# Algebra 1 Honors Vocabulary

## 150 terms

### Variable

A letter that is used to represent one or more numbers.

### Algebraic Expression

An expression that includes at least one variable.

### Power

An expression that represents repeated multiplication of the same factor.

### Base of a Power

The number or expression that is used as a factor in a repeated multiplication.

### Exponent

The number or variable that represents the number of times the base of a power is used as a factor.

### Order of Operations

Rules for evaluating an expression involving more than one operation.

### Verbal Model

Describes real-world situation using words as labels and using math symbols to relate the words.

### Rate

A fraction that compares two quantities measured in different units.

### Unit Rate

A rate in which the denominator of the fraction is 1 unit.

### Open Sentence

An equation or an inequality that contains an algebraic expression.

### Equation

a mathematical sentence formed by placing the = between two expressions.

### Inequality

A mathematical sentence formed by placing one of the symbols <, >, ≤,or ≥ between two expressions.

### Solution of an Equation

A number that produces a true statement when substituted for the variable in the equation.

### Solution of an Inequality

A number that produces a true statement when it is substituted for the variable in the inequality.

### Formula

An equation that relates two or more quantities.

### Function

It consists of:
1. A set called the domain containing numbers called inputs, and a set called the range containing numbers called outputs.

2. A pairing of inputs with outputs such that each input is paired with exactly one output.

### Domain

The set of all inputs of a function.

### Range

The set of all outputs of a function

### Independent Variable

The input variable of a function.

### Dependent Variable

The output variable of a function.

### Relation

Any pairing of a set of inputs with a set of outputs.

### Whole Numbers

The numbers 0,1,2,3...

### Integers

The numbers ...-3,-2,-1,0,1,2,3...

### Rational Number

A number that can be written as a/b where a and b are integers and b is not equal to 0.

### Opposites

Two numbers that are the same distance from zero on a number line but are on opposite sides of 0.

### Absolute Value

The distance between a number and 0 on a number line.

### Conditional Statement

A statement with a hypothesis and a conclusion

### Set

A collection of distinct objects.

### Element of a Set

Each object in a set.

### Empty Set

A set with no elements.

### Universal Set

The set of all elements under consideration.

### Union

Of two sets A and B is the set of all elements in either A or B written in A U B.

### Intersection

Of two sets A and B is the set of all elements in both A and B written in A (upside down U) B

### Complement of a Set

Of set A is the set of all elements in the universal set U that are not in A.

### Cross Product of Two Sets

Of two sets A and B, written as A X B, is the set of all possible ordered pairs of the form (x,y) where x is an element of A and y is an element of B.

The number 0, because the sum of any number and 0 is the number.

The opposite of a number, the sum of a number and its opposite is 0.

### Multiplicative Identity

The number 1, because the product of any number and 1 is the number.

### Equivalent Expressions

Two expressions that have the same value for all values of the variable.

### Distributive Property

A property that can be used to find the product of a number and a sum or difference.

### Term

The parts of an expression that are added together.

### Coefficient

The number part of a term with a variable part.

### Constant term

A term with a number part but no variable part.

### Like Terms

Terms that have the same variable parts.

### Multiplicative Inverse

The reciprocal of a nonzero number.

### Square Root

A number that when multiplied by itself equals a given number.

The number or expression inside a radical symbol.

### Perfect Square

A number that is the square of an integer.

### Irrational Number

A number that cannot be written as the quotient of two integers.

### Real Numbers

The set of all rational and irrational numbers.

### Cube Root

A number that when multiplied three times equals a given number.

### Inverse Operations

Two operations that undo each other.

### Equivalent Equations

Equations that have the same solution.

### Identity

An equation that is true for all values of the variable.

### Ratio

A comparison of two numbers using division.

### Proportion

An equation that states that two ratios are equivalent.

### Cross Product

The product of the numerator of one ratio and the denominator of the other ratio.

### Scale Drawing

A two-dimensional drawing in which the dimensions of the drawing are in proportion to the dimensions of the object.

### Scale Model

A three-dimensional model in which the dimensions of the model are in proportion to the dimensions of the object.

### Scale

A ratio that relates the dimensions of a scale drawing or model and the actual dimensions.

### Percent of Change

A percent that indicates how much a quantity increases or decreases with respect to the original amount.

### Percent of Increase

The percent of change in a quantity when the new amount of the quantity is greater than the original amount.

### Percent of Decrese

The percent of change in a quantity when the new amount of the quantity is less that the original amount.

### Literal Equation

An equation in which letters are used to replace the coefficients and constants of another equation.

The four regions into which the coordinate plane is dived by the x-axis and the y-axis.

### Transformation

It produces an image by applying a rule to the coordinates of each point on the graph.

### Translation

It moves every point on a graph the same distance in the same direction

### Vertical Stretch

Moves a point away from the x-axis.

### Vertical Shrink

Moves a point toward the x-axis.

### Reflection

Flips a point in a line.

### Standard Form of a Linear Equation

Ax + By = C, where A,B, and C are real numbers and A and B are not both zero.

### Linear Function

The equation Ax + By = C provided B does not equal 0.

### Discrete Function

A function with a graph that consists of isolated points.

### Continuous Function

A function with a graph that is unbroken.

### X-Intercept

The x-coordinate of the point where a graph crosses the x-axis.

### Y-Intercept

The y-coordinate of a point where a graph crosses the y-axis.

### Slope

The ratio of the vertical change to the horizontal change between any two points (x₁,y₁) and (x₂,y₂) on the line.

### Rate of Change

A comparison of a change in one quantity with a change in another quantity.

