Honors Algebra 1 All Year Vocab

Vocab for whole year of Algebra 1

Numerical Expression

a mathematical phrase involving numbers and operation symbols, but no variables. There’s NO EQUAL SIGN. Ex. 5 - 3

Exponent

indicates the number of times a number is being multiplied by itself.

Base

in a power, the number being multiplied by itself.

Evaluate

find the value of an expression by simplifying using the order of operations.

Variable

a letter that represents an unspecified number or value.

Algebraic Expression

a mathematical phrase that includes one or more variables. There is NO EQUAL SIGN in an expression. Ex. y + 4

Term

is a number, a variable, or the product or quotient of a number and one or more variables.

Variable term

a term that contains a variable.

Constant term

a term that does not contain a variable.

Defining a variable

choosing a variable to represent the unknown in the problem.

Coefficient

a numerical factor of a term.

Like Terms

having the same variable factors with the same exponent.

Simplest form

writing an expression with no like terms or parentheses.

Equivalent Expressions

two algebraic expressions that have the same value for all values of the variable(s).

Absolute Value

the distance a number is from 0 on a number line

Reciprocal

a numbers multiplicative inverse that is used for dividing fractions.

Equation

a mathematical statement that contains two expressions and an equal sign.

Solve an equation

find all values of the variable that make it true.

Solution

each value that makes an equation true.

Equivalent equations

have the same solution.

Multi-step equation

this uses more than one property of equality to solve it.

Identity

an equation that is true for all values of its variables.

Proportion

an equation stating that two ratios are equivalent.

Formula

an equation that expresses a relationship between certain quantities.

Literal equation

a formula or equation that involves more than one variable.

Relation

a set of ordered pairs.

Domain

the set of the first numbers of the ordered pairs in a relation.

Range

the set of second numbers of the ordered pairs in a relation.

Mapping

an illustration that shows how each element of the domain is paired with an element in the range.

Independent variable

does not change and is subject to choice.

Dependent variable

changes in response to another variable.

Scale

the distance between tick marks on the x- and y-axes.

Function

a relation in which each domain value is matched with exactly one element of the range.

Function notation

a way of writing an equation so that y = f(x).

x-intercept

the coordinate where the graph crosses the x-axis.

y-intercept

the coordinate where the graph crosses the y-axis.

Positive

where the graph of a function lies above the x-axis.

Negative

where the graph of a function lies below the x-axis.

Root

a solution of an equation.

Zero

an x-intercept of the graph of a function.

Rate of change

how a quantity is changing with respect to a change in another quantity.

Slope

the rate of change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run) for points on a line.

Parameter

a value in the equation of a function that can be varied to yield a family of functions.

Constant function

a linear function of the form y = b.

Family of graphs

graphs and equations of graphs that have at least one characteristic in common.

Parent function

the simplest of functions in a family.

Absolute value function

A function in which f(x) > 0 for all values of x.

Vertex

either the lowest or highest point of a function.

Parallel lines

nonvertical lines in the same plane that have the same shape.

Perpendicular lines

nonvertical lines in the same plane for which the product of the slopes is -1.

Bivariate data

data that consists of pairs of values.

Scatter plot

a graph of bivariate data that consists of ordered pairs on a coordinate plane.

Trend

a general pattern of data.

Positive correlation

bivariate data in which y increases as x increases.

Negative correlation

bivariate data in which y decreases as x increases.

No correlation

bivariate data in which x and y are not related.

Line of fit

a lines used to describe the trend of the data in a scatter plot.

Linear extrapolation

the use of a linear equation to predict values that are outside the range of data.

Linear interpolation

the use of a linear equation to predict values that are inside the range of data.

Causation

when a change in one variable produces a change in another variable.

Best-fit line

the line that most closely approximates the data in a scatter plot.

Linear regression

an algorithm used to find a precise line of fit for a set of data.

Correlation coefficient

a measure that shows how well data are modeled by a regression function.

Inverse relations

two relations, one of which contains points of the form (a, b) while the other contains points of the form (b, a).

Inverse functions

two functions, one of which contains points of the form (a, b) while the other contains points of the form (b, a).

Inequality

a mathematical sentence that contains

Interval notation

a method to represent an interval on a number line using different brackets.

Compound inequality

two or more inequalities that are connected by the words and or or.

Intersection

the graph of a compound inequality containing and.

Union

the graph of a compound inequality containing or.

Boundary

the edge of the graph of an inequality that separates the coordinate plane into regions

Half-plane

a region of the graph of an inequality on one side of a boundary.

Open half-plane

the solution of a linear inequality that does not include the boundary line.

Closed half-plane

the solution of a linear inequality that includes the boundary line.