Chapter 1-Arithmetic (40 Practice Problems but there are more problems after each section of the chapters)This chapter focused mainly on arithmetic. Below are the topics covered.
Chapter one focused on the basics of arithmetic math on the GMAT such as addition and subtraction on the number line as well as the direction of positive and negative numbers on it. The book also breaks down the terminology so you can gain a better understanding of the concepts. For example, it stated to focus on “like terms” which meant it contains very similar “stuff.” Then it explains how an expression does not contain any addition or subtraction and how a term is just a bunch of things multiplied together.
• Basic numbers, Digits(0,1,2,3,4,5,6,7,8, and 9), and Units Digit, and Place Value (how much a digit in a specific position is worth)
• Number Line
• Multiplying (negatives and positives) and Dividing
• Distributing and Factoring
• PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition,Subtraction)
There is a section in the book that really helps the reader because it breaks down the concepts. Below is an example. It kept the explanations simple and it broke it down so it didn’t confuse the reader.
What you see.............................What you say...............................What it means
x+y.............................................x plus y..............................x plus y, or the sum of x and y
Chapter 2-Divisibility (42 Practice Problems)• It covered divisibility by 2,3,5,9, and 10.
• It links factors and divisibility-Factors are Divisors.
• Prime numbers and Prime Factorization using prime trees.
• Factor Foundation Rule-every number is divisible by the factors of its factors.
• How to factor with unknown numbers.
• Factors of X with No Common Primes
Chapter 3-Exponents and Roots (63 Practice Problems)• What is an Exponent
• It tells you to memorize certain Perfect Squares and Cubes
• Also it tells you to memorize Powers of 2,3,4,5 and 10.
• Multiplying Exponential Terms with Same Base
• Dividing Exponential Terms with Same Base
• Negative Powers
• Applying Two Exponents
• Applying an Exponent to a Product
• Adding or Subtracting Terms with the Same Base
• Square Roots and Cube Roots
• Multiplying Square Roots and Simplifying Roots
• Addition and Subtraction with Roots
Here is another example of how the authors did a really good job. They used the format below to better explain and break down the concepts. This helped the most when I was studying the chapters.
If you........................................................................Then you.......................................Like this:
Raise something to two successive powers...............Multiply the powers............................(a²)^4=a^8
Chapter 4-Fractions (66 Practice Problems)• Numerator and Denominator
• Adding Fractions with the Same Denominator and Adding Fractions with Different Denominators
• Cross Multiplying and Improper Fractions
• How to change a Mixed Number To an Improper Fractions
• Simplifying Fractions and Multiplying them
• Squaring Fractions means it gets Smaller
• Dividing by a Fraction and Addition in the numerator and denominator
Chapter 5-Fractions, Decimals, Percents, and Ratios (77 Practice Problems)Chapter was very useful because it helps you convert decimals, fractions, and percentage making them easier to work with.
• Converting Decimals to Percentages and vice versa (Very Helpful)
• Converting Fractions to Decimals or Percents
• Multiplying a Decimal by a Power of 10
• Addition and Subtraction of Decimals as well as Multiplying Two Decimals
• Multiplying a Decimal and a Big Number and Dividing by Two Decimals
• How to determine Percentages of Dollars
• Percent Change
• Ratios (Part:Part:Whole Ratios)
Chapter 6-Equations (49 Practice Problems)Chapter 6 covered equations and expressions. This chapter was very helpful for me because I needed to brush up on equations.
• Deals with simplifying equations
• How an equation is a complete sentence
• Golden Rule of Equations-Changing the value of the left and right sides
• Isolating a Variable and Cleaning Up a Variable
• Variables in the Exponent
• Solving Two Equations and Two Unknowns by Isolating (then Substitute) or Combining Equations
• Working with Three or More Variables
Chapter 7-Quadratic Equations (25 Practice Problems)• What is a Quadratic Expression
• FOIL (First, Outer, Inner, Last)
• Factoring expressions such x2+5x+6
• Solving Quadratic Equations with No X Term, with Squared Parentheses (y+1)2
Chapter 8-Inequalities and Absolute Values (55 Practice Problems)• Inequalities with Variables
• Solving Inequalities
• Multiplying Inequalities by a Negative
Chapter 9-Word Problems (55 Practice Problems)• It gives Four Steps to Turning Words Into Math-What do they want, What do they give me, How do I turn this information into equations, and How do I solve those equations for the desired value.
Refer to GMAT Club on Word Problems
Chapter 10-Geometry (60 Practice Problems)• It covered the Radius, Diameter, Circumference, and Area of a Circle
• Sectors of a Circle including the Arc Length and Central Angle
• Triangles (Sum of Any Two Sides > Third Side)
• Sum of Three Angles=180 Degrees
• Same Sides=Same Angles
• Isosceles and Equilateral Triangles
• Perimeter of a Triangle
• Identifying the Base and height of a Triangle
• Parallelograms and Rectangles
• Coordinate Plane (X and Y Coordinates)
Most of the chapters were very helpful because I haven't done Algebra or Geometry in over 12 years! They also provide a lot of practice questions, which can be good and bad. The most useful chapters were chapter 2,3,4,5,6, and 8 except Chapter 9 on Word Problems. It did not really help me as much as I thought. I would check out this thread (
word-problems-made-easy-87346.html). He should have wrote Chapter 9. LOL. I also completed all the practice problems (or drill sets) at the end of each chapter. It took about two weeks for me to complete
Foundations of GMAT Math but I took notes while reading. I would definitely recommend this book to someone that needs to re-learn the basics for the GMAT. Now I am going through the Number Properties book more easily. Let me know if this format is helpful or not. I am sick at this moment so my thoughts are scattered everywhere. I feel bad I can't study but nothing beats a cold better than rest.