# Academic Support Center

## Algebra Vocabulary

**Absolute Value**

A number's distance from zero on a number line. The absolute value of 4, written
|4|, and the absolute value of -4, written |-4|, are both equal to 4.

**Acute Angle**

An angle with a measure of less than 90 degrees.

**Additive Identity**

Adding the number zero does not change a number's vale (e.g. *5 + 0 = 5*).

**Additive Inverse Property**

A number and its additive inverse have a sum of zero (e.g. in the equation *3 + -3 = 0* both the number 3 and -3 are additive inverses).

**Algebraic Equation**

A mathematical sequence in which two expressions are connected by an equality symbol
(e.g. *x^2 = 8x + 9*).

**Algebraic Expression**

An expression containing numbers and variables (e.g. *7x*) and operations that involve numbers and variables (e.g. *2**x** + **y *or *3**a** - 4*). Algebraic expressions do not contain equality or inequality symbols (e.g. *= < >*).

**Algebraic Order of Operations**

The order in which to complete algebraic operations within an expression. Begin
with anything inside grouping symbols (e.g. parenthesis), and anything above and below
fraction bars. Compute from left to right in the following order: FIRST exponents
(e.g. x^2), SECOND multiplication and division (e.g. *3 x 4* or *7 ÷ 8*), THIRD addition and subtraction (e.g. *1 + 2* or *3 - 4*).

**Algebraic Rule**

A mathematical expression that contains variables and describes a pattern or relationship.

**Angle**The shape made by two rays extending from a common end point, the vertex. Measures
of angles are described using the degree system.

**Area**

The inside region of a two-dimensional figure measured in square units (e.g. a rectangle
with sides of 4 units by 6 units contains 24 square units or has an area 24 square
units).

**Associative Property**

The way in which three or more numbers are grouped for addition or multiplication
does not change their sum or product (e.g. *2 + 3 = 3 + 2* or *4 x 7 = 7 x 4*).

**Axes**

The horizontal and vertical number lines used in a rectangular graph or coordinate
grid system.

**Base**

The line or plane upon which a figure is thought of as a resting.

**Break**

A zigzag on the line of the *x*- or *y*-axis in a line or a bar graph indicating that the data being displayed does not include
all of the values that exist on the number line being used. Also called a Squiggle.

**Capacity**

The amount of space that can be filled. Both capacity and volume are used to measure
three-dimensional spaces. However, capacity usually refers to fluids, whereas volume
usually refers to solids.

**Circumference**

The perimeter of a circle is called its circumference. Equal to twice the radius
of the circle multiplied by Pi, or *C = 2** π r*.

**Closed Figure**

A two-dimensional figure whose beginning and ending points meet, such that the plane
in which the figure lies is divided into two parts -- the part inside the figure and
the part outside the figure (e.g. circles, squares, rectangles).

**Commutative Property**

The order in which two numbers are added or multiplied does not change their sum
or product (e.g. *2 + 3 = 3 + 2* or *4 x 7 = 7 x 4*).

**Complementary Angles**Two angles, the sum of which is exactly 90 degrees.

**Composite**A whole number that has no more than two factors.

**Concrete Representations of Numbers**

Having a definite form or relating to an actual thing.

**Congruent**

Figures or objects that are the same shape and the same size.

**Coordinate System (Grid)**A network of evenly spaced, parallel horizontal and vertical lines especially designed
for locating points, displaying data, or drawing maps.

**Coordinates**

Numbers that correspond to points on a coordinate system or graph in the form (*x , y).*

**Customary Units**

The units of measure developed and used in the United States. Customary units for
length are inches, feet, yards and miles. Customary units for volume are cubic inches,
cubic feet, and cubic yards. Customary units for capacity or fluid ounces, cups, pints,
quarts, and gallons.

**Data Displays**

Different ways of displaying data in tables, charts, or graphs, including pictographs,
circle graphs, single, double, or triple bar and line graphs, histograms, stem-and-leaf
plots, and scatter plots.

**Decimal Number**

Any number written with a decimal point in the number. A decimal number falls between
two whole numbers (e.g. 1.5 falls between 1 and 2). Decimal numbers smaller than 1
are sometimes called decimal fractions (e.g. three-tenths is written 0.3).

**Diameter**

A line segment from any point on the circle passing through the center to another
point on the circle.

**Direct Measure**

Obtaining the measure of an object by using measuring devices, either standard devices
of the customary or metric systems, or nonstandard devices such as a paper clip or
pencil.

**Distributive Property**

For any real numbers *a, b, *and *x* the expression *x(a + b)* can be written as *ax + bx*.

**Effects of Operations**

The results of applying an operation to given numbers (e.g. adding two whole numbers
results in a number greater than or equal to the original numbers).

**Enlargement**

An increase in size in all directions by a uniform amount.

