 7 page 8 Unit 1 Basic Equations and Inequalities. 1.1 Order of Operations.
1.1 evaluating expressions 2017 ink.notebook page 7 page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 page 10 Lesson Objectives Standards 1.1 Order of Operations Press the tabs
More informationObjective Simplify expressions using the properties of exponents.
Pre-Algebra: Exponent Properties Objective Simplify expressions using the properties of exponents. Exponents are used to simplify expressions. For example, a*a*a*a*a*a*a is the expanded expression of a
More informationIntro to Animation. Introduction: Frames and Keyframes. Blender Lesson: Grade Level: Lesson Description: Goals/Objectives: Materials/Tools: 4th and up
Blender Lesson: Intro to Animation Grade Level: 4th and up Lesson Description: This lesson serves as an introduction to animation with Blender. The lesson begins by talking about some core concepts of
More informationAdvanced Functions Unit 4
Advanced Functions Unit 4 Absolute Value Functions Absolute Value is defined by:, 0, if if 0 0 - (), if 0 The graph of this piecewise function consists of rays, is V-shaped and opens up. To the left of
More informationProperties and Definitions
Section 0.1 Contents: Operations Defined Multiplication as an Abbreviation Visualizing Multiplication Commutative Properties Parentheses Associative Properties Identities Zero Product Answers to Exercises
More informationUnit 1 and Unit 2 Concept Overview
Unit 1 and Unit 2 Concept Overview Unit 1 Do you recognize your basic parent functions? Transformations a. Inside Parameters i. Horizontal ii. Shift (do the opposite of what feels right) 1. f(x+h)=left
More informationSlide 1 / 180. Radicals and Rational Exponents
Slide 1 / 180 Radicals and Rational Exponents Slide 2 / 180 Roots and Radicals Table of Contents: Square Roots Intro to Cube Roots n th Roots Irrational Roots Rational Exponents Operations with Radicals
More informationChapter 1 & 2 Calculator Test Study Guide
Chapter 1 & 2 Calculator Test Study Guide Powers and Exponents 1) To put a number to the second power, simply hit the x 2 key, then enter. 2) To put a number to the third or a higher power, key in base,
More informationFactoring. Factor: Change an addition expression into a multiplication expression.
Factoring Factor: Change an addition expression into a multiplication expression. 1. Always look for a common factor a. immediately take it out to the front of the expression, take out all common factors
More informationAlgebra 2 Semester 1 (#2221)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the 2016-2017 Course Guides for the following course: Algebra 2 Semester
More informationImportant Things to Remember on the SOL
Notes Important Things to Remember on the SOL Evaluating Expressions *To evaluate an expression, replace all of the variables in the given problem with the replacement values and use (order of operations)
More informationLesson 13: Exploring Factored Form
Opening Activity Below is a graph of the equation y = 6(x 3)(x + 2). It is also the graph of: y = 3(2x 6)(x + 2) y = 2(3x 9)(x + 2) y = 2(x 3)(3x + 6) y = 3(x 3)(2x + 4) y = (3x 9)(2x + 4) y = (2x 6)(3x
More informationName Course Days/Start Time
Name Course Days/Start Time Mini-Project : The Library of Functions In your previous math class, you learned to graph equations containing two variables by finding and plotting points. In this class, we
More informationSection 0.3 The Order of Operations
Section 0.3 The Contents: Evaluating an Expression Grouping Symbols OPERATIONS The Distributive Property Answers Focus Exercises Let s be reminded of those operations seen thus far in the course: Operation
More informationIntegers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not.
