I suggest a very cheap book: Algebra I (Cliffs Study Solver), by Mary Jane Sterling. ISBN: 0764537636
I break the contents down below, so scan for the topics you were looking for. I already colored some topics green that I think you might want to read.
Cliffs Study Solver: Algebra I
No GMAT specific books thoroughly review Algebra, the most important math skill tested on the GMAT. While Princeton Review
, and others try to teach “tricks” around doing math, The GMAT Guru expects students to learn and apply the skills taught in this book. Full of worked practice problems and themes directly relevant to the GMAT, this will be the student’s go-to resource for Algebra review.
Chapter By Chapter Review:
Introduction: Don’t worry about irrational numbers, improper fractions, or the symbol for infinity. All other material in this section is directly relevant to the GMAT.
Pretest: 90% of the skills tested are relevant to the GMAT. Scientific notation (55-57), tedious polynomial division (71), non-integer solutions to quadratics (114-116, 118,120), non-linear (curved) functions (126,127) and domain/range (131-134) are unlikely to be tested on the GMAT. Do all questions except for those noted above. If the test directs you to a particular section in the book, check my comments on that section to make sure that this section is really important.
Chapter 1: Basics
1. Order of Operations (31-44): Most of these should seem very basic. Don’t spend much time on this section unless you need clarification or extra work on one of the included topics.
2. Exponents and Roots (44-58): All of these sections are relevant. Make sure you know your exponent rules cold. You are unlikely to have worked much with exponents since high school and are probably rusty.
3. Divisibility Rules (58-61): Reducing fractions will be very important on the GMAT. You can’t reduce if you don’t know what numbers go into the numerator and the denominator. These rules are very helpful.
4. Prime Factors and Prime Factorization (61-67): Despite being in the “basics” section, understanding prime numbers and prime factorization is considered to be a very advanced topic on the GMAT, especially on questions that ask you about the factors or divisors of a particular number. For a glimpse of how complicated prime factorization can be, see “Prime Factorization Worksheet” in the Advanced Quant Chapter of The GMAT Guru Guide.
Chapter 2: Numbers
1. Signed Numbers (73-86): You don’t need to understand interval notation. You DO need to understand how inequalities can be graphed on a number line. Pay particular attention to how signs change when numbers are multiplied and divided (80). This concept will often be tested in Data Sufficiency. For more practice with how signed numbers multiply and divide, see “Odds Evens Negatives and Positives” in the Problem Solving chapter of this document.
2. Fractions (86-94): Throughout the GMAT you will be rewarded for reducing fractions (and punished if you don’t). Always look to put fraction into lowest terms.
3. Decimals (94-97): Working with fractions on the GMAT is much easier than working with decimals, so make sure you are comfortable converting decimals into fractions (95). In particular, you should always convert decimals representing fourths (.25,.5,.75, etc.) and fifths (.2,.4,.6,.8, etc.) into fractions.
4. Percents (97-99): This section isn’t as comprehensive as it should be for GMAT study. Percents are VERY common on Problem Solving questions, especially for students around the 50% percentile. Arco’s Master the GMAT has a more extensive discussion on percents and how to use the proportion method to easily solve percent based word problems. For examples, see “Percents and Equivalent Fractions” in the Problem Solving Chapter of this book.
5. Scientific Notation (99-101): This is not very important on the GMAT. You do need to understand how exponents work, however.
Chapter 3: Linear Equations and Algebraic Fractions
1. Solving Linear Equations (107-110): This is VERY basic and probably can be skipped. The main idea is that you can add, subtract, multiply, and divide both sides of an equation.
2. More than One Operation (111-116): Make sure you can do all of these except for the repeating decimal questions (not on the GMAT)
3. Solving Linear Formulas (116-120): Do several of these to make sure you are comfortable solving equations with many variables. On the GMAT, questions that are testing this concept will usually ask something like “solve for x in terms of y and z.”
4. Ratios and Proportions (120-125): Helpful in its discussion of the multiple ways you can reduce equivalent fractions.
5. Operations with Algebraic Fractions (125-128): This is where the material starts getting a little more difficult. Reducing algebraic fractions requires that you know how to factor the numerator and denominator. Reducing is important in and of itself. It is particularly important when multiplying multiple terms. Make sure you understand this section well.
6. Adding and Subtracting Algebraic Fractions (128-131): This is a very good discussion of finding common denominators. The problems are difficult, but are good practice.
7. Equations with fractions (131-134): Note: Clearing fractions by multiplying by the LCD works particularly well for problems where the numerator in one or more of the fractions is composed of multiple terms (2y-1)/5. Chapter 4: Polynomials and Factoring
1. Multiplying Monomials (145-148): Yes, you need to know how to do this.
2. Multiplying Polynomials, FOIL Method (148-149): Need to know FOIL, not only for its own sake, but also so that you can work in the other direction and solve for the binomial factors of quadratic equations (Reverse-FOIL)
3. Other Products (149-150): Not nearly as important as FOIL, but not to be ignored either.
4. Special Products (151-156): You need to know special products #1 and #2. (#3 and #4 are not tested on the GMAT.)
5. Dividing Polynomials (156-161): Study “Divisors with One Term.” Skip the other sections.
6. Factoring (162-165): Yes, you need to know this.
7. Factoring Binomials (165-168): Need to know difference of binomials, but not difference of cubes or sum of cubes. Do example problems 1-3 and 6. Do Work Problems 2 and 3.
