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198 Cards in this Set

  • Front
  • Back
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
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
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
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
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
(x + 3)2= x2 + 6x + 9 is a binomial expansion
Central angle
An angle whose vertex is the center of a circle
The numerical factor when a term has a variable. The number next to a letter
5 is the coefficient and y is the variable
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.
Objects that are the same size and the same shape. The symbol for congruent is an equal sign with a squiggle over it.
a value or number that never changes
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 x-axis is the horizontal axis and the y-axis is the vertical axis. The two axes meet at the origin (0,0)
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
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
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 y-axis.
y = 5x2 + 2
A raised number that represents repeated multiplication of a factor
34 = 3 • 3 • 3 • 3
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.
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
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
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
A bar graph that shows the frequency of data. The height of each bar shows the number of items in each interval
A set of points that are equidistant from a foci. The graph looks a lot like two parabolas on their side.
In a right triangle, the side opposite the right angle. The longest side in a right triangle
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
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
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
The whole numbers and their opposites
... - 3, -2, -1, 0, 1, 2, 3, ...
Lines intersect when they cross. The point where they cross is called the intersection.
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 three-dimensional 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
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
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.
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 y-intercept. An alternate form is Ax + By = C

y = 2x - 3
2x - y = 3
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
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
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
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 x-axis and the y-axis. It must pass through the origin.
One-to-one function
A function where the range elements (the y's) are used only once.
y = 2x + 3 is one-to-one
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
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
(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
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
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 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
A flat surface that extends forever in all directions. Planes have no thickness.
A location in space that has no size. Any point can be uniquely identified by a set of coordinates (x, y).
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.
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
The coordinate x-y 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)

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
A geometric figure with four sides and four angles
A rectangle is quadrilateral
A unit of measure for angles, used in trigonometry, calculus, and advanced math and physics.
1 radian = 180°
A square root sign or any other root, like a cube root or fourth root
In a circle, any segment that has one endpoint at the center of the circle and the other endpoint on the circle
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
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
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
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.
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 non-adjacent angles
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.
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 10-2
Sector of a circle
The portion of the interior of a circle intercepted by a central angle. Like a piece of a round pie
Part of a line consisting of two endpoints and all the points between them
Exactly half a circle
Skew lines
Two lines that are not in the same plane. They do not intersect and they are not parallel.
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
Slope-Intercept form
A linear equation written in the form y = mx + b, where m is the slope and b is the y-intercept

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.
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
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
When a graph is shifted in a horizontal or vertical direction.
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
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
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.
Variable expression
A mathematical phrase that contains at least one variable
8 - x is a variable expression
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 non-negative integers including zero
0, 1, 2, 3, 4, 5, 6, ...
The horizontal axis of the coordinate plane
The first number in an ordered pair. It indicates the distance left or right horizontally from the origin.
(5, 3)
5 is the x-coordinate
The x-coordinate of the point where a line crosses the x-axis
The x-intercept of
y = 2x + 4 is 4
The vertical axis of the coordinate plane
The second number in an ordered pair. It indicates the distance up or down vertically from the origin.
(5, 3)
3 is the y-coordinate
The y-coordinate of the point where a line crosses the y-axis
The y-intercept 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.
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).