EMTeachline interactive hyperbolic software - solving hyperbolic problems
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EMMentor Hyperbolic

EMMentor Hyperbolic
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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_Hyperbolic
Number of problems:
33508
Number of similar variants:
3
Languages of interface:
English, German
Price:
174 EUR
Size of archive:
7121 kb

Abstract. EMMentor_Hyperbolic 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 hyperbolic problems: computational problems, proofs of identities and solutions of equations. Thematically, this program integrates Hyperbolic_Calculation, Hyperbolic_Identity and Hyperbolic_Equations. The program includes 33508 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: Hyperbolic

back 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.


back Contents of the program

Themes

Chapters and sections
back Hyperbolic expressions. Computational problems
Chapters
Sections

Evaluation of linear expressions and expressions reduced to them

  • Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Distributive law. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law. Evaluation

Evaluation of quadratic expressions and expressions reduced to them

  • Evaluation of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Integer coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Formulas of short multiplication. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Rational coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Factorization of quadratic trinomial. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Properties of powers. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients. Evaluation

Comparison of values of linear expressions and expressions reduced to them

  • Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities
  • Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Distributive law
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of powers. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients. Comparison of values

Comparison of values of quadratic expressions and expressions reduced to them

  • Comparison of values of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Comparison
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare quadratic expressions containing fractions
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Integer coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Formulas of short multiplication
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Rational coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Factorization of quadratic trinomial
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Properties of powers
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Grouping method
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients

back Hyperbolic expressions. Transformations and proofs
Chapters
Sections

Transformation of linear expressions and expressions reduced to them

  • Transformation of linear expressions and expressions reduced to them. Elementary linear expressions
  • Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers
  • Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication

Transformation of quadratic algebraic expressions and expressions reduced to them

  • Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

Transformation of algebraic high-degree expressions

  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Irrational roots
  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
  • Transformation of algebraic high-degree expressions. High degrees. Grouping method
  • Transformation of algebraic high-degree expressions. High degrees. Perfect square
  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
  • Transformation of algebraic high-degree expressions. High degrees. Formulas of short multiplication
  • Transformation of algebraic high-degree expressions. High degrees. Difference of squares
  • Transformation of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial
  • Transformation of algebraic high-degree expressions. High degrees. Properties of fractions
  • Transformation of algebraic high-degree expressions. High degrees. Difference and sum of cubes
  • Transformation of algebraic high-degree expressions. High degrees. Method of substitution

Factorization of linear expressions and expressions reduced to them

  • Factorization of linear expressions and expressions reduced to them. Elementary linear expressions
  • Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers
  • Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication

Factorization of quadratic expressions and expressions reduced to them

  • Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

Factorization of algebraic high-degree expressions

  • Factorization of algebraic high-degree expressions. High degrees. Grouping method
  • Factorization of algebraic high-degree expressions. High degrees. Perfect square
  • Factorization of algebraic high-degree expressions. High degrees. Difference of squares
  • Factorization of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial
  • Factorization of algebraic high-degree expressions. High degrees. Properties of fractions
  • Factorization of algebraic high-degree expressions. High degrees. Difference and sum of cubes

Proof of identities related with linear expressions and expressions reduced to them

  • Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions
  • Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Distributive law
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of powers
  • Proof of identities related with linear expressions and expressions reduced to them. Expressions reduced to linear expressions
  • Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
  • Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
  • Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
  • Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
  • Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law

Proof of identities related with quadratic expressions and expressions reduced to them

  • Proof of identities related with quadratic expressions and expressions reduced to them. Elementary quadratic expressions
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

Proof of identities related with high-degree expressions

  • Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
  • Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Irrational roots
  • Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
  • Proof of identities related with high-degree expressions. High degrees. Grouping method
  • Proof of identities related with high-degree expressions. High degrees. Perfect square
  • Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
  • Proof of identities related with high-degree expressions. High degrees. Formulas of short multiplication
  • Proof of identities related with high-degree expressions. High degrees. Difference of squares
  • Proof of identities related with high-degree expressions. High degrees. Factorization of quadratic trinomial
  • Proof of identities related with high-degree expressions. High degrees. Properties of fractions
  • Proof of identities related with high-degree expressions. High degrees. Difference and sum of cubes
  • Proof of identities related with high-degree expressions. High degrees. Method of substitution