### Slope-Intercept Form

y=mx+b where m is the slope and b is the y-intercept of the equation's graph.

### Parallel Lines

Two lines in the same plane that do not intersect.

### Direct Variation

The relationship of two variable x and y if there is a nonzero number a such that y =ax.

### Constant of Variation

The nonzero constant a in a direct or inverse variation equation.

### Function Notation

A way to name a function using the symbol f(x) instead of y.

### Family of Functions

A group of functions with similar characteristics.

### Parent Linear Function

The function f(x) = x, which is the most basic function in the family of linear functions.

### Point-Slope Form

y − y₁= m(x − x₁) that passes through a given point (x₁, y₁) with a slope of m.

### Sequence

An ordered list of numbers.

### Arithmetic Sequence

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

### Common difference

The constant difference between consecutive terms of an arithmetic sequence.

### Converse

The statement formed by interchanging the hypothesis and conclusion of the conditional.

### Perpendicular Lines

Two lines in the same planes that intersect to form a right angle.

### Scatter Plot

A graph used to determine whether there is a relationship or trend between paired data.

### Correlation

The relationship between paired data.

### Line of Fit

A line used model the trend in data having a positive or negative correlation.

### Best-Fitting Line

The line that most closely follows a trend in data.

### Linear Regression

The process of finding the best-fitting line to model a set of data.

### Linear Interpolation

Using a line or its equation to approximate a value between two known values.

### Linear Extrapolation

Using a line or its equation to approximate a value outside the range of known values

### Zero of a Function

An x-value for which f(x) = 0.

### Graph of an Inequality

On a number line, the set of points that represent all solutions of the inequality.

### Equivalent Inequalities

Inequalities that have the same solution

### Compound Inequality

Two inequalities joined by "and" or "or"

### Absolute Value Equation

An equation that contains an absolute value expression.

### Absolute Deviation

A number x from a given value is the absolute value of the difference of x and the given value.

### Linear Inequality in Two Variables

An inequality that is the result of replacing the = sign in a linear equation with <, ≤, >, or ≥.

### Graph of an Inequality in Two Variables

In a coordinate plane, the set of points that represent all solutions of the inequality.

### System of Linear Equations

Two or more linear equations in the same variables.

### Solution of a System of Linear Equations

An ordered pair that is a solution of each equation in the system.

### Consistent Independent System

A linear system with exactly one solution.

### Inconsistent System

A linear system with no solution.

### Consistent Dependent System

A linear system with infinitely many solutions.

### System of Linear Inequalities

Two or more linear inequalities in the same variables.

### Solution of a System of Linear Inequalities

An ordered pair that is a solution of each inequality in the system.

### Graph of a System of Linear Inequalities

The graph of all solutions of the system.

### Order of Magnitude

The power of 10 nearest the quantity.

### Scientific Notation

Numbers are written in the form c x 10^n where 1≤c<10 and n is an integer.

### Monomial

A number, variable, or the product of a number and one or more variables with whole number exponents.

### Degree of a Monomial

The sum of the exponents of the variables in the monomial

### Degree of a Polynomial

The greatest degree of the terms of the polynomial.

### Polynomial

A monomial or sum of monomials.

The coefficient of the forest term.

### Binomial

A polynomial with two terms.

### Trinomial

A polynomial with three terms.

### Roots

The solutions of a polynomial equation.

### Vertical Motion Model

A model for the height of an object that is propelled into the air but has no power to keep itself up in the air.

### Perfect Square Trinomial

Trinomials of the form a²+2ab+b² or a²- 2ab+b².

### Factor by Grouping

Factor a common monomial from pairs of terms and then look for a common binomial factor.

### Factor Completely

A factorable polynomial with integer coefficients when it is written as a product of unfactorable polynomials with integer coefficients.

A nonlinear function that can be written in the standard form y=ax²+bx+c where a≠0.

### Parabola

The U-shaped graph of a quadratic function.

The function y=x².

### Vertex

The lowest or highest point on a parabola.

### Axis of Symmetry

The line that passes through the vertex and divides the parabola into two symmetric parts.

### Minimum Value

The y-coordinate of the vertex for y= ax²+bx+c, where a>0.

### Maximum Value

The y-coordinate of the vertex for y=ax²+bx+c when a<0.

### Intercept Form of a Quadratic Function

A quadratic function in the form y=a(x-p)(x-q).

An equation that can be written in the standard form ax² + bx + c = 0, where a ≠ 0.

### Completing the Square

The process of rewriting a quadratic expression so that it is a perfect square trinomial.

### Vertex Form of a Quadratic Function

A quadratic function in the form y=a(x-h)²+k.

The formula x=(-b±√b²-4ac)/2a can be used to find the solutions of the quadratic equation ax²+bx+c=0 where a≠0 and b²-4ac≥0

### Discriminant

The expression b² - 4ac of the associated equation ax² + bx + c = 0.

### Simplest Form of Radical Expression

A radical expression that has no perfect square factors other than 1 in the radicand, no fractions in the radicand, and no radicands appearing in the denominator of the fraction.

### Rationalizing the Denominator

The process of eliminating a radical from an expression's denominator.

### Inverse Variation

The relationship of two variables x and y if there is a nonzero number a such that y=a/x

### Hyperbola

The graph of the inverse variation equation y=a/x.

### Branches of a Hyperbola

The two symmetrical parts of a hyperbola.

### Asymptotes of a Hyperbola

Lines that a hyperbola approaches but does not intersect.

### Rational Expression

An expression that can be written as the ratio of two polynomials where the denominator is not 0.

### Excluded Value

A number that makes a rational expression undefined.

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