Confucius said, Education without understanding is a futile exercise.


 Gwenda Todd
 2 years ago
 Views:
Transcription
1 Welcome to Introduction to Statistics! This book is written for introductory Statistics courses both on line and in classroom. You should read this entire preface carefully. Either taking this course on line or in classroom, you will greatly benefit from what is stated in this preface. That is my guarantee. Confucius said, Education without understanding is a futile exercise. Understanding is the key to success in this course, in college, and in life. There is no substitute for understanding. If you memorize something without understanding, you often cannot use it correctly or effectively. In mathematics and Statistics, to learn and understand new materials, you need to use materials that you have learned and understood. So, do not try to get through this course by memorization. Please study the course materials to understand them. You should understand everything in the textbook. If you do, there is no problem but fun in this course. Generally, learning math and Statistics is easy and fun with understanding; everything becomes obvious. You should understand things given in bold letters, examples (especially those reference examples), definitions, formulas and, in fact, everything in this textbook. The tests and exams are based on the textbook. That is, you can find the answers and how to find the answers for test/exam questions in this book. Of course, you need certain things (like sets, inequalities and such) from the prerequisite. Other than that, you need nothing else to answer test and exam questions. A reference book is suggested in the course syllabus. Almost any introductory Statistics book could serve as a reference (check its topics, though). If there is a difference between this book and other books, we go by this textbook. You should read the textbook, for the sections of the next test, at least several times to understand as much (if not all) as possible before taking the test. If you read the textbook just to find answers for test questions (without trying to understand its contents), you would get in trouble fast. You cannot get through this course that
2 way. You should read the textbook several times and understand the materials given in the textbook before taking a test for the first time. The exams are for evaluation purposes only. However, the tests are for evaluation and learning purposes. That is, you use the tests to learn the materials, which is a reason why you are allowed to take each test many times before its deadline. You can ask me about test questions too, by or during the office hours. If you think that your answer for a question is correct but that it is graded to be incorrect, then please ask me about it. In fact, if you have four or five questions that you cannot answer correctly in a test after taking the test several times, ask me about them. I will help you. This means that you have no excuse for not getting excellent, if not perfect, scores on the tests. Exercise questions are given at the end of each section. They are used to check whether or not you have understood the materials given in the section. You can find all the answers (or how to find answers) in the section. If you truly understand the material that an exercise question is asking about, you can answer the question without any trouble. In fact, you know your answer is correct if you have understood the material that the question is asking about. This is a reason why the answers for these exercise questions are not given anywhere. If you are not sure about your answer or have no idea what an exercise question is asking about, then you have failed to understand the material that it is asking about. You need to go back to the textbook and study the material till you understand it. You can find answers or how to find answers for all the questions in the textbook. However, if you need to find the answers for numerical/computational questions or any exercise questions, please contact me; I am happy to help. You may discuss exercise questions with other students while you are prohibited to discuss, with any other students or anyone, on specific questions in any test before its deadline. Like any applied mathematics, Statistics consists of the math component (mathematical definitions, notations, formulae, computations, and such) and the application component (practical purposes, practical functions, practical application,