Proof of identities related with fractional algebraic expressions

  • Proof of identities related with fractional algebraic expressions. Elementary fractional algebraic expressions
  • Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator
  • Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
  • Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator
  • Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator
  • Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator
  • Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

back Hyperbolic equations
Chapters
Sections

Hyperbolic equations reduced to rational equations. Function sh

  • Hyperbolic equations reduced to rational equations. Function sh. Elementary linear equations
  • Hyperbolic equations reduced to rational equations. Function sh. Equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function sh. Equations reduced to linear equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function sh. Linear equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function sh. Linear equations. Formulas of short multiplication. Cubes
  • Hyperbolic equations reduced to rational equations. Function sh. Linear equations. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function sh. Linear equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function sh. Homographic equations with rational coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function sh. Homographic equations with integer coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function sh. Homographic equations with rational coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function sh. Homographic equations with integer coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function sh. Equations reduced to linear. Method of substitution. Distributive law
  • Hyperbolic equations reduced to rational equations. Function sh. Elementary quadratic equations
  • Hyperbolic equations reduced to rational equations. Function sh. Equations with integer coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function sh. Quadratic equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function sh. Quadratic equations with rational coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function sh. Equations reduced to quadratic. Factorization of quadratic trinomial
  • Hyperbolic equations reduced to rational equations. Function sh. Equations reduced to quadratic. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function sh. Fractional algebraic equations reduced to quadratic equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function sh. Quadratic equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function sh. Equations. Grouping method
  • Hyperbolic equations reduced to rational equations. Function sh. Equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function sh. Equations. Method of substitution. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function sh. Fractional equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function sh. High-degree equations. Perfect square
  • Hyperbolic equations reduced to rational equations. Function sh. Fractional algebraic equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function sh. Fractional algebraic equations reduced to quadratic equations
  • Hyperbolic equations reduced to rational equations. Function sh. Elementary fractional algebraic equations
  • Hyperbolic equations reduced to rational equations. Function sh. Fractional algebraic equations reduced to quadratic equations. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function sh. Fractional algebraic equations. Method of substitution

Hyperbolic equations reduced to rational equations. Function ch

  • Hyperbolic equations reduced to rational equations. Function ch. Elementary linear equations
  • Hyperbolic equations reduced to rational equations. Function ch. Equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function ch. Equations reduced to linear equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function ch. Linear equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function ch. Linear equations. Formulas of short multiplication. Cubes
  • Hyperbolic equations reduced to rational equations. Function ch. Linear equations. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function ch. Linear equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function ch. Homographic equations with rational coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function ch. Homographic equations with integer coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function ch. Homographic equations with rational coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function ch. Homographic equations with integer coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function ch. Equations reduced to linear. Method of substitution. Distributive law
  • Hyperbolic equations reduced to rational equations. Function ch. Elementary quadratic equations
  • Hyperbolic equations reduced to rational equations. Function ch. Equations with integer coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function ch. Quadratic equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function ch. Quadratic equations with rational coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function ch. Equations reduced to quadratic. Factorization of quadratic trinomial
  • Hyperbolic equations reduced to rational equations. Function ch. Equations reduced to quadratic. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function ch. Fractional algebraic equations reduced to quadratic equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function ch. Quadratic equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function ch. Equations. Grouping method
  • Hyperbolic equations reduced to rational equations. Function ch. Equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function ch. Equations. Method of substitution. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function ch. Fractional equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function ch. High-degree equations. Perfect square
  • Hyperbolic equations reduced to rational equations. Function ch. Fractional algebraic equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function ch. Fractional algebraic equations reduced to quadratic equations
  • Hyperbolic equations reduced to rational equations. Function ch. Elementary fractional algebraic equations
  • Hyperbolic equations reduced to rational equations. Function ch. Fractional algebraic equations reduced to quadratic equations. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function ch. Fractional algebraic equations. Method of substitution

