Bob Miller's Math for the ACT - Softcover

Miller, Bob

Softcover

ISBN 10: 0738610968 ISBN 13: 9780738610962

Verlag: RES & EDUCATION ASSN, 2012

Inhaltsangabe

Maximize Your Math Score on the ACT with Bob Miller!

Bob Miller's Math for the ACT* helps high school students master math and get into the college of their dreams!

Bob Miller has taught math to thousands of students at all educational levels for 30 years. His proven teaching methods will help you master the math portion of the ACT and boost your score!

Written in a lively and unique format that students embrace, Bob Miller’s Math for the ACT prepares ACT test-takers with everything they need to know to solve the math problems that typify the math portion of the ACT. Unlike some dull test preps that merely present the material, Bob actually teaches and explains math concepts and ideas. His no-nonsense, no-stress style and decades of experience as a math teacher help students boost their ACT math score.

Bob breaks down math and puts it back together in an easy-to-follow, step-by-step format. Each chapter is devoted to a specific topic and is packed with examples and exercises that reinforce math skills.

Some of the topics covered include:
- Exponents
- Square Roots
- Algebraic Manipulations
- Equations and Inequalities
- Geometry

Packed with Bob Miller’s engaging examples, practice questions, plus test-taking tips and advice, this book is a must for any student preparing for the ACT!

Remember, if you’re taking the ACT and need help with math, Bob Miller’s got your number!

Über diesen Titel

Über die Autorin bzw. den Autor

Bob Miller received his B.S. in the Unified Honors Program sponsored by the Ford Foundation and his M.S. in math from Polytechnic University. After the first class he taught (as a substitute for a full-time professor), he overheard one student say to another, “At least we have someone who can teach the stuff.” From that moment on, he was hooked on teaching.

Since then, Bob has taught at virtually every educational level, and has brought his math skills to classrooms at C.U.N.Y., Westfield State College, Rutgers, and Poly. Bob says, “I always feel great when students tell me they used to hate math or couldn’t do math and now they like it more and can do it better.”

Bob considers teaching to be exceptionally rewarding, and he has broadened his teaching horizons to include math students beyond the classroom. His math test preps are specifically written in a fun and easy-to-follow style that students embrace.

Bob says his goal as an author, teacher, and mathematician is to help students understand math so they can get the scores they need to excel on the ACT exam. With his numerous success stories, best-selling test preps, and over 30 years of experience, Bob has proven that his teaching methods get results!

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Don’t let poor math skills drag your ACT* score down! Use BOB MILLER’S MATH FOR THE ACT* and get into the college of your choice!Bob Miller’s Math for the ACT* – All the Math You Need for a Higher Score!The Most Complete ACT* Math Review
Everything you need to know for the math portion of the ACT*. Our easy-to-understand review chapters cover number operations, fractions, word problems, linear equations, geometry, and trigonometry. Step-by-step examples and exercises throughout the book build skills and explain key ACT* concepts.The Best ACT* Practice Exams Available
Includes 4 practice tests based on official ACT* exam questions to help you pinpoint your math strengths and weaknesses. Each practice exam includes every topic you can expect to see on the math portion of the ACT*.ACT* Math from an Expert
Bob Miller has been teaching math for 30 years. His no-stress, no-nonsense style explains ACT* math concepts in a step-by-step format that makes math easier. Bob takes the confusion out of math and teaches it from the ground up so anyone can learn ACT* math quickly and painlessly. Studying ACT* math from this book is like having your own personal tutor. About the Author
Author, teacher, and renowned mathematician Bob Miller has taught at virtually every educational level. Bob says: "In this book, I break down ACT* math and put it back together in step-by-step fashion. I teach ACT* math from the inside out so it sticks to your ribs. Welcome to my world of math. If you need help with math, I’ve got your number."

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Bob Miller's Math for the Act

By Bob Miller

Research & Education Association

Copyright © 2013 Research & Education Association, Inc.
All rights reserved.

ISBN: 978-0-7386-1096-2

Contents

Acknowledgments, 
Biography, 
Other Books, 
About REA, 
About This Book, 
CHAPTER 1: Basic Basics, 
CHAPTER 2: We Must Look at Arithmetic, 
CHAPTER 3: Exponents, the Powers That Be, 
CHAPTER 4: Radical Radicals, 
CHAPTER 5: Algebraic Skills, 
CHAPTER 6: Equations and Inequalities, 
CHAPTER 7: Problems with Words, 
CHAPTER 8: Working with Two or More Unknowns, 
CHAPTER 9: Points and Lines, 
CHAPTER 10: All Kinds of Angles and All About Triangles, 
CHAPTER 11: More Two-Dimensional Figures, 
CHAPTER 12: Circle to the Left, 
CHAPTER 13: Three-Dimensional Figures, 
CHAPTER 14: Other Algebraic Topics, 
CHAPTER 15: Trigonometry, 
CHAPTER 16: Important Miscellany, 
CHAPTER 17: Four Sample ACT Math Exams with Answers, 
CHAPTER 18: What To Do Now, 
Answer Sheets, 
ACT Math Glossary, 
Index, 

CHAPTER 1

Basic Basics

"All math begins with whole numbers. Master them and you will begin to speak the language of math."

Our great adventure begins with our basic terms. It is very important to understand what a question asks as well as how to answer it. The word numbers has many meanings, as we start to see here.

NUMBERS

Whole numbers: 0, 1, 2, 3, 4, ...

