154 terms

Absolute Value

The distance a value is from zero

Additive inverse

Two numbers whose sum is 0 are additive inverses of one another. Example 3 and -3 are additive inverses of one another because 3 + (-3) = 0.

Integer

A number expressible in the for a or -a for some whole number a.

Rational number

A number expressible in the form of a/b or -a/b for some fraction a/b. The rational numbers include the integers.

Whole numbers

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

rational numbers

a number expressible in the form a/b or -a/b for some fraction a/b. The rational numbers include the integers.

integers

a number expressible in the form a or -a for some whole number a.

constant

a number that does not change.

expression

a mathematical phrase that contains operations, numbers, and/or variables.

evaluate

To find the value of a numerical or algebraic expression.

equivalent expressions

expressions having the same value.

equation

a mathematical sentence that shows that two expressions are equivalent.

additive inverses

two numbers whose sum is 0 are additive inverses of one another.

additive identity property of zero

The property that states the sum of zero and any number is that number.

addition property of opposites

the property that states that the sum of a number and its opposite equals zero.

subtraction property of equality

the property that states that if you subtract the same number from both sides of an equation, the new equation will have the same solution.

distributive property

the property that states if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products.

addition property of equality

the property that states that if you add the same number to both sides of an equation, the new equation will have the same solution.

multiplication property of equality

the property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution.

division property of equality

the property that states that if you divide both sides of an equation by the same nonzero number, the new equation will have the same solution.

Inequality

a mathematical sentence that shows the relationship between quantities that are not equivalent.

algebraic inequality

an inequality that contains at least one variable.

solution set

the set of values that make a statement true.

Equation

a mathematical sentence that shows that two expressions are equivalent

denominator

the denominator tells how many parts there are in a whole. Within a fraction, the denominator is located below the fraction bar.

Numerator

the numerator tells how many parts of a whole are being considered. Within a fraction, the numerator is the number located above the fraction bar.

Convert

cause to change form

rational number

a number expressible in the form a/b where a and b are integers and b is not equal to 0

repeating decimal

a decimal in which one or more digits repeat infinitely

terminating decimal

a decimal is called terminating if its repeating digit is 0

terminating decimal

a decimal is called terminating if its repeating digit is 0.

sum

an amount obtained as a result of adding numbers

addend

a number added to one or more other numbers to form a sum

difference

an amount obtained as a result of subtracting numbers

fraction

a number expressible in the form a/b where a and b are integers

proper fraction

a fraction where the numerator is smaller than the denominator

improper fraction

a fraction in which the numerator is greater than or equal to the denominator

mixed number

a number that has a fraction and an integer

multiplicative inverses

two numbers whose product is 1. . Example 3/4 x 4/3 = 1

numerator

Tells how many parts of a whole are being considered. Within a fraction, the numerator is the number located above the fraction bar (top number).

rational number

a number expressible in the form a/b or -a/b. Rational numbers include integers.

additive inverse

Two numbers whose sum is 0 are additive inverses of one another.

common denominator

A denominator that is the same value between two fractions

equivalent fractions

Fractions that have the same value or fractions that name the same amount. They represent the same part of a whole. When subtracting fractions or mixed numbers, equivalent fractions can be generated using the process of regrouping or renaming.

fraction

A number expressible in the form a/b where a and b are integers.

improper fraction

An improper fraction is a fraction in which the numerator is greater than or equal to the denominator.

least common denominator

The smallest whole number that is divisible by each of the denominators.

mixed number

A mixed number is an integer and a fraction.

numerator

The numerator tells how many parts of a whole are being considered. Within a fraction, the numerator is the number located above the fraction bar (top number).

Rate

a ratio that compares quantities in different units

Proportion

an equality of two ratios

Constant of Proportionality

the constant unit rate associated with the different pairs of measurements in a proportional relationship

Unit Rate

a rate that has a denominator of 1

Ratio

a comparison of two quantities by division

Percent

a ratio that compares a number to 100

Tax

a percent of the cost of an item, which is charged by governments to raise money

Tip

the amount of money added to a bill for service; usually a percent of the bill

Commission

pay that is equal to a percent of sales

Mark-Up

added cost of merchandise to arrive at the selling price of an item

Discount

the amount by which a price is decreased

Percent Change

the amount stated as a percent that a number increases or decreases

Percent Error

percentage value that tells how close or how far off a measured (experimental) value is from the predicted (accepted) value.

Predicted Value

the value in a situation that is the real, accepted, and true value

Measured Value

the value in a situation that is the experimental or actual value

interest (I)

an amount that is collected or paid for the use of money.

principal (p)

the amount of money deposited, borrowed, or invested.

rate (r)

rate of interest per year (as a decimal). Interest rates are typically expressed as percents, so they must be written as decimals to be used in the formula I = prt.

time (t)

time, in years, that the money earns interest.

Balance

the principal plus the interest

simple interest

the formula to calculate simple interest is I = prt, where I is the interest, p is the principal, r is the interest rate per year, and t is the time in years.

