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198 Cards in this Set
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Absolute Value

Distance of a number from zero on a number line. Since distance is positive, the absolute value of any number must be positive.
 5  = 5  5 = 5 

Acute angle

An angle that measures between 0 and 90 degrees
0° < x < 90° 

Acute triangle

All angles in the triangle are acute
A 40  60  80 triangle is acute 

Additive Inverse

A number and its opposite
When you add them they equal zero. 5 and 5 are inverses because 5 + (5) = 0 

Adjacent angles

Two coplanar angles with a common side, a common vertex, and no common interior points


Adjacent arcs

Two arcs in the same circle that have exactly one point in common.


Algebraic expression

A collection of letters (variables) and real numbers (constants) combined using the operations of addition, subtraction, multiplication, division, and exponentiation.


Amplitude of a periodic function

Half the difference between the maximum and minimum values of the function


Angle

The shape formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle). In geometry an angle can be defined by the vertex or by the rays and vertex.


Angle bisector

A ray that divides an angle into two congruent (equal) angles


Arc

Part of a circle
Exactly half the circle is called a semicircle. Less than half is a minor arc and more than half is a major arc. 

Arithmetic Sequence

A sequence where the difference between consecutive terms is a constant
The arithmetic sequence 1, 4, 7, 10, 13, ... has a common difference of 3 

Associative Property

Changing the grouping of addends or factors does not change the sum or product. Grouping doesn't matter when adding or multiplying
(2 + 3) + 4 = 5 + 4 = 9 2 + (3 + 4) = 2 + 7 = 9 (2 x 6) x 5 = 12 x 5 = 60 2 x (6 x 5) = 2 x 30 = 60 

Asymptote

A line the graph of a function gets close to but does not cross


Axis of Symmetry

The line about which you can reflect a graph onto itself
When you fold a graph on the axis of symmetry, both sides match For the parabola, y = x2 + 2x  1 the axis of symmetry is the line x = 1 

Beta Β β

Greek letter frequently used to represent angles


Binomial

Expression with two terms  bi means two
2x + 3 

Binomial Experiment

A experiment that has only two possible outcomes
Tossing one coin is binomial because you only get heads or tails 

Binomial Theorem

(a+b)^n
(x + 3)2= x2 + 6x + 9 is a binomial expansion 

Central angle

An angle whose vertex is the center of a circle


Coefficient

The numerical factor when a term has a variable. The number next to a letter
5y 5 is the coefficient and y is the variable 

Collinear

Points that lie on the same line
Points that all line up 

Common Factors

Numbers, variables, and any products formed from the prime factors that appear in all terms of an expression
For 2x2 6x 2 and x are the common factors 

Commutative Property

Changing the order of addends or factors does not change the sum or product. Order doesn't matter when adding or multiplying
2 + 3 = 3 + 2 = 5 5 x 4 = 4 x 5 = 20 

Complementary angles

Two positive angles whose measures add to 90 degrees
A + B = 90° 

Complex fraction

A fraction where the numerator, denominator, or both has a fraction
5 = 20 ¾ 3 

Complex Number

A number of the form a + bi, where a and b are real numbers and i is the square root of 1. Also called an imaginary number


Concave polygon

When a diagonal contains points outside the polygon.


Congruent

Objects that are the same size and the same shape. The symbol for congruent is an equal sign with a squiggle over it.


Constant

a value or number that never changes
5 3.7 

Constant Term

A term that has no variable factor. A number that stands alone
7x + 3 3 is the constant term 

Convex polygon

No diagonal contains points outside the polygon


Coordinate of a point

On a number line, it is the distance of the point from the origin. On a coordinate axis is is the pair (x, y) that defines the location.


