Math needed for GRE

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Math Help for the GRE General Test

If you need help in preparing for the math part of the GRE general test, you have come to the right place. Note that you do not have to be a student at WTAMU to use this study session. It was created as a service to anyone who needs help getting ready for this test.

If this is your first visit to our website, please read the disclaimer.

The math part of the GRE General Test is split into four main areas:

arithmetic

algebra

geometry

data analysis

Below are the specific concepts you need to know about each of those areas. This list was compiled from researching the Math Review for Practicing to Take the GRE General Test (you need acrobat Reader to download) webpage at the official GRE website created by the Educational Testing Services.

Under each specific concept, you will find links to in-depth tutorials that will help learn and review the material. These tutorials come from the WTAMU Virtual Math Lab, which I created. Within these tutorials, you will find pertinent definitions, formulas, step-by-step explanations, an answer/discussion section with step-by-step solutions, and links to other credible webpages that can help you further with that topic.

In math, when you study a specific topic, a lot of times you are incorporating other mathematical topics into solving the problem. Some of the tutorials will overlap each other. This will help reinforce the concepts you need to know for the GRE.

HOW TO EFFECTIVELY USE THIS WEBPAGE:

Under the arithmetic, geometry and data analysis areas, you need to go to all the links that are under each topic to get the full benefit.

Under the algebra area, there is a lot of overlapping between the different levels (beginning, intermediate, and college) of tutorials. Find the algebra level that agrees with you most and do all of the tutorials under that level. If you start below college level algebra, make sure that you make your way up through college algebra before you take the GRE general test.

When you are done with a tutorial, you can come back to this webpage by clicking on the back arrow link marked GRE Math Help Page found on the top left corner of the tutorial page OR clicking on the back arrow on the top left of your Internet window until you are back to this page.

Arithmetic

The first area that we will be looking at is arithmetic. You know, fun things like making sure you have the negative in the right place and remembering when you have to find the common denominator of your fractions. Don't worry, I have the utmost confidence that you will do much better with arithmetic than Calvin.

SPECIAL NOTE:
You need to go to all the links that are under each topic for arithmetic to get the full benefit.

The arithmetic area covers:

integers

ordering and the real number line

absolute value

fractions

decimals

exponents

square roots

percents

Integers, Ordering and the Real Number Line, Absolute Value, Fractions, and Decimals

Beginning Algebra Tutorial 2: Symbols and Sets of Numbers

This tutorial covers:

sets
elements
equal and inequality signs
various sets of numbers

including integers and real numbers

Order Property for Real Numbers
absolute value of a number

Intermediate Algebra Tutorial 3: Sets of Numbers

This tutorial covers:

graphing a point on a real number line
knowing what a set and an element are
indicating if something is an element or is not an element of a set
subsets
roster
set builder forms of sets
the empty set and how to notate it
identifying what numbers belong to the set of:

natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers

finding the absolute value of a number
finding the opposite of a number

Beginning Algebra Tutorial 3: Fractions

This tutorial covers:

numerators and denominators of a fraction
the prime factorization of a number
simplifying a fraction
finding the least common denominator of given fractions
multiplying, dividing, adding and subtracting fractions

Beginning Algebra Tutorial 5: Adding Real Numbers

This tutorial covers:

adding real numbers
finding the additive inverse or the opposite of a number

Keep in mind that real numbers include integers, fractions and decimals as well as other types of numbers.

Beginning Algebra Tutorial 6: Subtracting Real Numbers

This tutorial covers:

subtracting real numbers

Keep in mind that real numbers include integers, fractions and decimals as well as other types of numbers.

Beginning Algebra Tutorial 7: Multiplying and Dividing Real Numbers

This tutorial covers:

finding the reciprocal of a number
multiplying and dividing real numbers
multiplying by zero
the fact that dividing by zero is undefined

Keep in mind that real numbers include integers, fractions and decimals as well as other types of numbers.

Exponents and Square Roots

Intermediate Algebra Tutorial 4: Operations on Real Numbers

This tutorial covers:

adding, subtracting, multiplying, and dividing real numbers
evaluating a numeric exponential expression
evaluating a numeric radical expression
using the order of operations appropriately

This is a good tutorial to review the topics covered above as well as teaching you about exponents and square roots.

Percent

Beginning Algebra Tutorial 16: Percent and Problem Solving

This tutorial covers:

converting percents into decimal numbers
converting decimal numbers into percents
solving word problems involving percents
pie charts with percents
tables with percents

Algebra

It's back!!!!!! Just when you thought it was safe to come back to school, POW, another math test with ALGEBRA!!! I'm hoping that with this section of tutorials, I will convert some of you who are math atheists (you know who you are).

