Algebra

Basic Concepts in Algebra

  • Understanding the concept of variables, which are symbols representing unspecified numbers or values.
  • Familiarization with algebraic expressions, which contain variables, constants, and mathematical operators.
  • Mastery of the basic operations such as addition, subtraction, multiplication, and division as applied to algebraic expressions.
  • Grasping the principle of equivalent expressions, or expressions that denote the same number for any value of the variables.

Simplifying Algebraic Expressions

  • Learning to combine like terms to simplify algebraic expressions.
  • Applying the distributive, associative, and commutative properties to simplify expressions.
  • Skillful manipulation of complex or fractions algebraic expressions.
  • Ability to correctly use brackets to simplify expressions.

Solving Basic Equations and Inequalities

  • Understanding the process of solving algebraic equations and inequalities.
  • Learning how to apply mathematical operations to both sides of an equation to maintain balance.
  • Familiarity with the concepts of zero product property and identity property.
  • Understanding absolute value concepts in inequalities.

Polynomials

  • Understanding what makes a polynomial, including terminology such as terms, degree, and coefficients.
  • Ability to classify polynomials according to their degree and the number of terms.
  • The process of adding, subtracting, multiplying, and dividing polynomials.
  • Comprehending the zero product property to solve polynomial equations.

Quadratic Equations

  • Understanding what distinguishes an equation as quadratic.
  • Mastering the quadratic formula and its application in solving quadratic equations.
  • Skill in completing the square to solve quadratic equations.
  • Learning how to factor quadratic equations to find solutions.

Algebraic Fractions

  • Understanding how to simplify complex fractions and rational expressions.
  • Proficiency in performing operations like addition, subtraction, multiplication, and division on algebraic fractions.
  • Mastery over solving equations involving algebraic fractions.

Functions and Graphs

  • Grasping the concept of a function and how it represents a mathematical relationship between variables.
  • Skill in plotting and interpreting function graphs.
  • Understanding the role of the x-intercept, y-intercept, and slope in linear functions.
  • Interpretation of quadratic function graphs, and understanding of concepts such as vertex, axis of symmetry, and discriminant.