Algebra Concepts and Definitions

Algebra Concepts and Definitions

• FOIL: Method to multiply two binomials; stands for first, outer, inner, last terms.
• Point-Slope Form: Equation of a line expressed as (y - y_1 = m(x - x_1)), where (m) is the slope and ((x_1, y_1)) is a point on the line.
• Absolute Value: Indicates the distance a number is from zero on a number line, always non-negative.
• Real Numbers: The set that includes all rational (e.g., integers, fractions) and irrational numbers (e.g., square roots of non-perfect squares).
• Rational Numbers: Numbers that can be represented as (a/b), where (a) and (b) are integers, and (b \neq 0); in decimal form, they either terminate or repeat.
• Irrational Numbers: Numbers that cannot be expressed as the quotient of two integers; their decimal forms neither terminate nor repeat.
• Symbol of Conclusion: Symbol that groups numbers, variables, and operations into a single term.
• Square Roots: A number that, when multiplied by itself, yields a given product.
• Probability: A measure reflecting how likely an event occurs, typically expressed as a percentage.
• Distributive Property: A property that allows the multiplication of a term across a sum or difference within parentheses to simplify expressions.
• Variable Expressions: Algebraic expressions that include letters representing numbers.
• Translating Algebraic Expressions: The process of converting words into symbolic expressions to enhance understanding.
• Combining Like Terms: The process of adding or subtracting terms that have identical variables or exponents.
• One-Step Equations: Equations that can be solved in a single operation.
• Graphing on a Coordinate Plane: The process of determining the orientation of a line (horizontal or vertical) and plotting it accurately.
• Two-Step Equations: Equations requiring two steps to isolate the variable and find the solution.
• Decimal Equations: Algebraic equations that include decimal numbers; converting fractions to decimals for easier solving is a common strategy.
• Relations: Describes how two or more mathematical concepts interact or are connected.
• Functions: Describe the role or output of a number in an algebraic expression.
• Multi-Step Equations: Equations that require three or more operations to solve for the variable.
• Misleading Representations of Data: Data that is distorted and does not accurately reflect true facts or statistics.
• Solving Equations with Variables on Both Sides: Requires elimination methods to isolate variables and resolve the equation.
• Literal Equations: Equations where variables symbolize known quantities.
• Graphic Function: A collection of ordered pairs representing a function visually.
• Rates: Measurements that express a quantity in relation to another quantity.
• Ratios: A quantitative comparison between two amounts reflecting how many times one value contains another.
• Proportions: A statement that two ratios are equal, expressing a comparative relation to a whole.
• Arithmetic Sequences: A sequence of numbers with a consistent difference between consecutive terms.
• Intercepts: Points where a line crosses the axes, integral to understanding linear equations.
• Scientific Notation: A method to express large or small numbers by using powers of ten, simplifying mathematical computations.
• Power Property of Exponents: When multiplying like bases, sum the exponents.
• Percent Problems: Involves expressing quantities as a fraction of 100.
• Rational Expression: A fraction where both the numerator and/or denominator are polynomials.
• Percent Change: The rate of increase or decrease represented as a percentage of the original amount.
• Measure of Central Tendency: A statistic that represents the center of a data set, typically including the mean, median, and mode.
• Slope-Intercept Form: The equation of a line written as (y = mx + b), where (m) is the slope and (b) is the y-intercept.
• Polynomials: Expressions consisting of multiple terms combined using addition, subtraction, and multiplication.
• Linear Equation: An equation involving two variables that results in a straight line when plotted on a graph.
• Direct Variation: A relationship where two variables change proportionally, typically expressed as (y = kx) where (k) is a constant.