3 and such). This course and the textbook emphasize both components, unlikely may other Statistics courses and textbooks. This book does not have a glossary because you construct a glossary in your head as you study and understand the materials in the course and this textbook. If you need a hard copy, make it yourself as you study. You need only materials that you have studied and understood in order to learn and understand new materials because of the sequential structure of mathematics (Statistics). By the way, you can take a glossary in your head to the exams and use it but cannot do so with a hard copy. This book does not have an index either. By studying and understanding the materials, you should know where you can find certain materials in the book. Of course, you can construct a hard copy of an index, if you need one, which could be a good learning process. Again, to study and understand new materials, you do not need anything that you have not studied (that is, you need only what you have studied and understood) because of the sequential structure of this book. For those who are taking a course in classroom, lectures are based on this book. You see the same definitions, examples and such along with more explanations and examples in the lectures. You should go over your lecture notes and make sure you understand everything in the notes before your next lecture; I am available to answer any questions by or during my office hours for every student. Finally, do not memorize formulae; study and understand them. If you understand formulae, you can recall and use them anytime you need or want to. Often, you can compute or obtain what you are looking for without its formula once you understand it. I have a couple of examples with the formulae of the sample mean and the sample standard deviation at the end of this preface. After studying the formulae, please come back and read the examples. It should make a lot more sense to you then. Do not memorize it but do understand it. This is generally true even outside mathematics and Statistics. There is a lot of trouble with memorization; easy to forget it, unable to regain it if forgotten, unable to memorize many things, easy to
4 get confused, and so on. However, the biggest problem is being unable to recognize when to use it (which one to use) and when not to use it. Also, often, you cannot use it correctly even when used. These problems can be avoided by understanding. So, study to understand and avoid memorization in this course. You cannot get through this course by memorizing this book. Confucius said, He who memorizes is buying a car without engine. It does not take him too far. EXAMPLES WITH THE FORMULAS OF SAMPLE MEAN AND STANDARD DEVIATION: One of the purposes of the sample mean (sample average) is to indicate the center of data. If data consist of two numbers, the center of the data is their midpoint. This midpoint is obtained by adding these two numbers and dividing the sum by two. With three numbers, their center is obtained by adding them up and dividing the sum by three. You can check that it indeed gives you the center of the numbers. Add three numbers and divide it by three. Subtract the sample mean from each number and add the three differences. It comes out to be zero (this is a definition of the center). Yes, the sample mean is the center of the data. So, if you have n numbers in data, then add them up and divide the sum by n. This is the formula for the sample mean. No need to be given to students who understand the sample mean (as the center of data) and its formula. The formula of the sample mean is simple. Let us try the formula of the sample variance, one of complicated formulas in introductory Statistics. A purpose of sample variance is to measure the amount of variation in data. So, let us measure the variation (difference) of each datum or number from the center of the data (the sample mean) by subtracting the sample mean from each datum. To get the total variation, add all the differences. However, the sum turns out always zero (a problem caused by these negative differences). So, square each of those differences (with that, they are all positive) and add them up.
5 Here is another problem. If there are many numbers in data, the sum becomes large even if they are tightly clustered (less variation). This is not fair. So, let us use average variation (per datum) to solve this unfairness. Divide the sum of squared differences by the sample size n. This is the formula of the sample variance. If you want to measure the amount of variation in the same unit as that of the original data, take the squareroot of the sample variance, which is the formula of the sample standard deviation. You do not have to be given these formulae. In fact, you do not need the formulae to compute sample variation and standard deviation. The great thing about this is that you know exactly how the sample standard deviation can get the value zero (or a large value) and what its value zero (or large) means. You do not have to memorize what a zero (or a large value) means. As a result, you do not have