PSAT 8th grade Math vocabulary with Formulas

function

1. A relationship from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. 2. The action or actions that an item is designed to perform.

Transformation

A change in the size or position of a figure

Histogram

A graph of vertical bars representing the frequency distribution of a set of data.

bar graph

A graph that uses horizontal or vertical bars to display data

Scatter Plots

A graph with points plotted to show a possible relationship between two sets of data.

Equation

A mathematical statement with variables and constants which contains an equal sign

rate

A ratio that compares two quantities measured in different units

Angle Bisector

A ray that divides an angle into two congruent angles

Ratio

A relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4.

negative linear relationship

A relationship in which increases in the values of the first variable are accompanied by decreases in the values of the second variable.

Translation

A side of a figure along a strait line

Sphere Volume

A sphere is a set of points in space that are a given distance r from the center.

stem and leaf plot

A system used to condense a set of data where the greatest place value of the data forms the stem and the next greatest place value forms the leaves.

Two-Way Frequency Table

A table that displays the frequencies of data in two different categories

infinite solutions

An equation that has infinite solutions

linear equation

An equation whose graph is a line

Rational numbers

Any number that can be expressed as a fraction

irrational numbers

Any real number which cant be expressed as a fraction of two integers

Similar Solids

Are solids that have the same shape and proportional corresponding dimensions.

rate of change

Distance or change of a line

Exponent Zero Property

Everything to the power of zero will equal 1.

Data

Facts and statistics collected together for reference or analysis

Congruent Figures

Figures that have the same shape and size.

Congruent

Having the same size and shape

standard form of a linear equation

In this kind of equation, x and y are variables and A, B, and C are integers. Ax+By=C

Scale Factor

In two similar geometric figures, the ratio of their corresponding sides is called the scale factor.

slope

Is the rate of change between any two points on a line. It is the measure of the steepness of the line.

Multiplying powers with the same base

Keep the base and add the exponents then simplify

negative slope

Line falls from left to right

No Solution and inconsistent

No solution would mean that there is no answer to the equation.

cube root

One of three equal factors of a number.

Domains

Possible values of x.

range

Possible values of y

Evaluating Functions

Replace (substitute) its variable with a given number or expression.

Box Plot (Box and Whisker Plot)

Shows distribution of data values on a number line. Divided into quartiles.

Proportional

The definition of geometrical proportion is the relationship between two things when the quantities of the two are equal in ratios. An example of geometrical proportion is when 4 is to 2 as 8 is to 4 - a square 4x2 and a square 8x4.

no relationship between variables

The points show no pattern

Slope of a line definition

The ratio of change in Y (vertical change) to the change in X (horizontal change. Slope= Change Y/ Change X

direct variation

The relationship between two variable quantities that have a constant ratio.

slope formula

The slope is calculated by counting the rise and then counting the run. We then write the slope as a fraction.

marginal frequency

The sums of the rows and columns in a two-way table

Volume of a cylinder

The volume V of a cylinder is the product of the area of the base and the height of the cylinder.

cone

The volume V of cone is one-third the product of the area of the base and the height of the cone

Product of Powers Property

To multiply powers with the same base, add their exponents

Similar

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

Ordered pair/Coordinate

Two numbers that tell you a location on the coordinate plane

Volume of a Cone Formula

V=1/3πr²h

Sphere Volume Formula

V=4/3πr³

Volume of a cylinder Formula

V=πr²h

Evaluating Functions / Example

What is the value of y= 2x + 5 when x=3 , Y=2(3) + 5, Y=6+5, Y=11

Negative Exponents in a denominator

When there is a negative exponent, take the reciprocal of the base

Negative Exponents in a numerator

When there is a negative exponent, take the reciprocal of the base

Volumes of Similar Solids

When two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

constant of variation

a constant ratio in a direct variation

image

a figure resulting from a transformation

linear function

a function in which the graph of the solutions forms a line

line graph

a graph that uses one or more lines to show changes in statistics over time or space

Dot Plot

a graphical display of data using dots

square root

a number that when multiplied by itself equals a given number

nonlinear relationship

a relationship between two variables that produces a curved line on a line graph; equations of the form represent nonlinear relationships

system of equations

a set of two or more equations containing the same variables. Example Y= x + 1

Cylinder

a solid geometric figure with straight parallel sides and a circular or oval cross section.

Rotation

a transformation in which a figure is turned around a point

reflection

a transformation of a figure that flips the figure across a line

dialations

a transformation that enlarges or reduces a figure

two-way relative frequency table

a two-way table that displays relative frequencies

Pythagorean Theorem -FORMULA

a² + b² = c²

corresponding angles

congruent angles in the same relative position within two figures

congruent solids

exactly the same shape and exactly the same size

solving linear equations by graphing

he solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

zero slope

horizontal line

positive linear relationship

increases in the values of one variable are accompanied by increases in the values of the second variable

solving systems of equations

is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. Example Y= 2x + 5

perfect square

is a number with integers as its square root

power

name given to a base combined with an exponent

Base

number used as a factor

exponent

number used to tell how many times to multiply the base

preimage

oringinal figure in a transformation

positive slope

rises from left to right

Writing algebraic expressions using exponents

s * s * s * s = s⁴

point slope form

the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line

vertical angles

the non-adjacent angles formed by the intersection of two lines

real numbers

the set of all rational and irrational numbers

undefined slope

the slope of a vertical line

Pythagorean Theorem

the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

x-intercept

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

Input

the x-values (domain) of a relationship, the value substituted into an expression or function

y-intercept

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

outputs/inputs

the y-values (range) of a situation, The results of the operation of a formula.

adjacent angles

two angles in a plane that share a common side and share a common vertex but have no interior points in common (do not overlap)

supplementary angles

two angles the sum of whose degree measures is 180

complementary angles

two angles the sum of whose degree measures is 90

SSS triangle congruence

two triangles are congruent if the three sided of one triangle are congruent respectively, to the three sided of the other

ASA triangle congruence

two triangles are congruent if two angles and the included side of one triangle are congruent, respectively, to two angles and the included sided of the other

SAS triangle congruence

two triangles are congruent if two sides and the included angle of one triangle are congruent, respectively, to two sides and the included angle of the other

One-solution equations

when solving an equation the variable equals a number

solving system of linear equations substitution

works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.

direct variation equation

y=kx

slope-intercept form

y=mx+b, where m is the slope and b is the y-intercept of the line.

solve system of linear equations elimination

you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.