What is an INTEGER/NONINTEGER? Integers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not. What is a REAL/IMAGINARY number? A real number is
More informationSection 3.1 Factors and Multiples of Whole Numbers:
Chapter Notes Math 0 Chapter : Factors and Products: Skill Builder: Some Divisibility Rules We can use rules to find out if a number is a factor of another. To find out if, 5, or 0 is a factor look at
More informationGraphing Calculator Overview
Graphing Calculator Overview Workshop One Objectives Learn the general layout of the calculator Learn how to navigate the menus Learn basic operating procedures Perform linear regression LEARNING CENTER
More informationPRE-ALGEBRA BY MYRL SHIREMAN
PRE-ALGEBRA BY MYRL SHIREMAN COPYRIGHT 1994 Mark Twain Media, Inc. ISBN 10-digit: 1-58037-064-0 13-digit: 978-1-58037-064-6 Printing No. CD-1876 Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa
More informationThe Anatomy of a Man in the Middle Attack
Before we dig into this tutorial, lets take an opportunity to cover a fundamental ARP based attack, the Man in the Middle. We re going to cover how this attack works and then we re going to launch this
More informationCH 87 FUNCTIONS: TABLES AND MAPPINGS
CH 87 FUNCTIONS: TABLES AND MAPPINGS INTRODUCTION T he notion of a function is much more abstract than most of the algebra concepts you ve seen so far, so we ll start with three specific non-math examples.
More informationPrime Time (Factors and Multiples)
CONFIDENCE LEVEL: Prime Time Knowledge Map for 6 th Grade Math Prime Time (Factors and Multiples). A factor is a whole numbers that is multiplied by another whole number to get a product. (Ex: x 5 = ;
More informationThe Foundation. Review in an instant
The Foundation Review in an instant Table of contents Introduction 1 Basic use of Excel 2 - Important Excel terms - Important toolbars - Inserting and deleting columns and rows - Copy and paste Calculations
More informationObjective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions
Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions Variable is a letter or symbol that represents a number. Variable (algebraic)
More informationReading on the Accumulation Buffer: Motion Blur, Anti-Aliasing, and Depth of Field
Reading on the Accumulation Buffer: Motion Blur, Anti-Aliasing, and Depth of Field 1 The Accumulation Buffer There are a number of effects that can be achieved if you can draw a scene more than once. You
More informationSeeing an Object. 6: Geometric Optics (Chapters 34)
Seeing an Object 6: Geometric Optics (Chapters 34) Phys130, A01 Dr. Robert MacDonald Light rays from each point on the go everywhere. Some light from each point reaches the. 2 virtual image As long as
More informationMath 10- Chapter 2 Review
Math 10- Chapter 2 Review [By Christy Chan, Irene Xu, and Henry Luan] Knowledge required for understanding this chapter: 1. Simple calculation skills: addition, subtraction, multiplication, and division
More informationThe figures below are all prisms. The bases of these prisms are shaded, and the height (altitude) of each prism marked by a dashed line:
Prisms Most of the solids you ll see on the Math IIC test are prisms or variations on prisms. A prism is defined as a geometric solid with two congruent bases that lie in parallel planes. You can create
More informationCSC148H Week 3. Sadia Sharmin. May 24, /20
CSC148H Week 3 Sadia Sharmin May 24, 2017 1/20 Client vs. Developer I For the first couple of weeks, we have played the role of class designer I However, you are also often in the opposite role: when a
More informationSpecial Products on Factoring
Special Products on Factoring What Is This Module About? This module is a continuation of the module on polnomials. In the module entitled Studing Polnomials, ou learned what polnomials are as well as
More informationMotivation for B-Trees
1 Motivation for Assume that we use an AVL tree to store about 20 million records We end up with a very deep binary tree with lots of different disk accesses; log2 20,000,000 is about 24, so this takes
More informationExample: Which of the following expressions must be an even integer if x is an integer? a. x + 5
8th Grade Honors Basic Operations Part 1 1 NUMBER DEFINITIONS UNDEFINED On the ACT, when something is divided by zero, it is considered undefined. For example, the expression a bc is undefined if either
More informationRandom input testing with R
Random input testing with R Patrick Burns http://www.burns-stat.com stat.com 2011 August Given at user!2011 at the University of Warwick on 2011 August 17 in the Programming session, Uwe Ligges presiding.