Hyperbolic equations reduced to rational equations. Function th

  • Hyperbolic equations reduced to rational equations. Function th. Elementary linear equations
  • Hyperbolic equations reduced to rational equations. Function th. Equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function th. Equations reduced to linear equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function th. Linear equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function th. Linear equations. Formulas of short multiplication. Cubes
  • Hyperbolic equations reduced to rational equations. Function th. Linear equations. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function th. Linear equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function th. Homographic equations with rational coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function th. Homographic equations with integer coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function th. Homographic equations with rational coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function th. Homographic equations with integer coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function th. Equations reduced to linear. Method of substitution. Distributive law
  • Hyperbolic equations reduced to rational equations. Function th. Elementary quadratic equations
  • Hyperbolic equations reduced to rational equations. Function th. Equations with integer coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function th. Quadratic equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function th. Quadratic equations with rational coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function th. Equations reduced to quadratic. Factorization of quadratic trinomial
  • Hyperbolic equations reduced to rational equations. Function th. Equations reduced to quadratic. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function th. Fractional algebraic equations reduced to quadratic equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function th. Quadratic equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function th. Equations. Grouping method
  • Hyperbolic equations reduced to rational equations. Function th. Equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function th. Equations. Method of substitution. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function th. Fractional equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function th. High-degree equations. Perfect square
  • Hyperbolic equations reduced to rational equations. Function th. Fractional algebraic equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function th. Fractional algebraic equations reduced to quadratic equations
  • Hyperbolic equations reduced to rational equations. Function th. Elementary fractional algebraic equations
  • Hyperbolic equations reduced to rational equations. Function th. Fractional algebraic equations reduced to quadratic equations. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function th. Fractional algebraic equations. Method of substitution

Hyperbolic equations reduced to rational equations. Function cth

  • Hyperbolic equations reduced to rational equations. Function cth. Elementary linear equations
  • Hyperbolic equations reduced to rational equations. Function cth. Equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function cth. Equations reduced to linear equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function cth. Linear equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function cth. Linear equations. Formulas of short multiplication. Cubes
  • Hyperbolic equations reduced to rational equations. Function cth. Linear equations. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function cth. Linear equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function cth. Homographic equations with rational coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function cth. Homographic equations with integer coefficients. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function cth. Homographic equations with rational coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function cth. Homographic equations with integer coefficients. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function cth. Equations reduced to linear. Method of substitution. Distributive law
  • Hyperbolic equations reduced to rational equations. Function cth. Elementary quadratic equations
  • Hyperbolic equations reduced to rational equations. Function cth. Equations with integer coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function cth. Quadratic equations. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function cth. Quadratic equations with rational coefficients. Distributive law
  • Hyperbolic equations reduced to rational equations. Function cth. Equations reduced to quadratic. Factorization of quadratic trinomial
  • Hyperbolic equations reduced to rational equations. Function cth. Equations reduced to quadratic. Properties of powers
  • Hyperbolic equations reduced to rational equations. Function cth. Fractional algebraic equations reduced to quadratic equations. Distributive law
  • Hyperbolic equations reduced to rational equations. Function cth. Quadratic equations containing fractions
  • Hyperbolic equations reduced to rational equations. Function cth. Equations. Grouping method
  • Hyperbolic equations reduced to rational equations. Function cth. Equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function cth. Equations. Method of substitution. Properties of fractions
  • Hyperbolic equations reduced to rational equations. Function cth. Fractional equations. Method of substitution. Formulas of short multiplication
  • Hyperbolic equations reduced to rational equations. Function cth. High-degree equations. Perfect square
  • Hyperbolic equations reduced to rational equations. Function cth. Fractional algebraic equations reduced to linear equations
  • Hyperbolic equations reduced to rational equations. Function cth. Fractional algebraic equations reduced to quadratic equations
  • Hyperbolic equations reduced to rational equations. Function cth. Elementary fractional algebraic equations
  • Hyperbolic equations reduced to rational equations. Function cth. Fractional algebraic equations reduced to quadratic equations. Method of substitution
  • Hyperbolic equations reduced to rational equations. Function cth. Fractional algebraic equations. Method of substitution

Hyperbolic equations reducible to quadratic equations

  • Hyperbolic equations reducible to quadratic equations. Fundamental identity
  • Hyperbolic equations reducible to quadratic equations. Double angle
  • Hyperbolic equations reducible to quadratic equations. Fundamental identity. Double angle

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