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- Herausgeber: John Wiley & Sons
- Kategorie: Bildung
- Sprache: Englisch
- Veröffentlichungsjahr: 2011
Multiply your chances of success on the ACT Math Test The ACT Mathematics Test is a 60-question, 60-minute subtest designed to measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade, and is generally considered to be the most challenging section of the ACT. ACT Math For Dummies is an approachable, easy-to-follow study guide specific to the Math section, complete with practice problems and strategies to help you prepare for exam day. * Review chapters for algebra, geometry, and trigonometry * Three practice tests modeled from questions off the most recent ACT tests * Packed with tips, useful information, and strategies ACT Math For Dummies is your one-stop guide to learn, review, and practice for the test!
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ACT® Math For Dummies®
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Table of Contents
ACT® Math For Dummies®
by Mark Zegarelli
ACT® Math For Dummies®
Published byWiley Publishing, Inc.111 River St.Hoboken, NJ 07030-5774www.wiley.com
Copyright © 2011 by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.
Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries, and may not be used without written permission. ACT is a registered trademark of ACT, Inc. All other trademarks are the property of their respective owners. Wiley Publishing, Inc., is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation warranties of fitness for a particular purpose. No warranty may be created or extended by sales or promotional materials. The advice and strategies contained herein may not be suitable for every situation. This work is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional services. If professional assistance is required, the services of a competent professional person should be sought. Neither the publisher nor the author shall be liable for damages arising herefrom. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read.
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Library of Congress Control Number: 2011927309
ISBN: 978-1-118-00154-7
Manufactured in the United States of America
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About the Author
Mark Zegarelli is the author of Basic Math and Pre-Algebra For Dummies (Wiley), SAT Math For Dummies (Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher.
Mark lives in San Francisco, California, and Long Branch, New Jersey.
Dedication
For my good friend David Feaster — as always, with love, laughter, and light.
Author’s Acknowledgments
This is my seventh For Dummies book, and my seventh positive experience working with a first-rate team of editors who make the process of writing so very pleasurable and productive. Thanks so much to my Wiley editors Chrissy Guthrie, Jessica Smith, and Lindsay Lefevere. More thanks to technical editors Sarah Weaver and Amy Nicklin for keeping me on track, accurate, and finely tuned to the needs of readers who are studying for the ACT.
And thanks to Annie Koziol, Steven Satyricon, and all the rest of the friendly folks at Maxfield’s House of Caffeine for their contribution in helping to make this book good to the last drop.
Publisher’s Acknowledgments
We’re proud of this book; please send us your comments through our online registration form located at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.
Some of the people who helped bring this book to market include the following:
Acquisitions, Editorial, and Media Development
Senior Project Editor: Christina Guthrie
Executive Editor: Lindsay Lefevere
Copy Editor: Jessica Smith
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Editorial Program Coordinator: Joe Niesen
Technical Editors: Amy Nicklin, Sarah Weaver
Editorial Manager: Christine Meloy Beck
Editorial Assistants: Rachelle Amick, Alexa Koschier
Cover Photos: © iStockphoto.com/design 56
Cartoons: Rich Tennant (www.the5thwave.com)
Composition Services
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Layout and Graphics: Carrie A. Cesavice, Corrie Socolovitch, Christin Swinford
Proofreaders: Laura Albert, Lindsay Amones, Sossity R. Smith
Indexer: Potomac Indexing, LLC
Special Help: Caitie Copple
Publishing and Editorial for Consumer Dummies
Diane Graves Steele, Vice President and Publisher, Consumer Dummies
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Introduction
Almost half of all graduating students in the United States (an estimated 45 percent) take the ACT. If you’re among this lucky bunch, you may be looking toward the future with a combination of anticipation and dread. You’re anticipating college, with its new experiences and first tastes of freedom, but you’re dreading the hoops you have to jump through to get there. Of course, the ACT is one of these hoops. If you do well on this test, you’re propelled to your first-choice college; if you do poorly, maybe not.