SPECIAL NOTE:
Note that most of the topics under Algebra contain tutorials from three levels (lowest to highest): beginning, intermediate, and college.

Ideally, for the Algebra section, you want to be able to work the college level by the time you take the GRE test.

There will be some overlapping between the levels. If a topic has tutorials in more than one level, try going under the highest level first. If that is too hard for you, go to the tutorials of the next level down, if available. If that is too hard for you, go to the tutorials of the next level down, if available.

Once you find a level to start with, make sure that if it is below college level, in the end you work your way up to college algebra.

The beauty of this is it is individualized. You can go at your own pace at the comfort of your own computer. You know better than anyone else what your algebra skills are.

The algebra area covers:

operations with algebraic expressions

factoring

solving linear equations

translating words into algebraic expressions and applications

inequalities

coordinate geometry

rules of exponents

solving quadratic equations

Operations with
Algebraic Expressions

Beginning Algebra Tutorial 11: Simplifying Algebraic Expressions

This tutorial covers:

combining like terms
simplifying an expression using distributive property

Beginning Algebra Tutorial 27: Adding and Subtracting Polynomials

This tutorial covers:

identifying a term, coefficient, constant term, and polynomial
telling the difference between a monomial, binomial, and trinomial
finding the degree of a term and polynomial
combining like terms
adding and subtracting polynomials

Beginning Algebra Tutorial 28: Multiplying Polynomials

This tutorial covers:

multiplying any polynomial times any other polynomial
using the FOIL method to multiply a binomial times a binomial

Intermediate Algebra Tutorial 25: Polynomials and Polynomial Functions

This tutorial covers:

identifying a term, coefficient, constant term, and polynomial
telling the difference between a monomial, binomial, and trinomial
finding the degree of a term and polynomial
evaluating a polynomial function
combine like terms
adding and subtracting polynomials

Intermediate Algebra Tutorial 26: Multiplying Polynomials

This tutorial covers:

multiplying any polynomial times any other polynomial
using the FOIL method to multiply a binomial times a binomial
using special product rules to multiply a binomial squared and a product of a sum and difference of two terms

College Algebra Tutorial 6: Polynomials

This tutorial covers:

identifying a term, coefficient, constant term, and polynomial
telling the difference between a monomial, binomial, and trinomial
finding the degree of a term and polynomial
evaluating a polynomial function
combining like terms
adding and subtract polynomials
multiplying any polynomial times any other polynomial
using the FOIL method to multiply a binomial times a binomial
using special product rules to multiply a binomial squared and a product of a sum and difference of two terms

Factoring

Intermediate Algebra Tutorial 27: The GCF and Factoring by Grouping

This tutorial covers:

finding the Greatest Common Factor (GCF) of a polynomial
factoring out the GCF of a polynomial
factoring a polynomial with four terms by grouping

Intermediate Algebra Tutorial 28: Factoring Trinomials

This tutorial covers:

factoring trinomials
factoring using substitution
indicating if a polynomial is a prime polynomial

Intermediate Algebra Tutorial 29: Factoring Special Products

This tutorial covers:

factoring a perfect square trinomial
factoring a difference of squares
factoring a sum or difference of cubes
applying the factoring strategy to factor a polynomial completely

College Algebra Tutorial 7: Factoring Polynomials

This tutorial covers:

finding the Greatest Common Factor (GCF) of a polynomial
factoring out the GCF of a polynomial
factoring a polynomial with four terms by grouping
factoring a trinomial
indicating if a polynomial is a prime polynomial
factoring a perfect square trinomial
factoring a difference of squares
factoring a sum or difference of cubes
applying the factoring strategy to factor a polynomial completely

Solving Linear Equations

Beginning Algebra Tutorial 12: Addition Property of Equality

This tutorial covers:

knowing what a linear equation is
knowing if a value is a solution or not

Beginning Algebra Tutorial 13: Multiplication Property of Equality

This tutorial covers:

using the multiplication and division properties of equalities to solve linear equations
solving an equation using more than one property
knowing how to express consecutive integers in terms of x, if the first integer is x
knowing how to express even consecutive integers in terms of x, if the first even integer is x
knowing how to express odd consecutive integers in terms of x, if the first odd integer is x

Beginning Algebra Tutorial 14: Solving Linear Equations

This tutorial covers:

solving linear equations by using a combination of simplifying and various properties of equality

Intermediate Algebra Tutorial 7: Linear Equations in One Variable

This tutorial covers:

knowing what a linear equation is
knowing if a value is a solution or not
using the addition, subtraction, multiplication, and division properties of equalities to solve linear equations
knowing when an equation has no solution
knowing when an equation has all real numbers as a solution