Ray

A part of a line. It has exactly one endpoint

Angle

A figure formed by two rays with a common endpoint

Vertex

Corner or intersection of geometric points

Side

One of the rays forming the exterior of an angle or polygon

Right Angle

An angle that measures 90 degrees

Acute Angle

An angle that measures less than 90 degrees

Obtuse Angle

An angle that measures more than 90 degrees but less than 180 degrees

Straight Angle

An angle that measures 180 degrees

Complementary Angles

Two angles whose sum is 90 degrees

Supplementary Angles

Two angles whose sum is 180 degrees

Congruent Angles

Angles that have the same measure

Adjacent Angles

Angles that share a vertex and a side but no points in their interiors

Vertical Angles

Angles formed by two intersecting lines and are opposite each other. Vertical angles are congruent.

Triangle

A three sided polygon

Equilateral Triangle

A triangle with three congruent sides

Isosceles Triangle

A triangle with two congruent sides

Scalene Triangle

A triangle with no congruent sides

Right Triangle

A triangle containing a right angle

Acute Triangle

A triangle with all angles measuring less than 90 degrees

Obtuse Triangle

A triangle containing one obtuse angle

Square

a parallelogram with four right angles and four congruent sides

Rectangle

a parallelogram with four right angles

Parallelogram

a quadrilateral with both pairs of opposite sides parallel

Trapezoid

a quadrilateral with exactly one pair of parallel sides

Triangle

a polygon with three sides

Rhombus

a parallelogram with four congruent sides

Perimeter

the distance around the figure

Area

the number of square units it encloses

Circle

the set of all points in a plane that are equidistant from a given point, called the center

Chord

a segment whose endpoints are on the circle

Diameter

a chord that passes through the center of the circle

Radius

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

Circumference

the distance around a circle. You calculate the circumference of a circle by multiplying the diameter by π

Similar Figures

Figures whose corresponding sides are proportional and corresponding angles are congruent

Corresponding

Sides or angles that lie in the same location on different figures

Proportions

An equality of two ratios

Scale Factor

The ratio used to enlarge or reduce similar figures. The scale factor comes from simplifying the ratio between two corresponding parts

Scale Model

A proportional model of a three-dimensional object. The model's dimensions are related to the dimensions of the actual object by a ratio called the scale factor.

Scale

The ratio between two sets of measurements. Scales can use the same units or different units.

Prism

A three dimensional figure with two parallel bases that are congruent polygons, and lateral faces that are parallelograms. A prism is named for the shape of its base.

Surface Area

the sum of the areas of the base(s) and the lateral faces of a space figure

Volume

the number of cubic units needed to fill a three-dimensional figure

Pyramid

a space figure with triangular faces that meet at a vertex, and a base that is a polygon. A pyramid is named for the shape of its base.

Cross-Section

The two-dimensional face that is the result of a three-dimensional shape being intersected by a plane.

Data

Values such as counts, ratings, measurements, or opinions that are gathered to answer questions.

Line Plot

A quick, simple way to organize data along a number line where the X's (or other symbols) above a number represent how often each value is mentioned

Mean

A value that represents the "evening out" of the values in a set of data

Measures of Center

Establish a central location in the data set

Measures of Variability

Establish the degree of variability (or scatter) of the individual data values and their deviations from the measures of center

Median

The number that is the midpoint of a set of data

Mode

The data value that occurs the most

Range

The difference between the least value and the greatest value in a data set

Statistics

The practice of collecting and analyzing data in large quantities

Cluster

a group of things or persons close together

Distribution

The arrangement of values in a data set

Frequency Table

A list of items or intervals that shows the number of times, or frequency, with which they occur.

Gap

a break or opening

Histogram

A display that shows the distribution of numeric data. The range of data values, divided into intervals, is displayed on the horizontal axis. The vertical axis shows frequency.

interval

is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set

Peak

being at the point of maximum frequency, intensity, use, etc.

Box Plot

a method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data

Five-Number Summary

The minimum, value, lower quartile, median, upper quartile, and maximum value

Inter-Quartile Range

a measure of variation in a set of numerical data, the inter-quartile range is the distance between the first and third quartiles of the data set

Lower Quartile

for a data set with median m, the first quartile is the median of the data values less than m

Maximum Value

The greatest value in a data set

Minimum Value

The lowest value in a data set

Outlier

a value that lies far from the "center" of a distribution

Quartiles

one of the values of a variable that divides the distribution of the variable into four groups having equal frequencies

Upper Quartile

for a data set with median m, the third quartile is the median of the data values greater than m

Mean Absolute Deviation

The average distance of all data values from the mean of the set

Variability

Degree to which data are spread out around a center value

Representative Sample

A sample in which every member of the population has an equal chance of being included in the sample. Random sampling is the best way to produce a representative sample that will support valid inferences.

Measures of Center

Mean, median, and mode

Range

The difference between the maximum and minimum values in a distribution

Outliers

Values significantly higher or lower than the other data values in a data set.

Outcome

A possible result.

Probability

A number between 0 and 1 that describes the likelihood that an outcome will occur.

Experimental Probability

A probability that is determined through experimentation.

Theoretical Probability

A probability obtained by analyzing a situation.

Tree Diagram

A diagram used to determine the number of possible outcomes in a probability situation.

Payoff

The number of points (or dollars or other objects of value) a player in a game receives for a particular outcome.

Area Model

A diagram in which fractions of the area of the diagram correspond to probabilities in a situation.

Expected Value

The average payoff over the long run.

Binomial Probability

The probability of getting one of two outcomes.