ATI TEAS MATH

finding the percentage

% = p (part)/ w (whole)

finding the part

p (part) = w (whole) x %

finding the whole

w (whole) = p (part) / %

percent increase

percent increase = new amount - original amount / original amount x 100

mean

found by adding all numbers in a set together and dividing that by the number of the numbers in a set

median

arrange numbers from least to greatest and then find the middle number; when there are an even amount of numbers in a set, find the average (mean) of those two numbers

mode

arrange numbers from least to greatest, then find the number (s) that occurs the most often

range

subtract the smallest number from the highest number in a set

standard deviation

a measure of variability that describes the average distance of every score from the mean

low standard deviation

data is tightly clustered around the mean

high standard deviation

data is loosely spread over a range of values

symmetry

data is equally distributed on either side of a line or point

number of peaks

when data has multiple local maxima or minima; data can be bimodal (two peaks), unimodal (one peak), or multimodal (more and two peaks)

skewness

when data is not equally distributed on either side of a line or point

uniform data

When the frequency of each value of a variable in a graph is evenly spread out across the values of all variables.

types of trends

linear, exponential, and quadratic

direction of trends

positive (increasing), negative (negative), no change (flat)

rate of change

describes how a quantity is changing over time

linear trend

a straight line (line of best fit) can be drawn through the data

exponential trend

A trend with a constant growth rate; curved line

quadratic trend

increase in change but then stabilizes and decreases

probability

likelihood that a particular event will occur; formula - p(event) = (number of desired outcomes) / (total outcomes)

dependent variable

a variable (often denoted by y ) whose value depends on that of another.

independent variable

a variable (often denoted by x ) whose variation does not depend on that of another.

positive correlation

A correlation where as one variable increases, the other also increases, or as one decreases so does the other. Both variables move in the same direction.

negative correlation

as one variable increases, the other decreases

no correlation

There is no relationship between data sets.

direct relationship

a relationship in which one variable increases with an increase in another variable; y=mx

inverse relationship

a relationship in which one variable decreases when another variable increases; y=m/x

perimeter

p=s+s+s.... (s= side)

circumference

c=πd (d= diameter)

area of a rectangle

A=lw (l=length ; w=width)

area of a triangle

A=1/2bh (b=base ; h=height)

area of a circle

A=πr² (r=radius)

area of a parallelogram

A=bh (b=base ; h=height)

area of a trapezoid

A=1/2h(b1+b2) ((b1= smallest base b2= largest base; h=height)

volume of a rectangular prism

V=lwh (l=length ; w=width ; h=height)

volume of a triangular prism

V=(1/2bh)h

volume of a cylinder

V=πr²h (r= radius ; h= height)

volume of a rectangular pyramid

V=1/3lwh

volume of a cone

V=1/3πr²h

Decimal Placement/Converting

- Value greater than 1, Move decimal to right till you get whole number.

- Number becomes numerator and 1 becomes denominator with the number of 0's that matches number of moves for decimal. = Fraction

- Value less than 1. Use whole number as numerator and the Place value of last decimal Digit as denominator. =Fraction

Percentage Convert to/from Decimal

TO - Divide % by 100 then remove % symbol

FROM - Multiply by 100 then add % symbol

Divide % by 100

How do you convert a percent into a decimal?

Percentage Convert to/from Fraction

TO - Convert to decimal first (divide by 100) then put into simplest form

FROM - Convert to decimal (multiply to get 100 in denominator then divide by denominator) then put decimal into %

Fraction Convert to Decimal

Divide numerator by denominator

Compare and Order Rational Numbers

-Rational Numbers: -6 (-6/1), 5 (5/1), 100 (100/1)

-Irrational Numbers: Square root (any prime number), pi

-Numeric Order: Least to Greatest, Greatest to Least. Best in decimal form. Line them up vertically.

-Fraction/Fraction Form: 5 2/7 (put into decimal) Divide 2 by 7 to get .2857 which will equal 5.2857

<, _<_

Less than, IS fewer than

Less than or equal to, is at most, is no more than

>, _>_

Greater than, IS more than

Greater than or equal to, is at least, is no less than

Common Denominator

1. Find least on on multiple of denominator

2. Change each fraction to make their denominator the same as least common denominator

~List multiples of each denominator and find SMALLEST number

~Multiply numerator by multiple of LCD, Use LCD as denominator

Solve Equations in One Variable

Collecting all variable terms to one side of the equal sign and all the constants on the other side, using addition or subtraction. Once all like terms are combined, last step is to divide. Could also be multiplication by the reciprocal ( One divided by original number).

Extraneous

Incorrect

Story that is interesting containing details that aren't necessary to tell you what happened.

