The San Diego Math Tutor (Juan Carlos Castaneda, MS)

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This page is for easy reference when my students ask me about test prep books and other math books.

Recommended SAT Preparation Books

The official guide
by the College Board
889 pages
ISBN: 0874477182
Gruber's Guide 2008
Author: Gary Gruber
1080 pages
ISBN: 1402211341
Barron's SAT 2400
by Linda Carnevale
and Roselyn Teukolsky
384 pages
ISBN: 0764132695

SAT verbal preparation in a fun way

Confessions of a High School Word Nerd
(Laugh Your Gluteus Off and Increase Your SAT Verbal Score)

I only tutor for the math section of the test but I list this book here because sometimes my students ask me if I know of a good book to prepare for the verbal part of the test. I think reading the short, real stories in “Confessions of a High School Word Nerd” will be a fun way for you to get familiar with many of the words tested for, not only in the SAT but also in the GMAT, GRE, and other standardized tests.
The book is a collection of personal essays written by recent Ivy League graduates. Their stories incorporate many SAT vocabulary words. These words come in bolded text, and they are defined at the bottom of each page. Check out the reviews in

By Arianne Cohen,
and Colleen Kinder
Penguin Books (January 2, 2007)
Paperback: 224 pages
ISBN: 0143038362

Recommended CBEST Preparation Books

Cracking the CBEST, 2nd Edition
Princeton Review
by Rick Sliter
400 pages
ISBN: 0375762639
Cliffs Test Prep
by Jerry Bobrow, Ph.D
448 pages
ISBN: 0764586084
Barron's CBEST
by Steve Reiss
and Kathryn Henkins
464 pages
ISBN: 0764135899

Recommended GRE Preparation Books

Kaplan Gre & Gmat Exams Math Workbook
by Kaplan
352 pages
ISBN: 0743241290
Practicing to Take the General Test
Educational Testing Service (ETS)
443 pages
ISBN: 0886852129
Gre Prep Course
Nova Press
With Software
624 pages
ISBN: 188905710X
The Ultimate Math Refresher for the Gre, Gmat & Sat
Lighthouse Review Inc.
256 pages
ISBN: 0967759404

Recommended ELM Preparation Books

The Best Test Prep for the Entry Level Mathematics Exam
by Archibald Sia,
Hugo Sun,
& Robert S. Wilson
448 pages
ISBN: 0738600164
CliffsTestPrep ELM & EPT
by Jerry Bobrow
Cliffs Notes series
247 pages
ISBN: 0471786780

Exercise Books with Solved, Fully Worked Problems Ordered by Difficulty Level

(How these books help improving your problem-solving performance)

Schaum's Outline of
Elementary Algebra
McGraw-Hill; 3rd edition
2000+ solved problems
Paperback; 400 pages
ISBN: 007141083X
Table of Contents
Schaum's Outline of
McGraw-Hill; 3rd edition
712 solved problems
Paperback; 367 pages
ISBN: 0070527660
Table of Contents
Schaum's Outline of
McGraw-Hill; 2nd edition
430 solved problems
Paperback; 311 pages
ISBN: 0071352031
Table of Contents

Recommended Calculus Books

Calculus: Early
by Ron Larson,
Robert P. Hostetler,
& Bruce H. Edwards
Houghton Mifflin Co.
4th edition
Hardcover: 1328 pages
ISBN: 0618606246
by James Stewart
Brooks Cole; 5th edition
Hardcover: 1368 pages
ISBN: 053439339X
Schaum's Outline of
by Elliott Mendelson
& Frank Ayres
McGraw-Hill; 4th edition
1103 solved problems
Paperback; 578 pages
ISBN: 0070419736
by Michael Spivak
Cambridge University
Hardcover; 682 pages
ISBN: 0521867444
Applied Calculus for
and Engineers
by Frank Blume
& Calvin E. Piston
Jones & Bartlett
Hardcover; 869 pages
ISBN: 0763728772
e: The Story of
a Number
by Eli Maor
Princeton U. Press
Paperback: 232 pages
ISBN: 0691058547
Vector Calculus
by Jerrold E. Marsden
& Anthony Tromba
Freeman; 5th edition
Hardcover: 704 pages
ISBN: 0716749920
Div, Grad, Curl,
and All That
by H. M Schey
Norton; 4th edition
Paperback: 176 pages
ISBN: 0393925161

Train Your Brain: 60 Days to a Better Brain

Improve your mental calculation speed.

In a standardized test like the GMAT, you will not be able to use a calculator.
Any way to speed up the problem-solving process is a great advantage in a timed test. These days many students are so used to their pocket calculators they really slow down when they have to perform numerical calculations in their head.
Are you in this situation? How confident are you in your ability to add, subtract, multiply, and divide numbers in your head, fast and accurately? This ability is a great asset to have during a timed test. You really don’t want to waste any time figuring out the result of (15)(8), or 47+25, or trying to remember how it’s done. You want to go ahead and just do it in your head in a couple seconds or less, without any hesitation as to the accuracy of your result.

This book is a good tool to help you improve towards that performance level, if you are not there yet. The book is a guided 12-week program for you to increase your speed at numerical calculations. The author, neurologist Ryuta Kawashima, says the increased brain activity resulting from doing the exercises in this book may help improving your memory too.
Take a look inside this book and read the introduction to learn about the science behind it.

