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# Algebra I Vocabulary Flashcards

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@SlickBinary8749

### 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?

<p>A math sentence that contains numbers, variables, and operations</p> Signup and view all the answers

### Define an arithmetic sequence.

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

### What does ascending order mean?

<p>Arranged in order from least to greatest</p> Signup and view all the answers

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

<p>Associative property</p> Signup and view all the answers

### What are axes in a coordinate plane?

<p>Two perpendicular lines that form the coordinate plane</p> Signup and view all the answers

### What is the axis of symmetry?

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

### Define a binomial.

<p>The sum or difference of two monomials</p> Signup and view all the answers

### What is a boundary in math?

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

### What does a box-and-whisker plot summarize?

<p>Data using median, upper quartile, lower quartile, and extreme values</p> Signup and view all the answers

### Define a circle graph.

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

### What is a coefficient in algebra?

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

### What is a common difference?

<p>The difference between the terms in an arithmetic sequence</p> Signup and view all the answers

### Define common ratio.

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

### What does the commutative property state?

<p>Changing the order does not change the sum or product</p> Signup and view all the answers

### What is a composite number?

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

### What is compound interest?

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

### Define conjugates in algebra.

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

### What are consecutive integers?

<p>Integers in counting order</p> Signup and view all the answers

### What does consistent mean in systems of equations?

<p>If graphs intersect or coincide</p> Signup and view all the answers

### What is meant by a constant?

<p>Monomial that is a real number; the number without a variable</p> Signup and view all the answers

### What is the coordinate plane?

<p>The plane containing the x-axis and the y-axis</p> Signup and view all the answers

### Define a coordinate system.

<p>A grid formed by the intersection of two number lines</p> Signup and view all the answers

### What is the cube root?

<p>One of the three identical factors of a number</p> Signup and view all the answers

### What does data refer to in statistics?

<p>Numerical information gathered for statistical purposes</p> Signup and view all the answers

### What is the degree of a monomial?

<p>The sum of the exponents of all its variables</p> Signup and view all the answers

### What is the degree of a polynomial?

<p>The greatest degree of any term in the polynomial</p> Signup and view all the answers

### What is a dependent variable?

<p>The variable that depends on the independent variable</p> Signup and view all the answers

### Define dependent in terms of systems of equations.

<p>Infinitely many solutions in a system of equations</p> Signup and view all the answers

### What does descending order mean?

<p>Arranged in order from greatest to least</p> Signup and view all the answers

### Define the difference of squares.

<p>Two perfect squares separated by a subtraction sign</p> Signup and view all the answers

### What is dilation in geometry?

<p>A figure is enlarged or reduced</p> Signup and view all the answers

### What is direct variation?

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

### What does a discount refer to?

<p>The amount by which the regular price is reduced</p> Signup and view all the answers

### What is the distance formula?

<p>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)</p> Signup and view all the answers

### What is the distributive property?

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

### What does domain refer to in functions?

<p>The set of first numbers in an ordered pair</p> Signup and view all the answers

### What is an element in set theory?

<p>Each object or number in a set</p> Signup and view all the answers

### Define elimination in the context of solving equations.

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

### What is an equation?

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

### What does evaluate mean in mathematics?

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

### What are excluded values?

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

### Define exponential decay.

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

### What is an exponential function?

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

### What does exponential growth refer to?

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

### What is an extraneous solution?

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

### Define factored form.

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

### What is factoring by grouping?

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

### What does factoring mean in algebra?

<p>To express a polynomial as the product of monomials and polynomials</p> Signup and view all the answers

### What is a family of graphs?

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

### What does the FOIL method stand for?

<p>First, Outer, Inner, and Last terms</p> Signup and view all the answers

### What is a formula in mathematics?

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

### What does frequency mean in statistics?

<p>How often a piece of data occurs</p> Signup and view all the answers

### Define function notation.

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

### What is a function?

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

### What are geometric means?

<p>Missing terms between two nonconsecutive terms in a geometric sequence</p> Signup and view all the answers

### Define a geometric sequence.

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

### What is a graph in mathematics?

<p>Visual representations of data</p> Signup and view all the answers

### What is the greatest common factor (GCF)?

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

### What is a half-plane in geometry?

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

### What is a hypotenuse?

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

### What is identity in mathematics?

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

### Define image in transformation.

<p>The position of the figure after the transformation</p> Signup and view all the answers

### What does inconsistent mean in system solving?

<p>If graphs are parallel</p> Signup and view all the answers

### What is an independent variable?

<p>A variable whose value determines the value of another variable</p> Signup and view all the answers

### What is an independent system of equations?

<p>Exactly one solution in a system of equations</p> Signup and view all the answers

### Define inductive reasoning.

<p>A conclusion based on a pattern of examples</p> Signup and view all the answers

### What is an inequality?

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

### Define an integer.

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

### What is interest in finance?

<p>The amount of money paid or earned for the use of money</p> Signup and view all the answers

### What is interquartile range?

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

### What is the inverse relation?

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

### Define inverse variation.

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

### What is an irrational number?

<p>A number that cannot be expressed as a fraction</p> Signup and view all the answers

### What are legs in a right triangle?

<p>The sides that form the right angle</p> Signup and view all the answers

### What are like terms in algebra?

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

### What is a line graph?

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

### What is a line of best fit?

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

### What is a linear equation?

<p>An equation whose graph is a straight line</p> Signup and view all the answers

### What is linear extrapolation?

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

### What is linear interpolation?

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

### What is the lower quartile (LQ)?

<p>The median of the lower half of the set of data</p> Signup and view all the answers

### What is mapping in relation to functions?

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

### What is markup?

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

### What is a matrix?

<p>A rectangular arrangement of numbers in rows and columns</p> Signup and view all the answers

### What is maximum in graphing?

<p>The highest point on the graph of a parabola</p> Signup and view all the answers

### Define mean in mathematics.

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

### What are measures of central tendency?

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

### Define measures of variation.

<p>Numbers used to describe the distribution of data</p> Signup and view all the answers

### What is the median?

<p>The middle of the data, or the mean of the two middle numbers</p> Signup and view all the answers

### What is a midpoint?

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

### Define minimum in graphing.

<p>The lowest point on the graph of a parabola</p> Signup and view all the answers

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

### What is a mixture problem in mathematics?

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

### What does mode refer to in statistics?

<p>The number or numbers that occur the most often</p> Signup and view all the answers

### Define a monomial.

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

### What is the multiplicative identity property?

<p>Any number or variable multiplied by one is that number or variable</p> Signup and view all the answers

### What is the multiplicative inverse property?

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

## Study Notes

### Absolute Value

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

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

• 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.

• 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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## Description

Explore key terms in Algebra I with these flashcards. Each card contains a word along with its definition to help you understand fundamental concepts in algebra. Perfect for students looking to reinforce their vocabulary skills.

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