8. Factoring Trinomials/Factoring Other Polynomials (168-173): You will likely only need to solve trinomials with no coefficients in front of the first term. (Work problem 1, pg 171) or expressions that can be reduced to such an expression by dividing out a common factor (Work problem 2, pg 172). The GMAT very rarely will ask you to factor a trinomial with fractional answers (Work Problem 3 and 4, pg 171: Notice that if these were quadratics set to “0”, that the answer for #3 would be x=4/3, ¾). For more practice solving GMAT like quadratic equations, see “Reverse Foil Drill” in the Problem Solving chapter of this book.
9. Factoring by Grouping (173-175): Skip this section and any questions in the back of the chapter that are solved with this method.
Chapter 5: Inequalities, Absolute Value Inequalities, and Radicals
1. Inequalities (183-192): Many students try to pick numbers when they are faced with inequalities, especially on Data Sufficiency. If you have confidence solving inequalities, you will be at a distinct advantage. Often, the GMAT will try to obscure information about “x” by presenting an inequality with multiple terms and fractions. If you solve this inequality, you will know exactly how “x” relates to the number line.
2. Absolute Value Equations/ Absolute Value Inequalities (192-203): These two sections solve inequalities and equations using the concept that absolute value really represents two equations/inequalities in one. 3. Simplifying Square Roots (203-206): This section really should be in the chapter on exponents, but do it anyway. Roots ARE exponents and follow all the same rules.
4. Simplifying Other Roots (206-208): On the GMAT, you need to be able to recognize all perfect squares through 13 13 = 169. You should know perfect cubes for the first 5 integers. Because so many GMAT questions ask about populations or other groups “doubling,” you should know the first few powers of 2 (through 2 2 2 2=16)
5. Radical Equations (208-214): Knowing that you can not only add, subtract, multiply, and divide, but also square both sides of an equation is the key lesson in this section.
Chapter 6: Introducing Quadratic Equations:
1. Introduction: (221-222): We will be focusing almost completely on factoring as a method of solving quadratic equations. The only important take away from this first section is that the solutions to a quadratic equation are the numbers that “work” when you plug them in. If really stuck on the GMAT, you can do this, but it isn’t very efficient to plug in 10 numbers into a quadratic to see which two work. (2 solutions for each of 5 answers = 10)
2. Solving Quadratic Equations by Factoring (224-228): Remember that you are most likely to see integer solutions to quadratics on the GMAT. This means that the first term will have a coefficient of 1, or could be reduced to have a coefficient of 1. Work Problems 1,3, and 4 on page 227 are typical quadratics you would see on a GMAT.
3. Solving Quadratics with the Quadratic Formula/ by Completing the Square (228-237): You DO NOT need to know either of these two methods. Skip them if you like.
4. Solving Quadratic-Like Equations (237-231): Yes, you should learn to recognize the common trinomial equations (x+y)(x+y) = ….. even if the x and the y have exponents. On the GMAT, however, the first and last terms would be perfect squares. None of the examples given are like this, so you can skip this section.
5. Quadratic and Other Inequalities (241-245): SKIP. Nothing even remotely like this should be on the GMAT
6. Radical Equations with Quadratics (245-248): This is a good section because many students totally freeze up when they see radicals on one side of the equation. Remember, the only way to clear radicals is to square both sides. Don’t be shy!
Chapter 7: Graphing and Systems of Equations:
1. Coordinate System: (259-272) This is an extremely important section for students who want to score above 650. Coordinate Geometry is becoming more and more important on the GMAT. Be sure to be able to graph coordinate points, draw equations as lines, and translate two points into the equation of a line.
2. Graphing Other Curves (273-282): You don’t need to know how to do this. From a conceptual standpoint, however, you should note that quadratic ( ) and
cubic ( ) lines are curved and, therefore, can cross in more than one place. This means they have multiple solutions (two equations are not enough to solve for two variables), a lesson that will be valuable in Data Sufficiency.
3. Finding the Equation of a Line/ Graphing Inequalities (283-290): Finding the equation of a line is probably the most important part of Coordinate Geometry. Know this section well.
4. Systems of Equations – Linear and Quadratic (290-298): Notice that two different equations (lines) only cross in one place. This is why you need two equations to solve for two variables. Do not use graphing to solve on the GMAT, but it is a good way to understand roughly where the solutions should be. You will never be given two equations that do not have a solution (parallel lines), but you do need to know that parallel lines have the same slope. Pay particular attention to the “addition method” for solving two equations. For more practice solving two equations and two variables, see the Problem Solving Worksheets in The GMAT Guru Guide.
Chapter 8: Functions SKIP THIS ENTIRE CHAPTER
Charpter 9: Story Problems (333-355):
1. Other than the first section on “number problems,” these story problems are very GMAT like.
2. The main point of this book has been to learn how to calculate/solve equations. In this section you need to take a step further and learn how to actually write the equation before you even solve it. This will be a great last step before you begin GMAT specific math preparation.
Customized Full Length Exam (363-383):
1. Do all questions except for the following: 9,10, 29,30, 57-60, 85-86,91,92,94,115-118,121,125-128,135-142
2. Restudy materials as directed.
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