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Questions and Answers

What does the addition property of equality state?

When equal values are added to both sides of a true equation, the equation continues to be true.

What is an arithmetic sequence?

A number sequence in which the difference between two consecutive terms is a constant.

What is the axis of symmetry in a parabola?

An imaginary vertical line that passes through the vertex of a parabola.

What is the base in an exponential expression?

The number being raised to a power. Signup and view all the answers

Define binomial.

A polynomial with only two terms. Signup and view all the answers

What is a box plot?

A graphical way to summarize data. Signup and view all the answers

What is the elimination method?

A way of solving a system of linear equations by eliminating one of the variables. Signup and view all the answers

What is an equation?

Two mathematical expressions with an equals sign between them. Signup and view all the answers

Define exponential equation.

An equation in which the variable is an exponent. Signup and view all the answers

What is an exponential function?

A function in which the variable is an exponent. Signup and view all the answers

What defines an expression?

Numbers and variables that are combined with the operations from math. Signup and view all the answers

What does factoring a polynomial involve?

Finding two polynomials that can be multiplied to become another polynomial. Signup and view all the answers

Define factors.

The polynomials that evenly divide into a polynomial. Signup and view all the answers

What is the first quartile?

The number in a data set that is bigger than just 25% of the numbers in the set. Signup and view all the answers

What is FOIL?

A method for multiplying two binomials of the form (a + b)(c + d). Signup and view all the answers

Define a function.

Something that takes numbers as inputs and outputs numbers. Signup and view all the answers

What is a geometric sequence?

A number sequence in which the ratio between two consecutive terms is a constant. Signup and view all the answers

What is a graph in mathematics?

A visual way to describe the solution set to an equation. Signup and view all the answers

What is the greatest common factor?

The largest expression that divides evenly into two or more monomials. Signup and view all the answers

What does growth rate refer to in an exponential expression?

In an expression of the form a × b^x, the b is the growth rate. Signup and view all the answers

Define a histogram.

A way of representing data with repeated values. Signup and view all the answers

What does increasing mean in terms of functions?

A function is increasing on an interval if making the input value larger also makes the y output larger. Signup and view all the answers

What is an inequality?

Like an equation, but there are <, ≤, >, or ≥ signs between the two expressions. Signup and view all the answers

What is interquartile range?

The difference between the third quartile and the first quartile of a data set. Signup and view all the answers

What does isolating a variable mean?

A variable is isolated when it is by itself on one side of an equation. Signup and view all the answers

Define like terms.

Terms that have the same variable part. Signup and view all the answers

What is the line of best fit?

A line that comes closest to the set of points in a scatter plot. Signup and view all the answers

What is a linear equation?

An equation in which the greatest exponent is 1. Signup and view all the answers

What is a linear function?

A function in which the greatest exponent is 1. Signup and view all the answers

What does mean refer to in data?

The average of the numbers in a data set. Signup and view all the answers

Define median.

The middle number in a data set after it has been arranged from least to greatest. Signup and view all the answers

What is mode in statistics?

The most frequent number in a data set. Signup and view all the answers

Define monomial.

A mathematical expression that has a coefficient and/or a variable part. Signup and view all the answers

What does the multiplication property of equality state?

When equal values are multiplied by both sides of a true equation, the equation continues to be true. Signup and view all the answers

Define an ordered pair.

Two numbers written in the form (x,y). Signup and view all the answers

What is a parabola?

A 'U'-shaped curve that is the graph of the solution set of a quadratic equation. Signup and view all the answers

Define perfect square trinomial.

A quadratic trinomial of the form x^2 + bx + (b/2)^2. Signup and view all the answers

What is a piecewise function?

A function that has multiple rules for determining output values based on input values. Signup and view all the answers

Define polynomial.

The sum of one or more monomials. Signup and view all the answers

What is a quadratic equation?

An equation in which the highest power on a variable is 2. Signup and view all the answers

What is the quadratic formula?

The formula x = (-b +/- square root(b^2 - 4ac)) / 2a. Signup and view all the answers

Define quadratic function.

A function in which the highest power on a variable is 2. Signup and view all the answers

What is a quadratic polynomial?

A polynomial in which the highest power on a variable is 2. Signup and view all the answers

What is the range of a function?

The set of values that can be output from a function. Signup and view all the answers

Define recursively defined sequence.

A sequence in which the first term or terms are given and a formula is used for calculating the next term based on previous terms. Signup and view all the answers

What does regression mean in data analysis?

Finding a curve that best fits a scatter plot. Signup and view all the answers

What is a residual plot?