More informationThe counting numbers or natural numbers are the same as the whole numbers, except they do not include zero.,
Factors, Divisibility, and Exponential Notation Terminology The whole numbers start with zero and continue infinitely., The counting numbers or natural numbers are the same as the whole numbers, except
More informationMath 083 Final Exam Practice
Math 083 Final Exam Practice Name: 1. Simplify the expression. Remember, negative exponents give reciprocals.. Combine the expressions. 3. Write the expression in simplified form. (Assume the variables
More informationHow to Do Word Problems. Building the Foundation
Building the Foundation The notion that Mathematics is a language, is held by many mathematicians and is being expressed on frequent occasions. Mathematics is the language of science. It is unique among
More informationNFC ACADEMY MATH 600 COURSE OVERVIEW
NFC ACADEMY MATH 600 COURSE OVERVIEW Math 600 is a full-year elementary math course focusing on number skills and numerical literacy, with an introduction to rational numbers and the skills needed for
More informationPage 1 CCM6 Unit 10 Graphing UNIT 10 COORDINATE PLANE. CCM Name: Math Teacher: Projected Test Date:
Page 1 CCM6 Unit 10 Graphing UNIT 10 COORDINATE PLANE CCM6 2016-17 Name: Math Teacher: Projected Test Date: Main Concept Page(s) Vocabulary 2 Coordinate Plane Introduction graph and label 3-6 Reflect across
More informationAre you ready for Beast Academy 4B?
re you ready for east cademy 4? Step 1. he student should try to answer every question without a calculator and without help. Step 2. heck the student s answers using the solutions at the end of this document.
More informationIntro to Programming. Unit 7. What is Programming? What is Programming? Intro to Programming
Intro to Programming Unit 7 Intro to Programming 1 What is Programming? 1. Programming Languages 2. Markup vs. Programming 1. Introduction 2. Print Statement 3. Strings 4. Types and Values 5. Math Externals
More informationFraction to Percents Change the fraction to a decimal (see above) and then change the decimal to a percent (see above).
PEMDAS This is an acronym for the order of operations. Order of operations is the order in which you complete problems with more than one operation. o P parenthesis o E exponents o M multiplication OR
More informationRectangle Sums
Rectangle Sums --208 You can approximate the area under a curve using rectangles. To do this, divide the base interval into pieces subintervals). Then on each subinterval, build a rectangle that goes up
More informationAlgebra II Chapter 4: Quadratic Functions and Factoring Part 1
Algebra II Chapter 4: Quadratic Functions and Factoring Part 1 Chapter 4 Lesson 1 Graph Quadratic Functions in Standard Form Vocabulary 1 Example 1: Graph a Function of the Form y = ax 2 Steps: 1. Make
More informationMAT 003 Brian Killough s Instructor Notes Saint Leo University
MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
More informationCongruence Arithmetic
Module 4 Congruence Arithmetic Popper 4 Introduction to what is like Modulus choices Partitions by modulus Mod 5 Mod 7 Mod 30 Modular Arithmetic Addition Subtraction Multiplication INTEGERS! Mod 12 Cayley
More informationIs the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd
Is the statement sufficient? If both x and y are odd, is xy odd? Is x < 0? 1) xy 2 < 0 Positives & Negatives Answer: Yes, xy is odd Odd numbers can be represented as 2m + 1 or 2n + 1, where m and n are
More informationSquare Roots: Introduction & Simplification
Square Roots: Introduction & Simplification You already know about squaring. For instance, 2 2 = 4, 3 2 = 9, etc. The backwards of squaring is square-rooting. The symbol for square-rooting is " ", the
More informationGraphing Techniques. Domain (, ) Range (, ) Squaring Function f(x) = x 2 Domain (, ) Range [, ) f( x) = x 2
Graphing Techniques In this chapter, we will take our knowledge of graphs of basic functions and expand our ability to graph polynomial and rational functions using common sense, zeros, y-intercepts, stretching
More information/633 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Priority Queues / Heaps Date: 9/27/17
01.433/33 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Priority Queues / Heaps Date: 9/2/1.1 Introduction In this lecture we ll talk about a useful abstraction, priority queues, which are
More informationCCBC Math 081 Order of Operations Section 1.7. Step 2: Exponents and Roots Simplify any numbers being raised to a power and any numbers under the
CCBC Math 081 Order of Operations 1.7 1.7 Order of Operations Now you know how to perform all the operations addition, subtraction, multiplication, division, exponents, and roots. But what if we have a
More informationSection 1.8. Simplifying Expressions
Section 1.8 Simplifying Expressions But, first Commutative property: a + b = b + a; a * b = b * a Associative property: (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) Distributive property: a * (b
More informationChapter 2: Polynomial and Rational Functions Power Standard #7
Chapter 2: Polynomial and Rational s Power Standard #7 2.1 Quadratic s Lets glance at the finals. Learning Objective: In this lesson you learned how to sketch and analyze graphs of quadratic functions.