Coordinate Plane

Formed when two number lines intersect at right angles. The xaxis is the horizontal axis and the yaxis is the vertical axis. The two axes meet at the origin (0,0)


Coplanar

Points and lines that are in the same plane


Corresponding parts

Matching sides and angles in a polygon


Coterminal Angles

Two angles that share two sides in standard position. The sum of the absolute values of the angles adds to 360°.
150° and 210° are coterminal angles 

Cubic Equation

An equation in the form
ax3 + bx2 + cx + d = y, where a, b, c, and d are real numbers and a ≠ 0. Largest exponent is 3 2x3 + 3x2 5x + 7 = y 

Delta Δ δ

Greek letter frequently used to represent variables that change


Dependent variable

A variable that relies on the value of another variable
for y = x + 2, the value of y depends on the value of x 

Diameter

In a circle, any segment that contains the center of the circle and has both endpoints on the circle.


Difference of two squares

A quadratic binomial of the form a2  b2, it factors to
(a + b)(a  b) Perfect square minus a perfect square x2  9 4x2  25 

Direct variation

A linear function of the form y = kx, where k ≠ 0
A straight line that passes through (0,0) with slope k y = 5x y = 2x 

Discrete Data

Involves a count of data items. Things that can be counted.
heart beats in a minute, daily temperature at noon 

Distributive property

For all real numbers a, b, and c:
a(b + c) = ab + ac a(b  c) = ab  ac Multiply everything inside the parenthesis by the thing in front of the parentheses 5(x + 2) = 5x + 10 4(x  2) = 4x  8 

Domain

The set of all possible input values  the independent variable in a function. For functions in x and y, the possible x values are the domain.
For y = 2x + 6, the domain is all real numbers For y = 7/x, the domain is all real numbers except 0 because you can't divide by zero 

Equiangular polygon

A polygon where all the angles are congruent
All angles equal 

Equilateral polygon

A polygon where all the sides are congruent
All sides equal 

Equilateral triangle

A triangle where all the sides are congruent
All sides equal 

Even function

A function graph whose axis of symmetry is the yaxis.
y = 5x2 + 2 

Exponent

A raised number that represents repeated multiplication of a factor
34 = 3 • 3 • 3 • 3 

Expression

Any combination of values and operations (no = sign)
4x2 + 2x 

Exterior angle

In a polygon, the angle formed by a side and an extension of a side.


Factoring

Breaking a polynomial equation down into the product of several factors
y = x2  3x + 2 Original problem y = (x  2)(x  1) Factored form 

Factorial !

n! is the product of all the whole numbers from n down to 1  used in probability
3! = 3• 2 • 1 = 6 4! = 4 • 3• 2 • 1 = 24 

Factors

Whole numbers that are multiplied together to equal another number.
2 and 5 are the factors of 10 because 10 = 2 • 5 

Factored Form

A polynomial written as the product of polynomials of lower degree
y = (x + 4)(x  3) is the factored form of y= x2 + x  12 

Function

A relation that assigns exactly one value of the dependent variable to each value of the independent variable. Rule that matches one input to only one answer
y = x + 5 is a function if you pick x = 3 you get one answer, y = 8 

Function notation

A function written using the symbol f(x) in place of y. Another name for a function, read f of x
f(x) = 2x + 3 y = 2x + 3 

Geometric Sequence

A series of numbers where each consecutive number is the prior number times a constant called the common ration.
¼, ½, 1, 2, 4, 8, ... has a common ratio of 2  each number is 2 times the one before 

Greatest common factor GCF

The largest number that is a factor of two or more whole numbers.
7 is the GCF of 14 and 21 

Histogram

A bar graph that shows the frequency of data. The height of each bar shows the number of items in each interval


Hyperbola

A set of points that are equidistant from a foci. The graph looks a lot like two parabolas on their side.


