COUNTING IS THE BASIC MATHEMATICAL
|
|
|
- Richard Atkins
- 5 years ago
- Views:
Transcription
1
2 COUNTING IS THE BASIC MATHEMATICAL ACTIVITY EVERY HUMAN ACTIVITY, DAY IN AND DAY OUT INVOLVES THIS COUNTING, IN ONEWAY OR THE OTHER. House wife in the kitchen to A space scientist Farmer on the field to AN industrialist A petty hawker to A great economist All of them play paywt with numbers sto achieve their targets.
3 As the human Endeavors advanced simple counting has become computation, calculations and estimations. To make calculations, computations and estimations, easier and quicker, operations on numbers are used.
4 An operation is said to be well defined in a set, if it is possible to effect the execution of the process of operation.
5 IT IS ABSOLUTELY NECESSARY TO HAVE THE SET OF ELEMENTS TO OPERATE WITH AND TO KNOW THE PROCESS OF EXECUTION OF THE OPERATION
6 ALGEBRA An ALGEBRA is a structure, consisting of a non empty set, along with well defined operation (s) in it. Example: SET OF NATURAL NUMBERS WITH ADDITION OPERATIONS [N,+] SET OF REAL NUMBERS WITH MUILTIPLICATION OPERATIONS [R, ] ]
7 ALGEBRE REAL NUMBER ALGEBRA VECTOR ALGEBRA MATRIX ALGEBRA COMPLEX ALGEBRA ALGEBRA OF FUNCTION etc
8 The fundamental operations on set of real numbers widely accepted are ADDITION SUBTRACTION MULTIPLICATION DIVISION
9 ADDITION is the process of counting the elements of two sets taken TOGETHER Eg: Adding the number of students of section A & B of class 10 of aparticular school
10 SUBTRACTION is the process of counting the remaining elements of a given set, after TAKING AWAY a few elements from it. Eg: How many students of class consisting 50 students are left, after 15 students leave the school.
11 MULTIPLICATION is a process of REPEATED ADDITION OF THE SAME NUMBER Eg: is same 6 times 4 6 4=24
12 DIVISION is the process of SUCCESSIVE SUBTRACTION of the same number. Eg: = 0 4 can be successively subtracted 6 times from 24 to get the reminder 0 24/4 = 6
13 All fundamental operations on Real numbers involve two facts at a time. Basic operations are denoted by symbols in mathematical sentences The most basic operation on Real numbers is Addition Other operations are derived from addition SUBTRACTION NEGETIVE ADDITION MULTIPLICATION REPEATED ADDITION DIVISION SUCCESSIVE SUBTRACTION
14 THE PROPERTIES OF OPERATIONS ON REAL NUMBERS CLOSURE PROPERTY: If the result of the operations is a member of the set on which the operation is effected, the operations is said to have closure property. Eg: Addition in the set, of Natural numbers has the closure property 4+7 = 11
15 COMMUTATIVE PROPERTY: If the result of the operations remain same, when the facts are inter change, the operations has commutative property Eg: Multiplication of Real numbers is commutative 7 5 = 5 7 = 35
16 ASSOCIATIVE PROPERTY: if the result of the operations is independent of the association of facts the operation is said to have associative property. Eg: Addition of Natural numbers is Associative (4+5)+7 = 4+(5+7)
17 DISTRIBUTIVE PROPERTY: In this property two operations are involved Addition and Multiplication. Eg: 3 (7+5) = 36 (3 7)+(3 5) = 36 Multiplication is distributive over Addition Note: Addition is not distributive over Multiplication in the set of Real numbers
18 UNARY OPERATIONS These operations involve only one fact at a time. For Eg: 81=9, 64=8, 6.25=2.5, 5 4=2 5² = 25, 10³ = 1000 Note: every positive Real number has a unique real square root
19 Operations on Real numbers need not be basic operations only We can define other operations with defined symbols Eg: a*b = a/b + b/a a,b 0 x y= x + y x,y> 0 p q= p² q²
20 All operations on Real numbers essentially consist fundamental operations ADDITION SUBTRACTION MULTIPLICATION DIVISION
Sect Properties of Real Numbers and Simplifying Expressions
Sect 1.7 - Properties of Real Numbers and Simplifying Expressions Concept #1 Commutative Properties of Real Numbers Ex. 1a 9.34 + 2.5 Ex. 1b 2.5 + ( 9.34) Ex. 1c 6.3(4.2) Ex. 1d 4.2( 6.3) a) 9.34 + 2.5
MATH ALGEBRA AND FUNCTIONS
Students: 1. Use letters, boxes, or other symbols to stand for any number in simple expressions or equations. 1. Students use and interpret variables, mathematical symbols and properties to write and simplify
Properties of Real Numbers. Unit 1 Lesson 4
Properties of Real Numbers Unit 1 Lesson 4 Students will be able to: Recognize and use the properties of real numbers. Key Vocabulary: Identity Property Inverse Property Equality Property Associative Property
Note: An algebraic expression is made of one or more terms. The terms in an algebraic expression are connected with either addition or subtraction.
.4 Combining Like Terms Term A term is a single number or variable, or it can be a product of a number (called its coefficient) and one or more variables. Examples of terms:, x, a, xy, 4 a bc, 5, xyz coefficient
Skills Practice Skills Practice for Lesson 4.1
Skills Practice Skills Practice for Lesson.1 Name Date Thinking About Numbers Counting Numbers, Whole Numbers, Integers, Rational and Irrational Numbers Vocabulary Define each term in your own words. 1.
2. Associative Law: A binary operator * on a set S is said to be associated whenever (A*B)*C = A*(B*C) for all A,B,C S.
BOOLEAN ALGEBRA 2.1 Introduction Binary logic deals with variables that have two discrete values: 1 for TRUE and 0 for FALSE. A simple switching circuit containing active elements such as a diode and transistor
Expressions, Equations and Inequalities Guided Notes
Expressions, Equations and Inequalities Guided Notes Standards: Alg1.M.A.SSE.A.01a - The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression.
Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating
Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating
Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.
Real Numbers and The Number Line Properties of Real Numbers Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers. Square root, radicand,
bc7f2306 Page 1 Name:
Name: Questions 1 through 4 refer to the following: Solve the given inequality and represent the solution set using set notation: 1) 3x 1 < 2(x + 4) or 7x 3 2(x + 1) Questions 5 and 6 refer to the following:
Properties of Real Numbers
Properties of Real Numbers Essential Understanding. Relationships that are always true for real numbers are called properties, which are rules used to rewrite and compare expressions. Two algebraic expressions
Numbers and Operations
Numbers and Operations George E. Hrabovsky MAST Mathematics as the study of objects, their relationships, and the structures created by their relationships Mathematics is the abstract study of objects
Eureka Math Module 4 Topic G Solving Equations
Eureka Math Module 4 Topic G Solving Equations Lessons 23-27 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make
Precalculus Chapter P.1 Part 2 of 3. Mr. Chapman Manchester High School
Precalculus Chapter P.1 Part of 3 Mr. Chapman Manchester High School Algebraic Expressions Evaluating Algebraic Expressions Using the Basic Rules and Properties of Algebra Definition of an Algebraic Expression:
Concept: Solving Equations
Concept: Solving Equations EQ: How do we justify how we solve equations? REI. 1 Vocabulary: Properties of Equality Properties of Operation Justify 1 Solve the equations below, provide an explanation for
5.2 Algebraic Properties
5.2 Algebraic Properties Your friend s birthday is next weekend, and you are sending her a birthday card. As usual, you will put a return address label in the upper left corner of the envelope and a stamp
Bishop Kelley High School Summer Math Program Course: Algebra II B
016 017 Summer Math Program Course: NAME: DIRECTIONS: Show all work in the packet. You may not use a calculator. No matter when you have math, this packet is due on the first day of class This material
CHAPTER 1 REVIEW Section 1 - Algebraic Expressions
CHAPTER 1 REVIEW Section 1 - Algebraic Expressions A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable. The terms of an expression are the parts
Discrete Mathematics. CS204: Spring, Jong C. Park Computer Science Department KAIST
Discrete Mathematics CS204: Spring, 2008 Jong C. Park Computer Science Department KAIST Today s Topics Combinatorial Circuits Properties of Combinatorial Circuits Boolean Algebras Boolean Functions and
Assignment for Whole Numbers
Assignment for Whole Numbers 1 Question 1 Write the smallest natural and smallest whole number. Question 2 Match the column Closure Property If a and b are any two whole numbers, then a+b = b+a and a b
Section 1.1 Notes. Real Numbers
Section 1.1 Notes Real Numbers 1 Types of Real Numbers The Natural Numbers 1,,, 4, 5, 6,... These are also sometimes called counting numbers. Denoted by the symbol N Integers..., 6, 5, 4,,, 1, 0, 1,,,
Chapter. Algebra techniques. Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations.
Chapter 2 Algebra techniques Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations. Page 1 2.1 What is algebra? In order to extend the usefulness of mathematical
Ch 1 The Language of Algebra. 1.1 Writing Expressions and Equations. Variable: Algebraic Expression: Numerical Expression: Multiplication: Division:
Ch 1 The Language of Algebra 1.1 Writing Expressions and Equations Variable: Algebraic Expression: Numerical Expression: Multiplication: Division: Words for Addition: Subtraction: Multiplication: Division:
CHAPTER 5: ALGEBRA CHAPTER 5 CONTENTS
CHAPTER 5: ALGEBRA Image from www.coolmath.com CHAPTER 5 CONTENTS 5. Introduction to Algebra 5. Algebraic Properties 5. Distributive Property 5.4 Solving Equations Using the Addition Property of Equality
MATH STUDENT BOOK. 11th Grade Unit 10
MATH STUDENT BOOK 11th Grade Unit 10 Unit 10 ALGEBRA II REVIEW MATH 1110 ALGEBRA II REVIEW INTRODUCTION 3 1. INTEGERS, OPEN SENTENCES, AND GRAPHS 5 INTEGERS 5 OPEN SENTENCES 10 GRAPHS 18 SELF TEST 1 24
UNIT 4 NOTES: PROPERTIES & EXPRESSIONS
UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics
irst we need to know that there are many ways to indicate multiplication; for example the product of 5 and 7 can be written in a variety of ways:
CH 2 VARIABLES INTRODUCTION F irst we need to know that there are many ways to indicate multiplication; for example the product of 5 and 7 can be written in a variety of ways: 5 7 5 7 5(7) (5)7 (5)(7)
2. Two binary operations (addition, denoted + and multiplication, denoted
Chapter 2 The Structure of R The purpose of this chapter is to explain to the reader why the set of real numbers is so special. By the end of this chapter, the reader should understand the difference between
Calendar Squares Ten Frames 0-10
K.CC.A Know number names and the count sequence. K.CC.1 Count to 100 by ones and tens. (0-10) K.CC.3 Write numbers from 0-20. Represent a number of objects with a written numeral 0-20 (with 0 representing
SYNA INTERNATIONAL SCHOOL LEARNING PAPERS CLASS 8 SUBJECT MATHEMATICS
CLASS 8 Page 1 SYNA INTERNATIONAL SCHOOL LEARNING PAPERS CLASS 8 SUBJECT MATHEMATICS 1 x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 3
DO NOT USE WITHOUT PERMISSION
PROGRESSION FOR DEVELOPING ALGEBRA UNDERSTANDING THROUGH GENERALIZING ARITHMETIC ACROSS GRADES 3-7: This curricular progression is intended to develop algebra understanding through generalizing arithmetic.
REVIEW Chapter 1 The Real Number System
REVIEW Chapter The Real Number System In class work: Complete all statements. Solve all exercises. (Section.4) A set is a collection of objects (elements). The Set of Natural Numbers N N = {,,, 4, 5, }
ALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations
ALGEBRA 1 Interactive Notebook Chapter 2: Linear Equations 1 TO WRITE AN EQUATION: 1. Identify the unknown (the variable which you are looking to find) 2. Write the sentence as an equation 3. Look for
7.12 The student will represent relationships with tables, graphs, rules, and words.
7.12 The student will represent relationships with tables, graphs, rules, and words. HINTS & NOTES Relation- is a set of ordered pairs. Remember to always start from the origin. Origin is (0,0) Move horizontally
Properties of Real Numbers
Pre-Algebra Properties of Real Numbers Identity Properties Addition: Multiplication: Commutative Properties Addition: Multiplication: Associative Properties Inverse Properties Distributive Properties Properties
2.1: Algebraic Expressions
.1: Algebraic Expressions Algebra uses letters, called variables, such as x and y, to represent numbers. Algebraic expressions are combinations of variables and numbers using the operations of addition,
hp calculators HP 35s Using Register Arithmetic Variables and Memory Registers Practice Examples: Calculating Using STO Arithmetic
Variables and Memory Registers Practice Examples: Calculating Using STO Arithmetic Calculating Using RCL Arithmetic in RPN mode Storage Arithmetic in a Program Variables and Memory Registers The purpose
CHAPTER 1 POLYNOMIALS
1 CHAPTER 1 POLYNOMIALS 1.1 Removing Nested Symbols of Grouping Simplify. 1. 4x + 3( x ) + 4( x + 1). ( ) 3x + 4 5 x 3 + x 3. 3 5( y 4) + 6 y ( y + 3) 4. 3 n ( n + 5) 4 ( n + 8) 5. ( x + 5) x + 3( x 6)
COLLEGE ALGEBRA. Properties of Real Numbers with Clock Arithmetic
COLLEGE ALGEBRA By: Sister Mary Rebekah www.survivormath.weebly.com Cornell-Style Fill in the Blank Notes and Teacher s Key Properties of Real Numbers with Clock Arithmetic 1 Topic: Clock Arithmetic Addition
Chapter 1 Review of Equations and Inequalities
Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve
Northwest High School s Geometry
Northwest High School s Geometry Summer Math Packet (For 2013-2014) DUE THE FIRST DAY OF SCHOOL Student Name: - 1 - This packet has been designed to help you review various mathematical topics that will
Name Date Class California Standards Prep for 4.0. Variables and Expressions
California Standards Prep for 4.0 To translate words into algebraic expressions, find words like these that tell you the operation. add subtract multiply divide sum difference product quotient more less
1. Revision Description Reflect and Review Teasers Answers Recall of Rational Numbers:
1. Revision Description Reflect Review Teasers Answers Recall of Rational Numbers: A rational number is of the form, where p q are integers q 0. Addition or subtraction of rational numbers is possible
DO NOT USE WITHOUT PERMISSION
PROGRESSION FOR DEVELOPING ALGEBRA UNDERSTANDING FOR EQUALITY, EXPRESSIONS, EQUATIONS, AND INEQUALITIES 1 This curricular progression is intended to develop algebra understanding through a study of the
Mr. Gallo Algebra 2 1 2: PROPERTIES OF REAL NUMBERS. Real Number Review
Mr. Gallo Algebra 2 1 2: PROPERTIES OF REAL NUMBERS Real Number Review 1 Subsets of the Real Numbers Classifying Variables Example 1: What set of numbers would best describe the number of participants
Unit 1: Equations & Inequalities in One Variable
Date Period Unit 1: Equations & Inequalities in One Variable Day Topic 1 Properties of Real Numbers Algebraic Expressions Solving Equations 3 Solving Inequalities 4 QUIZ 5 Absolute Value Equations 6 Double
PROBLEM SET 32. To find the least common multiple, we need to factor each number and make sure all factors are present in our LCM.
PROBLEM SET To find the least common multiple, we need to factor each number and make sure all factors are present in our LCM. Find the least common multiples: 0,,, Least common multiple 0 00 Least common
CURRICULUM CATALOG. Algebra I (3130) VA
2018-19 CURRICULUM CATALOG Table of Contents COURSE OVERVIEW... 1 UNIT 1: FOUNDATIONS OF ALGEBRA... 1 UNIT 2: LINEAR EQUATIONS... 2 UNIT 3: FUNCTIONS... 2 UNIT 4: INEQUALITIES AND LINEAR SYSTEMS... 2 UNIT
Correlations to the Common Core State Standards: Kindergarten
Correlations to the Common Core State s: Kindergarten L-1, Building the Hundreds Counting and Cardinality Know number names and the count sequence. K.CC.1. Count to 100 by ones and by tens. K.CC.2. Count
Algebra SECTION 1: THE MEANING AND USE OF SIGNED NUMBERS; THE SET OF INTEGERS
Algebra Introduction: About how many days each year does the temperature in Oklahoma City drop below zero? Water freezes at 0ϒC. How would you write a temperature below zero? You can write 1ϒC above zero
Chapter 6: Rational Expr., Eq., and Functions Lecture notes Math 1010
Section 6.1: Rational Expressions and Functions Definition of a rational expression Let u and v be polynomials. The algebraic expression u v is a rational expression. The domain of this rational expression
2.1 Matrices. 3 5 Solve for the variables in the following matrix equation.
2.1 Matrices Reminder: A matrix with m rows and n columns has size m x n. (This is also sometimes referred to as the order of the matrix.) The entry in the ith row and jth column of a matrix A is denoted
Mini-Lecture 2.1 Simplifying Algebraic Expressions
Copyright 01 Pearson Education, Inc. Mini-Lecture.1 Simplifying Algebraic Expressions 1. Identify terms, like terms, and unlike terms.. Combine like terms.. Use the distributive property to remove parentheses.
Number Axioms. P. Danziger. A Group is a set S together with a binary operation (*) on S, denoted a b such that for all a, b. a b S.
Appendix A Number Axioms P. Danziger 1 Number Axioms 1.1 Groups Definition 1 A Group is a set S together with a binary operation (*) on S, denoted a b such that for all a, b and c S 0. (Closure) 1. (Associativity)
Algebra Review. Terrametra Resources. Lynn Patten
Terrametra Resources Lynn Patten ALGEBRAIC EXPRESSION A combination of ordinary numbers, letter symbols, variables, grouping symbols and operation symbols. Numbers remain fixed in value and are referred
Reteach 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
Math 7.2, Period. Using Set notation: 4, 4 is the set containing 4 and 4 and is the solution set to the equation listed above.
Solutions to Equations and Inequalities Study Guide SOLUTIONS TO EQUATIONS Solutions to Equations are expressed in 3 ways: In Words: the equation x! = 16 has solutions of 4 and 4. Or, x! = 16 is a true
GCSE AQA Mathematics. Numbers
GCSE Mathematics Numbers Md Marufur Rahman Msc Sustainable Energy Systems Beng (Hons) Mechanical Engineering Bsc (Hons) Computer science & engineering GCSE AQA Mathematics 215/16 Table of Contents Introduction:...
A number that can be written as, where p and q are integers and q Number.
RATIONAL NUMBERS 1.1 Definition of Rational Numbers: What are rational numbers? A number that can be written as, where p and q are integers and q Number. 0, is known as Rational Example:, 12, -18 etc.
Northwest High School s Algebra 1
Northwest High School s Algebra 1 Summer Review Packet 2015 DUE THE FIRST DAY OF SCHOOL Student Name This packet has been designed to help you review various mathematical topics that will be necessary
WUCT121. Discrete Mathematics. Numbers
WUCT121 Discrete Mathematics Numbers 1. Natural Numbers 2. Integers and Real Numbers 3. The Principle of Mathematical Induction 4. Elementary Number Theory 5. Congruence Arithmetic WUCT121 Numbers 1 Section
Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models
Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic expressions.. Translate English phrases into algebraic expressions.. Determine whether a number is a solution
Ch 1. The Language of Algebra
Ch 1 The Language of Algebra 1-1 Writing Expressions and Equations Writing Expressions Buying CDs: 1 CD = $15 2 CD = $15 x 2 3 CD = $15 x 3 n number of CDs? $15 x n Algebraic Expression Writing Expressions
Math 90 Lecture Notes Chapter 1
Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,
LESSON OBJECTIVES NCTM MATH STANDARDS: GRADES 6 8 NCTM
NCTM Number and Operations Standard; Hands On Equations(R) Learning System: Algebra; Problem Solving; Communication; Level I Representation Lesson 1 Students will use a symbol to represent an unknown.
Turing Machines. The Language Hierarchy. Context-Free Languages. Regular Languages. Courtesy Costas Busch - RPI 1
Turing Machines a n b n c The anguage Hierarchy n? ww? Context-Free anguages a n b n egular anguages a * a *b* ww Courtesy Costas Busch - PI a n b n c n Turing Machines anguages accepted by Turing Machines
1.1 Variables and Expressions How can a verbal expression be translated to an algebraic expression?
1.1 Variables and Expressions How can a verbal expression be translated to an algebraic expression? Recall: Variable: Algebraic Expression: Examples of Algebraic Expressions: Different ways to show multiplication:
Math Lecture 3 Notes
Math 1010 - Lecture 3 Notes Dylan Zwick Fall 2009 1 Operations with Real Numbers In our last lecture we covered some basic operations with real numbers like addition, subtraction and multiplication. This
Lesson 1.3: Algebra and Scientific Notation with Small Numbers
Specific Objectives Students will understand that in algebra, numbers and variables can be combined to produce expressions, equations and inequalities. numbers between 0 and 1 can be written using scientific
1-2 Study Guide and Intervention
1- Study Guide and Intervention Real Numbers All real numbers can be classified as either rational or irrational. The set of rational numbers includes several subsets: natural numbers, whole numbers, and
SECTION Types of Real Numbers The natural numbers, positive integers, or counting numbers, are
SECTION.-.3. Types of Real Numbers The natural numbers, positive integers, or counting numbers, are The negative integers are N = {, 2, 3,...}. {..., 4, 3, 2, } The integers are the positive integers,
Algebra I Notes Unit Two: Variables
Syllabus Objectives:. The student will use order of operations to evaluate expressions.. The student will evaluate formulas and algebraic expressions using rational numbers (with and without technology).
Algebra II First Semester Assignment #5 (Review of Sections 1.1 through 1.8)
Algebra II First Semester Assignment #5 (Review of Sections 1.1 through 1.8) Do not rely solely on this review to prepare for the test. These problems are meant only as a means to remind you of the types
Northwest High School s Algebra 1
Northwest High School s Algebra 1 Summer Review Packet 2011 DUE WEDNESDAY, SEPTEMBER 2, 2011 Student Name This packet has been designed to help you review various mathematical topics that will be necessary
SEVENTH EDITION and EXPANDED SEVENTH EDITION
SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 10-1 Chapter 10 Mathematical Systems 10.1 Groups Definitions A mathematical system consists of a set of elements and at least one binary operation. A
SOLUTIONS TO ALL IN-SECTION and END-OF-SECTION EXERCISES
CHAPTER. SECTION. SOLUTIONS TO ALL IN-SECTION and END-OF-SECTION EXERCISES ESSENTIAL PRELIMINARIES The Language of Mathematics Expressions versus Sentences IN-SECTION EXERCISES: EXERCISE. A mathematical
Intro to Algebra Today. We will learn names for the properties of real numbers. Homework Next Week. Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38
Intro to Algebra Today We will learn names for the properties of real numbers. Homework Next Week Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38 Due Thursday Pages 51-53/ 19-24, 29-36, *48-50, 60-65
5.1 Introduction to Matrices
5.1 Introduction to Matrices Reminder: A matrix with m rows and n columns has size m x n. (This is also sometimes referred to as the order of the matrix.) The entry in the ith row and jth column of a matrix
Unit 4, Ongoing Activity, Little Black Book of Algebra II Properties
Unit 4, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 4 - Radicals & the Complex Number System 4.1 Radical Terminology define radical sign,
Parenthesis and other grouping symbols. Exponential expressions. Multiplication & Division Addition & Subtraction.
NAME SADDLE BROOK HIGH SCHOOL HONORS ALGEBRA II SUMMER PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their
Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12
Equation A mathematical sentence formed by setting two expressions equal to each other Example 1: 3 6 = 18 Example 2: 7 + x = 12 Variable A symbol, usually a letter, that is used to represent one or more
CURRICULUM CATALOG. Algebra I (2052) WA
2018-19 CURRICULUM CATALOG Table of Contents Course Overview... 1 UNIT 1: FOUNDATIONS OF ALGEBRA... 1 UNIT 2: LINEAR EQUATIONS... 1 UNIT 3: FUNCTIONS... 2 UNIT 4: INEQUALITIES... 2 UNIT 5: LINEAR SYSTEMS...
Chapter 2: Boolean Algebra and Logic Gates
Chapter 2: Boolean Algebra and Logic Gates Mathematical methods that simplify binary logics or circuits rely primarily on Boolean algebra. Boolean algebra: a set of elements, a set of operators, and a
Math-2 Section 1-1. Number Systems
Math- Section 1-1 Number Systems Natural Numbers Whole Numbers Lesson 1-1 Vocabulary Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers Complex Numbers Closure Why do we need numbers?
3 + 1 = 4. First Grade. Addition: Combining two or more numbers to find a total.
First Grade 425 Addition: Combining two or more numbers to find a total. + = 3 + 1 = 4 Arithmetic: The basic math that we do in everyday life involving addition, subtraction, multiplication and/or division.
1.8 INTRODUCTION TO SOLVING LINEAR EQUATIONS
1.8 INTRODUCTION TO SOLVING LINEAR EQUATIONS Combining Like Terms In algebra we often deal with terms such as 4y or 7x. What do we mean by terms? A term is a number, a variable, or a product of a number
03 Review of First-Order Logic
CAS 734 Winter 2014 03 Review of First-Order Logic William M. Farmer Department of Computing and Software McMaster University 18 January 2014 What is First-Order Logic? First-order logic is the study of
Core Mathematics 2 Algebra
Core Mathematics 2 Algebra Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Algebra 1 Algebra and functions Simple algebraic division; use of the Factor Theorem and the Remainder Theorem.
Section-A. Short Questions
Section-A Short Questions Question1: Define Problem? : A Problem is defined as a cultural artifact, which is especially visible in a society s economic and industrial decision making process. Those managers
Chapter 2. Boolean Algebra and Logic Gates
Chapter 2 Boolean Algebra and Logic Gates Basic Definitions A binary operator defined on a set S of elements is a rule that assigns, to each pair of elements from S, a unique element from S. The most common
6-4 Adding and Subtracting Polynomials 6-4. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1 1Algebra 1
6-4 Adding and Subtracting Polynomials Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 1Algebra 1 Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p 5p
Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4)
NAME HONORS ALGEBRA II REVIEW PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their Algebra I course. In
Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.
Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical
JUST THE MATHS UNIT NUMBER 1.6. ALGEBRA 6 (Formulae and algebraic equations) A.J.Hobson
JUST THE MATHS UNIT NUMBER 1.6 ALGEBRA 6 (Formulae and algebraic equations) by A.J.Hobson 1.6.1 Transposition of formulae 1.6. of linear equations 1.6.3 of quadratic equations 1.6. Exercises 1.6.5 Answers
Math 260 Lecture Notes Ch Solving Equations Using Addition and Subtraction Properties of Equality
2.3 Solving Equations Using Addition and Subtraction Properties of Equality Let s play a game of are in the envelope? Here are the rules: 1. The same number of counters are placed on the left side and
Unit One Algebraic Thinking (Part A Number Relationships) 1.2 Powers *I can write and understand numerical expressions involving
1.2 Powers *I can write and understand numerical expressions involving and Exponents whole number exponents. Discuss with your group how do you THINK you would find the value? Exponential Form: base 4
Extra Problems: Unit 0
Extra Problems: Unit 0 These are example problems, mostly from tests and quizzes that I have given in the past. Make sure you understand and can do all assigned textbook problems, activities, problems
NPTEL web course on Complex Analysis. A. Swaminathan I.I.T. Roorkee, India. and. V.K. Katiyar I.I.T. Roorkee, India
NPTEL web course on Complex Analysis A. Swaminathan I.I.T. Roorkee, India and V.K. Katiyar I.I.T. Roorkee, India A.Swaminathan and V.K.Katiyar (NPTEL) Complex Analysis 1 / 14 Complex Analysis Module: 1:
GRADE 7 MATH LEARNING GUIDE
GRADE 7 MATH Lesson 5: Properties of the Operations on Integers Time: 1.5 hours Prerequisite Concepts: Addition, Subtraction, Multiplication and Division of Integers About the Lesson: This lesson will
Definition For a set F, a polynomial over F with variable x is of the form
*6. Polynomials Definition For a set F, a polynomial over F with variable x is of the form a n x n + a n 1 x n 1 + a n 2 x n 2 +... + a 1 x + a 0, where a n, a n 1,..., a 1, a 0 F. The a i, 0 i n are the