to memorize formulae and anything connected with formulae. You do not have to be given formulae either. You should learn formulae in math and Statistics this way (understand them); that is, no need for memorization and no need to be given formulae in mathematics and Statistics courses. Note: The common formula for the sample variance (or sample standard deviation) uses the divisor (n1), instead of n. There are two reasons for this. One is the unbiasedness of the estimator. Another reason is to prevent someone from using the formula to measure variation from one datum. One number does not contain any information about the variation and cannot and should not be used for measuring variation. If someone tries to use the formula with one datum, he has n = 1 and n 1 = 0. When the denominator is 0, it is undefined as it should be. By the way, when data are large enough, dividing the sum by n or n 1 would not result in any significant difference numerically. What is given in these examples might not be clear to you now. However, after learning about sample variance and standard deviation, please come back and read these examples again. They should make a lot of sense to you, then. 08/08/11
Order 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 informationCommon Core Mathematics Challenge
Level: Domain: Cluster: Grade Five Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. Standard Add and subtract fraction with unlike denominators (including
More informationThe NotFormula Book for C1
Not The NotFormula Book for C1 Everything you need to know for Core 1 that won t be in the formula book Examination Board: AQA Brief This document is intended as an aid for revision. Although it includes
More informationExponential Notation and the Order of Operations
1.7 Exponential Notation and the Order of Operations 1.7 OBJECTIVES 1. Use exponent notation 2. Evaluate expressions containing powers of whole numbers 3. Know the order of operations 4. Evaluate expressions
More informationGrade 7/8 Math Circles October 7/8, Exponents and Roots  SOLUTIONS
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 7/8, 2014 Exponents and Roots  SOLUTIONS This file has all the missing
More informationImproper Fractions and Mixed Numbers
This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All
More informationSpringfield Technical Community College School of Mathematics, Sciences & Engineering Transfer
Springfield Technical Community College School of Mathematics, Sciences & Engineering Transfer Department: Mathematics Course Title: Algebra 2 Course Number: MAT097 Semester: Fall 2015 Credits: 3 NonGraduation
More informationHow to Study Mathematics Written by Paul Dawkins
How to Study Mathematics Written by Paul Dawkins Before I get into the tips for how to study math let me first say that everyone studies differently and there is no one right way to study for a math class.
More informationLAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS DEPARTMENT Fall 2014
1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS DEPARTMENT Fall 2014 MAT 097: Algebra 6 Lecture Hours, 2 Educo Lab Hours, 2 Tutoring Lab Hours, 0 Credits Catalog Description This
More information8 th Grade Summer Mathematics Review Packet
8 th Grade Summer Mathematics Review Packet Table of Contents Topic One: Adding and Subtracting Integers Topic Two: Multiplying and Dividing Integers Topic Three: Order of Operations Topic Four: Solving
More informationFive 5. Rational Expressions and Equations C H A P T E R
Five C H A P T E R Rational Epressions and Equations. Rational Epressions and Functions. Multiplication and Division of Rational Epressions. Addition and Subtraction of Rational Epressions.4 Comple Fractions.
More informationSolving Equations with One Variable Type  The Algebraic Approach. Solving Equations with a Variable in the Denominator  The Algebraic Approach
3 Solving Equations Concepts: Number Lines The Definitions of Absolute Value Equivalent Equations Solving Equations with One Variable Type  The Algebraic Approach Solving Equations with a Variable in
More informationQuadratic Equations and Inequalities
MA 134 Lecture Notes August 20, 2012 Introduction The purpose of this lecture is to... Introduction The purpose of this lecture is to... Learn about different types of equations Introduction The purpose
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 informationExam Preparation Tips & TestTaking Strategies  Action Plan
Exam Preparation Tips & TestTaking Strategies  Action Plan According to the workshop presenter, it is important to focus on learning the information and not simply memorizing it. Learning means that
More informationDIVISION OF NATURAL SCIENCES AND MATHEMATICS TIDEWATER COMMUNITY COLLEGE VIRGINIA BEACH CAMPUS COURSE PLAN