College Algebra Tutorial 14: Linear Equations in One Variable

This tutorial covers:

knowing what a linear equation is
knowing if a value is a solution or not
using the addition, subtraction, multiplication, and division properties of equalities to solve linear equations
knowing when an equation has no solution
knowing when an equation has all real numbers as a solution

Translating Words into Algebraic Expressions and Applications

Beginning Algebra Tutorial 15: Introduction to Problem Solving

This tutorial covers:

using Polya's four step process to solve word problems involving numbers, rectangles, supplementary angles, and complementary angles

Beginning Algebra Tutorial 17: Further Problem Solving

This tutorial covers:

using Polya's four step process to solve word problems involving geometry concepts, distance, mixtures and interest

Intermediate Algebra Tutorial 2: Algebraic Expressions

This tutorial covers:

knowing what a variable is
knowing what an algebraic expression is
evaluating an algebraic expression given a value for a variable
translating an English phrase into an algebraic expression

Intermediate Algebra Tutorial 8: Introduction to Problem Solving

This tutorial covers:

using Polya's four step process to solve word problems involving numbers, percents, rectangles, supplementary angles, complementary angles, consecutive integers, and breaking even

Intermediate Algebra Tutorial 9: Formulas and Problem Solving

This tutorial covers:

solving a formula for a given variable
using Polya's four step process to solve word problems involving formulas

College Algebra Tutorial 16: Formulas and Applications

This tutorial covers:

translating an English phrase into an algebraic expression
using Polya's four step process to solve word problems
solving a formula for a given variable

Inequalities

Beginning Algebra Tutorial 18: Solving Linear Inequalities

This tutorial covers:

using the addition, subtraction, multiplication, and division properties of inequalities to solve linear inequalities
drawing a graph to give a visual answer to an inequality problem

Intermediate Algebra Tutorial 10: Linear Inequalities

This tutorial covers:

using the addition, subtraction, multiplication, and division properties of inequalities to solve linear inequalities
writing the answer to an inequality using interval notation
drawing a graph to give a visual answer to an inequality problem

College Algebra Tutorial 22: Linear Inequalities

This tutorial covers:

using the addition, subtraction, multiplication, and division properties of inequalities to solve linear inequalities
solving linear inequalities involving absolute values
writing the answer to an inequality using interval notation
drawing a graph to give a visual answer to an inequality problem

Coordinate Geometry

Beginning Algebra Tutorial 20: The Rectangular Coordinate System

This tutorial covers:

plotting points on a rectangular coordinate system
identifying what quadrant or axis a point lies on
telling if an ordered pair is a solution of an equation in two variables or not
completing an ordered pair that has one missing value

Beginning Algebra Tutorial 21: Graphing Linear Equations

This tutorial covers:

recognizing when an equation in two variables is a linear equation
graphing a linear equation

Beginning Algebra Tutorial 22: Intercepts

This tutorial covers:

finding the x- and y-intercepts of a linear function
graphing a linear function using the x- and y-intercepts
graphing vertical and horizontal lines

Beginning Algebra Tutorial 23: Slope

This tutorial covers:

finding the slope given a graph or two points
knowing the relationship between slopes of parallel lines as well as slopes of perpendicular lines

Intermediate Algebra Tutorial 12: Graphing Equations

This tutorial covers:

plotting points on a rectangular coordinate system
identifying what quadrant or axis a point lies on
knowing if an equation is a linear equation
telling if an ordered pair is a solution of an equation in two variables or not
graphing an equation by plotting points

Intermediate Algebra Tutorial 14: Graphing Linear Equations

This tutorial covers:

finding the x- and y-intercepts of a linear function
graphing a linear function using the x- and y-intercepts
graphing vertical and horizontal lines

Intermediate Algebra Tutorial 15: The Slope of a Line

This tutorial covers:

finding the slope given a graph, two points or an equation
writing a linear equation in slope/intercept form
determining if two lines are parallel, perpendicular, or neither

College Algebra Tutorial 25: Slope of a Line

This tutorial covers:

knowing when a line rises, falls, is horizontal or is vertical
finding the slope given two points on the line

College Algebra Tutorial 27: Graphing Lines

This tutorial covers:

graphing a straight line using the y-intercept and slope
graphing vertical and horizontal lines

Rules of Exponents

Beginning Algebra Tutorial 26: Exponents

This tutorial covers:

using the definition of exponents
simplifying exponential expressions involving multiplying like bases, zero as an exponent, dividing like bases, raising a base to two exponents, raising a product to an exponent and raising a quotient to an exponent

Intermediate Algebra Tutorial 23: Exponents and Scientific Notation Part I

This tutorial covers:

using the definition of exponents, simplifying exponential expressions involving multiplying like bases, zero as an exponent, dividing like bases, and negative exponents
writing a number in scientific notation
writing a number in standard notation, without exponents