A set of points that represents how far points on a graph deviate from a curve of best fit. Signup and view all the answers

What are roots in an equation?

The values that solve that equation. Signup and view all the answers

Define sequence.

A list of numbers that usually have some kind of pattern. Signup and view all the answers

What is a slope?

A measure of a line's steepness. Signup and view all the answers

What is slope-intercept form?

An equation in the form y = mx + b. Signup and view all the answers

Define solution set.

The set of numbers or ordered pairs that satisfy an equation. Signup and view all the answers

What is the substitution method?

A method for solving a system of equations where one variable is isolated and substituted into the other equation. Signup and view all the answers

What does the subtraction property of equality state?

When equal values are subtracted from both sides of a true equation, the equation continues to be true. Signup and view all the answers

What is a system of equations?

Two or more equations with two or more unknowns to solve for. Signup and view all the answers

What is the third quartile?

The number in a data set that is greater than just 75% of the numbers in the set. Signup and view all the answers

Define translation in graphing.

A shift of the points on a graph in the same direction by the same amount. Signup and view all the answers

What is a trinomial?

A polynomial with three terms. Signup and view all the answers

Define a variable in mathematics.

A letter, often x, y, or z, that represents a value. Signup and view all the answers

What is a vertex in terms of a parabola?

The turning point of a parabola. Signup and view all the answers

What is the vertical line test?

A test to see if a graph can represent a function. Signup and view all the answers

Define x-intercept.

The location where a curve crosses the x-axis. Signup and view all the answers

What is the y-intercept?

The location where a curve crosses the y-axis. Signup and view all the answers

What are zeros of a function?

The numbers that can be input into the function so that 0 is output. Signup and view all the answers

What is a closed form defined sequence?

A formula that defines the nth term of a sequence. Signup and view all the answers

Define coefficient.

A number multiplied by a variable expression. Signup and view all the answers

What is a common difference in arithmetic sequence?

The difference between consecutive terms. Signup and view all the answers

What is a common ratio in a geometric sequence?

The ratio between consecutive terms. Signup and view all the answers

What does the commutative property of addition or multiplication state?

The order in which two numbers are added or multiplied does not matter. Signup and view all the answers

What does completing the square involve?

Turning one side of a quadratic equation into a perfect square trinomial. Signup and view all the answers

Define a constant in mathematics.

A number that does not have a variable part. Signup and view all the answers

What is the correlation coefficient?

A number represented by r that measures how well a curve fits the points in a scatter plot. Signup and view all the answers

What is the degree of a polynomial?

The exponent on the highest power of a polynomial. Signup and view all the answers

What is the difference of perfect squares?

Factoring a quadratic binomial in the form x^2 - a^2 into (x - a)(x + a). Signup and view all the answers

What does the distributive property of multiplication over addition state?

Expressions of the form a(b + c) can become a × b + a × c. Signup and view all the answers

What does the division property of equality state?

When both sides of a true equation are divided by the same non-zero number, the equation continues to be true. Signup and view all the answers

Define domain in relation to functions.

The numbers that can be input into a function. Signup and view all the answers

What is a dot plot?

A graphical way of representing a data set where each piece of data is represented with a dot. Signup and view all the answers