Effective Fall 2011 DIVISION OF NATURAL SCIENCES AND MATHEMATICS TIDEWATER COMMUNITY COLLEGE VIRGINIA BEACH CAMPUS COURSE PLAN Course Number and Title: MTH 158College Algebra Online Sections Lecture Hours:
More informationCSE 107 Course Information
Computer Science and Engineering, UCSD Fa17 CSE 107: Introduction to Modern Cryptography Instructor: Mihir Bellare Course Information January 10, 2017 CSE 107 Course Information Lectures: T and Th, 8:00
More informationSQ3R Modified for Math
SQ3R Modified for Math Overview: Math classes are very difficult for most people. Part of the reason why is that the text can be extremely complex to read. By using the SQ3R reading strategy modified for
More informationCourse Title: Math A Elementary Algebra
Course Title: Math A Elementary Algebra Unit 0: Course Introduction In this unit you will get familiar with important course documents, such as syllabus and communication policy. You will register on MyMathLab
More informationCHAPTER 3 Numbers and Numeral Systems
CHAPTER 3 Numbers and Numeral Systems Numbers play an important role in almost all areas of mathematics, not least in calculus. Virtually all calculus books contain a thorough description of the natural,
More informationDescriptive Statistics: Measures of Central Tendency and Crosstabulation. 789mct_dispersion_asmp.pdf
789mct_dispersion_asmp.pdf Michael Hallstone, Ph.D. hallston@hawaii.edu Lectures 79: Measures of Central Tendency, Dispersion, and Assumptions Lecture 7: Descriptive Statistics: Measures of Central Tendency
More informationDetermining When an Expression Is Undefined
Determining When an Expression Is Undefined Connections Have you ever... Tried to use a calculator to divide by zero and gotten an error Tried to figure out the square root of a negative number Expressions
More informationMath: Study Skills, Note Taking Skills, And Test Taking Strategies
Math: Study Skills, Note Taking Skills, And Test Taking Strategies Math Study Skill Active Study vs. Passive Study Be actively involved in managing the learning process, the mathematics and your study
More informationSummation Algebra. x i
2 Summation Algebra In the next 3 chapters, we deal with the very basic results in summation algebra, descriptive statistics, and matrix algebra that are prerequisites for the study of SEM theory. You
More informationDECIMALS are special fractions whose denominators are powers of 10.
DECIMALS DECIMALS are special fractions whose denominators are powers of 10. Since decimals are special fractions, then all the rules we have already learned for fractions should work for decimals. The
More informationBasic numerical skills: EQUATIONS AND HOW TO SOLVE THEM. x + 5 = 7 2 + 52 = 72 5 + (22) = 72 5 = 5. x + 55 = 75. x + 0 = 20.
Basic numerical skills: EQUATIONS AND HOW TO SOLVE THEM 1. Introduction (really easy) An equation represents the equivalence between two quantities. The two sides of the equation are in balance, and solving
More informationSquare Roots. Learning Objectives. PreActivity
Section 1. PreActivity Preparation Square Roots Our number system has two important sets of numbers: rational and irrational. The most common irrational numbers result from taking the square root of nonperfect
More informationMATH 143 Precalculus Algebra and Analytic Geometry
MATH 143 Precalculus Algebra and Analytic Geometry Course Guide Selfpaced study. Anytime. Anywhere! Math 143 Precalculus Algebra and Analytic Geometry University of Idaho 3 SemesterHour Credits Prepared
More informationEast Los Angeles College. Section 1806 C2 127A MT ThF 10:35AM 12:00noon MyMathLab CourseID:
East Los Angeles College MATH 105 Arithmetic Section 1806 C2 127A MT ThF 10:35AM 12:00noon MyMathLab CourseID: faradineh12885 Instructor: Office Hours: Rahim Faradineh, Phone: 3232608129, email: rfaradineh@gmail.com
More informationMAT 096, ELEMENTARY ALGEBRA 6 PERIODS, 5 LECTURES, 1 LAB, 0 CREDITS
1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS, ENGINEERING and COMPUTER SCIENCE DEPARTMENT FALL 2015 MAT 096, ELEMENTARY ALGEBRA 6 PERIODS, 5 LECTURES, 1 LAB, 0 CREDITS Catalog
More informationStudy Skills in Mathematics
Study Skills in Mathematics From the Skills Team, University of Hull Studying maths Studying maths is different from studying other subjects. A very important part of learning maths is doing problems.
More informationGrade 6 Math Circles. Exponents
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles November 4/5, 2014 Exponents Quick Warmup Evaluate the following: 1. 4 + 4 + 4 +
More informationPrime Numbers and Divisibility
2.1 Prime Numbers and Divisibility 2.1 OBJECTIVES 1. Find the factors of a number 2. Determine whether a number is prime, composite, or neither 3. Determine whether a number is divisible by 2, 3, or 5
More informationOrder of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A.