Erroneous

Irrelevant

Story might contain conflicting accounts of what happened due to having multiple observers.

Terms Related to Operations

Sum (+) , Difference (-) , Product (x) , Quotient ( / ) , Per 100 (#% _<_ 100%), Is or Of (#% _>_ 100%)

Order of Operations

-PEMDAS

-Parentheses FIRST

-Multiplication and Division SECOND (Left to Right)

-Addition and Subtraction THIRD (Left to Right)

=

Equal, equal to, is, was, were, will be, yields, becomes

Rational Numbers can be represented by?

By fractions

Includes: Whole Numbers, Positives/Negatives, Zero, and all decimals that either terminate or repeat.

~Irrational numbers will not concern us at this point

Percent Increase Equation

- Percent Increase

~ PI= new amount - original amount/ original amount X 100%

Percent Decrease Equation

PD = original amount - new amount/ original amount X 100%

Rounding Rules

- 5 or LARGER, round UP (decimals)

- 5 or SMALLER, Round DOWN (decimals)

- Numerator is GREATER THAN OR EQUAL TO 1/2 the denominator, then round whole # UP

- Numerator is LESS THAN OR EQUAL TO 1/2 the denominator, then round whole # DOWN

Proportions

Ratio in fraction form set equal to another ratio in fraction form.

~Example:

50mi/1cm = X/12.6cm (cross multiply) -> 50mix12.6cm/1cm=Xx12.6cm/12.6cm (cancel out 12.6cm on Num. and Den.) -> 50mix12.6cm/1cm (cancel out cm) = X -> 630mi = X

Constant of Proportionality

Also known as Rate of Change

Ratio between two quantities

~Y=k*x (k is constant, y and X are direct proportion)

~One variable is always the product of the other and a constant, the two are said to be directly proportional.

Bar Graph

Which graph is used to compare data (has scale)?

Area

What is the amount of space inside a 2 dimensional shape

Line Graph

Which graph is used to show data INCREASE or DECREASE over time (has legend)?

Pictograph

Which graph shows pics or symbols to show data (legend)?

Pie Chart

Which graph is a diagram to compare parts as a whole (labeled,legend)?

Histogram

What graph is like a bar graph with grouped data that is touching?

Stem and leaf plot

This graph outlines groups of data that fall into range (small to large, left=stem, right=leaf)

Scatter plot

This graph functions with data, finding simple regression.

4 different types: positive, negative, nonlinear exponential, nonlinear quadratic

Mean

Which measure of tendency is when you add all #, then divide by how many # there are? Also known as the average.

Median

Which measure of tendency is when you put the middle # of ordered (Least to Greatest) list, and if # are even, then the 2 middle # averaged out?

Mode

Which measure of tendency is the number that occurs the most and can be more than one?

Range

Which measure of tendency is when you subtract the minimum value from maximum value?

Outlier

What is a data point that is distinctly separated from other values and is considered unexpected value? This value "lies outside" (is much smaller or larger than) most of the other values in a set of data

Data trend

What is the term for the general tendency of numbers in a set?

Symmetry

Which shape of distribution is divided at the center with each side having half the data?

Unimodal

Which shape of distribution has a single clear peak?

Bimodal

Which shape of distribution has TWO clear peaks?

Bell Shaped

Which shape of distribution has a single peak at the center?

Skewed Right

Which shape of distribution has fewer observations on the right (towards higher values)?

Skewed Left

Which shape of distribution has fewer observations on the left (towards lower values)?

Uniform distribution

Which shape of distribution has observations in a data set that are spread equally across the range of the distribution?

Covariance

What is the term that explains the way two variables change together?

Dependent Variable

What kind of variable depends on at least one other variable?

Independent Variable

What kind of variable determines the value of another variable?

Length

Which geometric quantity is measured with ruler or tape measure?

Length

Inches, feet, yard, miles, centimeters, meter, and kilometers are all units of?

C=2 x PIE x r

How is the circumference (distance around a circle) calculated?

Pie x r squared

How do you find the area of a circle?

Length of half a circle

What does this formula cover?

C=2 PIE r then multiply by the fraction central angle measure/360

Perimeter

What is the term for the distance around a 2 dimensional shape?

Add all the sides

How do you find the perimeter of a shape?

Subtract the width and height of the other sides.

How do you find the perimeter of a shape that is missing a side?

A= l x l

What is the formula for a square?

A= l x w

What is the formula for a rectangle?

A= 1/2 x b x h

What is the formula for a triangle?

A= h x b

What is the formula for a parallelogram?

A= 1/2 x h x (b1 + b2)

What is the formula for a trapezoid?

A= PIE x R squared

What is the formula for a circle?