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Math Help for the THEA or ACCUPLACER Test


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desk Introduction


 

If you need help in preparing for the math part of the THEA or ACCUPLACER 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.


Special note to those taking the math part of the ACCUPLACER test:

Even though I refer to the THEA test throughout this webpage, if you are planning to take the ACCUPLACER test this page can also help you.  The content of the math part of the THEA and the ACCUPLACER tests are similar, they just may be labeled differently.

I believe that if you have the mathematical concepts down, then you should be able to answer a wide variety of questions that use those concepts no matter how the questions are asked.


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


The math part of the THEA test is split into four main areas:



Below are the specific concepts you need to know about each of those areas.   This list was compiled from researching the Mathematics Skill Descriptions webpage at the official THEA website created by the National Evaluation Systems.

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 THEA test.


 

HOW TO EFFECTIVELY USE THIS WEBPAGE:
 
 
Under the Fundamental Mathematics, Geometry and Problem Solving 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 and  intermediate) of tutorials.  Find the algebra level that agrees with you most and do all of the tutorials under that level.  If you start at the beginning level algebra, make sure that you make your way up through intermediate algebra before you take the THEA or ACCUPLACER test.

When you are done with a tutorial, you can come back to this webpage by clicking on the back arrow link marked THEA 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.



desk Fundamental Mathematics


 


The first area that we will be looking at is fundamental mathematics.  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 fundamental mathematics to get the full benefit.


The fundamental mathematics area covers:




 

Integers, Fractions, Decimals, and Units of Measurements


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.


 

Problems Involving Data Interpretation and Analysis

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

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



desk 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 two levels (lowest to highest): beginning and intermediate. 

Ideally, for the Algebra section, you want to be able to work the intermediate level by the time you take the THEA 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.  

Once you find a level to start with, make sure that if it is beginning algebra, in the end you work your way up to intermediate 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:


 

Graphs of Number Relationships


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 

Beginning Algebra Tutorial 24: Graphing Linear Inequalities
 

This tutorial covers:
  •  graphing linear inequalities in two variables

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


Intermediate Algebra Tutorial 17: Graphing Linear Inequalities
 

This tutorial covers:
  • graphing linear inequalities in two variables
  • graphing the union of two linear inequalities in two variables
  • graphing the intersection of two linear inequalities in two variables 

 

One and Two Variable 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
  • using the addition and subtraction properties of equalities to solve linear equations


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.

Intermediate Algebra Tutorial 19: Solving Systems of Linear Equations in Two Variables
 

This tutorial covers:
  • knowing if an ordered pair is a solution to a system of linear equations in two variables or not
  • solving a system of linear equations in two variables by graphing
  • solving a system of linear equations in two variables by the substitution method
  • solving a system of linear equations in two variables by the elimination method

 

Word Problems With Variables

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 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 21: Systems of Linear Equations and Problem Solving

This tutorial covers:
  • using Polya's four step process to solve various problems involving systems of linear equations in both two and three variables


 

Algebraic Expressions and Functional Notation

Beginning Algebra Tutorial 11: Simplifying Algebraic Expressions
 

This tutorial covers:
  • combining like terms
  • simplifying an expression using distributive property


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


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


Beginning Algebra Tutorial 29: Negative Exponents and Scientific Notation
 

This tutorial covers:
  • simplifying exponential expressions involving negative exponents
  • writing a number in scientific notation
  • writing a number in standard notation, without exponents

Intermediate Algebra Tutorial 13:  Introduction to Functions

This tutorial covers:
  • knowing what a relation, function, domain and range is
  • finding the domain and range of a relation
  • identifying if a relation is a function or not
  • knowing how to use the vertical line test
  • evaluating functional values


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 

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.

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


 

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 

 


desk 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 fundamental mathematics to get the full benefit.



The geometry area covers:


  


Problems with Geometric 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

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

 

 

Problems with Geometric Concepts

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 



desk Problem Solving


 

Whether you like it or not, whether you are going to be a mother, father, teacher, computer programmer, scientist, researcher, business owner, coach, mathematician, manager, doctor, lawyer, banker (the list can go on and on) problem solving is everywhere.  Some people think that you either can do it or you can't.  Contrary to that belief, it can be a learned trade.  Even the best athletes and musicians had some coaching along the way and lots of practice. That's what it also takes to be good at problem solving.  So don't savor the mystery of a good problem, but get in there and solve it!


SPECIAL NOTE: 

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



The problem solving area covers:


 
 Reasoning Skills

Beginning Algebra Tutorial 35: Reasoning Skills
 

This tutorial covers:
  • using inductive reasoning to solve problems
  • finding the next terms in a sequence
  • using deductive reasoning to solve problems 


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WTAMU > Virtual Math Lab > THEA/ACCUPLACER


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 Seward 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. 

THEA is the registered trademark of National Evaluation Systems, Inc. (NES). The material here has neither been reviewed nor endorsed by NES.

ACCUPLACER is the registered trademark of the College Entrance Examination Board (CEEB).  The material here has neither been reviewed nor endorsed by the CEEB.

Throughout this website, we link to various outside sources.  WTAMU and Kim Seward do not have any ownership to any of these outside websites and cannot give you permission to make any kind of copies of anything found at any of these websites that we link to.  It is purely for you to link to for information or fun as you go through the study session. Each of these websites have a copy right clause that you need to read carefully if you are wanting to do anything other than go to the website and read it. We discourage any illegal use of the webpages found at these sites. 


All contents copyright (C) 2003 - 2008, WTAMU and Kim Seward. All rights reserved. 
Last revised on August 8, 2008 by Kim Seward.