Order of Operations Section 1: Introduction You know from previous courses that if two quantities are added, it does not make a difference which quantity is added to which. For example, 5 + 6 = 6 + 5.
More informationMath 131 College Algebra Fall 2015
Math 131 College Algebra Fall 2015 Instructor's Name: Office Location: Office Hours: Office Phone: Email: Course Description This course has a minimal review of algebraic skills followed by a study of
More informationSample Problems. Lecture Notes Equations with Parameters page 1
Lecture Notes Equations with Parameters page Sample Problems. In each of the parametric equations given, nd the value of the parameter m so that the equation has exactly one real solution. a) x + mx m
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 informationCommunity College of Philadelphia Spring 2010 Math 017Elementary Algebra SYLLABUS
SYLLABUS Instructor: *********************************************************************** Course Number: Math 017 CRN: 11837 Section: 027 Class ime: uesday and hursday between 5:15 pm and 6:35 pm Classroom:
More informationMAKING FRIENDS WITH MATH
MAKING FRIENDS WITH MATH Workshop sponsored by: The Dr. Mack Gipson, Jr., Tutorial and Enrichment Center Presented by: Carole Overton, Director The Dr. Mack Gipson, Jr., Tutorial and Enrichment Center
More informationIntroduction to Finite Systems: Z 6 and Z 7
Introduction to : Z 6 and Z 7 The main objective of this discussion is to learn more about solving linear and quadratic equations. The reader is no doubt familiar with techniques for solving these equations
More informationChapter 1.1 Rational and Irrational Numbers
Chapter 1.1 Rational and Irrational Numbers A rational number is a number that can be written as a ratio or the quotient of two integers a and b written a/b where b 0. Integers, fractions and mixed numbers,
More informationCourse notes on Number Theory
Course notes on Number Theory In Number Theory, we make the decision to work entirely with whole numbers. There are many reasons for this besides just mathematical interest, not the least of which is that
More informationExpressions and Equations Understand the connections between proportional relationships, lines, and linear equations.
Performance Assessment Task Squares and Circles Grade 8 The task challenges a student to demonstrate understanding of the concepts of linear equations. A student must understand relations and functions,
More informationMath 016. Materials With Exercises
Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of
More informationACKING THE STANDARDS FOR UNDERSTANDING
TEACHING GUIDE Module 1: Quadratic Equations and Inequalities A. Learning Outcomes Content Standard: The learner demonstrates understanding of key concepts of quadratic equations, quadratic inequalities,
More informationACCESS Study Skills Tip of the Week
ACCESS Study Skills Tip of the Week Are You Prepared for THE EXAM? If you believe in miracles, then you may think that you can pass examinations without studying for them. For most of us, however, that
More informationGrade 7  Chapter 1 Recall Prior Knowledge
MATH IN FOCUS Grade 7  Chapter 1 Recall Prior Knowledge REFRESH YOUR MEMORY! CHAPTER 1 Recall Prior Knowledge In order to be successful with the new information in Chapter 1, it is necessary to remember
More informationMathematics. What to expect Resources Study Strategies Helpful Preparation Tips Problem Solving Strategies and Hints Test taking strategies
Mathematics Before reading this section, make sure you have read the appropriate description of the mathematics section test (computerized or paper) to understand what is expected of you in the mathematics
More informationStrategies for Winning at Math. Student Success Workshop
Strategies for Winning at Math Student Success Workshop Just the Facts Poor performance in math is NOT due to a lack of intelligence. The key to success in math is having the right approach to studying
More informationLesson Plan. N.RN.3: Use properties of rational and irrational numbers.
