EMTeachline interactive software - algebraic inequalities - solutions proofs

EMMentor Inequalities

EMTeachline Mathematics Software - interactive math problem solving, test authoring

Get a private math tutor right on your desk! All students need help at some point, so be sure to get the help you need. With dozens of interactive learning techniques and a unique system of error analysis, EMMentor provides a qualified training of problem solving skills. He will offer you a task, ask you questions, give you hints as you need them, analyse your answers, trace your errors, detect gaps in your theoretical knowledge and problem solving skills and generate optimal exercises to close these gaps. EMMentor is here to help you figure out how to learn math for yourself. Those who stick with EMMentor will come away with a stronger understanding of fundamental math concepts, improved higher-level thinking skills and excellent practical skills in solving math problems! Free fully functional downloadable version of EMMentor is available. Our online demos enable you to try a number of training techniques and observe examples of error analysis.

Parameters of the program

Name of program:	EMMentor_Inequalities
Number of problems:	25683
Number of similar variants:	5
Languages of interface:	English, German
Price:	164 EUR
Size of archive:	4597 kb

Abstract. EMMentor_Inequalities is a new generation interactive training program that offers a large number of math problems, a variety of appropriate techniques to solve problems and a unique system of performance analysis with methodical feedback. Students at all levels can practice at their own pace, review their own work, monitor their weaknesses and achievements, and get methodical recommendations for building missing math knowledge and skills.Considered are solutions of algebraic, trigonometric and hyperbolic inequalities. Thematically, this program integrates Algebra_Inequalities, Trigonometry_Inequalities and Hyperbolic_Inequalities. The program includes 25683 math problems of 11 levels of complexity, from basic to advanced. For each math problem, EMMentor offers a set of methodical tasks to be discharged at each step of problem solution. Your work will be throughly analysed with respect to multiple parameters. You can review the distributions of your errors throughout the solution steps, over formulas and other math concepts, over topics, etc. Based on this joint error distribution, EMMentor provides an optimal set of tasks for error correction. In addition, EMMentor offers a number of test authoring options that automate creation of math tests, quizzes, homeworks and exams of varied complexity and enable automatic generation of a number of variants around each test. The tests with or without the solutions can be printed out or stored in a file and re-used. Dozens of variant tests are ready for students to review and reinforce their math skills. Each definition, rule etc can be instantly translated to German or another available language.

System Requirements:

Pentium 2 or higher

64 MB RAM

Windows 98 or higher

Internet Explorer 5.5 or higher

Plug-in MathPlayer (downloadable from here)

Program's detail

●	Examples
●	Press release
●	Contents of the program
●	Characteristics of similar programs

Examples

An online sample of math problems and problem solutions from this program is provided below:

●	Problems: Algebra
●	Problems: Algebra Inequalities
●	Problems: Algebra Inequalities advanced
●	Problems: Algebra Inequalities basic

EMTEACHLINE MATHEMATICS SOFTWARE - YOUR PERSONAL MATH TEACHER

Press release

ABSTRACT. EMTeachline Software has released a PC-based interactive mathematics software brand EMMentor that tutors in solving math problems. This encyclopedic software contains hundreds thousands of fully explained step by step solutions to math problems from basic to advanced and thousands of related definitions, rules, formulas and theorems. Based on a unique teaching technology, EMMentor controls, analyses and grades your performance, detects gaps in your theoretical knowledge and problem-solving skills, and generates an optimal set of tasks to close the revealed gaps. This software helps kids grasp math concepts and build problem solving skills much more effectively than any classroom teacher. For teachers and parents, EMMentor offers a comprehensive objective analysis of children's performance, with tables and plots, and methodical recommendations for error correction. Easy-to-use authoring options automate development of math tests and homeworks. The software is designed for mathematics self-study. Provides an ideal help for math teachers. Suitable for elementary, middle and high school use.

1. SOFTWARE OVERVIEW

The EMTeachline Interactive Mathematics Software EMMentor provides kids and teens with the chance to build outstanding problem-solving skills in math without any external help. Based on a brand-new teaching technology, this highly interactive software will help you much more effectively than any classroom teacher.

EMMentor includes a set of original interactive training techniques and a unique system of performance analysis with methodical feedbacks. Each technique consists of a set of questions asked at each step of task performance and a system of multiple choice answers with hints. Based on an analysis of your answers, the software detects gaps in your theoretical knowledge and problem-solving skills and summarises your errors. To correct errors and develop missing skills, EMMentor offers an optimal set of exercises.