Hypotenuse

In a right triangle, the side opposite the right angle. The longest side in a right triangle


Identity

An equation that is true for every value of the variable
An equation that is true for every value of the variable x + 1 = 1 + x 

Identity Property of Addition

The sum of any number and zero is that number
Anything + 0 = Itself a + 0 = a 

Identity Property of Multiplication

The product of any number and one is that number
Anything x 1 = Itself a • 1 = a 

Imaginary Number

A number of the form a + bi, where i is the square root of 1 and i2 = 1
√(4) = 2i 

Improper fraction

A fraction where the numerator is larger than the denominator. In arithmetic, you are trained to change these to a mixed number. In Algebra, you should leave it alone.
7 = 1 ¾ 4 improper mixed 

Independent Events

In probability, when the outcome of one event does not affect the outcome of a second event, the events are independent


Independent Variable

A variable that does not depend on another variable.
The input variable For y = x + 3 x is independent 

Inductive Reasoning

A method used to reach conclusions based on an observed pattern.
For the pattern 2, 4, 6, 8 you can induce that since they are all even numbers, the next number must be 10 

Inequality

One expression that is not equal to another
x > 7 means x is greater than 7 2 < x means negative 2 is less than x 4 < x means x is 4 or bigger 

Integer

The whole numbers and their opposites
...  3, 2, 1, 0, 1, 2, 3, ... 

Intersect

Lines intersect when they cross. The point where they cross is called the intersection.


Interval

A portion of the real number line that may or may not include the end points. The ends of the interval are called the boundaries.


Interval notation

A short way to define an interval. Brackets [ are used if the end point is part of the interval. Parentheses ( means the end point is not included in the interval.
[3, 5) means 3 < x 5 

Inverse Operation

Operations that undo each other  they are opposite operations
addition and subtraction are inverses multiplication and division are inverses 

Inverse Variation

A function that can be written in the form xy = k or y = k/x
As one variable gets bigger, the other gets smaller 

Irrational number

A number that cannot be written as a fraction.
A decimal that does not truncate (end) or repeat. π = 3.14159... √7 = 2.6457... 

Isometric drawing

The drawing of a threedimensional object that shows the corners.


Isosceles trapezoid

A trapezoid whose nonparallel sides are congruent


Isosceles triangle

A triangle where at least two sides are congruent
Two or more sides equal 

Kite

A parallelogram with two pairs of adjacent sides congruent and no opposite sides congruent


Like terms

Terms with exactly the same variable factors
6y and 3y are like terms 2ab and 5ab are like terms 

Line

A series of points that extends forever in two directions. A line is uniquely defined if you know two points on the line.


Line graph

A graph that has data points connected by lines


Line of best fit

The trend line that most closely matches your data points on a scatter plot.


Line segment

Part of a line consisting of two endpoints and all the points between them.


Linear

Something that graphs as a straight line, may be an equation or a term within an equation.
y = 3x  2 is a line 

Linear equation

An equation with one variable no exponents
7 = 2x  3 

Linear function

A function that graphs as a straight line. Its form is usually y = mx + b where m is the slope and b is the yintercept. An alternate form is Ax + By = C
y = 2x  3 or 2x  y = 3 

Matrix

A rectangular arrangement of numbers, it uses big brackets to define the matrix. The size of a matrix is # of rows by the # of columns.


Maximum value

The largest value a function can reach.
for y =  x2 + 2 the maximum value is 2 

Midpoint

The point that divides a line into two equal pieces. For the line with end points at A(x1,y1) and B(x2,y2), the midpoint is located at:
x1 + x2 , y1 + y2 2 2 The midpoint of a line with ends at (2,5) and (4,7) is at (3,6) 

Minimum value

The smallest value a function can reach.
for y = x2 + 5 the minimum value is 5 

Mode

The data item that occurs most frequently in a set of numbers. A set may have more than one mode.
for 1, 3, 4, 6 and 6 the mode is 6 

Multiplicative inverse

Two numbers that multiply to equal one
Reciprocal inverse of a fraction is the fraction turned upside down ½ and 2 are inverses because ½ • 2 = 1 

Multiplication counting principle

If there are m ways to make a first selection and n ways to make a second selection, then there are m x n ways to make the two selections.
If there are 3 kinds of crust and 6 kinds of topping, then there are 3 x 6 = 18 different pizza choices 

Natural number

The counting numbers  the first numbers learned by very small children
1, 2, 3, 4, 5, ... 