More informationA triangle that has three acute angles Example:
1. acute angle : An angle that measures less than a right angle (90 ). 2. acute triangle : A triangle that has three acute angles 3. angle : A figure formed by two rays that meet at a common endpoint 4.
More informationA. Incorrect! To simplify this expression you need to find the product of 7 and 4, not the sum.
Problem Solving Drill 05: Exponents and Radicals Question No. 1 of 10 Question 1. Simplify: 7u v 4u 3 v 6 Question #01 (A) 11u 5 v 7 (B) 8u 6 v 6 (C) 8u 5 v 7 (D) 8u 3 v 9 To simplify this expression you
More informationUnit 4: Multiplication
Math Fundamentals for Statistics I (Math 52) Unit 4: Multiplication By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike
More informationMath 1314 Lesson 2: An Introduction to Geogebra (GGB) Before we introduce calculus, let s look at a brief introduction to GGB.
Math 1314 Lesson : An Introduction to Geogebra (GGB) Before we introduce calculus, let s look at a brief introduction to GGB. GeoGebra (GGB) is a FREE software package that we will use throughout the semester.
More informationFUNDAMENTAL ARITHMETIC
FUNDAMENTAL ARITHMETIC Prime Numbers Prime numbers are any whole numbers greater than that can only be divided by and itself. Below is the list of all prime numbers between and 00: Prime Factorization
More information7th Grade Accelerated Math Unit 1 Number Sense Learning Targets. 7th Grade Number Sense (Operations with Fractions and Integers)
7th Grade Accelerated Math Unit 1 Number Sense Learning Targets 7th Grade Number Sense (Operations with Fractions and Integers) Integer Learning Targets (Positive and Negative Whole Numbers) 1. I can describe
More informationGAP CLOSING. Grade 9. Facilitator s Guide
GAP CLOSING Grade 9 Facilitator s Guide Topic 3 Integers Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions solutions... 5 Using Intervention Materials...8
More informationLesson 26: Volume of Composite Three-Dimensional Objects
Lesson 26: Volume of Composite Three-Dimensional Objects Student Outcomes Students compute volumes of three-dimensional objects composed of right prisms by using the fact that volume is additive. Lesson
More informationCP1 Math 2 Cumulative Exam Review
Name February 9-10, 2016 If you already printed the online copy of this document, there are answer corrections on pages 4 and 8 (shaded). Deductive Geometry (Ch. 6) Writing geometric proofs Triangle congruence
More informationMini-Lesson 1. Section 1.1: Order of Operations PEMDAS
Name: Date: 1 Section 1.1: Order of Operations PEMDAS If we are working with a mathematical expression that contains more than one operation, then we need to understand how to simplify. The acronym PEMDAS
More informationAlgebra 2 Common Core Summer Skills Packet
Algebra 2 Common Core Summer Skills Packet Our Purpose: Completion of this packet over the summer before beginning Algebra 2 will be of great value to helping students successfully meet the academic challenges
More informationAdding and Subtracting Integers
Quarterly 1 Review Sheet (NOTE: This may not include everything you need to know for tomorrow about every topic. It is student created and I am just sharing it in case you find it helpful) Page 1: Adding
More informationinteger not an integer Directions: Classify each number as an integer or not an integer. September 19, 2014
Directions: Classify each number as an integer or not an integer. 0 9 3¾ π ½ 3.2 5 1 65 6 6.32 21 ¾ integer not an integer 1 Directions: Insert an equality symbol() between the following signed numbers:
More informationTable of Contents. Foundations 5p Vocabulary List
Table of Contents Objective 1: Review (Natural Numbers)... 3 Objective 2: Reading and Writing Natural Numbers... 5 Objective 3: Lines: Rays, and Line Segments... 6 Objective 4: Comparing Natural Numbers...