The error analysis is made for a particular task performance, as well as for a number of tasks performed during the selected period of time. EMMentor shows, in tables and on plots, how many errors were made and how many hints were used at each step of solution within one technique, the distributions of errors and hints throughout the techniques, over formulas and other math categories, the total number of errors per topic, etc. The concluding methodical recommendations are based on an objective analysis of these joint error distributions. Any teacher or tutor will find this function to be extremely useful.

As a multilingual tutoring program, EMMentor offers a way for children to learn math lexicon in a foreign language. Translation of any text to German or another available language is easily obtained by double-clicking on it. Those kids who study not in a native language will find this option invaluable.

Covered subject areas are arithmetic, pre-algebra, algebra, trigonometry and hyperbolic trigonometry. All math problems are graded in 11 complexity classes from basic to advanced and provided with fully explained step by step solutions. Comprehensive tutoring material is provided for each solution step. The available test authoring options automate development of tests, quizzes, homeworks and exams. All developed materials can be printed out or stored in a file and re-used.

2. SKILLS COVERED

Arithmetic and Pre-Algebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problem-solving. Solving arithmetic problems using algebraic formulas.

Algebra: Polynomial and fractional rational expressions: transformation, simplification, evaluation. Solution of linear, quadratic, cubic, biquadratic, reciprocal and fractional algebraic equations and inequalities. Proofs of algebraic identities. Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more. Related theory: definitions and rules, proof of algebraic formulas and theorems.

Trigonometry and Hyperbolic Trigonometry: trigonometric and hyperbolic functions, arcus functions. Trigonometric and hyperbolic expressions: transformation, simplification, evaluation. Solution of trigonometric and hyperbolic equations. Proofs of trigonometric and hyperbolic identities. Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more. Related theory: definitions and rules, proof of trigonometric and hyperbolic formulas.

3. USER OPTIONS

For math students: You will get a diagnosis of all vacancies in your math skills. You can train the missing problem solving skills with the help of dozens of interactive training techniques. You can effectively learn definitions, rules and other math concepts, study solution methods, pick up skills of verbal formulation of math transformations, learn proofs of math formulas and theorems, develop reasoning skills etc. And in parallel, you can learn math lexicon in a foreign language!

For math teachers: You can use an extensive bank of math problems; arrange problems by topic, complexity level, solution method and type of task; compile math tests, quizzes, homeworks and exams of varied complexity; create your own didactic materials and problem-solving lesson plans; generate numerous similar variants of math tests; use dozens of ready variant tests. For each student of yours, you can get an objective analysis of his/her work, revealing his/her weak and strong points, together with an optimal set of tasks for error correction.

Contents of the program

Themes

Rational expressions. Proofs of inequalities
Rational inequalities

Chapters and sections

Rational expressions. Proofs of inequalities
Chapters	Sections
Proof of strict inequalities. Linear expressions and expressions reduced to them	Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Distributive law Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Properties of powers Proof of strict inequalities. Linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Properties of powers
Proof of strict inequalities. Quadratic expressions	Proof of strict inequalities. Quadratic expressions. Elementary quadratic inequalities Proof of strict inequalities. Quadratic expressions. Quadratic inequalities containing fractions Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Distributive law. Integer coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Grouping method Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Integer coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Rational coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Grouping method Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Factorization of quadratic trinomial Proof of strict inequalities. Quadratic expressions. Fractional inequalities. Method of substitution. Distributive law. Integer coefficients
Proof of strict inequalities. Algebraic high-degree expressions	Proof of strict inequalities. Algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Proof of strict inequalities. Algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems
Proof of strict inequalities. Fractional algebraic expressions	Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. To prove inequality Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. To prove inequality