Negative angle

An angle formed by a clockwise rotation around the vertex.


Negative square root

 √
 √25 =  5 is the negative square root of 25 

Normal distribution

A statistical frequency distribution that graphs in the shape of a bell curve


Oblique triangle

Any triangle that is not a right triangle


Observational data

In statistics, data that is from seeing something happen or asking someone (doing a survey) about what happened.


Obtuse angle

An angle that measures between 90 and 180 degrees
90° < x < 180° 

Obtuse triangle

A triangle with one obtuse angle
One angle bigger than 90° 

Odd Function

A function graph whose axis of symmetry is both the xaxis and the yaxis. It must pass through the origin.


Onetoone function

A function where the range elements (the y's) are used only once.
y = 2x + 3 is onetoone 

Open interval

An interval that does not include the endpoints
(4, 5) is the interval between 4 and 5 

Opposite rays

Two collinear rays that share the same endpoint and together form a straight line


Order of operations

do any operation inside grouping symbols, like parentheses, absolute values, square root signs or the numerator or denominator of a complex fraction
simplify terms with exponents multiply and divide in order from left to right add and subtract in order from left to right PEMDAS 

Ordered numbers

Numbers that are arranged in order from smallest to largest or from largest to smallest
5 < 7 < 8.5 6 > 2 > 1 

Ordered pair

The location of a point on a coordinate axis
(6, 1) is a point 6 units to the right and 1 unit down from the origin 

Origin

(0, 0)
The place where the x axis and y axis intersect in a coordinate plane 

Orthogonal vectors

Vectors that are perpendicular, meaning the angle between the two vectors is 90°


Orthographic drawing

A drawing that represents a three dimensional object by showing separate drawings for the front, top and right side views


Parabola

The curved shape you get when you graph a quadratic function


Parallel lines

Lines that are always the same distance apart, they never cross. Lines that have the same slope
y = 3x + 1 and y = 3x  5 are parallel because they both have slope = 3 

Parallelogram

A quadrilateral where the opposite sides are parallel
Rectangles, squares, and diamonds are parallelograms 

Pascal's Triangle

A pattern for finding the coefficients of the terms in a binomial expansion. It is also used in probability.
1 1 1 1 2 1 1 3 3 1 

Perfect squares

Numbers whose square roots are rational numbers
1, 4, 9, 16, 25, 36, and 49 are perfect squares ¼ is also a perfect square 

Perpendicular bisector

A line, segment, or ray that is perpendicular to the original segment at its midpoint


Perpendicular lines

Lines that cross at right angles. The product of the slopes is 1.
y = 2x + 1 and y = ½x  5 are perpendicular because 2 • (½) = 1 

Plane

A flat surface that extends forever in all directions. Planes have no thickness.


Point

A location in space that has no size. Any point can be uniquely identified by a set of coordinates (x, y).


Polynomial

A statement with one or more terms  poly means many
5x2, 72, and 3x2 + 2x  1 are polynomials 

Position vector

A vector with its initial point at the origin


Positive angle

An angle formed by counter clockwise rotation about its endpoint.


Proportion

A statement that two ratios are equal  two fractions that are equal
1 = 3 5 15 

Pure imaginary number

A complex number a + bi, where a = 0 and b is not zero


Pythagorean theorem

In a right triangle, the sum of the squares of the lengths of the two sides (legs a and b) is equal to the square of the length of the hypotenuse (c)
a2 + b2 = c2 

Quadrants

The coordinate xy plane is divided into four quadrants by the x axis and y axis. Quad means four. The quadrants are usually labeled with roman numerals.


