Algebra I Vocabulary Flashcards

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Questions and Answers

What is the definition of absolute value?

The sum of the exponents of all its variables

The distance a number is from zero on a number line (correct)

The longest side of a right triangle

The opposite of a number

What does the additive identity property state?

Any number subtracted from itself is zero

The sum of any number and one is that number plus one

Any number or variable added to zero is that number or variable (correct)

The sum of two positive numbers is positive

What is the additive inverse?

The opposite of a number

What is an algebraic expression?

A math sentence that contains numbers, variables, and operations Signup and view all the answers

Define an arithmetic sequence.

A numerical pattern that increases or decreases at a constant rate or value Signup and view all the answers

What does ascending order mean?

Arranged in order from least to greatest Signup and view all the answers

Which property states that changing the grouping does not change the sum or product?

Associative property Signup and view all the answers

What are axes in a coordinate plane?

Two perpendicular lines that form the coordinate plane Signup and view all the answers

What is the axis of symmetry?

The vertical line containing the vertex of a parabola; the equation x = -b/2a Signup and view all the answers

Define a binomial.

The sum or difference of two monomials Signup and view all the answers

What is a boundary in math?

A line or curve that separates the coordinate plane into regions Signup and view all the answers

What does a box-and-whisker plot summarize?

Data using median, upper quartile, lower quartile, and extreme values Signup and view all the answers

Define a circle graph.

A graph used to show data as parts of a whole Signup and view all the answers

What is a coefficient in algebra?

The numerical factor in a term; the number in front of the variable Signup and view all the answers

What is a common difference?

The difference between the terms in an arithmetic sequence Signup and view all the answers

Define common ratio.

The number by which each term in a geometric sequence is multiplied Signup and view all the answers

What does the commutative property state?

Changing the order does not change the sum or product Signup and view all the answers

What is a composite number?

A positive whole number greater than 1 that has more than two factors Signup and view all the answers

What is compound interest?

An equation that is a special application of exponential growth associated with investments; A = P (1 + (r/n))^(nt) Signup and view all the answers

Define conjugates in algebra.

Binomials of the form a√b + c√d and a√b - c√d whose product is always a rational number with no radicals Signup and view all the answers

What are consecutive integers?

Integers in counting order Signup and view all the answers

What does consistent mean in systems of equations?

If graphs intersect or coincide Signup and view all the answers

What is meant by a constant?

Monomial that is a real number; the number without a variable Signup and view all the answers

What is the coordinate plane?

The plane containing the x-axis and the y-axis Signup and view all the answers

Define a coordinate system.

A grid formed by the intersection of two number lines Signup and view all the answers

What is the cube root?

One of the three identical factors of a number Signup and view all the answers

What does data refer to in statistics?

Numerical information gathered for statistical purposes Signup and view all the answers

What is the degree of a monomial?

The sum of the exponents of all its variables Signup and view all the answers

What is the degree of a polynomial?

The greatest degree of any term in the polynomial Signup and view all the answers

What is a dependent variable?

The variable that depends on the independent variable Signup and view all the answers

Define dependent in terms of systems of equations.

Infinitely many solutions in a system of equations Signup and view all the answers

What does descending order mean?

Arranged in order from greatest to least Signup and view all the answers

Define the difference of squares.

Two perfect squares separated by a subtraction sign Signup and view all the answers

What is dilation in geometry?

A figure is enlarged or reduced Signup and view all the answers

What is direct variation?

An equation of the form y = kx, where k is not equal to zero Signup and view all the answers

What does a discount refer to?

The amount by which the regular price is reduced Signup and view all the answers

What is the distance formula?

The distance, d, between any two points with coordinates (x1, y1) and (x2, y2) is given by the formula d = √((x2 - x1)² + (y2 - y1)²) Signup and view all the answers

What is the distributive property?

a(b + c) = ab + ac; a number outside the parentheses can be multiplied to each term within the parentheses Signup and view all the answers

What does domain refer to in functions?

The set of first numbers in an ordered pair Signup and view all the answers

What is an element in set theory?

Each object or number in a set Signup and view all the answers

Define elimination in the context of solving equations.

A method of solving systems of equations by adding or subtracting two equations in order to eliminate one variable Signup and view all the answers

What is an equation?

A math sentence that states two quantities are equal using an equal sign Signup and view all the answers

What does evaluate mean in mathematics?

To find the value of an expression by replacing the variable with a number Signup and view all the answers

What are excluded values?

Any values of a variable that result in a denominator of 0, which must be excluded from the domain of that variable Signup and view all the answers

Define exponential decay.

An equation in which the initial amount C decreases by the same percent over a period of time; y = C (1 - r)^t Signup and view all the answers

What is an exponential function?

A function that can be described by an equation of the form y = a*b^x, where b > 0 and b ≠ 1 Signup and view all the answers

What does exponential growth refer to?

An equation in which the initial amount C increases by the same percent over a period of time; y = C (1 + r)^t Signup and view all the answers

What is an extraneous solution?

A result that is not a solution to the original equation Signup and view all the answers

Define factored form.