Rational inequalities
Chapters	Sections
Weak linear inequalities	Weak linear inequalities. Elementary linear weak inequalities Weak linear inequalities. Linear weak inequalities containing fractions Weak linear inequalities. Homographic weak inequalities. Method of substitution. Rational coefficients Weak linear inequalities. Linear weak inequalities. Distributive law Weak linear inequalities. Weak inequalities reduced to linear inequalities. Formulas of short multiplication Weak linear inequalities. Linear weak inequalities. Formulas of short multiplication. Cubes Weak linear inequalities. Linear weak inequalities. Properties of fractions Weak linear inequalities. Linear weak inequalities. Factorization of quadratic trinomial Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Distributive law Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Properties of powers Weak linear inequalities. Linear weak inequalities. Properties of powers Weak linear inequalities. Weak inequalities reduced to linear inequalities Weak linear inequalities. Fractional weak inequalities reduced to linear inequalities Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Rational coefficients Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Integer coefficients Weak linear inequalities. Homographic weak inequalities. Method of substitution. Integer coefficients Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Distributive law Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Properties of powers Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial
Strict linear inequalities	Strict linear inequalities. Elementary strict linear inequalities Strict linear inequalities. Strict linear inequalities containing fractions Strict linear inequalities. Strict linear inequalities. Distributive law Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication. Cubes Strict linear inequalities. Strict linear inequalities. Properties of fractions Strict linear inequalities. Strict linear inequalities. Properties of powers Strict linear inequalities. Strict inequalities reduced to linear inequalities Strict linear inequalities. Strict fractional inequalities reduced to linear inequalities Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Rational coefficients Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Integer coefficients Strict linear inequalities. Strict homographic inequalities. Method of substitution. Integer coefficients Strict linear inequalities. Strict homographic inequalities. Method of substitution. Rational coefficients Strict linear inequalities. Strict linear inequalities. Factorization of quadratic trinomial Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Distributive law Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Properties of powers Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Distributive law Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Properties of powers Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial
Strict quadratic inequalities	Strict quadratic inequalities. Elementary quadratic strict inequalities Strict quadratic inequalities. Quadratic strict inequalities containing fractions Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Rational coefficients Strict quadratic inequalities. Strict inequalities. Distributive law. Integer coefficients Strict quadratic inequalities. Strict inequalities. Formulas of short multiplication Strict quadratic inequalities. Strict inequalities. Distributive law. Rational coefficients Strict quadratic inequalities. Strict inequalities. Factorization of quadratic trinomial Strict quadratic inequalities. Strict inequalities. Properties of powers Strict quadratic inequalities. Fractional strict algebraic inequalities reduced to quadratic inequalities Strict quadratic inequalities. Strict inequalities. Grouping method Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Integer coefficients Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients Strict quadratic inequalities. Strict inequalities. Method of substitution. Factorization of quadratic trinomial Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Integer coefficients Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Rational coefficients Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
Weak quadratic inequalities	Weak quadratic inequalities. Elementary quadratic weak inequalities Weak quadratic inequalities. Quadratic weak inequalities containing fractions Weak quadratic inequalities. Weak inequalities. Distributive law. Integer coefficients Weak quadratic inequalities. Weak inequalities. Formulas of short multiplication Weak quadratic inequalities. Weak inequalities. Distributive law. Rational coefficients Weak quadratic inequalities. Weak inequalities. Factorization of quadratic trinomial Weak quadratic inequalities. Weak inequalities. Properties of powers Weak quadratic inequalities. Fractional algebraic weak inequalities reduced to quadratic inequalities Weak quadratic inequalities. Weak inequalities. Grouping method Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Integer coefficients Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Rational coefficients Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Integer coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Rational coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
Strict algebraic high-degree inequalities	Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Integer roots Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Irrational roots Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Integer roots Strict algebraic high-degree inequalities. Strict high-degree inequalities. Grouping method Strict algebraic high-degree inequalities. Strict high-degree inequalities. Perfect square Strict algebraic high-degree inequalities. Strict inequalities. Formulas of short multiplication Strict algebraic high-degree inequalities. Strict inequalities. Difference of squares Strict algebraic high-degree inequalities. Strict inequalities. Factorization of quadratic trinomial Strict algebraic high-degree inequalities. Strict inequalities. Properties of fractions Strict algebraic high-degree inequalities. Strict inequalities. Difference and sum of cubes
Weak algebraic high-degree inequalities	Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Integer roots Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Irrational roots Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Integer roots Weak algebraic high-degree inequalities. Weak high-degree inequalities. Grouping method Weak algebraic high-degree inequalities. Weak high-degree inequalities. Perfect square Weak algebraic high-degree inequalities. Weak inequalities. Formula of difference of squares Weak algebraic high-degree inequalities. Weak inequalities. Factorization of quadratic trinomial Weak algebraic high-degree inequalities. Weak inequalities. Properties of fractions Weak algebraic high-degree inequalities. Weak inequalities. Difference and sum of cubes
Strict fractional inequalities	Strict fractional inequalities. Elementary fractional strict algebraic inequalities Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict linear inequalities Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities. Method of substitution
Weak fractional inequalities	Weak fractional inequalities. Elementary fractional weak algebraic inequalities Weak fractional inequalities. Fractional weak algebraic inequalities reduced to linear inequalities Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities. Method of substitution

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