Quadratic equation

An equation written in the form ax2 + bx + c = 0 where a, b, and c are real numbers and a ≠ 0
The largest exponent is 2 2x2  3x + 4 = 0 

Quadratic formula

if ax2 + bx + c = 0 and a ≠ 0, then
x = b ± √(b2  4ac) 2a 

Quadratic function

A function with an equation written in the form y = ax2 + bx + c where a ≠ 0
Graph as a parabola  the largest exponent is 2 y = 2x2  3x + 4 

Quadrilateral

A geometric figure with four sides and four angles
A rectangle is quadrilateral 

Radian

A unit of measure for angles, used in trigonometry, calculus, and advanced math and physics.
1 radian = 180° 

Radical

A square root sign or any other root, like a cube root or fourth root
√5 

Radius

In a circle, any segment that has one endpoint at the center of the circle and the other endpoint on the circle


Range

The set of all possible output values of a function  the dependant variable. For functions in x and y, the possible y values are the range.
for y = x the range is all positive numbers and 0 

Ratio

Comparing two numbers by division
A fraction ¾ and 3:4 

Rational expression

An expression with fractions, especially when there is a variable in the denominator. The variable can not make the denominator equal to zero


Rational number

A number that can be written as a fraction. This includes whole numbers, fractions, and decimals that truncate (end) or repeat.
½, ¾, 2.5 and 3 are rational 

Rationalize the denominator

Make the denominator of a fraction a rational number without changing the value of the expression
Get rid of any √ signs in the denominator 3 = 3√5 √5 5 

Ray

The part of a line consisting of one endpoint and all the points extending forever in one direction


Real number

A number that is either rational or irrational. All numbers except imaginary numbers
√5, ½, ¾, 2.5, 0, π and 3 are real numbers 

Reciprocal

Multiplicative inverse of a nonzero number. The product of a number and its reciprocal is 1.
To get the reciprocal; Flip it! 2 and 3 3 2 are reciprocals because 2 • 3 = 1 3 2 

Regular polygon

A polygon that is both equilateral and equiangular.


Relation

Any set of ordered pairs


Relationship symbols

Symbols that compare two numbers. This includes the equal sign.
5 < 7 2 > 8 

Remote interior angles

For each exterior angle of a triangle, the two nonadjacent angles


Rhombus

A parallelogram with four congruent sides
A diamond is a rhombus 

Right Triangle

A triangle that has one 90° angle. The other two angles will add up to 90°


Sanple Space

In probability, all the possible ways that an event can happen.


Scalar

A quantity that represents a magnitude. It can be represented by a real number.


Scalene triangle

A triangle with no sides congruent. All sides are different length


Scatter plot

A graph that relates ordered sets of data. Scatter plots frequently have dots or x's


Scientific Notation

A number expressed in the form a x 10n where n is an integer and 1 < a < 10. For a number between 0 and 1, the exponent n will be a negative.
3450 = 3.45 x 103 0.052 = 5.2 x 102 

Sector of a circle

The portion of the interior of a circle intercepted by a central angle. Like a piece of a round pie


Segment

Part of a line consisting of two endpoints and all the points between them


Semicircle

Exactly half a circle


Skew lines

Two lines that are not in the same plane. They do not intersect and they are not parallel.


Slope

The measure of the steepness of a line. Slope is the change in y (up and down) divided by the change in x (left and right).
Slope is abbreviated m. slope = m = Δy Δx 

SlopeIntercept form

A linear equation written in the form y = mx + b, where m is the slope and b is the yintercept
y = 2x + 4 

Solution set

The set of all numbers that satisfy an equation (make it true).


Standard Form of a Polynomial

When the degree of the terms in a polynomial decrease from left to right.
5x3 + 3x2  x + 8 

Straight angle

An angle that measures 180°, a straight line.
x = 180° 

Supplementary angles

Two positive angles whose measures add to 180 degrees, a straight line.
A + B = 180° 

System of Linear Equations

Two or more linear equations for which a common solution is sought.
The solution is where the two lines cross when graphed. 