**Equation**

A mathematical sentence (e.g. *2**x** = 10*) that equates one expression *2**x* to another expression *10*.

**Equivalent Expressions**

Expressions that have the same value but are represented in a different format using
the properties of numbers (e.g. *ax + bx = x(a +b)*).

**Equivalent Forms of a Number**

Expressions that have the same value but are represented in a different format using
the properties of numbers (e.g., *ax + bx = x(a + b)*).

**Estimation**

The use of rounding and/or other strategies to determine a reasonably accurate approximation,
without calculating an exact answer.

**Evaluate an Expression**

Substitute numbers for variables in the expression and follow the operation symbols
to find the numerical value of the expression.

**Explain in Words**

Directions requesting a written description of the procedures for finding the solution
to the problem presented.

**Exponent (Exponential Form)**

The number of times the base occurs as a factor. For example, 2^3 is the exponential
form of 2 x 2 x 2. The numeral two is called the base, and the numeral three is called
the exponent.

**Expression**

A collection of numbers, symbols, and/or operation signs that stands for a number.

**Extrapolate**

To estimate or infer a value or quantity beyond the known range.

**Face**

One of the plane surfaces bounding a three-dimensional figure (a side).

**Factor**

A number or expression that divides exactly another number (e.g. 1, 2, 4, 5, 10 and
20 are factors of 20).

**Finite Graph**

A graph having definable limits.

**Flip**A transformation that produces the mirror image of a geometric figure. Also called
a reflection.

**Fraction**Any part of a whole is called a fraction (e.g. one-half written in fractional form
is 1/2.

**Function**

The relationship between two sets (e.g. sets of numbers) in which each element of
one set has one assigned element in the other set.

**Function table**

A table of *x- *and *y-*values (ordered pairs) that represents the function, pattern, relationship, or sequence
between the two variables.

**Grid**

A network of evenly spaced, parallel horizontal and vertical lines.

**Height**

A line segment extending from the vertex or apex of a figure to its base and forming
a right angle with the base or basal plane.

**Hypothesis**

A proposition or supposition developed to provide a basis for further investigation
or research.

**Indirect Measure**

Obtaining the measurement of an object through the known measure of another object.

**Inequality**

A sentence that states one expression is greater than or equal to, less than, less
than or equal to another expression (e.g., *A is not = 5 * or *x < 7* ).

**Integers**

The numbers in the set {...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...}.

**Intercept**

The value of a variable when all other variables in the equation equal zero. On a
graph, the values where a function crosses the axes.

**Intersection**

The point at which two lines meet.

**Inverse Operation**

An action that cancels a previously applied action. For example, subtraction is the
inverse operation of addition.

**Irrational Number**A real number that can not be expressed as a ratio of two numbers (e.g.

*20 = 2(*

*w*

*+4) + 2*

*w*and

*y*

*= 3*

*x*

*+ 4*).

**Labels (for a Graph)**

The titles given to a graph, the axes of a graph, or to the scales on the axes of
a graph.

**Length**

A one-dimensional measure that is the measurable property of line segments.

**Likelihood**

The chance that something is likely to happen.

**Line**

A straight line that is endless in length.

**Line Segment**A portion of a line that has a defined beginning and end (e.g. the line segment AB
is between point A and point B).

**Linear Equation**An algebraic equation in which the variable quantify or quantities are in the first
power and the graph is a straight line (e.g.

*20 = 2(w + 4) + 2*

*w*and

*y*

*= 3*

*x*

*+ 4*).

**Mean**

The arithmetic average of a set of ordered numbers where half of the numbers are
above the median and half are below it.

**Median**

The middle point of a set of ordered numbers where half are below it.

**Metric Units**

The units of measure developed in Europe and used in most of the world. Like the
decimal system, the metric system uses the base 10. Metric units for length are millimeters,
centimeters, meters, kilometers. Metric units for weight are milligrams, grams, and
kilograms. Metric units for volume are cubic millimeters, cubic centimeters, and cubic
meters. Metric units for capacity are milliliters, centiliters, liters, and kiloliters.

**Midpoint of a Line Segment**

The point on a line segment that divides it into two equal parts.

**Mode**

The score or data point found most often in a set of numbers.

**Multiples**

The numbers that result from multiplying a given number by the set of whole numbers
(e.g. the multiples of 15 are 0, 15, 30, 45, 60, 75, etc . . .).

**Multiplicative Identity**

The number one, that is, multiplying by 1 does not change a number's value
(e.g. *5 x 1= 5*).

**Multiplicative Inverse ****(Reciprocal)**

Any two numbers with a product of 1. (e.g. *4 and 1/4*).

**Natural Numbers ****(Counting Numbers)**The numbers in the set {1, 2, 3, 4, 5, ...}.

**Negative Exponent**

Used in scientific notation to designate a number smaller than one (e.g. 3.45 x 10^-2
equals 0.0345).