Integers: 0, ± 1, ±2, ±3, ±4, ..., where ±3 stands for both +3 and -3.

Positive integers are integers that are greater than 0. In symbols, x > 0, x an integer.

Negative integers are integers that are less than 0. In symbols, x< 0, x an integer.

Even integers: 0, ±2, ±4, ±6, ...

Odd integers: ±1, ±3, ±5, ±7, ...

Inequalities

For any numbers represented by a, b, c, or d on the number line:

[ILLUSTRATION OMITTED]

We say c >d (c is greater than d) if c is to the right of d on the number line.

We say d < c (d is less than c) if d is to the left of c on the number line.

c >d is equivalent to d < c.

a ≤ b means a < b or a = b; likewise, a ≥ b means a > b or a = b.

Example 1: 4 ≤ 7 is true because 4 < 7; 9 ≤ 9 is true because 9 = 9; but 7 ≤ 2 is false because 7 > 2.

Example 2: Find all integers between -4 and 5.

Solution: {-3, -2, -1, 0, 1, 2, 3, 4}.

Notice that the word between does not include the endpoints.

Example 3: Graph all the multiples of five between 20 and 40 inclusive.

Solution:

[ILLUSTRATION OMITTED]

Notice that inclusive means to include the endpoints.

Odd and Even Numbers

Here are some facts about odd and even integers that you should know.

• The sum of two even integers is even.

• The sum of two odd integers is even.

• The sum of an even integer and an odd integer is odd.

• The product of two even integers is even.

• The product of two odd integers is odd.

• The product of an even integer and an odd integer is even.

• If n is even, n2 is even. If n2 is even and n is an integer, then n is even.

• If n is odd, n2 is odd. If n2 is odd and n is an integer, then n is odd.

OPERATIONS ON NUMBERS

Product is the answer in multiplication, quotient is the answer in division, sum is the answer in addition, and difference is the answer in subtraction.

Because 3 × 4 = 12, 3 and 4 are said to be factors or divisors of 12, and 12 is both a multiple of 3 and a multiple of 4.

A prime is a positive integer with exactly two distinct factors, itself and 1. The number 1 is not a prime because only 1 × 1 = 1. It might be a good idea to memorize the first eight primes:

2, 3, 5, 7, 11, 13, 17, and 19

The number 4 has more than two factors: 1, 2, and 4. Numbers with more than two factors are called composites. The number 28 is a perfect number because if we add the factors less than 28, they add to 28.

Example 4: Write all the factors of 28.

Solution: 1, 2, 4, 7, 14, and 28.

Example 5: Write 28 as the product of prime factors.

Solution: 28 = 2 × 2 × 7.

Example 6: Find all the primes between 70 and 80.

Solution: 71, 73, 79. How do we find this easily? First, because 2 is the only even prime, we have to check only the odd numbers. Next, we have to know the divisibility rules:

• A number is divisible by 2 if it ends in an even number. We don't need this here because then it can't be prime.

• A number is divisible by 3 (or 9) if the sum of the digits is divisible by 3 (or 9). For example, 456 is divisible by 3 because the sum of the digits is 15, which is divisible by 3 (it's not divisible by 9, but that's okay).

• A number is divisible by 4 if the number named by the last two digits is divisible by 4. For example, 3936 is divisible by 4 because 36 is divisible by 4.

• A number is divisible by 5 if the last digit is 0 or 5.

• The rule for 6 is a combination of the rules for 2 and 3.

• It is easier to divide by 7 than to learn the rule for 7.

• A number is divisible by 8 if the number named by the last three digits are divisible by 8.

• A number is divisible by 10 if it ends in a zero, as you know.

• A number is divisible by 11 if the difference between the sum of the even-place digits (2nd, 4th, 6th, etc.) and the sum of the odd-place digits (1st, 3rd, 5th, etc.) is a multiple of 11. For example, for the number 928, 193, 926: the sum of the odd digits (9, 8, 9, 9, and 6) is 41; the sum of the even digits (2, 1, 3, 2) is 8; and 41 — 8 is 33, which is divisible by 11. So 928, 193, 926 is divisible by 11.

That was a long digression!!!!! Let's get back to example 6.

We have to check only 71, 73, 75, 77, and 79. The number 75 is not a prime because it ends in a 5. The number 77 is not a prime because it is divisible by 7. To see if the other three are prime, for any number less than 100 you have to divide by the primes 2, 3, 5, and 7 only. You will quickly find they are primes.

Rules for Operations on Numbers

Note () are called parentheses (singular: parenthesis); [] are called brackets; {} are called braces.

Rules for adding signed numbers

1. If all the signs are the same, add the numbers and use that sign.

2. If two signs are different, subtract them, and use the sign of the larger numeral.

Example 7:a. 3 + 7 + 2 + 4 =+ 16

b. -3 -5 -7 -9= -24

c. 5 - 9 + 11 - 14 = 16 - 23 = -7

d. 2 - 6 + 11 - 1 = 13 - 7 = +6

Rules for multiplying and dividing signed numbers

Look at the minus signs only.

1. Odd number of minus signs — the answer is minus.

2. Even number of minus signs — the answer is plus.

Example 8:...

Details zur Ausgabe

• Verlag: RES & EDUCATION ASSN
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 0738610968
• ISBN 13: 9780738610962
• Einband: Taschenbuch
• Anzahl der Seiten: 316
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar