Algebra I Vocabulary Flashcards

Absolute Value

• Measures the distance of a number from zero on a number line.

Additive Identity Property

• States that any number or variable added to zero remains unchanged.

Additive Inverse

• Refers to the opposite of a number, when added together they yield zero.

Algebraic Expression

• A mathematical phrase that includes numbers, variables, and operations.

Arithmetic Sequence

• A sequence where each term is generated by adding or subtracting a constant value.

Ascending Order

• Arrangement of numbers from least to greatest.

Associative Property

• Demonstrates that grouping does not affect the sum or product, expressed as (a+b) + c = a + (b+c).

Axes

• The two perpendicular lines (x-axis and y-axis) that create the coordinate plane.

Axis of Symmetry

• The vertical line that divides a parabola into two mirrored halves; determined by the formula x = -b/2a.

Binomial

• A sum or difference comprised of two monomials.

Boundary

• A line or curve that distinguishes different regions within the coordinate plane.

Box-and-Whisker Plot

• Visual representation summarizing data through median, quartiles, and extremes.

Circle Graph

• A circular diagram that illustrates data proportions relative to a whole.

Coefficient

• The numerical factor preceding a variable in a term.

Common Difference

• The consistent difference between consecutive terms in an arithmetic sequence.

Common Ratio

• The constant factor by which each term in a geometric sequence is multiplied.

Commutative Property

• Indicates that changing the order of addition or multiplication does not affect the outcome, such as a + b = b + a.

Composite Number

• A whole number greater than 1 with more than two factors.

Compound Interest

• Investment growth described by the formula A = P (1 + (r/n))^(nt), representing interest accrued on principal over time.

Conjugates

• Binomials structured as a√b + c√d and a√b - c√d, whose product yields a rational number.

Consecutive Integers

• A sequence of integers listed in counting order.

Consistent

• Refers to systems of equations with intersecting or coinciding graphs.

Constant

• A monomial representing a real number without any variable.

Coordinate Plane

• The two-dimensional space created by the intersection of the x-axis and y-axis.

Coordinate System

• A grid formed by two intersecting number lines.

Cube Root

• One of the three identical factors of a given number.

Data

• Quantitative information collected for analysis.

Degree of a Monomial

• Calculated as the total of all variable exponents in the term.

Degree of a Polynomial

• Defined by the highest degree of any individual term within the polynomial.

Dependent Variable

• A variable whose value is influenced by another variable.

Dependent

• Situations with infinitely many solutions in systems of equations.

Descending Order

• Arrangement of numbers from greatest to least.

Difference of Squares

• Formed by the subtraction of two perfect squares.

Dilation

• Transformation that enlarges or reduces a figure.

Direct Variation

• Expressed as y = kx, with a constant k not equal to zero.

Discount

• The reduction applied to the regular price of an item.

Distance Formula

• Formula to calculate distance between two points: d = √((x2 - x1)² + (y2 - y1)²).

Distributive Property

• States a(b + c) = ab + ac, allowing distribution of a term across terms within parentheses.

Domain

• The set of all possible first components in ordered pairs.

Element

• Each individual object or number within a set.

Elimination

• A method solving systems of equations by eliminating one variable through addition or subtraction.

Equation

• A mathematical statement asserting that two quantities are equal.

Evaluate

• The process of substituting variable values to determine an expression's outcome.

Excluded Values

• Values that create a denominator of zero must be excluded from the variable's domain.

Exponential Decay

• Describes situations where an initial quantity diminishes over time, represented by y = C (1 - r)^t.

Exponential Function

• Can be represented mathematically as y = a*b^x, where b > 0 and b ≠ 1.

Exponential Growth

• Depicts a situation in which an initial amount increases consistently over time: y = C (1 + r)^t.

Extraneous Solution

• An outcome derived from an equation that does not satisfy the original problem.

Factored Form

• Represents a monomial as a product of primes and variables with no variable exponent exceeding one.

Factoring by Grouping

• Utilizes the distributive property to factor polynomials with four or more terms.

Factoring

• The process of expressing a polynomial as a product of monomials or lower-degree polynomials.

Family of Graphs

• Graphs sharing at least one common characteristic.

FOIL Method

• A technique for multiplying two binomials through specific term pairing; stands for First, Outer, Inner, Last.

Formula

• An equation that describes the relationship between specific quantities.

Frequency

• The occurrences of specific data within a set.

Function Notation

• A method of naming functions represented by equations.

Function

• A relation where each input correlates to exactly one output.

Geometric Means

• Terms inserted between nonconsecutive terms in a geometric sequence to maintain proportionality.

Geometric Sequence

• A sequence where each term follows by multiplying by a constant factor post the first non-zero term.

Graph

• Visual depictions representing data relationships.

Greatest Common Factor (GCF)

• The product of shared prime factors among two or more monomials.

Half-Plane

• The section of a graph representing a half-region defined by an inequality.

Hypotenuse

• Longest side of a right triangle, opposite the right angle.

Identity

• An equation valid for all variable values.

Image

• The result of a transformation of a geometric figure.

Inconsistent

• Occurs when graphed equations do not intersect and are parallel.

Independent Variable

• A variable that influences or determines others' values.

Independent

• System of equations yielding exactly one solution.

Inductive Reasoning

• Forming conclusions based on observed patterns.

Inequality

• A comparison of two quantities using inequality symbols (<, >, ≤, ≥).

Integer

• Whole numbers that can be negative, positive, or zero, excluding fractions and decimals.

Interest

• Fees earned or paid for the utilization of capital.

Interquartile Range

• The difference between upper (UQ) and lower quartiles (LQ) of a data set.

Inverse Relation

• Ordered pairs created by switching original pair coordinates.

Inverse Variation

• Expressed as y = k/x, with k not equal to zero.

Irrational Number

• A number that cannot be precisely represented as a fraction.

Legs

• The sides that create the right angle in a right triangle.

Like Terms

• Terms sharing identical variables, with corresponding exponents remaining the same.

Line Graph

• A graph illustrating data variations over time.

Line of Best Fit

• A line on a scatter plot indicating correlation between two data sets, synonymous with a regression line.

Linear Equation

• An equation yielding a straight-line graph.

Linear Extrapolation

• Using a linear equation to predict values outside the data range.

Linear Interpolation

• Using a linear equation to estimate values within the data range.

Lower Quartile (LQ)

• Median of the lower segment of a dataset.

Mapping

• Illustration of domain elements paired with range counterparts.

Markup

• The increase in an item's price over its cost.

Matrix

• A structured arrangement of numbers presented in rows and columns.

Maximum

• The highest value on a parabola's graph.

Mean

• The average value calculated by the total of data divided by the data count.

Measures of Central Tendency

• Statistical values representing a dataset's overall characteristics.

Measures of Variation

• Figures showcasing the data's spread or distribution.

Median

• The central value of a dataset; average of the two center values if needed.

Midpoint

• The precise halfway point between two endpoints on a line segment.

Minimum

• The lowest point on a parabola’s graph.

Misleading Graphs

• Graphs with improper construction that lead to misunderstanding and incorrect interpretations.

Mixture Problem

• A scenario where multiple components are blended to form a complete entity.

Mode

• The value(s) that appear most frequently in a dataset.

Monomial

• Consists of a single number, variable, or a product comprising numbers and variables.

Multiplicative Identity Property

• Any number multiplied by one remains unchanged.

Multiplicative Inverse Property

• A relationship where the product of a number and its reciprocal equals one.