**Nonstandard Units of Measure**

Units such as blocks, paper clips, crayons, or pencils that can be used to obtain
a measure.

**Number Line**

A line on which numbers can be written or visualized.

**Obtuse Angle**

An angle with a measure of more than 90 degrees but less than 180 degrees.

**Odds**

The ratio of an event occurring to it not occurring.

**Operation**

Any mathematical process, such as addition, subtraction, multiplication, division,
exponents, or square roots.

**Operational Shortcut**

A method having fewer arithmetic calculations.

**Ordered Pair**

The location of a single point on a rectangular coordinate system where the digits
represent the position relative to the *x*-axis and *y*-axis [e.g. *(**x,y**)* or *(3,4)*]

**Organize Data**

To arrange data in a display that is meaningful and that assists in the interpretation
of the data.

**Parallel Lines**

Two lines in the same plane that never meet. Also, lines with equal slopes.

**Pattern****(Relationship)**

A predictable or prescribed sequence of numbers, objects, etc. Patterns and relationships
may be described or presented using manipulatives, tables, graphics (pictures or drawings),
or algebraic rules (functions).

**Percent**

A special-case ratio in which the second term is always 100. The ratio is written
as a whole number followed by a percent sign (e.g. *25%* means the ratio of *25 to 100*).

**Perimeter**

The length of the boundary around a figure.

**Perpendicular**

Forming a right angle.

**Pi (π)**

The symbol designating the ratio of the circumference of a circle to its diameter,
represented approximately as either the decimal 3.1415 or the fraction 22/7.

**Place Value**

The position of a single digit in a whole number or decimal number containing one
or more digits.

**Planar Cross Section**

The intersection of a plane and a three-dimensional figure.

**Plane**

An undefined, two-dimensional (no depth) geometric surface that has no boundaries
specified. A plane is determined by defining points or lines existing on the plane.

**Plane Figure**

A two-dimensional figure that lies entirely within a single plane.

**Point**

A location in space that has no length or width.

**Polygon**A closed plane figure whose sides are straight lines and do not cross.

**Prime Number**

Any whole number with only two factors, 1 and itself (e.g. 2, 3, 5, 7, 11, etc .
. .).

**Prism**

A three-dimensional figure (polyhedron) with congruent polygonal bases and lateral
faces that are all parallelograms.

**Probability**

The likelihood of an event happening. An impossible event has a probability of zero.
An event that will occur with absolute certainty is assigned a probability of one.
Every event that is neither certain nor impossible has a probability that is between
zero and one, and is obtained by dividing the number of favorable outcomes of an event
by the total number of possible outcomes.

**Probability, Empirical**

The likelihood of an event happening that is based on experience and observation
rather than on theory.

**Probability, Theoretical**

The likelihood of an event happening that is based on theory rather than on experience
and observation.

**Proof**

A set of steps that demonstrates the truth of a given statement. Each step can be
justified with a reason, such as a given, a definition, an axiom, or a previously
proven property.

**Pythagorean Theorem**

The square of the hypotenuse (*c*) of a right triangle is equal to the sum of the square of the legs (*a* and *b*), as shown by the equation *a*^2+*b*^2=c^2.

**Quadrant**

Any of the four regions formed by the axes in a rectangular coordinate system.

**Radical Sign**

The symbol used before a number to show that the number is radicand.

**Radicand**

A number that appears with a radical sign.

**Radius**

A line segment extending from the center of a circle or sphere to a point on the
circle or sphere.

**Range of a Set of Numbers**

The difference between the highest (H) and the lowest (L) value in a set of data.
Also, the values that a function takes when evaluated over a domain.

**Rate/Distance**

Calculations involving rates, distances, and time intervals, based on the distance,
rate, time formula *D =** r t*.

**Ratio**

The compression of two quantities (e.g. the ratio of *a* to *b* is a/b, where *b* doesn't equal zero).

**Rational Number**

A real number that can be expressed as a ratio of two integers.

**Ray**

A portion of a line that begins at a point and goes on forever in one direction.

**Real Numbers**All rational and irrational numbers.

**Reciprocal**

see Multiplicative Inverse

**Reflection**

see Flip

**Reflexive Axiom of Equality**

A number or expression is equal to itself (e.g. *ab** = **ab*).

**Regular Polygon**

A polygon that is both equilateral and equi-angular.

**Relation (Relationship)**

see Pattern

**Relative Size**

The size of one number in comparison to the size of another number or numbers.

**Right Angle**

An angle whose measure is exactly 90 degrees.

**Right Circular Cylinder**

A cylinder in which the bases are parallel circles perpendicular to the side of the
cylinder.