You’re not alone. And I’m here to help. As the author of Basic Math and Pre-Algebra For Dummies (Wiley) and SAT Math For Dummies (Wiley), I’ve already helped thousands of would-be college students get through the arduous testing process and move into the exciting life that awaits them in college.
If you’re willing to keep the faith and do the work in front of you, I’m confident that you can be among those who succeed on the ACT and take one step forward into your dreams. Let this book be your guide.
About This Book
Although you certainly want to do well on all four sections of the ACT (as well as the optional writing test), this book focuses exclusively on math. The reason I’m playing favorites is simple: For many students (and possibly you, too), math is the toughest section of the test. Because your composite score on the ACT is based in part on your math score, you don’t want math to drag down an otherwise good score.
The math you need to know to do well on the ACT is basically what’s covered in high school: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. If you’re thinking of college, the good news is that you’ve probably studied a lot of this material already. The bad news is that you may have forgotten it or never felt entirely comfortable with it in the first place.
This situation is perfectly normal, and most students who aren’t math geniuses feel roughly the same as you. So your task is to find a realistic strategy to pull together the stuff you already know — even if you’re not currently confident that you know it — and tie in the more advanced topics that may have eluded you. Luckily, you’ve come to the right place.
Everything in this book is designed to take the small amount of math you may remember and build on it so you can use it to tackle typical questions that appear on the ACT. If you’ve laid the groundwork in school and you’re willing to practice, I’ll get you through the test.
My approach in this book is simple: practice, practice, and more practice. The focus is specifically on the types of questions that appear over and over again on the ACT. Even if math isn’t your strong suit, when you become comfortable with this core material, you stand a much better chance of getting the kind of ACT score you want to see. And the best part is that you don’t necessarily have to read this book from cover to cover. You can hop and skip around to whatever topics you need to work on most.
Conventions Used in This Book
Here are a few conventions to keep in mind as you make your way through this book:
Variables (such as x and y)and newly defined terms are in italics.
Keywords in bulleted lists, action parts of numbered steps, and answers in the practice tests are in bold.
Web sites are in monofont.
I alternate the range of the answer choices throughout the book. In one question, you see Choices (A), (B), (C), (D), and (E), and then in the one after it you see Choices (F), (G), (H), (J), (K). Because the ACT itself uses this pattern, I want you to become familiar with it before test day. And, yes, test-designers skip the letter I. Why? Probably to avoid confusion because it looks like the number 1.
Foolish Assumptions
I’m going out on a limb here, but if you’ve bought this book, my first assumption is that you or somebody you know is thinking about taking the ACT. If not, you can certainly use it to improve your knowledge of high school math. And beyond that, it also makes a useful doorstop or something to stick under the leg of a very wobbly table.
My second assumption is that you’ve taken a year of algebra, whether in high school, junior college, or some other place. You don’t actually have to feel like you know algebra. In fact, the point of this book is to build these very skills. But if you’ve at least sat through an algebra class, you probably know a lot more than you think you know. Really!
How This Book Is Organized
ACT Math For Dummies is divided into six parts, each of which focuses on a different math topic you may encounter on the ACT. In this section, I give you a basic overview of these parts so you have a better idea of where you’d like to begin.
Part I: Getting into the Act: An Overview of ACT Math Basics
Chapter 1 provides an introduction to ACT math, giving you the most basic information about the test. It also includes a road map of the rest of the book. In Chapter 2, I discuss test-taking skills that aren’t strictly math-related but are still necessary to do well on the ACT. In particular, I focus on some ways to work with multiple-choice questions, including plugging in answers. I also show you how to use your calculator to your advantage, rule out answers and guess wisely, and know when to jump over questions that look long or difficult.
In Chapter 3, I discuss a variety of problem-solving strategies. These include looking for a pattern by drawing a chart or picture, memorizing basic math ideas, working with math formulas, setting up word problems, and making a plan to answer difficult questions.
