United University

Algebra Grade 8. Square roots. Real numbers. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 25 hors
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Unlock the world of numbers with our engaging Algebra Grade 8 course! Delve into the fascinating realm of square roots and real numbers. Through interactive lessons, practice problems, and real-world applications, you'll develop a solid understanding of these fundamental mathematical concepts.

Why choose our course:

  • Interactive learning: Engage with the content through interactive quizzes and exercises.
  • Visual learning: Understand complex concepts through clear and concise visual representations.
  • Real-world applications: Connect mathematical concepts to everyday life.
  • Comprehensive coverage: Explore all key topics in square roots and real numbers.

Course Content:

  • Module 1: Square roots. Real numbers
    Lessons 13-19

Expected Outcomes by Course End:

    • Provides examples of: sets, the "element belongs to (does not belong to) a set" relation, numerical sets, rational numbers, irrational numbers, real numbers, relationships between quantities described by functions y = x^2, y =√x.
    • Recognizes functions: y = x^2, y =√x among others.
    • Explains:
      • What a set, a rational number, an irrational number, and a real number are.
      • What is meant by a subset of a given set.
      • What the union and intersection of sets are.
    • Understands:
      • The concept of an arithmetic square root.
      • The essence of the properties of an arithmetic square root.
      • Which numerical sets form the set of real numbers.
      • How the numerical sets N, Z, Q, R are interconnected.
      • The proof of the properties of an arithmetic square root.
    • Formulates:
      • The definition of the arithmetic square root of a number.
      • The properties of the arithmetic square root.
      • Distinguishes between a square root and an arithmetic square root.
      • Describes the properties of the functions y = x^2, y =√x based on their graphs.
      • Understands that the functions y = x^2, y =√x can serve as mathematical models of real-life situations.
    • Solves problems that involve:
      • Applying the concept of an arithmetic square root to calculate the values of expressions, simplify expressions, solve equations, and compare the values of expressions.
      • Finding the union and intersection of sets.
      • Transforming expressions using the extraction of a factor from under the radical, inserting a factor under the radical, reducing fractions, and rationalizing the denominator.
      • Constructing graphs of the functions y = x^2, y =√x and using them to find the square of a number and the arithmetic square root of a number.
      • Determining individual characteristics of the functions y = x^2, y =√x based on their graphs (zeros, positive values, negative values).
      • Analyzing the relationships between numerical sets and their elements.
      • Using the functions y = x^2, y =√x and their graphs to model real-world processes.

By the end of this course, you will have a strong foundation in square roots and real numbers, enabling you to confidently tackle more advanced mathematical concepts.

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