United University

Algebra Grade 11. Exponential and logarithmic functions. Collection 1.

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 16 hours

Algebra and the Elements of Analysis for Grade 11
The topic “Exponential and Logarithmic Functions” covers key concepts, including transforming expressions and solving related equations and inequalities. The material is structured with theory, examples, exercises of varying difficulty, and interactive tests with automated assessment. Life Mathematics sections show practical applications, while Challenging Tasks develop creative, non-standard thinking.

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Embark on an in-depth journey through advanced algebra! Our "Algebra Grade 11. Exponential and logarithmic functions. Collection 1" course provides students with comprehensive knowledge in algebra and introductory analysis, covering functions, equations, inequalities, integral calculus, combinatorics, and probability theory. The course develops logical and abstract thinking, practical application of mathematical knowledge, and prepares students for further studies and successful exam performance.

Why choose our course:

  • Interactive tests and exercises: Strengthen your understanding with homework assignments, review tasks, and self-check exercises.
  • Expertly crafted content: Aligned with the State Standard of Basic Secondary Education and model educational programs for Grade 11.
  • Focus on logical thinking and analysis: Develop the ability to analyze functions, solve complex equations and inequalities, and apply mathematical concepts in practice.

Course Modules

Module 1: Exponential and logarithmic functions

  • §1. Real exponents. Exponential function, its properties, and graph
  • §2. Exponential equations
  • §3. Exponential inequalities
  • Homework assignment №1
  • Knowledge check tasks for §§1–3
  • §4. Concept of logarithm. Properties of logarithms
  • §5. Logarithmic function, its properties, and graph
  • §6. Logarithmic equations
  • Homework assignment №2
  • Knowledge check tasks for §§4–6
  • §7. Logarithmic inequalities
  • §8. Systems of exponential and logarithmic equations and inequalities
  • §9. Exponential and logarithmic equations and inequalities with parameters
  • §10. Derivatives of exponential, logarithmic, and power functions
  • Homework assignment №3
  • Knowledge check tasks for §10
  • Revision exercises for Module 1
  • Ukrainians in the World

Expected Learning Outcomes

  • Understand and apply properties of exponential and logarithmic functions.
  • Solve exponential and logarithmic equations and inequalities, including systems and equations with parameters.
  • Analyze and construct graphs of exponential, logarithmic, and power functions.
  • Compute derivatives and apply them in problem-solving.
  • Develop logical and abstract thinking, spatial reasoning, and analytical skills.
  • Successfully complete practice assignments and tests aligned with state standards.

By the end of this course, students will have a solid foundation in advanced algebra, enhanced analytical skills, and the ability to solve complex mathematical problems, preparing them for further studies and exam success.

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