**Right Triangle Geometry**

Finding the measures of missing sides or angles of a right triangle when given the
measures of other sides or angles. See Pythagorean Theory

**Rise**

The change in *y* going from one point of *y* to another (the horizontal change on the graph).

**Rotation**

A transformation of a figure by turning it about a center point or axis. The amount
of rotation is usually expressed in the number of degrees (e.g. a 90 degree rotation).
Also called a Turn.

**Rule**

A mathematical expression that describes a pattern or relationship, or a written
description of the pattern or relationship.

**Run**

The change in *x* going from one point of *y* to another (the horizontal change on the graph).

**Scale Model**

A model or drawing based on a ratio of the dimensions for the model and the actual
object it represents (e.g. a map).

**Scales**

The numeric values assigned to the axes of a graph.

**Scatter Plot**

A graph of data points, usually from an experiment, that is used to observe the relationship
between two variables.

**Scientific Notation**

A shorthand method of writing very large or very small numbers using exponents in
which a number is expressed as the product of a power of 10 and a number that is greater
than or equal to one and less than 10 (e.g. 7.59 x 10^5=759,000). It is based on the
idea that is easier to read exponents than it is to count zeros. If a number is already
a power of 10, it is simply written 10^27 instead of 1 x 10^27.

**Sequence**

An ordered list with either a constant difference (arithmetic) or a constant ratio
(geometric).

**Side**

The edge of a geometric figure (e.g. a triangle has three sides).

**Similar Figures**

Two figures that are the same shape, have corresponding, congruent angles, and having
corresponding sides that are proportional in length.

**Similarity**

Figures that are the same shape are similar; they are not necessarily the same size
or in the same position.

**Slide**

To move along in constant contract with the surface in a vertical, horizontal, or
diagonal direction. Also called a Translation

**Slope**

The incline of a line, defined by the ratio of the change in units on the vertical
axis to the change in one unit on the horizontal axis.

**Solid Figures**

Three-dimensional figures that completely enclose a portion of space (e.g. a rectangular
solid, cube, sphere, right circular cylinder, right circular cone, and regular square
pyramid).

**Spatial Relationships**

Relationships of figures existing or happening in space.

**Square Root**

A positive real number that can be multiplied by itself to produce a given number
(e.g., the square root of 144 is 12 or *√144 = 12*).

**Squiggle**

see Break

**Standard Units of Measure**

The measurement of an object by using accepted measuring devices and units of the
customary or metric system.

**Straight Angle**

An angle whose measure is exactly 180 degrees.

**Supplementary Angles**

Two angles, the sum of which is exactly 180 degrees.

**Surface Area of a Geometric Solid**

The sum of the area of the faces of the figure that create the geometric solid.

**Symbolic Expression**A symbol or set of symbols expressing a mathematical quantity or operation (e.g.

*2*

*x*is equal to two times

*x*).

**Symbolic Representations of Numbers**Being expressed by symbols (e.g. circles shaded to represent 1/4, or variables used
to represent quantities).

**Symmetry**

When a line can be drawn through the center of a figure such that the two halves
are congruent.

**Systems of Equations**

A group of two or more equations that share variables. The solution to a system of
equations is an ordered number set that makes all of the equations true.

**Tessellation**

A covering of a plane with congruent copies of the same pattern with no holes and
no overlaps, like floor tiles.

**Transformation**

An operation on a geometric figure by which another image is created. Common transformations
include flips, slides, and turns.

**Transitive Property**

When the first element has a particular relationship to a third element that in turn
has the same relationship to a third element, the first has this same relationship
to the third element (e.g. if *a = b *and *b = c, *then* a = c*)*. *Identity and equality are transitive relationships.

**Translation**

see Slide

**Tree Diagram**

A diagram in which all the possible outcomes of a given event are displayed.

**Turn**

see Rotation

**Unorganized Data**

Data that are presented in a random manner.

**Variable**

Any symbol that could represent a number.

**Vertex**

The common endpoint from which two rays begin (e.g. the vertex of an angle) or the
point where two lines intersect; the point on a triangle or pyramid opposite to and
farthest from the base.

**Vertical Angles**

The opposite angles formed when two lines intersect.

**Volume**

The amount of space occupiedin three dimensions and expressed in cubic units. Both
capacity and volume are used to measure empty spaces; however, capacity usually refers
to fluids, whereas volume usually refers to solids.

**Weight**

Measures that represent the force that attracts an object to the center of Earth.
In the customary system, the basic unit of weight is the pound.

**Whole Numbers**

The numbers in the set {0, 1, 2, 3, 4,...}.

**X Intercept**The value of

*x*on a graph when

*y*is zero. The

*x*-axis is the horizontal number line on a rectangular coordinate system.

**Y Intercept**

The value of *y* on a graph when *x* is zero. The *y*-axis is the vertical number line on a rectangular coordinate system.