A monomial expressed as a product of prime numbers and variables, in which no variable has an exponent greater than 1 Signup and view all the answers

What is factoring by grouping?

The use of the distributive property to factor polynomials with four or more terms Signup and view all the answers

What does factoring mean in algebra?

To express a polynomial as the product of monomials and polynomials Signup and view all the answers

What is a family of graphs?

Graphs and equations of graphs that have at least one characteristic in common Signup and view all the answers

What does the FOIL method stand for?

First, Outer, Inner, and Last terms Signup and view all the answers

What is a formula in mathematics?

An equation that states a rule for the relationship between certain quantities Signup and view all the answers

What does frequency mean in statistics?

How often a piece of data occurs Signup and view all the answers

Define function notation.

A way to name a function that is defined by an equation Signup and view all the answers

What is a function?

A relationship between input and output values; there is exactly one input for each output Signup and view all the answers

What are geometric means?

Missing terms between two nonconsecutive terms in a geometric sequence Signup and view all the answers

Define a geometric sequence.

A sequence in which each term after the nonzero first term is found by multiplying the previous term by a constant Signup and view all the answers

What is a graph in mathematics?

Visual representations of data Signup and view all the answers

What is the greatest common factor (GCF)?

The product of prime factors common to 2 or more monomials Signup and view all the answers

What is a half-plane in geometry?

The region of the graph of an inequality on one side of a boundary Signup and view all the answers

What is a hypotenuse?

The longest side of a right triangle which is opposite the right angle Signup and view all the answers

What is identity in mathematics?

An equation that is true for every value of the variable Signup and view all the answers

Define image in transformation.

The position of the figure after the transformation Signup and view all the answers

What does inconsistent mean in system solving?

If graphs are parallel Signup and view all the answers

What is an independent variable?

A variable whose value determines the value of another variable Signup and view all the answers

What is an independent system of equations?

Exactly one solution in a system of equations Signup and view all the answers

Define inductive reasoning.

A conclusion based on a pattern of examples Signup and view all the answers

What is an inequality?

An open sentence that compares two quantities using less than, greater than, less than or equal to, greater than or equal to Signup and view all the answers

Define an integer.

A positive or negative number, including zero, that does not contain a fraction or decimal Signup and view all the answers

What is interest in finance?

The amount of money paid or earned for the use of money Signup and view all the answers

What is interquartile range?

The difference between the upper quartile and the lower quartile (UQ - LQ) Signup and view all the answers

What is the inverse relation?

A set of ordered pairs obtained by switching the coordinates in a relation Signup and view all the answers

Define inverse variation.

An equation of the form y = k/x, where k is not equal to zero Signup and view all the answers

What is an irrational number?

A number that cannot be expressed as a fraction Signup and view all the answers

What are legs in a right triangle?

The sides that form the right angle Signup and view all the answers

What are like terms in algebra?

Terms that contain the same variables, with corresponding variables having the same exponents Signup and view all the answers

What is a line graph?

A graph used to show change in data over time Signup and view all the answers

What is a line of best fit?

A line drawn on a scatter plot to show the correlation between two sets of values; also known as a regression line Signup and view all the answers

What is a linear equation?

An equation whose graph is a straight line Signup and view all the answers

What is linear extrapolation?

The use of a linear equation to predict values that are outside the range of data Signup and view all the answers

What is linear interpolation?

The use of a linear equation to predict values that are inside of the range of data Signup and view all the answers

What is the lower quartile (LQ)?

The median of the lower half of the set of data Signup and view all the answers

What is mapping in relation to functions?

Illustration of how each element of the domain is paired with an element in the range Signup and view all the answers

What is markup?

The amount the price of an item is increased above the price the store is paid for the item Signup and view all the answers

What is a matrix?

A rectangular arrangement of numbers in rows and columns Signup and view all the answers

What is maximum in graphing?

The highest point on the graph of a parabola Signup and view all the answers

Define mean in mathematics.

The sum of all the data divided by the number of pieces of data; average Signup and view all the answers

What are measures of central tendency?

Numbers or pieces of data that can represent the whole set of data Signup and view all the answers

Define measures of variation.

Numbers used to describe the distribution of data Signup and view all the answers

What is the median?

The middle of the data, or the mean of the two middle numbers Signup and view all the answers

What is a midpoint?

The point that lies exactly halfway between the two endpoints of a line segment Signup and view all the answers

Define minimum in graphing.

The lowest point on the graph of a parabola Signup and view all the answers

What are misleading graphs?

Graphs that are constructed incorrectly to cause confusion and can lead to false assumptions Signup and view all the answers

What is a mixture problem in mathematics?

Problem in which two or more parts are combined into a whole Signup and view all the answers

What does mode refer to in statistics?

The number or numbers that occur the most often Signup and view all the answers

Define a monomial.

A number, a variable, or a product of numbers and/or variables Signup and view all the answers

What is the multiplicative identity property?

Any number or variable multiplied by one is that number or variable Signup and view all the answers

What is the multiplicative inverse property?

a/b * b/a = 1; the product of a number and its reciprocal always equals one Signup and view all the answers

Study Notes

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.

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