Intermediate Algebra Tutorial 24: Exponents and Scientific Notation Part II

This tutorial covers:

simplifying exponential expressions involving raising a base to two exponents, raising a product to an exponent and raising a quotient to an exponent
multiplying and dividing numbers written in scientific notation

College Algebra Tutorial 2: Integer Exponents

This tutorial covers:

using the definition of exponents
simplifying exponential expressions involving multiplying like bases, zero as an exponent, dividing like bases, negative exponents, raising a base to two exponents, raising a product to an exponent and raising a quotient to an exponent

Solving Quadratic Equations

College Algebra Tutorial 17: Quadratic Equations

This tutorial covers:

solving quadratic equations by factoring
solving quadratic equations by the square root method
solving quadratic equations by completing the square
solving quadratic equations by using the quadratic formula
finding the discriminant of a quadratic equation and use it to tell how many and what type of solutions the equation has

Geometry

Ahhhhh, a relief from algebra. This section covers the basics of geometry. You do not need to know how to do geometry proofs for the test - YEAH!!! After completing this section, you will be able to write funny little cartoons like this one (ha, ha - I just couldn't resist).

SPECIAL NOTE:
You need to go to all the links that are under each topic for arithmetic to get the full benefit.

The geometry area covers:

lines

angles

polygons

triangles

quadrilaterals

circles

three-dimensional figures

SPECIAL NOTE - please read before starting this section:

You need to go to all the links that are under each topic for geometry to get the full benefit.

Lines, Angles, Polygons, Triangles, Quadrilaterals,
and Circles

Beginning Algebra Tutorial 33: Basic Geometry

This tutorial covers:

knowing what a line is
identifying the different types of angles
finding a complimentary angle to a given angle
finding a supplementary angle to a given angle
knowing what a polygon is
knowing what a quadrilateral is
identifying types of triangles
finding the value of a corresponding angle or side given congruent figures
finding the value of a corresponding angle or side given similar figures
knowing the relationship of the angles formed when a transversal cuts through two parallel lines
identifying parts of a circle

Formulas for Two- and Three-
Dimensional Figures

Beginning Algebra Tutorial 32: Formulas

This tutorial covers:

solving a formula for a given variable
solving problems involving formulas for two- and three- dimensional figures

Data Analysis

This is a very important area to know when going into graduate school. Most of you will be working on a thesis or a dissertation. No matter what field you are in you, chances are you will have to do data analysis on that work. I'm sure you will have better luck with probabilities than Frank and Ernest.

SPECIAL NOTE:
You need to go to all the links that are under each topic for arithmetic to get the full benefit.

The data analysis area covers:

measures of central location

measures of dispersion

frequency distributions

counting

permutations

combinations

probability

data representation and interpretation

SPECIAL NOTE - please read before starting this section:

You need to go to all the links that are under each topic for data analysis to get the full benefit.

Measures of Central Location, Measures of Dispersion,
and Frequency Distributions

Beginning Algebra Tutorial 34: Central Tendencies

This tutorial covers:

finding the mean, median, mode, range, standard deviation and frequency distribution of a list of values

Counting, Permutations,
and Combinations

College Algebra Tutorial 55: The Fundamental Counting Principle

This tutorial covers:

using the Fundamental Counting Principle to determine the number of outcomes in a problem

College Algebra Tutorial 56: Permutations

This tutorial covers:

using permutations to solve a counting problem involving order

College Algebra Tutorial 57: Combinations

This tutorial covers:

using combinations to solve a counting problem involving groups

Probability

College Algebra Tutorial 58: Probability

This tutorial covers:

finding the probability of an empirical event
finding a theoretical probability
knowing when two events are mutually exclusive
using basic properties of probability to find various probabilities
knowing when two events are independent of each other
knowing how to find the probability of the intersection of two independent events

Data Representation and Interpretation

Beginning Algebra Tutorial 9: Reading Graphs

This tutorial covers:

reading a bar graph
reading a line graph
reading a double line graph
drawing and reading a Venn diagram

Beginning Algebra Tutorial 16: Percent and Problem Solving

This tutorial covers:

converting percents into decimal numbers
converting decimal numbers into percents
solving word problems involving percents
pie charts with percents
tables with percents

Note that this tutorial is also found under Arithmetic/Percents above. For Data Representation and Interpretation go to the pie charts and tables in this tutorial.

Disclaimer:
Note that we can not guarantee that you will pass your test after going through any of the tutorials in this website. However, it will definitely help you to better understand the topics covered. WTAMU and Kim Peppard are not responsible for how a student does on any test for any reason including not being able to access the website due to any technology problems.

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