United University

Algebra Grade 10. Functions, polynomials, equations and inequalities. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 40 hours

Embark on an exciting journey through algebra! Our "Algebra Grade 10. Functions, polynomials, equations and inequalities" course offers a dynamic learning experience that brings the principles of advanced algebra to life. Through interactive lessons, quizzes, and engaging activities, students will gain a deep understanding of sets, functions, polynomials, equations, and inequalities.

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Embark on an exciting journey through algebra! Our "Algebra Grade 10. Functions, polynomials, equations and inequalities" course offers a dynamic learning experience that brings the principles of advanced algebra to life. Through interactive lessons, quizzes, and engaging activities, students will gain a deep understanding of sets, functions, polynomials, equations, and inequalities.

Why choose our course:

  • Interactive tests: Test your knowledge and reinforce learning with engaging and challenging quizzes.
  • Expertly crafted content: Developed by experienced educators to ensure high-quality and effective learning.
  • Focus on mathematical analysis: Encourage students to analyze functions, apply mathematical properties, and develop logical reasoning.

Course Modules

Module 1: Functions, polynomials, equations and inequalities

  • Introduction
  • §1. Sets. Operations on Sets (Parts 1, 2, 3)
  • §2. Numerical Functions. Domain and Range. Ways of Defining Functions (Parts 1, 2)
  • §3. Properties of Functions (Parts 1, 2)
  • §4. Properties and Graphs of Basic Types of Functions. Constructing Function Graphs Using Geometric Transformations. Inverse Function (Parts 1, 2)
  • §5. Equations (Parts 1, 2)
  • §6. Inequalities (Parts 1, 2)
  • §7. Division of Polynomials. Bezout's Theorem and its Corollaries (Parts 1, 2)
  • §8. Method of Mathematical Induction (Parts 1, 2)
  • Ukrainians in the World

Expected Learning Outcomes

  • Illustrates the union and intersection of sets on diagrams or a number line.
  • Formulates the definitions of a subset, union, and intersection of sets.
  • Finds the union and intersection of numerical sets.
  • Uses different ways of defining functions.
  • Formulates the definitions of a numerical function, increasing and decreasing functions, and even and odd functions.
  • Finds the domain and range of functions, function values for given arguments, and argument values for which the function takes a given value.
  • Establishes function properties from a graph.
  • Performs and explains transformations of function graphs.
  • Investigates functions and uses the results to construct graphs.
  • Performs polynomial division with a remainder and uses Bezout's theorem to solve equations and inequalities.
  • Solves simple equations with parameters and inequalities using the interval method.
  • Uses the method of mathematical induction to prove statements.

By the end of this course, students will have a thorough understanding of advanced algebraic concepts, their applications, and methods for solving various types of problems.

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