Paperback: 172 pages
Publisher: Kumon Publishing North America (August 2005)
Language: English
ISBN: 1933241152

Exercise Books with Solved, Fully Worked Problems Ordered by Difficulty Level

When you are preparing for a standardized test like the GMAT, GRE, CBEST, ELM or SAT, you want to cover all your bases and master the fundamentals. Even though this is not enough in and of itself, it is an absolute requirement.

During the exam you want to breeze through the simple operational stuff. You do not want to get stuck wasting your time figuring out how to solve for a variable, how to add two fractions or how to expand the square of a sum.

By test time you want to be ready and have all those small operational steps down and out of the way, so you can focus on reading the problems, understanding them, and developing solutions.

The best way to become effective, proficient, fast and accurate at doing the routine calculations is by “practice, practice, practice.” You want a good source of practice problems, many of the same kind, ordered by subject, from easiest to hardest, with answers and examples.

The books in the Schaum’s Outline series are excellent sources of practice problems and self-explanatory exercises. They have all most students need to master this fundamental aspect of their mathematical performance. Each book in this series is comprehensive in the subject matter indicated by its title, and it is also very well organized.

Here are a few of them, some of the most useful for standardized test preparation:

Schaum's Outline of Elementary Algebra (Paperback)

(More than 2000 fully-solved problems)
  • Chapter 1) From Arithmetic to Algebra
  • Chapter 2) Simple Equations and Their Solutions
  • Chapter 3) Signed Numbers
  • Chapter 4) Introduction to Monomials and Polynomials
  • Chapter 5) First-Degree Equations
  • Chapter 6) Formulas
  • Chapter 7) Graphs of Linear Equations
  • Chapter 8) Introduction to Simultaneous Equations
  • Chapter 9) Problem Solving and Mathematical Modeling
  • Chapter 10) Products and Factoring
  • Chapter 11) Fractions
  • Chapter 12) Roots and Radicals
  • Chapter 13) Quadratic Equations
  • Chapter 14) The Pythagorean Theorem and Similar Triangles
  • Chapter 15) Introduction to Trigonometry
  • Chapter 16) Introduction to Geometry
Paperback: 400 pages
Publisher: McGraw-Hill; 3 edition (January 5, 2004)
Language: English
ISBN: 007141083X

Schaum's Outline of Geometry (Paperback)

(712 fully-solved problems)
  • Chapter 1) Fundamentals of Algebra: Laws and Operations
  • Chapter 2) Fundamentals of Algebra: Equations and Formulas
  • Chapter 3) Lines, Angles, and Triangles
  • Chapter 4) Methods of Proof
  • Chapter 5) Congruent Triangles
  • Chapter 6) Parallel Lines, Distances, and Angle Sums
  • Chapter 7) Paralelograms, Trapezoids, Medians, and Midpoints
  • Chapter 8) Circles
  • Chapter 9) Similarity
  • Chapter 10) Areas
  • Chapter 11) Regular Polygons and the Circle
  • Chapter 12) Locus
  • Chapter 13) Inequalities and Indirect Reasoning
  • Chapter 14) Improvement of Reasoning
  • Chapter 15) Constructions
  • Chapter 16) Proofs of Important Theorems
  • Chapter 17) Transformational Geometry
Paperback: 367 pages
Publisher: McGraw-Hill; 3 edition (December 6, 1999)
Language: English
ISBN: 0070527660

Schaum's Outline of Probability, 2nd Edition (Paperback)

The GMAT and the GRE have only a few questions on probability, but they sure affect the student’s score as any other question.
In my experience, several students prepare for probability only at the end of the preparation period, when it may be too late to adequately cover this important subject.
One common difficulty comes from the small number of probability questions in the standard prep books. That is the reason why I often recommend getting one probability book with as many examples and exercises as possible.
The Schaum’s Outline of Probability covers all the basic probability concepts you will face in the GMAT and GRE exams.
Some reviews of this book –posted in complain that the book does not include any calculus material, and that the problems are too complicated and too basic at the same time. In my opinion, that is exactly why this book is a good problem source for GMAT and GRE preparation. That is the same way the GMAT and GRE problems are designed. They are complicated and convoluted while using only the most basic concepts available from theory.
So, while this book may not be the best textbook for a math or science college class, I think it is a very good working reference for GMAT and GRE prep.
In Chapters 2, 3, 5 and 6, plus Appendix A, you will find more than enough material, problems and examples to prepare yourself well for the GMAT and GRE in the area of probability. When preparing for the GMAT or GRE you should familiarize yourself at least with some of the material covered in Chapters 2 and 3, and Appendix A.

(430 fully-solved problems)

  • Chapter 1) Set theory
  • Chapter 2) Techniques of Counting
  • Chapter 3) Introduction to Probability
  • Chapter 4) Conditional Probability and Independence
  • Chapter 5) Random Variables
  • Chapter 6) Binomial and Normal Distributions
  • Chapter 7) Markov Processes
  • Appendix A) Descriptive Statistics
  • Appendix B) Chi-Square Distribution
Paperback: 311 pages
Publisher: McGraw-Hill; 2 edition (March 21, 2000)
Language: English
ISBN: 0071352031
Recommended Books

»Test Prep Books«

Other Math Books


Other Pages

Calculator TI-89

Tower of Hanoi

Factored Integers




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Last review: June 5, 2011