N.RN.3: Use properties of rational irrational numbers. N.RN.3: Use Properties of Rational Irrational Numbers Use properties of rational irrational numbers. 3. Explain why the sum or product of two rational
More informationPractice 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 informationRules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER
Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the
More informationGrade Level Year Total Points Core Points % At Standard 9 2003 10 5 7 %
Performance Assessment Task Number Towers Grade 9 The task challenges a student to demonstrate understanding of the concepts of algebraic properties and representations. A student must make sense of the
More informationSOUTHWEST COLLEGE Department of Mathematics
SOUTHWEST COLLEGE Department of Mathematics COURSE SYLLABUS MATH 0312: Intermediate Algebra  Online INSTRUCTOR: CONFERENCE TIMES: CONTACT INFORMATION: Emmanuel Usen TBA Emmanuel.usen@hccs.edu 7137188062
More informationAlgebra I. Copyright 2014 Fuel Education LLC. All rights reserved.
Algebra I COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics, with an emphasis
More informationIntegers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
More informationWelcome to Math 19500 Video Lessons. Stanley Ocken. Department of Mathematics The City College of New York Fall 2013
Welcome to Math 19500 Video Lessons Prof. Department of Mathematics The City College of New York Fall 2013 An important feature of the following Beamer slide presentations is that you, the reader, move
More informationEQUATIONS. Main Overarching Questions: 1. What is a variable and what does it represent?
EQUATIONS Introduction to Variables, Algebraic Expressions, and Equations (2 days) Overview of Objectives, students should be able to: Main Overarching Questions: 1. Evaluate algebraic expressions given
More informationBERGEN COMMUNITY COLLEGE DIVISION OF MATHEMATICS, SCIENCE AND TECHNOLOGY DEPARTMENT OF DEVELOPMENTAL MATHEMATICS COURSE SYLLABUS
BERGEN COMMUNITY COLLEGE DIVISION OF MATHEMATICS, SCIENCE AND TECHNOLOGY DEPARTMENT OF DEVELOPMENTAL MATHEMATICS COURSE SYLLABUS MAT040 Algebra for Liberal Arts INSTRUCTOR: OFFICE EMAIL: PHONE: COURSE
More informationIntroduction to Modular Arithmetic, the rings Z 6 and Z 7
Introduction to Modular Arithmetic, the rings Z 6 and Z 7 The main objective of this discussion is to learn modular arithmetic. We do this by building two systems using modular arithmetic and then by solving
More informationSolving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
More informationSuccess Center Directed Learning Activity (DLA) Quadratic Formula M109.1
Success Center Directed Learning Activity (DLA) Quadratic Formula M109.1 Directed Learning Activity Quadratic Formula Description: In this Directed Learning Activity (DLA), you will learn about the Quadratic
More informationWelcome to Basic Math Skills!
Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots
More informationPlaying with Numbers
PLAYING WITH NUMBERS 249 Playing with Numbers CHAPTER 16 16.1 Introduction You have studied various types of numbers such as natural numbers, whole numbers, integers and rational numbers. You have also
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 information( ) 4, how many factors of 3 5
Exponents and Division LAUNCH (9 MIN) Before Why would you want more than one way to express the same value? During Should you begin by multiplying the factors in the numerator and the factors in the denominator?
More informationMath 1111 Journal Entries Unit I (Sections , )
Math 1111 Journal Entries Unit I (Sections 1.11.2, 1.41.6) Name Respond to each item, giving sufficient detail. You may handwrite your responses with neat penmanship. Your portfolio should be a collection
More informationYork Suburban Middle School Course Overview. Algebra 1
York Suburban Middle School Course Overview I. Course Description Algebra 1 1.0 Credit Length: School Year; Format: Meets Daily Prerequisite: PreAlgebra Algebra 1 The Larson Algebra 1brings math to life
More informationReading 7 : Program Correctness
CS/Math 240: Introduction to Discrete Mathematics Fall 2015 Instructors: Beck Hasti, Gautam Prakriya Reading 7 : Program Correctness 7.1 Program Correctness Showing that a program is correct means that
More informationCOURSE REQUIREMENTS AND EXPECTATIONS FOR ALL STUDENTS ENROLLED IN COLLEGE ALGEBRA ROWAN UNIVERSITY CAMDEN CAMPUS SPRING 2011
COURSE REQUIREMENTS AND EXPECTATIONS FOR ALL STUDENTS ENROLLED IN COLLEGE ALGEBRA ROWAN UNIVERSITY CAMDEN CAMPUS SPRING 2011 PROFESSOR JAY L. SCHIFFMAN email: schiffman@rowan.edu 1 IMPORTANT INFORMATION
More informationALGEBRA 1/ALGEBRA 1 HONORS
ALGEBRA 1/ALGEBRA 1 HONORS CREDIT HOURS: 1.0 COURSE LENGTH: 2 Semesters COURSE DESCRIPTION The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical
More informationLinear Equations and Inequalities
Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109  Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................
