Algebra Vocabulary Flashcards

Number Types

• Rational Number: Can be expressed as a ratio of integers.
• Irrational Number: Cannot be expressed as a ratio of integers.
• Integers: Whole numbers including negatives.
• Whole Numbers: Integers without negatives.
• Natural Numbers: Positive integers including zero.

Algebra Fundamentals

• Algebraic Expression: Combines integers, variables, and algebraic operations.
• Variable: Represents a constant or changing value, typically denoted as X or Y.
• Coefficient: A number multiplied by a variable in an expression.
• Equation: States that two mathematical expressions are equal.

Solving Equations

• Example of solution: For the equation (3x - 4 = 5), the objective is finding x.
• Like Terms: Terms sharing the same variable and exponent.
• Literal Equation: A formula where a specific variable is solved.

Ratios and Inequalities

• Proportion: Two ratios are equal, e.g., (1/2 = 5/10).
• Inequality: A relation indicating one expression is not equal to another (e.g., >, <).
• Compound Inequality: Combines two inequalities using "and" or "or."

Functions and Relations

• Relation: Set of ordered pairs from two different sets.
• Function: A relation mapping each input to exactly one output.
• Domain: Set of input values (X-axis).
• Range: Set of output values (Y-axis).
• Independent Variable: Input of a function.
• Dependent Variable: Output of a function.

Linear Equations & Functions

• Linear Equation (2 Variables): Example form (2x - 3y = 8).
• Linear Function: Standard form (y = mx + b), where m is the slope.
• Standard Form: Written as (ax + by = c).

Graph Characteristics

• Slope: Indicates the steepness of a line.
• Slope Formula: Calculated as ((y1 - y2) / (x1 - x2)).
• X-intercept: Point where the line crosses the x-axis ((x, 0)).
• Y-intercept: Point where the line crosses the y-axis ((0, y)).

Special Forms and Systems

• Slope-Intercept Form: (y = mx + b).
• Point-Slope Form: ((y - y1) = m(x - x1)).
• Absolute Value Function: Involves expressions containing absolute values.
• Scatter Plot: Graph shows potential relationships between two data sets.

Systems of Equations

• Solution of a System: Any ordered pair that satisfies all equations in the system.
• Types of Systems:
  • One Solution: Exact value solution (e.g., (x = 7)).
  • No Solutions: Contradictory statements (e.g., (1 = 4)).
  • Many Solutions: Identities (e.g., (5 = 5)).

Exponential Functions

• Exponential Function: Defined by (f(x) = ab^x).
• Exponent: Indicates how many times the base is multiplied by itself.

Polynomials

• Monomial: A single term consisting of numbers and variables with whole number exponents.
• Binomial: A polynomial with two terms.
• Trinomial: A polynomial with three terms.
• Polynomial Definition: Composed of one or more terms.

Exponent Rules

• Multiply Powers: Applies when multiplying like bases, e.g., (x^2 \cdot x^2 = x^4).
• Power of Power: ((x^3)^2 = x^6).
• Power of Product: ((2ab)^2 = 4a^2b^2).
• Negative Exponent: Represents reciprocal, e.g., (2^{-1} = \frac{1}{2}).