Tangent

The ratio of the length of the side opposite an angle and the side adjacent to the angle in a right triangle. side opposite divided by side adjacent


Term

A grouping together of one or more factors (variables and/or number).
Multiplication or division connects letters to numbers in a term. Addition and subtraction symbols separate terms. 4xy is one term 3xy + 5x – 6 has three terms 

Theoretical Probability

The calculated chance that something will happen based on the number of ways possible.
in tossing a coin, the theoretical probability of getting heads is: P(heads) = ½ 

Translation

When a graph is shifted in a horizontal or vertical direction.


Trapezoid

A quadrilateral with exactly one pair of parallel sides. Two sides are parallel, other sides are not.


Trend Line

A line on a scatter plot that can be drawn to pass through the points. The trend line shows the correlation between the two sets of data.


Unit Circle

A circle with a radius r = 1 and its center is at the origin. The equation is x2 + y2 = 1


Unknown

The value represented by a letter in an equation. The unknown is also called the variable.


Unbounded intervals

Intervals with end points at + ∞ on the real number line used to define the domain of an inequality. See bounded intervals
[a,∞) means x > a (a,∞) means x > a, an open interval (∞,b] means x < b (∞,b) means x < b, an open interval (∞,∞) means the entire number line 

Variable

A letter that is used to represent a number. When a variable is used in an equation, the value of the variable can be solved for and its value becomes the solution to the equation.
x a z 

Variable expression

A mathematical phrase that contains at least one variable
8  x is a variable expression 

Vertex

The point on a parabola where the arch turns. If the parabola opens up, the vertex is the smallest value of the function.


Vertical angles

Two angles whose sides are opposite rays


Vertical line test

A method used to determine if the graph of a relation is a function. For all functions, a vertical line will never cross the graph more than once.


Whole Number

The nonnegative integers including zero
0, 1, 2, 3, 4, 5, 6, ... 

xaxis

The horizontal axis of the coordinate plane


xcoordinate

The first number in an ordered pair. It indicates the distance left or right horizontally from the origin.
(5, 3) 5 is the xcoordinate 

xintercept

The xcoordinate of the point where a line crosses the xaxis
The xintercept of y = 2x + 4 is 4 

yaxis

The vertical axis of the coordinate plane


ycoordinate

The second number in an ordered pair. It indicates the distance up or down vertically from the origin.
(5, 3) 3 is the ycoordinate 

yintercept

The ycoordinate of the point where a line crosses the yaxis
The yintercept of y = 2x + 4 is 2 

Zero Product Property

For any two real numbers multiplied together so the answer is zero, at least one of the numbers multiplied must be zero. Used when factoring to solve an equation.
If ab = 0, a or b or both must equal zero 

Arithmetic Mean

The most commonly used type of average. To find the arithmetic mean of a set of n numbers, add the numbers in the set and divide the sum by n.


Prime Number

Prime Number
A positive integer which has only 1 and the number itself as factors. For example, 2, 3, 5, 7, 11, 13, etc. are all primes. By convention, the number 1 is not prime. 

Composite Number

A positive integer that has factors other than just 1 and the number itself. For example, 4, 6, 8, 9, 10, 12, etc. are all composite numbers. The number 1 is not composite.


Circumference

A complete circular arc. Circumference also means the distance around the the outside of a circle.


FOIL Method

A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial. Then simplify the products and combine any like terms which may occur.
Example: (x + 2)(x + 5) = x·x + x·5 + 2·x + 2·5 First Outer Inner Last = x2 + 7x + 10 

Linear System of Equations

A system of equations in which each equation is linear.
For any linear system, exactly one of the following will be true: There is only one solution, there are infinitely may solutions (underdetermined), or there are no solutions (overdetermined or inconsistent). 