More informationContents. Introduction and Notes pages 23 (These are important and it s only 2 pages ~ please take the time to read them!)
Page Contents Introduction and Notes pages 23 (These are important and it s only 2 pages ~ please take the time to read them!) Systematic Search for a Change of Sign (Decimal Search) Method Explanation
More informationAccommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego
Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego Courtney O Donovan Class: Algebra 1 Day #: 67 Grade: 8th Number of Students: 25 Date: May 1213, 2011 Goal: Students will
More information2014 Assessment Report. Mathematics and Statistics. Calculus Level 3 Statistics Level 3
National Certificate of Educational Achievement 2014 Assessment Report Mathematics and Statistics Calculus Level 3 Statistics Level 3 91577 Apply the algebra of complex numbers in solving problems 91578
More informationGrade 7/8 Math Circles Fall 2012 Factors and Primes
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Factors and Primes Factors Definition: A factor of a number is a whole
More informationGrade 4 Number & Operations in Base Ten 4.NBT.13
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 4 Number & Operations in Base Ten 4.NBT.13 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES THE
More informationMarie has a winter hat made from a circle, a rectangular strip and eight trapezoid shaped pieces. y inches. 3 inches. 24 inches
Winter Hat This problem gives you the chance to: calculate the dimensions of material needed for a hat use circle, circumference and area, trapezoid and rectangle Marie has a winter hat made from a circle,
More informationMath Help and Additional Practice Websites
Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade7 http://www.softschools.com/grades/6th_and_7th.jsp
More informationMicrosoft Excel IF & AND Functions. By Stephen Groulx
Microsoft Excel IF & AND Functions By Stephen Groulx Excel IF & AND Functions Table of Contents Page Introduction... 3 IF Function, Simplified... 6 IF Function, Nested... 8 AND Function... 16 Assumptions
More informationSyllabus MAT0018 Developmental Mathematics I
Syllabus MAT0018 Developmental Mathematics I Term: Reference #: Instructor s Name: Email: Office: Math Lab, Room # 2223 Mailbox: Math Lab, Room # 2223 Office Hours: To leave a message for the instructor,
More informationDigital VLSI System Design Prof. S. Srinivasan Department of Electrical Engineering Indian Institute of Technology, Madras.
Digital VLSI System Design Prof. S. Srinivasan Department of Electrical Engineering Indian Institute of Technology, Madras Lecture  20 Example of System Design using Sequential Circuits (Continued) Slide
More informationIsolate the absolute value expression. Add 5 to both sides and then divide by 2.
