The document discusses the history and development of the Arabic numeral system. It explains that the numerals originated from the Phoenicians but were popularized by Arabs. It then provides a theory about how the shapes of the numerals may have been derived from representing different numbers of angles, showing examples. The document also briefly outlines some key developments in the history of algebra.
This document defines and explains key concepts related to real numbers and algebraic expressions. It introduces sets and subsets of real numbers like integers, rational numbers, and irrational numbers. It describes properties of real numbers including addition, multiplication, order, and absolute value. It also covers representing real numbers on a number line, algebraic expressions, and properties of negatives.
1) The document discusses the real number system, including identifying integers, rational numbers, and irrational numbers. Real numbers have important properties like closure under addition and multiplication.
2) Intervals of real numbers can be described using inequality notation like x ≥ 1 or -4 < x < 1, or interval notation like [1, +∞) or (-4, 1).
3) Absolute value of a real number a, written |a|, represents the distance of the number from the origin on the number line and is always non-negative.
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
This document defines and categorizes different types of numbers and explains their representation on a number line. It discusses natural numbers, negative numbers, rational numbers, irrational numbers, and real numbers. It also describes properties of the number line including that numbers increase in value as you move right and decrease as you move left, and how to determine the distance between points on the number line using absolute value.
TechMathII - 1.1 - The Set of Real Numberslmrhodes
The document defines and provides examples of different types of numerical sets:
- Natural numbers are counting numbers like 1, 2, 3, etc.
- Whole numbers include natural numbers and 0.
- Integers include all whole numbers and their negatives.
- Rational numbers are numbers that can be written as fractions like a/b where a and b are integers.
- Irrational numbers cannot be written as fractions and include numbers like the square root of numbers and pi.
- Real numbers include all numbers, both rational and irrational.
This document summarizes key concepts about expressions, equations, and inequalities in mathematics:
It defines variables, expressions, algebraic expressions, and different sets of real numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of real numbers like the additive inverse and multiplicative inverse. Examples are provided to illustrate graphing numbers and classifying them, as well as identifying properties from equations.
1. The document discusses real numbers and their properties, including subsets such as rational and irrational numbers.
2. Key topics covered include using a number line to graph and order real numbers, properties of number operations like closure and commutativity, and defining operations like addition, subtraction, multiplication and division.
3. Unit analysis is also introduced to check that units make sense when performing number operations for real-life applications.
This document defines and explains key concepts related to real numbers and algebraic expressions. It introduces sets and subsets of real numbers like integers, rational numbers, and irrational numbers. It describes properties of real numbers including addition, multiplication, order, and absolute value. It also covers representing real numbers on a number line, algebraic expressions, and properties of negatives.
1) The document discusses the real number system, including identifying integers, rational numbers, and irrational numbers. Real numbers have important properties like closure under addition and multiplication.
2) Intervals of real numbers can be described using inequality notation like x ≥ 1 or -4 < x < 1, or interval notation like [1, +∞) or (-4, 1).
3) Absolute value of a real number a, written |a|, represents the distance of the number from the origin on the number line and is always non-negative.
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
This document defines and categorizes different types of numbers and explains their representation on a number line. It discusses natural numbers, negative numbers, rational numbers, irrational numbers, and real numbers. It also describes properties of the number line including that numbers increase in value as you move right and decrease as you move left, and how to determine the distance between points on the number line using absolute value.
TechMathII - 1.1 - The Set of Real Numberslmrhodes
The document defines and provides examples of different types of numerical sets:
- Natural numbers are counting numbers like 1, 2, 3, etc.
- Whole numbers include natural numbers and 0.
- Integers include all whole numbers and their negatives.
- Rational numbers are numbers that can be written as fractions like a/b where a and b are integers.
- Irrational numbers cannot be written as fractions and include numbers like the square root of numbers and pi.
- Real numbers include all numbers, both rational and irrational.
This document summarizes key concepts about expressions, equations, and inequalities in mathematics:
It defines variables, expressions, algebraic expressions, and different sets of real numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of real numbers like the additive inverse and multiplicative inverse. Examples are provided to illustrate graphing numbers and classifying them, as well as identifying properties from equations.
1. The document discusses real numbers and their properties, including subsets such as rational and irrational numbers.
2. Key topics covered include using a number line to graph and order real numbers, properties of number operations like closure and commutativity, and defining operations like addition, subtraction, multiplication and division.
3. Unit analysis is also introduced to check that units make sense when performing number operations for real-life applications.
The document discusses several fundamental concepts of algebra including:
1. Different types of numbers such as integers, rational numbers, and irrational numbers.
2. Properties of operations like addition, subtraction, multiplication, and division.
3. Exponent rules for simplifying expressions with exponents like multiplying terms with the same base.
This chapter reviews real numbers including:
[1] Classifying numbers as natural numbers, integers, rational numbers, irrational numbers, and real numbers. Rational numbers can be written as fractions while irrational numbers cannot.
[2] Approximating irrational numbers like π as decimals to a given number of decimal places by rounding or truncating.
[3] How calculators handle decimals by either truncating or rounding values based on their display capabilities. A scientific or graphing calculator is recommended for this course.
Presentacion del informe expresiones algebraicas Vicente Gabriel Gutierrez y ...Vicente Gabriel Gutierrez
Informe: Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
The document discusses two types of log and exponential equations:
1) Equations that do not require calculators, which involve relating bases on both sides of the equation and can be simplified using properties of logarithms and exponents.
2) Numerical equations that do require calculators. It provides examples of solving each type, including consolidating bases, using logarithmic and exponential properties, and algebraic manipulation to isolate the variable.
This document discusses different types of number systems. It begins by introducing natural numbers, which are counting numbers formed by repeated addition of 1. Whole numbers include all natural numbers and 0. Integers extend whole numbers infinitely in both the positive and negative directions. Rational numbers are numbers that can be written as fractions p/q where p and q are integers. Irrational numbers have non-repeating decimal expansions and cannot be written as fractions. Real numbers include all rational and irrational numbers and are represented on the number line. Methods for finding rational numbers between two given numbers and representing different types of numbers on the number line are also described.
This document provides vocabulary terms and definitions that will be covered in Unit 2 of math class. It includes terms like variable, solve, one-step equation, two-step equation, distributive property, term, solution, like terms, infinitely many solutions, algebraic expression, inverse operation, constant, no solution, unique solution, coefficient, linear equation in one variable, addition property of equality, additive inverses, exponent, irrational, rational, scientific notation, perfect square, and square root. Students are expected to learn these terms and their definitions to understand the concepts covered in Unit 2.
This document provides an overview of algebraic expressions. It defines algebraic expressions as sets of numbers and letters combined using operations like addition, subtraction, multiplication, division, and parentheses. It describes the main elements of algebraic expressions as variables, coefficients, exponents, operators, and parentheses. It also discusses types of expressions like monomials and polynomials, and algebraic operations like addition, subtraction, multiplication, division, and factoring of expressions using notable products. It includes examples for each topic and a bibliography of additional resources.
Algebraic Mathematics of Linear Inequality & System of Linear InequalityJacqueline Chau
A brief, yet thorough look into the Linear Inequality & System of Linear Inequality and how these Math Concepts would be useful in solving our everyday life problems.
1. The document discusses subsets of real numbers including natural numbers, whole numbers, integers, and rational numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are formed by adding 0 to the natural numbers. Integers are formed by adding the negatives of natural numbers to whole numbers.
3. Rational numbers can be expressed as fractions a/b where a and b are integers and b is not equal to 0. Their decimal representations either terminate or repeat.
The document discusses operations with integers. It defines absolute value and covers addition, subtraction, multiplication, and division of integers through examples. Rules for integer operations are that the sign of the product is the product of the signs of the factors, and the sign of the quotient is the sign of the dividend. Division by zero is undefined.
The document provides definitions for mathematical terms that students in 5th/6th class primary school and junior cycle secondary school may encounter. It includes over 50 terms defined with diagrams and examples. The glossary is designed to inform students, parents, and teachers about the vocabulary and meanings of key mathematical terms as students transition between primary and post-primary education in Ireland.
This document discusses the real number system and its properties. It begins by describing how the set of real numbers is constructed by successive extensions of the natural numbers to include integers, rational numbers, and irrational numbers. It then establishes a one-to-one correspondence between real numbers and points on the real number line. Key properties of real numbers discussed include algebraic properties like closure under addition/multiplication, as well as properties of order and completeness. The document also covers intervals, inequalities, and the absolute value of real numbers.
The document discusses various methods for solving inequalities, including:
- Properties for adding, subtracting, multiplying, and dividing terms within an inequality
- Using set-builder and interval notation to describe the solution set of an inequality
- Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set
The document provides examples of applying these different techniques to solve specific inequalities.
This document defines sets and subsets, classifies different types of sets such as finite, infinite, empty and unit sets. It also discusses operations on sets like union and intersection. Real number sets such as natural, integer, rational and irrational numbers are defined. Inequalities, absolute value inequalities and their properties are explained. Intervals such as open, closed and infinite intervals are classified. The numeric plane and Cartesian product are defined. Graphical representations of conic sections like ellipses, circles, parabolas and hyperbolas are shown. Examples of solving inequalities and simplifying fractions are provided.
Mathematics power point presenttation on the topicMeghansh Gautam
This document provides an overview of mathematics and different types of numbers. It discusses what mathematics is, polynomials, algebraic identities, and various number systems including natural numbers, integers, rational numbers, real numbers, complex numbers, and computable numbers. It also briefly discusses the history of numbers, mentioning that tally marks found on bones and artifacts may be some of the earliest forms of counting and record keeping.
This document introduces real numbers and their properties. It discusses that real numbers can be divided into two kinds: rational numbers, which can be written as a ratio of integers, and irrational numbers, which cannot. It provides examples of rational numbers like fractions and decimals, as well as irrational numbers like square roots and pi. The document also defines integers, explains operations like exponents and identities, and illustrates the real number system.
The document discusses sets and operations involving sets of real numbers. It defines key sets such as the real numbers, rational numbers, integers, natural numbers, whole numbers, and irrational numbers. It also covers properties of real numbers like closure, commutativity, associativity, distributivity, identity, and inverse properties as they relate to addition and multiplication. Examples are provided to illustrate set notation and properties. The document contains exercises asking to identify which properties justify certain statements involving real number operations.
The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
The document discusses different number systems used in mathematics. It begins by explaining that a number system is defined by its base, or the number of unique symbols used to represent numbers. The most common system is decimal, which uses base-10. Other discussed systems include binary, octal, hexadecimal, and those used historically by cultures like the Babylonians. Rational and irrational numbers are also defined. Rational numbers can be written as fractions of integers, while irrational numbers cannot.
english mathematics dictionary
kamus bahassa inggris untuk matematika
oleh neneng
Nurwaningsih
(06081281520066)
Nurwaningsih30@gmail.com
PROGRAM STUDI PENDIDIKAN MATEMATIKA
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS SRIWIJAYA
INDRALAYA
2017
semoga bermanfaat
This document provides a summary of key terms in mathematical English for concepts in arithmetic, algebra, geometry, number theory, and more. Some key points covered include:
- Terms for integers, fractions, real and complex numbers, exponents, and basic arithmetic operations.
- Algebraic expressions, indices, matrices, inequalities, polynomial equations, and congruences.
- The use of definite and indefinite articles for theorems, conjectures, and mathematical concepts.
- Concepts in number theory like Fermat's Little Theorem and the Chinese Remainder Theorem.
- Terms for geometric concepts like points, lines, intersections, and rectangles.
The document discusses several fundamental concepts of algebra including:
1. Different types of numbers such as integers, rational numbers, and irrational numbers.
2. Properties of operations like addition, subtraction, multiplication, and division.
3. Exponent rules for simplifying expressions with exponents like multiplying terms with the same base.
This chapter reviews real numbers including:
[1] Classifying numbers as natural numbers, integers, rational numbers, irrational numbers, and real numbers. Rational numbers can be written as fractions while irrational numbers cannot.
[2] Approximating irrational numbers like π as decimals to a given number of decimal places by rounding or truncating.
[3] How calculators handle decimals by either truncating or rounding values based on their display capabilities. A scientific or graphing calculator is recommended for this course.
Presentacion del informe expresiones algebraicas Vicente Gabriel Gutierrez y ...Vicente Gabriel Gutierrez
Informe: Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
The document discusses two types of log and exponential equations:
1) Equations that do not require calculators, which involve relating bases on both sides of the equation and can be simplified using properties of logarithms and exponents.
2) Numerical equations that do require calculators. It provides examples of solving each type, including consolidating bases, using logarithmic and exponential properties, and algebraic manipulation to isolate the variable.
This document discusses different types of number systems. It begins by introducing natural numbers, which are counting numbers formed by repeated addition of 1. Whole numbers include all natural numbers and 0. Integers extend whole numbers infinitely in both the positive and negative directions. Rational numbers are numbers that can be written as fractions p/q where p and q are integers. Irrational numbers have non-repeating decimal expansions and cannot be written as fractions. Real numbers include all rational and irrational numbers and are represented on the number line. Methods for finding rational numbers between two given numbers and representing different types of numbers on the number line are also described.
This document provides vocabulary terms and definitions that will be covered in Unit 2 of math class. It includes terms like variable, solve, one-step equation, two-step equation, distributive property, term, solution, like terms, infinitely many solutions, algebraic expression, inverse operation, constant, no solution, unique solution, coefficient, linear equation in one variable, addition property of equality, additive inverses, exponent, irrational, rational, scientific notation, perfect square, and square root. Students are expected to learn these terms and their definitions to understand the concepts covered in Unit 2.
This document provides an overview of algebraic expressions. It defines algebraic expressions as sets of numbers and letters combined using operations like addition, subtraction, multiplication, division, and parentheses. It describes the main elements of algebraic expressions as variables, coefficients, exponents, operators, and parentheses. It also discusses types of expressions like monomials and polynomials, and algebraic operations like addition, subtraction, multiplication, division, and factoring of expressions using notable products. It includes examples for each topic and a bibliography of additional resources.
Algebraic Mathematics of Linear Inequality & System of Linear InequalityJacqueline Chau
A brief, yet thorough look into the Linear Inequality & System of Linear Inequality and how these Math Concepts would be useful in solving our everyday life problems.
1. The document discusses subsets of real numbers including natural numbers, whole numbers, integers, and rational numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are formed by adding 0 to the natural numbers. Integers are formed by adding the negatives of natural numbers to whole numbers.
3. Rational numbers can be expressed as fractions a/b where a and b are integers and b is not equal to 0. Their decimal representations either terminate or repeat.
The document discusses operations with integers. It defines absolute value and covers addition, subtraction, multiplication, and division of integers through examples. Rules for integer operations are that the sign of the product is the product of the signs of the factors, and the sign of the quotient is the sign of the dividend. Division by zero is undefined.
The document provides definitions for mathematical terms that students in 5th/6th class primary school and junior cycle secondary school may encounter. It includes over 50 terms defined with diagrams and examples. The glossary is designed to inform students, parents, and teachers about the vocabulary and meanings of key mathematical terms as students transition between primary and post-primary education in Ireland.
This document discusses the real number system and its properties. It begins by describing how the set of real numbers is constructed by successive extensions of the natural numbers to include integers, rational numbers, and irrational numbers. It then establishes a one-to-one correspondence between real numbers and points on the real number line. Key properties of real numbers discussed include algebraic properties like closure under addition/multiplication, as well as properties of order and completeness. The document also covers intervals, inequalities, and the absolute value of real numbers.
The document discusses various methods for solving inequalities, including:
- Properties for adding, subtracting, multiplying, and dividing terms within an inequality
- Using set-builder and interval notation to describe the solution set of an inequality
- Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set
The document provides examples of applying these different techniques to solve specific inequalities.
This document defines sets and subsets, classifies different types of sets such as finite, infinite, empty and unit sets. It also discusses operations on sets like union and intersection. Real number sets such as natural, integer, rational and irrational numbers are defined. Inequalities, absolute value inequalities and their properties are explained. Intervals such as open, closed and infinite intervals are classified. The numeric plane and Cartesian product are defined. Graphical representations of conic sections like ellipses, circles, parabolas and hyperbolas are shown. Examples of solving inequalities and simplifying fractions are provided.
Mathematics power point presenttation on the topicMeghansh Gautam
This document provides an overview of mathematics and different types of numbers. It discusses what mathematics is, polynomials, algebraic identities, and various number systems including natural numbers, integers, rational numbers, real numbers, complex numbers, and computable numbers. It also briefly discusses the history of numbers, mentioning that tally marks found on bones and artifacts may be some of the earliest forms of counting and record keeping.
This document introduces real numbers and their properties. It discusses that real numbers can be divided into two kinds: rational numbers, which can be written as a ratio of integers, and irrational numbers, which cannot. It provides examples of rational numbers like fractions and decimals, as well as irrational numbers like square roots and pi. The document also defines integers, explains operations like exponents and identities, and illustrates the real number system.
The document discusses sets and operations involving sets of real numbers. It defines key sets such as the real numbers, rational numbers, integers, natural numbers, whole numbers, and irrational numbers. It also covers properties of real numbers like closure, commutativity, associativity, distributivity, identity, and inverse properties as they relate to addition and multiplication. Examples are provided to illustrate set notation and properties. The document contains exercises asking to identify which properties justify certain statements involving real number operations.
The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
The document discusses different number systems used in mathematics. It begins by explaining that a number system is defined by its base, or the number of unique symbols used to represent numbers. The most common system is decimal, which uses base-10. Other discussed systems include binary, octal, hexadecimal, and those used historically by cultures like the Babylonians. Rational and irrational numbers are also defined. Rational numbers can be written as fractions of integers, while irrational numbers cannot.
english mathematics dictionary
kamus bahassa inggris untuk matematika
oleh neneng
Nurwaningsih
(06081281520066)
Nurwaningsih30@gmail.com
PROGRAM STUDI PENDIDIKAN MATEMATIKA
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS SRIWIJAYA
INDRALAYA
2017
semoga bermanfaat
This document provides a summary of key terms in mathematical English for concepts in arithmetic, algebra, geometry, number theory, and more. Some key points covered include:
- Terms for integers, fractions, real and complex numbers, exponents, and basic arithmetic operations.
- Algebraic expressions, indices, matrices, inequalities, polynomial equations, and congruences.
- The use of definite and indefinite articles for theorems, conjectures, and mathematical concepts.
- Concepts in number theory like Fermat's Little Theorem and the Chinese Remainder Theorem.
- Terms for geometric concepts like points, lines, intersections, and rectangles.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
This document discusses key concepts in the real number system including:
- Rational numbers that can be expressed as ratios of integers, and irrational numbers that cannot.
- Integers, including positive, negative and whole numbers.
- Properties of addition like commutativity, associativity and closure.
- Properties of multiplication like commutativity, associativity and distributivity.
- Absolute value and rules for performing operations on signed numbers like addition, subtraction, multiplication and division.
The document provides an overview of topics in number theory including:
- Number systems such as natural numbers, integers, and real numbers
- Properties of real numbers like closure, commutativity, associativity, identity, and inverse properties
- Rational and irrational numbers
- Order of operations
- Absolute value
- Intervals on the number line
- Finite and repeating decimals
- Converting between fractions and decimals
The document defines key concepts in real numbers and the number plane. It discusses the sets of natural numbers, integers, rational numbers, irrational numbers and their properties. It also covers operations like addition, subtraction, multiplication and distribution. Graphical representations of conic sections like circles, ellipses, parabolas and hyperbolas are shown. Examples of distance and midpoint on the number plane are provided, along with inequalities and absolute value exercises.
The document provides information on various topics in mathematics including:
- Number systems and notation for numbers written in words, Roman numerals, and different number bases.
- Interest calculation formulas for compound and continuous interest.
- Basic algebra concepts such as properties of addition/multiplication and the definition of conic sections.
- Geometric shapes including the definition of polygons, formulas for calculating polygon properties, and special polygon names.
This document defines various math terms across several categories:
1) It begins by defining types of numbers such as natural numbers, integers, decimals, and irrational numbers. It also defines basic math operations like addition, subtraction, multiplication, and division.
2) It then defines geometry terms like points, lines, angles, polygons, triangles, circles, and 3D shapes. It also covers perimeter, area, volume, and surface area.
3) Finally, it defines coordinate geometry terms like the coordinate plane, axes, ordered pairs, intercepts, slope, domain, and range. It discusses parallel and perpendicular lines on a graph.
This document defines and explains several concepts in mathematics including real numbers, absolute value, inequalities, sets, and set operations. It discusses how real numbers can be rational or irrational based on whether they have a periodic or non-periodic decimal expansion. Absolute value is defined as the distance from zero on the number line, and properties like non-negativity and the triangular inequality are covered. Inequalities and their properties like reflexivity and symmetry are also outlined. Sets are defined as collections of elements that share properties, and set operations like intersection, union, difference and complement are discussed. Examples are provided throughout to illustrate each concept.
This chapter discusses various types of errors that can occur in numerical analysis calculations, including:
- Round-off errors due to limitations in significant figures and binary representation in computers
- Truncation errors from using approximations instead of exact mathematical representations
- Error propagation when combining results with arithmetic operations
It also covers topics like accuracy vs precision, definitions of relative and absolute errors, floating point representation standards, and techniques to estimate errors like Taylor series expansions and machine epsilon values. The goal is to understand the sources and magnitudes of different errors to improve the reliability of numerical analysis methods.
1) The document provides an overview of properties and operations of real numbers including identifying different types of real numbers like integers, rational numbers, and irrational numbers.
2) It discusses ordering real numbers and using symbols like <, >, ≤, ≥ to compare them. Properties of addition, multiplication and other operations are also covered.
3) Examples are provided to illustrate concepts like using properties of real numbers to evaluate expressions and convert between units like miles and kilometers.
This document defines and explains various sets of numbers including natural numbers, integers, rational numbers, irrational numbers, and real numbers. It provides properties and examples of operations like addition, subtraction, multiplication, and division on real numbers. Key points covered include:
- The definitions of natural numbers, integers, rational numbers, irrational numbers, and real numbers as sets.
- Properties of addition, subtraction, multiplication, and division for real numbers like commutativity, associativity, identity elements, and opposites.
- Absolute value and inequalities involving absolute value.
ICSE class X maths booklet with model paper 2015APEX INSTITUTE
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
As It is very important to discover the basic weaknesses and problems of students not succeeding in IIT-JEE / PRE-MEDICAL exams. In fact, as question patterns are changing, now you need to have a different approach for these exams. As far as ENGG. / PRE-MEDICAL preparations is concerned, students have been wasting time and energy, studying Physics, Chemistry and Maths at different places. At APEX INSTITUTE, the scope of the subject has been deliberately made all- inclusive to free them of this burden. APEX INSTITUTE offers you complete preparation for IIT-JEE/PRE-MED. exams under one roof.
This document provides information on mathematical concepts and formulas relevant to economics, including:
- Exponential functions such as y=ex and their graphs showing exponential growth and decay
- Quadratic functions of the form y=ax2+bx+c and total cost functions
- Differentiation rules for common functions like exponentials, logarithms, and the product, quotient and chain rules
- Integration basics and formulas for integrating common functions
- Concepts like inverse functions, the mean, variance and standard deviation in statistics
- Information is also provided on fractions, ratios, percentages, and algebraic rules involving exponents, logarithms and sigma notation.
La siguiente presentación ejecutada por mi persona Angeli Dannielys Peña Suárez, estudiante de la Universidad Politécnica Territorial Andes Eloy Blanco te sera de gran ayuda para saber un poco mas acerca de de los conceptos y ejemplos de los conjuntos, pertenencia, agrupación, intersección, operaciones con conjuntos, los números reales y sus conjuntos, desigualdades, valor absoluto, desigualdades con valor absoluto, plano numérico y las cónicas.
Presentacion del informe expresiones algebraicas Vicente Gabriel Gutierrez y ...DanielGutierrez434
Informe: Suma, Resta y Valor numérico de Expresiones algebraicas.
Multiplicación y División de Expresiones algebraicas.
Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables.
The document discusses various topics in advanced algebra including inequalities, arithmetic progressions, geometric progressions, harmonic progressions, permutations, combinations, matrices, determinants, and solving systems of linear equations using matrices. Key properties and formulas are provided for each topic. Examples are included to demonstrate solving problems related to each concept.
This document discusses inequalities and interval notation in abstract algebra. It defines less than (<) and greater than (>) symbols to compare real numbers on a number line. Interval notation uses brackets [ ] or parentheses ( ) to indicate if endpoints are included or excluded from sets of real numbers. For example, the set of real numbers greater than or equal to 3 can be written as the closed interval [3, ∞). The document provides examples of writing set-builder and interval notations to represent sets of real numbers on a number line.
The document discusses exponents and order of operations. It defines exponents as indicating how many times the base is used as a factor. It provides examples of evaluating exponential expressions by writing repeated factors with exponents. Rules for exponents include: any number to the power of 0 equals 1; any number to the power of 1 equals the number; and multiplying exponents when the bases are the same. The order of operations is explained as: exponents, multiplication/division from left to right, and addition/subtraction from left to right. Grouping symbols like parentheses and fraction bars dictate that operations within are completed first. Several examples demonstrate applying these rules to simplify expressions.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
1. “… for a bit of review use the green buttons” INTEGERS
2. Main Menu Decimal (Standard) Form Mixed Number Exponential Form and Roots Fraction Scientific Notation Literal (written) Form Absolute Value Real Number Hierarchy Party in Mathland Parts of Operations Numerals Types of Whole Numbers Venn diagram Comparing Values Percent Conversion Number Properties
3. 013456… The numeral digits used for Numbers This seems to be the most likely theory but counting and writing numbers certainly developed earlier, if nothing more than scratching on a soft rock, bark, etc, 1 2 4 5 3
4. The numbers we write are made up of symbols, (1, 2, 3, 4, etc) called Arabic numerals, to distinguish them from the Roman numerals (I; II; III; IV; etc.). 013456… 1 2 4 5 3
5. 013456… The Arabs popularized these numerals, but their origin goes back to the Phoenician merchants that used them to count and do their commercial accounting. 1 2 4 5 3
6. 013456… Have you ever asked the question why 1 is “one”, 2 is “two”, 3 is “three”…..? 1 2 4 5 3
7. 013456… What is the logic that exists in the Arabic numerals? 1 2 4 5 3
13. 013456… And the most interesting and intelligent of all….. 1 2 4 5 3
14. 013456… No (zero) angles ! This is a theory.. unless there is a few–thousand–year old mathematician. BUT it sounds reasonable. 1 2 4 5 3
15. Known History of Algebra The origins of algebra can be traced to the cultures of the ancient Egyptians and Babylonians who used an early type of algebra to solve linear, quadratic (variable to power of 2), and indeterminate (variable) equations more than 3,000 years ago. Around 300 BC Greek mathematician Euclid in Book 2 of his Elements addresses quadratic equations, although in a strictly geometrical fashion. Around 100 BC Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters of Mathematical Art). Around 150 AD Greek mathematician Hero of Alexandria treats algebraic equations in three volumes of mathematics. Around 200 AD Greek mathematician Diophantus , often referred to as the "father of algebra", writes his famous Arithmetica , a work featuring solutions of algebraic equations and on the theory of numbers. The word algebra itself is derived from the name of the treatise first written by Persian mathematician Al-Khwarizmi in 820 AD titled: Kitab al-mukhtasar fi Hisab Al-Jabr wa-al-Moghabalah meaning ‘The book of summary concerning calculating by transposition and reduction’. The word al-jabr (from which algebra is derived) means "reunion", "connection”, or "completion". Algebra was introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci in 1202.
16. Venn Diagram A Venn diagram is a drawing, in which areas represent groups of items sharing common properties. The drawing consists of two or more shapes (usually circles or ellipses), each representing a specific group. This process of visualizing logical relationships was devised by John Venn (1834-1923). Set C Set C has some elements in both Set A and Set B All elements of Set D are in Set B What is the difference between Set C and Set D? What are the similarities between Set B and C? If elements of Set D are removed, what could this Venn represent? Set B Set A Set D
17. Types of Whole Numbers Primes to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 A Whole Number are positive integers ( 0 to ∞ ) A Prime Number has only 2 factors: “1” and itself. A Composite Number has 3 or more factors. “ 0” and “1” are not composite or prime numbers. WHOLE NUMBERS PRIME COMPOSITE 0 and 1
18. Real Numbers Venn diagram Venn diagram Real Numbers All Numbers (Rational and Irrational) Irrational Numbers PI (3.14….), Square root of a non-perfect square Any number that can be represented by a fraction: Integer Integer Rational Numbers Integers Positive and Negative numbers, and Zero; NO Decimals Whole Numbers Positive non-decimal numbers and Zero Natural (Counting) Numbers Positive non-decimal numbers ; NO Zero or Negative
19. Operation Parts Multiplication Addition Subtraction Division Also called: Multiplicand x Multiplier = Product Addition is the total of groups (sum) of the same and/or different size groups (addend). Subtraction is the amount left (difference) when a total of groups (minuend) is reduced by the same and/or different size groups (subtrahend). Multiplication is adding groups of a same size (multiplicand) so many groups (multiplier) to get the size of all groups (product), Division is subtracting the size of 1 group (divisor) from the total size of all groups (dividend) to get the number of groups (quotient) in the total (dividend). Addend + Addend = Sum 12 + 15 = 27; 2x + x = 3x Factor x Factor = Product 2 x 15 = 30; 3y x 2 = 6y Minuend – Subtrahend = Difference 37 – 15 = 22; 5t – 3t = 2t Dividend ÷ Divisor = Quotient 60 ÷ 15 = 4; 8x ÷ 4 = 2x
20. Operation Basics – Diagrams Division is subtracting groups of a same size ( divisor ) from the total size of all groups ( dividend ) to get the number of groups ( quotient ). Multiplication is adding groups of a same size ( multiplicand ) so many times, or groups ( multiplier ), to get the size of all groups ( product ). Addition is the total of groups ( sum ) of the same and/or different size groups ( addend ). Subtraction is the amount left ( difference ) when a total of groups ( minuend ) is reduced by the same and/or different size group ( subtrahend ). – = ● 3 = + = 3 ÷ = The multiplicand and multiplier can be switched, due to the commutative property, and both are typically referred to as factors .
21. Absolute Value The absolute value is the distance to 0. Absolute value can NEVER be negative ! Negative becomes positive … | –2 | = 2 ; | 2 – 3 | = 1 ; | –2 | 3 = 2 3 = 8 Positives remain positive … | 2 | = 2 ; | 3 – 2 | = 1 ; | 2 | 3 = 2 3 = 8 Examples: The symbol is | a |, where a is any value. -5 5 0 10 -10 7 7
22. Properties of Numbers Additive Identity a + 0 = a Multiplicative Identity a * 1 = a Additive Inverse a + (-a) = 0 Commutative of Addition a + b = b + a Multiplicative Inverse a * (1/a) = a / a = 1 (a ‡ 0) Commutative of Multiplication a * b = b * a Associative of Addition (a + b) + c = a + (b + c) Associative of Multiplication (a * b) * c = a * (b * c) Basis for solving equations and inequalities… isolates the variable by getting an identity number on one side Order of terms CHANGES Term Order does NOT CHANGE.. Grouping DOES = One group of 3 (a=3) = = = ( ) = ( ) + = nothing
23. Properties of Numbers –cont– Definition of Subtraction a - b = a + (-b) Distributive Property a(b + c) = ab + ac Definition of Division a / b = a(1/b) Zero Property of Multiplication a * 0 = 0 Adding a negative number is subtraction , so subtracting is adding a negative number Multiplying by a fraction is dividing by its denominator, so division is dividing by a common factor ex. No ( zero ) piles of 4 crates equals no ( zero ) piles of crates … where “ a ” is a common factor of “ b ” and “ c ” ex. 2( 3 – x ) = 6 – 2x ex. 4x + 2 = 4( x+ ½ ) ex. –x+2 = 2–x ex. x+(–2) = x–2 ex. 3 / 4 = 3● 1 / 4 ex. 3 / 4 = 3● 1 / 4 a - b = a + ( -b ) = a • a a b ( + ) = • + •
24. Fraction A fraction is division of 2 integers but used as one number. There are 2 types of fractions: Proper is < “1” so numerator is smaller than denominator Improper is ≥ “1” so numerator is greater than denominator Any integer can become an improper fraction with “1” as the denominator ex. –⅞, ⅔, ⅓ Ex. 8 / 7 , – 23 / 7 , 3 / 2 Ex. –8 = – 8 / 1 , 23 = 23 / 1 , 3 = 3 / 1 Repeating bar (ignore the “+” / “–” signs for this discussion) This is done because a fraction is more exact in value than a decimal 1 / 3 =0.33
25. Mixed Number The integer and proper fraction parts are added, so addition is implied … 3 ½ = 3 + ½ 10 + ¼ = 10 ¼ A mixed number is an improper fraction reduced to an integer and a proper fraction part, if needed. An improper fraction is in its lowest terms when it is reduced to an integer and its remaining proper fraction part is reduced. Integer part Fraction part
26. Decimal (Standard) Form All numbers have a decimal point. If there is NO decimal portion then the decimal point is implied after (to the right of) the last digit, and is not shown. A decimal (point) separates value greater or equal to “1” and that less than “1” in a number. In the number 12.3 “12” ≥ 1 and .3 < 1 30%= 30 . 0 % 23 = 23 . 0 –123 . 002 0 . 123 22 . 5 % All numbers have a decimal part (after decimal) and an integer part (before decimal) . If it needs to be shown it is followed by a zero(s). 23 = 23.0 = 23.00… This is called “padding” and does not change the value. (ignore the “+” / “–” signs for this discussion) decimal point
27. Exponential Form (Exponent) Exponential form is a short way of show multiplication of the same factor. It has 2 parts: Base: the only factor to be multiplied Exponent: the number of times the base is a factor The exponent identifies the number of times the base is used as a factor only!!! b e = 1 x b 1 x b 2 x b 3 x… b e = p where: b = the base which is any term (number) or Grouping symbols contents… this is the factor e = the exponent (power) which is the number of times to multiply the base by itself… this is not a factor p = the product of the exponential form “ p is the e th power of b ” 2 3 = 8 (3●4–1) 2 = 121 – 2 4 = –16 (–2) 4 = 16 4 -3 = ¼ ● ¼ ● ¼ = 3 / 4 “ b to the e th power equals p” A negative exponent means to use the reciprocal of the base as a factor
28. Exponential Form (examples) “ 1” (multiplicative identity) is always implied in multiplication 1; –1; 1 25 6.25 1 / 512 31,000 0.00031 3 8 8 – 8 – 4 – 8 4 2 exponent value calculation Find the value! 3(2+14.3 • 2÷x) 0 = 3(1) 3(2+14.3 • 2÷x) 0 3.10 x ( 1 / 10 x 1 / 10 x 1 / 10 x 1 / 10 ) 3.10 x 10 -4 3.10 x (10 x10 x10 x10) 3.10 x 10 4 (⅛)(⅛)(⅛) (⅛) 3 2.5 * 2.5 2.5 2 (3+1 • 2) 2 = (5) 2 (3+1 • 2) 2 1 ; -1 x 1; 1 2 0 ; -2 0 ; {2x+3 (12-2)} 0 1(2) 2 1 1x(-2) x (-2) (-2) 2 ; exponent is even 1x(-2) x (-2) x (-2) (-2) 3 ; exponent is odd -1(2 * 2) -2 2 ; exponent is even -1(2 * 2 * 2) -2 3 ; exponent is odd (2) x (2) x (2) (2) 3 2 * 2 * 2 2 3
29. Roots A root is the inverse operation of exponent form Exponential form : b e = 1 x b 1 x b 2 x b 3 x… b e = p where: “b” is the base , “e” is the exponent , and “p” is the product Root form : e p = b where: “b” is the base , “e” is the index , and “p” is the radicand If “e” (index) is not shown the root is assumed to be a square root (“e” = 2) Operations with roots and exponents
30. Scientific Notation very large numbers (a lot of trailing zeroes before decimal) 1,220,000,000,000 very small numbers (a lot of leading zeroes after the decimal) 0.00000000023 (1) The unit digit is always 1-9; AND it is the only digit to the left of the decimal point in the decimal factor. This factor is always ≥ 1 and <10. (2) An explicit multiplication symbol is present. Usually “X”, but also “ • ”, “ ”. Scientific Notation is a short way to show: A value in Scientific Notation form has 3 distinct characteristics (3) The other factor is an exponent with a base of “10”. = 1.22 X 10 12 = 2.3 ● 10 -10 Positive exponent when value ≥ 1 Negative exponent when value < 1 Multiplication of a decimal (>1 and <10) and an exponent
31. Literary (Written) Form Used in speech, thought, and word problems, they must be converted to/from algebraic expressions, inequalities, and equations. Solving math word problems: Translate the wording into a numeric equation, then solve the equation! An expression in Math is like a phrase in Grammar… no subject and verb. A sentence in Math is like a sentence in Grammar. The verb typically includes: is will was equals equal calculate sum estimate subtract can times It is very important to understand the word use in the context of the problem… like determining the meaning of a word when context reading.
32. Literal (Written) Examples There are many others! ( ),{},[] = Results - Reduce = Will be - Diminished Quantity = Equal - Difference % Percent = Was - Subtract 1:4, ¼ 1 of 4 = Is - Less than 3–2 Difference between 3 and two ≈ about - Decreased by 2 x Product of 2 and x /, ÷ Quotient + Greater 2÷4 Quotient of two and 4 /, ÷ Divide + In excess < Less than or equal to /, ÷ Per + Increased < Less than *,•,x Interest on + More than > Greater than or equal to *,•,x Product + In addition > Greater than *,•,x Percent of + Add ≠ Not equal to *,•,x Times + Sum
33. A number increased by 5 n + 5 4 decreased by the quotient of a number and 7 4 - n / 7 7 less than a number n - 7 7 less a number 7 – n The product of ½ and a number is 36 ½ • n = 36 3 more than twice a number is 15 2n + 3 = 15 When you see the words: ‘ less than ’ vs. ‘less in subtraction… switch it around. Literal (Written) Examples Important!
34. The Party in Mathland A dd, S ubtract, M ultiply, and D ivide positive and negative values (integers).
35. Multiply and Divide Party Everyone is happy and having a good time (they are ALL POSITIVE). Suddenly, who should appear but the GROUCH (ONE NEGATIVE)! The grouch goes around complaining to everyone about the food, the music, the room temperature, the other people.... Everyone feels a lot less happy... the party may be “negatized”!! ODD NUMBER OF NEGATIVES MAKES EVERYTHING NEGATIVE I feel odd here.
36. Multiply and Divide Party continues Everyone feels a lot less happy... the party may be doomed! Everyone is so negative! ... is that another guest arriving? Yes, another grouch (A SECOND NEGATIVE) appears? The two negative grouches pair up and gripe and moan to each other about what a horrible party it is and how miserable they are!! But look!! They are starting to smile; they're beginning to have a good time, themselves…is that a POSITIVE attitude!! PAIRS OF NEGATIVES BECOME POSITIVE Now that the two grouches are together the rest of the people (who were really positive all along) become positive again. The party is positive!!
37. The moral of the story Negatives in PAIRS are POSITIVE: Negatives NOT in pairs, they're NEGATIVE: When multiplying or dividing the number of positives doesn't matter … but watch out for those negatives!! To determine whether the outcome will be positive or negative , count the number of negatives : If there are an even number of negatives the answer will be positive If not ( odd number of negatives )... It will be negative – , + , – , – , + , + , – equals + , – , – , + , + , – equals + – + + +
38. Addition with the Same Signs If the signs are the same; the answer will keep the same sign. – 4 + ( –2 ) = –6 4 + 2 = 6 + = + = Positives Negatives + –
39. Addition with different signs (alias Subtraction) – 32 + 11 32 – 11 Wait a second! ... This is subtraction! What about… ? = – 21 32 – 11 21 32 – 11 21 = + 21 32 + ( –11 ) If the signs are different ; then subtract the absolute value of the small value from the larger value. The sign of the larger value is the answer’s sign. Oh yeah! Subtracting is adding a negative, so adding a negative is subtraction.
41. Scholarly Subtracting a Negative (adding a positive) Subtracting a negative is adding the subtrahend’s absolute value to the minuend Wait a second! ... This is addition! Oh yeah! Multiplying two negatives gives a positive product. 32 – (–11) – 32 – (–11) This is addition with different signs! Is the addition of 2 negatives subtracting a negative? No, when adding 2 negatives, like 2 positives, the sum’s sign is the same as the addends… –2+(–4) = –6 and 2+4=6. So, adding 2 negatives is adding 2 negatives. Subtracting a negative: –2–(–4) = –2+4 = 2 32 + 11 43 = 43 + 32 + 11 = –21 + – 32 + 11 32 – 11 21
42. Your Turn (reduce to decimal form or an expression/equation/inequality ) 23 2 – 9 103,000 0.4 – 8 2.25 – 8 4 – 12 – 72 12 – 4 v ÷ 3 =15 t > 30 ⅔ ● 12 |–23| = |4–2| = – 3 2 = 1.03 X 10 5 = 2 / 5 = -|–2| 3 = (–2) 3 = 12 less than 4 – 3 2 (2 3 ) = 12 less 4 Quotient of a value and 3 is 15. Total is greater than 6 groups of 5 . 2 ¼ = Two–thirds of a dozen
44. Decimal / Percent Conversion Converting to a percent from a decimal is dividing by 100 (or multiplying by 1 / 100 ). Since decimals are based on 10, we can move the decimal 2 places for conversion… do NOT forget to add / remove the “%”. Move decimal 2 places to the left for conversion from percent to decimal and remove the “%” % Shortcut! Add the percent symbol Move decimal 2 places to the right for conversion from decimal to percent and add the “%” 3.24% = 0.0324 5 ½ % = 0.05 ½ = 0.055 .02% = 0.0002 3.24 = 324% 5 1 / 3 = 5.33 = 533 1 / 3 % .02 = 2%
45. Comparing Values Use this method when not finding a more obvious way. With this method Least–to–Greatest and Greatest–to–Least mistakes are easily remedied. 2) Convert all values to decimal 3) Pad with zeroes all values to the same decimal position. 4) Number the increasing/decreasing values starting with one. 1) Write each value in a different row. Ex. 2.3%, 3 / 25 , 2.31 x 10 2 , 2 1 / 3, , 0.233 greatest–to–least 2.3%, 3 / 25 2.31 x 10 2 2 1 / 3 0.233 2.3 0.12 231 0.233 000 00 0 1 2 .0000 5 4 3 Oh No! I wanted least–to–greatest! Oh Yeah! I can reverse the order. least–to–greatest 2.3333