TEAS EXAM- MATH

Number

Quantify a set of entities that share some characteristic

*number is a quantity → a numeral is the symbol that represents the #

Natural numbers

1,2,3,4,5 - Counting numbers

Whole numbers

0,1,2,3,4,5 - Natural Numbers + 0

Integers

-3,-2,-1,0,1,2,3 - Whole numbers & all negative whole numbers

Real numbers

All numbers → the integer + all fraction/numbers in between decimal

Rational numbers

All real numbers that can be expressed as p/q where p&q are integers & q is nonzero

*natural whole & integers = rational

Irrational numbers

All real numbers that are not rational & irrational together constitute the entire set of real numbers

Number lines

Left/smallest → Right/greatest

Addition

Combining 2 or more numbers (+)

*when added you get a sum

*the order of numbers is irrelevant when adding

Subtraction

Opposite of addition (-) difference between the numbers

*when subtracting it creates a difference

Addition and Subtraction can only take place when…

Numbers have the same unit

ex: weight, volume, currencies

Multiplication

Replaces repeated addition of the same number with a single operation (X)

*result of multiplication is called the product

*order of numbers are irrelevant to the product

Division

inverse of multiplication

*division by 0 is undefined if it appears in an expression something is wrong

PEMDAS

Parentheses ()[]

Exponents

MD (X)(/)

AS(+)(-)

*Go from L→R

Exponents

imply an expression of repeated multiplication “power”

ex:6(2)

*any base to a power of 0=1

(-) value these expressions are considered fractions/decimals

Fraction

part of a whole number

*numerator is smaller for a proper fraction

ex: ½ 1→numerator 2→denominator

numerator is greater for an improper fraction

Improper Fraction

a whole number with a proper fraction

*compare fractions= denominators of fractions must be the same

Decimal

number that expresses part of a whole

Like Fractions

fractions with the same denominator

*to determine what the denominator should be= find the lowest common multiple between the numbers and convert to have the value as the denominator

*change the fraction to have a common denominator

The product (x) of a fraction by a fraction is…

always less than 1

Always change a mixed number to…

an improper fraction when multiplying by a mixed number

Percent (means ‘per hundred’)

represents a fraction of some quantity

Ratio

expresses the relationship between 2 numbers is expressed using a colon or fraction notation

*follows the rules or fractions

*avoid confusing standard ratios with odds both may use a colon but their meanings differ in general a ratio is the same as a fraction containing the same numbers

Proportion

equation of 2 ratios

ex:2 equivalent factors

Linear equation

equation where 2 expressions are set to equal each other

eq:ax+b=c

*only 1 solution

Addition property of equality

add the same number to both sides of the equation

Subtraction property of equality

subtract the same number from both sides of the equation

Multiplication property of equality

Multiply both sides of the equation by the same number

Division property of equality

Divide both sides of the equation by the same number

Two-step linear equation

ax+b=c

Multi-step linear equations

3 Steps

1. Simplify each side * remove parentheses remove fractions adding-like terms

2. Use (+) & (-)

3. Use (x) & (/) *infinite number of values

*variables can be placed on left or right sides

Addition property of inequality

Add the same number to both sides of inequality

Subtraction propert of inequality

Subtract the same number from both sides of the inequality

Multiplication property when (x) is a positive number

multiply both sides od the inequality by the same number

Division property when (x) by a positive number

divide both sides of the inequality by the same number

Multiplication property when (x) by a negative number

Multiply both sides of the inequality by the same number

Division property when (x) by a negative number

Divide both sides of inequality by the same number

*(x) & (/) both sides by a negative number reverses the sign

Estimations

rough calculations of a solution to a problem

ex: educated guess

Round a whole number

roud the value to the nearest ten or hundred

Power

exponents imply an expression of repeated multiplication

Square of a number

a number is the number raised to the power of 2

Square root

number is squared, gives that number

ex:10(10)=100

*most square roots & cube roots are not perfect roots

Perfect squares

numbers with whole number square roots

1,4,9,16,&25

Cube

a number is the number raised to the power of 3

Cube root

when the number is cubed gives that number

ex: 10(10)(10)=1,000

Perfect cube

numbers with whole number cube roots

1,8,27,64,&125

Scientific notation

a large or small number written in 2 parts

*a positive exponent=larger number

a negative exponent=small number

Polynomial

express that contains exponents as well as variables, constants & operations

Monomial

a polynomial of 1 term

Binomial

a polynomial of 2 terms

Trinomial

a polynomial of 3 terms

Squared Binomial expression

written in 2 different forms

ex:(a+b)2=a(2)+2ab+b(2)

(a-b)2=a(2)-2ab+b(2)

12 Inches =

1 Foot

1 Foot=

3 Feet

3 Feet=

1 Yard

5,280 Feet=

1 Mile

1 Pint=

16 Fluid Ounce’s

1 Quart=

2 Pints

1 Gallon=

4 Quarts

1,000 milliliters=

1 Liter

1,000 Liters=

1 Kiloliter

1,000 Milligrams=

1 Gram

100 Centigrams=

1 Gram

1 Kilogram=

1,000 Grams

1 Metric ton=

1,000 Kilograms

2.54 Centimeters=

1 Inch

1 Meter=

3.28 Feet

1.61 Kilometers=

1 Mile

1.06 Quarts=

1 Liter

3.79 Liters=

1 Gallons

28.3 Grams=

1 Ounce

1 Kilogram=

2.2 Pounds

Mean

Sum of all numbers in a data set divided by the number of elements in the set

Median

Middle number of a data set when written in order

Mode

Number or numbers that occur most often

Range

Difference between the highest & lowest values in a data set

Coordinate Plane

Two- dimensional number line with the horizontal axis→x-axis & verticall axis→y-axis

Area

Number of unit squares that fit inside a two-dimensional object

Rectangle Area

A= LW

Parallelogram Area

A=bh

Square Area

A=S(2)

Triangle Area

A=1/2 bh

Trapezoid Area

A=1/2h(b1+b2)

Regular Polygon Area

A=1/2ap

Cubes

made up of six congruent square faces

Right prism

made of 3 sets of congruent faces with at least 2 sets of congruent rectangles

Surface Area

any three-dimensional object is the sum of the area of all faces

Volume

any three-dimensional object is the amount of space inside the object

Circle

figure composed of points that are equidistant from a given point

Center

the point from which all points are equidistant

Chord

a segment whose endpoints are on the circle

Diameter

chord that goes through the center of the circle

Radius

a segment with one endpoint at the center of the circle and one endpoint on the circle

Arcs

have two endpoints on a circle between those endpoints

Circumference of a circle

is the perimeter or the distance around the circle

Area of a circle

is the amount of space inside a circle