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.

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.

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.

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.

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.

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.