ABEKA Algebra 2 Flashcards

Algebra Concepts

• Variables: Represent numbers that change, commonly denoted as x, y, or other letters.
• Constants: Fixed values, not associated with variables.
• Coefficients: Numbers directly adjacent to variables, indicating multiplication.

Operations and Functions

• Distribution: A process where a number outside parentheses multiplies all terms within the parentheses.
• Combining Like Terms: The method of simplifying algebraic expressions by grouping similar terms.
• Independent Variable (X): Represents inputs in equations; can vary independently.
• Dependent Variable (Y): Represents outputs in equations; changes in response to the independent variable.

Inequalities and Relations

• Inequality: A statement involving less than, greater than, or equivalent expressions.
• Greater Than and Less Than: Represented with open circles on a number line.
• Greater Than or Equal To & Less Than or Equal To: Indicated with closed circles, showing inclusive limits.

Graphing and Functions

• Relation: Composed of ordered pairs; includes an independent and a dependent variable.
• Function: A special relation where each X value corresponds to only one Y value, tested using the vertical line test.
• Ordered Pair: Coordinates used to designate points in a coordinate plane.

Types of Functions

• Linear Function: Graph results in a straight line, expressed as Y = MX + B.
• Quadratic Function: Formed as y = x², typically creating a parabolic shape.
• Solutions to a Quadratic: Referred to as roots, x-intercepts, or zeros.

Systems and Equations

• System of Linear Equations: Involves two or more linear functions that may have zero, one, or infinitely many solutions.

Special Terms in Algebra

• Radical: Equivalent to taking the square root of a number.
• Axis of Symmetry: A line that divides a shape or graph into two mirrored halves.
• Vertex: The point at which a quadratic function achieves its maximum or minimum value.

Advanced Concepts

• Binomial Theorem: Provides the coefficients of terms in polynomial expansions.
• Quadratic Formula: Used for solving quadratic equations, represented as b ± √(b² - 4ac) / 2a.
• FOIL Method: A technique for multiplying two binomials, standing for First, Outer, Inner, Last.
• Difference of Squares: An algebraic identity defined as b² = (a - b)(a + b).

Trigonometric Functions

• Imaginary Number: Indicated by a cursive i, used within square root expressions.
• Tangent: Defined as opposite side over adjacent side in a right triangle.
• Cosine: Ratio of the adjacent side over the hypotenuse.
• Sine: Ratio of the opposite side over the hypotenuse.

Test your knowledge of key algebraic concepts with these flashcards designed for ABEKA Algebra 2. Each card contains a definition and example of important terms such as variables, constants, coefficients, and distribution. Perfect for reinforcing your understanding before exams.