11 of 21 8/14/2014 2:35 PM of a variable expression. You can use the definition of absolute value to solve absolute value equations algebraically. Since then the equation ax + b = c is equivalent to (ax
More informationWhy do we measure central tendency? Basic Concepts in Statistical Analysis
Why do we measure central tendency? Basic Concepts in Statistical Analysis Chapter 4 Too many numbers Simplification of data Descriptive purposes What is central tendency? Measure of central tendency A
More informationCENTRAL TEXAS COLLEGE SYLLABUS FOR DSMA 0306 INTRODUCTORY ALGEBRA. Semester Hours Credit: 3
CENTRAL TEXAS COLLEGE SYLLABUS FOR DSMA 0306 INTRODUCTORY ALGEBRA Semester Hours Credit: 3 (This course is equivalent to DSMA 0301. The difference being that this course is offered only on those campuses
More information0.75 75% ! 3 40% 0.65 65% Percent Cards. This problem gives you the chance to: relate fractions, decimals and percents
Percent Cards This problem gives you the chance to: relate fractions, decimals and percents Mrs. Lopez makes sets of cards for her math class. All the cards in a set have the same value. Set A 3 4 0.75
More informationMATHEMATICS. Y5 Multiplication and Division 5330 Square numbers, prime numbers, factors and multiples. Equipment. MathSphere
MATHEMATICS Y5 Multiplication and Division 5330 Square numbers, prime numbers, factors and multiples Paper, pencil, ruler. Equipment MathSphere 5330 Square numbers, prime numbers, factors and multiples
More informationIT Introduction to IT Problem Solving Using Computer Programming revised
Applied Information Technology Department Course Syllabus IT 106  Introduction to IT Problem Solving Using Computer Programming revised 07.11.2014 Catalog Description Prerequisites Introduces techniques
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 informationHigh School Functions Interpreting Functions Understand the concept of a function and use function notation.
Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.
More informationAlgebra Revision Sheet Questions 2 and 3 of Paper 1
Algebra Revision Sheet Questions and of Paper Simple Equations Step Get rid of brackets or fractions Step Take the x s to one side of the equals sign and the numbers to the other (remember to change the
More informationStudent Guide and Syllabus for MAT100 Introductory Algebra
Course Information: MAT100 Introductory Algebra Section: 05C Section: 06C Section: 07C* Classroom: 341 Main Building Classroom: 341 Main Building Classroom: 341 Main Building Meeting Dates: Monday Thursday
More informationSolving Inequalities Examples
Solving Inequalities Examples 1. Joe and Katie are dancers. Suppose you compare their weights. You can make only one of the following statements. Joe s weight is less than Kate s weight. Joe s weight is
More informationLLCC Study Skills Center 88. Tips on How to Study Math. 2. Unlike many other textbooks, math textbooks have:
LLCC Study Skills Center 88 Tips on How to Study Math What s Different About Math Textbooks 1. Math textbooks must be studied very slowly. 2. Unlike many other textbooks, math textbooks have: No repetition
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 informationChapter 2 Formulas and Decimals
Chapter Formulas and Decimals Section A Rounding, Comparing, Adding and Subtracting Decimals Look at the following formulas. The first formula (P = A + B + C) is one we use to calculate perimeter of a
More informationPreviously, you learned the names of the parts of a multiplication problem. 1. a. 6 2 = 12 6 and 2 are the. b. 12 is the
Tallahassee Community College 13 PRIME NUMBERS AND FACTORING (Use your math book with this lab) I. Divisors and Factors of a Number Previously, you learned the names of the parts of a multiplication problem.
More informationStudent attitudes in firstsemester Calculus
Student attitudes in firstsemester Calculus David M. Bressoud This is the text of an article that appeared in MAA Focus, 1994, vol 14, pages 6 7 Abstract One of the large lecture sections 1 of firstsemester
More informationGCSE MATHEMATICS. 43602H Unit 2: Number and Algebra (Higher) Report on the Examination. Specification 4360 November 2014. Version: 1.
GCSE MATHEMATICS 43602H Unit 2: Number and Algebra (Higher) Report on the Examination Specification 4360 November 2014 Version: 1.0 Further copies of this Report are available from aqa.org.uk Copyright
More informationa) x 2 8x = 25 x 2 8x + 16 = (x 4) 2 = 41 x = 4 ± 41 x + 1 = ± 6 e) x 2 = 5 c) 2x 2 + 2x 7 = 0 2x 2 + 2x = 7 x 2 + x = 7 2
Solving Quadratic Equations By Square Root Method Solving Quadratic Equations By Completing The Square Consider the equation x = a, which we now solve: x = a x a = 0 (x a)(x + a) = 0 x a = 0 x + a = 0
More information