Study Notes

Algebra 1 Glossary of Terms

Addition Property of Equality: If equal values are added to both sides of an equation, the equation remains true.
Arithmetic Sequence: A sequence where the difference between consecutive terms is constant.
Axis of Symmetry: An imaginary vertical line that divides a parabola into two mirror-image halves.
Base: The number being raised to a power in an exponential expression.
Binomial: A polynomial comprised of exactly two terms.
Box Plot: A graphical summary that displays the distribution of data based on a five-number summary.
Elimination Method: A technique for solving systems of linear equations by eliminating one variable.
Equation: A mathematical statement asserting the equality of two expressions.
Exponential Equation: An equation where the variable appears as an exponent.
Exponential Function: A function characterized by an exponent variable.
Expression: A combination of numbers and variables linked by mathematical operations.
Factoring a Polynomial: The process of decomposing a polynomial into the product of two polynomials.
Factors: The polynomials that divide into another polynomial without leaving a remainder.
First Quartile: The value in a dataset that separates the lowest 25% of values.
FOIL: A method for multiplying two binomials, following the order: First, Outer, Inner, Last.
Function: A relation that assigns a unique output for each input.
Geometric Sequence: A sequence in which each term is derived from the previous term by multiplying by a constant ratio.
Graph: A visual representation of the solution set for an equation.
Greatest Common Factor (GCF): The largest expression that evenly divides multiple monomials.
Growth Rate: In the expression a × b^x, the b indicates the growth rate.
Histogram: A representation of data using bars to show the frequency of values within intervals.
Increasing Function: A function that produces larger outputs as the input increases on an interval.
Inequality: A mathematical statement comparing two expressions using symbols like <, >, ≤, or ≥.
Interquartile Range: The difference between the third quartile (75th percentile) and the first quartile (25th percentile).
Isolating Variable: The act of rearranging an equation so a variable stands alone on one side.
Like Terms: Terms within an expression that contain the same variable parts.
Line of Best Fit: A line that approximates the trend of data points in a scatter plot.
Linear Equation: An equation where the highest exponent of a variable is 1.
Linear Function: A function representing a straight line, with the highest variable exponent as 1.
Mean: The calculated average value of a dataset.
Median: The middle value in a dataset when arranged in ascending order.
Mode: The most frequently occurring number in a dataset.
Monomial: A polynomial with one term, comprising coefficients and/or variables.
Multiplication Property of Equality: When the same value is multiplied to both sides of an equation, the equation remains valid.
Ordered Pair: A pair of numbers written as (x,y) representing a point in a two-dimensional space.
Parabola: The U-shaped graph representing a quadratic function.
Perfect Square Trinomial: A trinomial that can be factored into the square of a binomial.
Piecewise Function: A function defined by different rules for different intervals of input values.
Polynomial: An expression formed by the sum of monomials.
Quadratic Equation: An equation where the highest power of a variable is 2.
Quadratic Formula: The formula used to solve quadratic equations: x = (-b ± √(b² - 4ac)) / (2a).
Quadratic Function: A function represented by a polynomial of degree 2.
Quadratic Polynomial: A polynomial in which the term with the highest degree is squared.
Range: The set of output values produced by a function.
Recursively Defined Sequence: A sequence defined where each term is derived based on prior terms, alongside given initial terms.
Regression: The technique of finding a curve that best fits a set of data points in a scatter plot.
Residual Plot: A graph depicting the discrepancies between observed values and values predicted by a model.
Roots: The solutions or values of a variable that satisfy an equation.
Sequence: An ordered list of numbers following a specific pattern.
Slope: The measure of steepness of a line, indicating how much y changes for a change in x.
Slope-Intercept Form: The equation format y = mx + b where m is the slope and b is the y-intercept.
Solution Set: The complete set of values or ordered pairs that satisfy an equation.
Substitution Method: A strategy for solving a system of equations by substituting one variable with an expression from another equation.
Subtraction Property of Equality: When equal amounts are subtracted from both sides of an equation, the equation stays valid.
System of Equations: A collection of two or more equations involving the same variables.
Third Quartile: The value separating the highest 25% of a dataset.
Translation: A transformation that shifts a graph's points uniformly in a specified direction.
Trinomial: A polynomial that includes three terms.
Variable: A symbol representing an unspecified number or value within an expression or equation.
Vertex: The point at which a parabola changes direction, its maximum or minimum point.
Vertical Line Test: A method to determine if a graph represents a function by checking if a vertical line intersects the graph at more than one point.
X-Intercept: The point where a graph intersects the x-axis.
Y-Intercept: The point where a graph intersects the y-axis.
Zeros: The values that, when inputted into a function, yield an output of zero.
Closed Form Defined Sequence: An expression that directly computes the nth term of a sequence.
Coefficient: The multiplicative factor in a term of an expression, generally a number before a variable.
Common Difference: The consistent difference between consecutive terms in an arithmetic sequence.
Common Ratio: The constant ratio between consecutive terms in a geometric sequence.
Commutative Property: The principle stating that the order of addition or multiplication does not affect the result.
Completing the Square: A technique used to form a perfect square trinomial in quadratic equations.
Constant: A fixed value that does not change, having no variable components.
Correlation Coefficient: A value (r) that quantifies the degree to which a curve fits a set of points in a scatter plot.
Degree of a Polynomial: The highest exponent found in a polynomial.
Difference of Perfect Squares: The factorization of expressions of the form x² - a² into (x - a)(x + a).
Distributive Property: The rule stating that a(b + c) = ab + ac for any numbers a, b, and c.
Division Property of Equality: The principle where dividing both sides of an equation by the same non-zero number maintains the equation's validity.
Domain: The complete set of input values permissible in a function.
Dot Plot: A visual representation where each data point is indicated by a dot, useful for displaying frequency.

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