Algebra Basics
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Questions and Answers

Trong đại số, khái niệm gì dùng để biểu thị các giá trị hoặc lượng chưa biết?

  • Constants
  • Variables (correct)
  • Algebraic expressions
  • Inequalities

    • Cách nào sau đây được sử dụng để đơn giản hóa các biểu thức đại số?

  • Multiplication
  • Graphing
  • Division
  • Addition and Subtraction (correct)

    • Loại phương trình nào sau đây có bậc cao nhất của biến là 1?

  • Linear Equations (correct)
  • Inequalities
  • Quadratic Equations
  • Systems of Equations

    • Cách nào sau đây được sử dụng để giải các hệ phương trình?

    <p>Elimination</p> Signup and view all the answers

    Phương trình nào sau đây có bậc cao nhất của biến là 2?

    <p>Quadratic Equations</p> Signup and view all the answers

    Biểu đồ là gì trong đại số?

    <p>Một đồ thị của phương trình trên mặt phẳng tọa độ</p> Signup and view all the answers

    Study Notes

    Algebra

    Definition and Scope

    • Algebra is a branch of mathematics that deals with the study of variables and their relationships.
    • It involves the use of symbols, equations, and formulas to solve problems and model real-world situations.

    Key Concepts

    • Variables: Letters or symbols that represent unknown values or quantities.
    • Constants: Numbers that do not change value.
    • Algebraic expressions: Combinations of variables, constants, and mathematical operations.
    • Equations: Statements that express the equality of two algebraic expressions.
    • Inequalities: Statements that express the relationship between two algebraic expressions using greater than, less than, or equal to.

    Operations

    • Addition and Subtraction: Combining like terms to simplify expressions.
    • Multiplication: Distributing numbers or variables over expressions.
    • Division: Reversing the multiplication process.

    Solving Equations and Inequalities

    • Linear Equations: Equations in which the highest power of the variable is 1.
      • Example: 2x + 3 = 5
      • Solution: x = 1
    • Quadratic Equations: Equations in which the highest power of the variable is 2.
      • Example: x^2 + 4x + 4 = 0
      • Solution: x = -2
    • Systems of Equations: Sets of two or more equations that must be solved simultaneously.
      • Example: 2x + 3y = 7, x - 2y = -3
      • Solution: x = 2, y = 1

    Graphing and Functions

    • Graphing: Visual representation of equations on a coordinate plane.
    • Functions: Relations between variables that assign a unique output to each input.
      • Example: f(x) = 2x + 1
      • Domain: All real numbers
      • Range: All real numbers

    Quadratic Formula and Functions

    • Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a
      • Used to solve quadratic equations of the form ax^2 + bx + c = 0
    • Quadratic Functions: Functions of the form f(x) = ax^2 + bx + c
      • Can be graphed as parabolas on a coordinate plane

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    Description

    Learn the fundamentals of algebra, including variables, equations, and functions. Practice solving linear and quadratic equations, graphing, and understanding quadratic formulas.

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