More informationName: Tutor s
Name: Tutor s Email: Bring a couple, just in case! Necessary Equipment: Black Pen Pencil Rubber Pencil Sharpener Scientific Calculator Ruler Protractor (Pair of) Compasses 018 AQA Exam Dates Paper 1 4
More informationPart II Composition of Functions
Part II Composition of Functions The big idea in this part of the book is deceptively simple. It s that we can take the value returned by one function and use it as an argument to another function. By
More informationCS 542G: Barnes-Hut. Robert Bridson. November 5, 2008
CS 54G: Barnes-Hut Robert Bridson November 5, 008 The Gravitational Potential While it s perfectly possible to derive all the following at the level of forces, it can be both convenient and useful to re-express
More informationConvert Your TiVo Shows
Convert Your TiVo Shows Watch TiVo recordings on your portable player, or save them to DVD, with the Roxio Video Capture & Convert utility. TiVos are great for time-shifting TV shows, but with Roxio Creator
More informationCollege Prep Algebra II Summer Packet
Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When
More informationMath 96--Radicals #1-- Simplify; Combine--page 1
Simplify; Combine--page 1 Part A Number Systems a. Whole Numbers = {0, 1, 2, 3,...} b. Integers = whole numbers and their opposites = {..., 3, 2, 1, 0, 1, 2, 3,...} c. Rational Numbers = quotient of integers
More informationMathematical Operations
CHAPTER 10 Mathematical Operations The basic approach for the problems of this type is more or less similar to that of coding and decoding. One has to study the symbols or the geometrical figures and their
More informationMath Glossary Numbers and Arithmetic
Math Glossary Numbers and Arithmetic Version 0.1.1 September 1, 200 Next release: On or before September 0, 200. E-mail edu@ezlink.com for the latest version. Copyright 200 by Brad Jolly All Rights Reserved
More informationYou may use a calculator for these practice questions. You may
660 Math Smart Practice Questions You may use a calculator for these practice questions. You may not know all the math to complete these practice questions yet, but try to think them through! 1. Eric lives
More informationPlace Value. 2. Rounding. 2 Divisibility Rules 17 Exponents. 3 Cubes & Roots.. 3, 15 Squares & Roots... 3, 15 Factors & Multiples.
Algebra..... - Steps of Algebra... Expressions.. Conversion Benchmarks. - Customary & Metric.. - Fractions/ Decimals/ Percents Gallon Guy Diagram. Volume Coordinate Plane.. 0 Data Analysis & Statistics..
More informationSolving Simple Quadratics 1.0 Topic: Solving Quadratics
Ns Solving Simple Quadratics 1.0 Topic: Solving Quadratics Date: Objectives: SWBAT (Solving Simple Quadratics and Application dealing with Quadratics) Main Ideas: Assignment: Square Root Property If x
More informationLecture 7: Lists, Version 2 (with Mutation)
Integrated Introduction to Computer Science Fisler Contents 1 The Impact of addfirst on Lists 1 2 The Challenge of Sharing Data Structures 2 2.1 Functional Lists in Memory................................
More informationOutputs. Inputs. the point where the graph starts, as we ll see on Example 1.
We ve seen how to work with functions algebraically, by finding domains as well as function values. In this set of notes we ll be working with functions graphically, and we ll see how to find the domain
More informationVisual Formula, Important Graphs, Inequalities, and Other Things
flynt_1598632914_ch10, 4/8/6, 12:3191 chapter 10 Visual Formula, Important Graphs, Inequalities, and Other Things The activities this chapter covers allow you to use Visual Formula to work with many of
More informationRising Geometry Students! Answer Key
Rising Geometry Students! Answer Key As a 7 th grader entering in to Geometry next year, it is very important that you have mastered the topics listed below. The majority of the topics were taught in Algebra
More information