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.