Analytical, graphical and functional methods of solving problems with parameter

What you will learn

### Challenge your mind with some of the most tricky and neat problems of basic mathematics

Description

This course will challenge your knowledge in high-school mathematics. You will learn new ways of solving problems with parameter and comparing ways of solving these problems and choosing the best one.

This course is first of all made for school and university teachers and technical university students, but anyone who wants to put their knowledge of basic mathematics in systematic order can take it.
The course covers three main ways of solving problems with parameter:

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1. Analytical method.You will learn about:
• linear equations and inequalities with parameter
• systems of linear equations and inequalities with parameter
• rational equations and inequalities with parameter
• quadratic equations and inequalities with parameter
• theorems about positions of the roots of quadratic equations and inequalities with parameter
• problems reducible to quadratic equations and inequalities with parameter
2. Graphical method.You will learn about:
• graphs of linear, quadratic, rational, modular, irrational, exponential, logarithmic and trigonometric functions
• transformations of graphs of functions
• graphs of equations and inequalities
• using graphs as a visualisation tool to solve problems with parameter
3. Functional method.

• monotonous functions
• limited functions
• even\odd functions
• using properties of functions to solve problems with parameter

In conclusion you will face some problems solvable in every mentioned way and learn to compare different ideas and choose the one that fits the best for every unique situation.

English
language

Content

### Introduction

Introduction
What is a problem with parameters?
What will you learn?

### Analytical solutions

Linear equations with parameters
Systems of linear equations
Linear inequalities