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:
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
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
Functional method.
You will learn about:
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.
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Math teacher from Russia
MIPT alumnus (Moscow institute of physics and technology)
Speaker at Umschool (one of the biggest online schools in Russia)
USE expert (unified state exam - state exam in Russia that school graduates take to enroll in universities. Consists of two parts: a test like SAT and a written part that requires a written solution that experts will evaluate)