Part II: Building Your Pre-Algebra and Elementary Algebra Skills
In Part II, I begin helping you build your math skills. In Chapter 4, for example, you review the basics of pre-algebra: number sequences; inequalities; absolute value; factors and multiples; percents, ratios, and proportions; powers and square roots; tables and graphs; basic statistics; and probability.
In Chapter 5, you focus on elementary algebra (Algebra I), including the following: understanding basic algebra concepts and vocabulary; evaluating, simplifying, and factoring expressions; solving a variety of equations, including rational equations and equations with absolute values, square roots, and exponents; and working with equations that have more than one variable.
Chapter 6 provides 30 practice questions, covering the material from Chapters 4 and 5. Each question includes a detailed explanation of how to answer that question.
Part III: Digging In to Intermediate Algebra and Coordinate Geometry
Part III adds on to the math skills you gain in Part II. Chapter 7 discusses intermediate algebra (Algebra II). You study these topics: inequalities, systems of equations, direct and inverse proportionality, quadratic equations, and functions.
Chapter 8 covers coordinate geometry, which usually is introduced in Algebra I and is continued in Algebra II. I discuss the following topics: graphing points and lines, the distance and midpoint formulas, the slope-intercept form of a line, parallel and perpendicular lines, quadratic functions, transformations, higher-order polynomial functions, and circles on the xy-graph.
Chapter 9 offers 30 practice questions focusing on the topics covered in Chapters 7 and 8, along with answers and step-by-step explanations for each.
Part IV: Visualizing Plane Geometry and Trigonometry
Part IV completes the math skills you need to know to get a good score on the ACT. Chapter 10 focuses on plane geometry: lines and angles; triangles, including the area formula and the Pythagorean theorem; quadrilaterals such as squares, rectangles, parallelograms, and trapezoids; circles, including the formulas for area and circumference, tangents, arc length, and chords; and solid geometry.
In Chapter 11, I cover a variety of advanced math topics: trigonometry, including trig ratios, radian measure, the graphing of trig functions, and basic identities; matrices, including matrix operations and determinants; logarithms; and imaginary and complex numbers.
Chapter 12 tests your understanding of the math you discover in Chapters 10 and 11 with 30 practice questions and fully worked-out explanations.
Part V: Tracking Your Progress with Practice Tests
Part V includes three full-length ACT mathematics tests. Chapters 13, 15, and 17 each contain a different test. Each has 60 questions that should be completed in 60 minutes. In Chapters 14, 16, and 18, you find the answer keys and detailed explanations of how to answer each question.
Part VI: The Part of Tens
In Part VI, I present two top-ten lists that provide useful information about the ACT. In Chapter 19, I outline ten key differences between the ACT and the SAT. And in Chapter 20, I give you a checklist of small but vital things to remember leading up to your test day.
Icons Used in This Book
Throughout this book, I use the following four icons to help you keep track of the different kinds of information. Here’s what each icon means:
This icon highlights essential information that you need to know, such as key ideas or formulas. Spending a few extra minutes studying these important points is time well spent. You also can use these icons to skim through a chapter you’ve already studied. Doing so helps solidify your understanding.
Each tip provides an insightful way to approach a question. You may find it especially helpful as a quick way to cut through a seemingly complicated problem.
This icon is like a flashing red light, drawing your attention to a sticky or subtle point that may trip you up if you’re not aware of it. Take an extra moment to slow down and make sure you understand the point being made so it doesn’t trip you up on the test.
When you see this icon, you know you’re ready to put pencil to paper. This book includes dozens of examples of ACT questions, showing you how to answer them from start to finish. Use these examples to better understand a specific type of problem and then refer to them when answering the practice questions.
Where to Go from Here
I’ve written this book as a complete reference to ACT math. You can start anywhere you like, dip in, clarify your understanding, and then hop back out with ease.
If you’re completely unfamiliar with the ACT, I recommend that you begin with Chapter 1 before branching out. In that chapter, I outline the basics of the math portion of the ACT and provide an overview of the topics that are covered on the test.
If you’re ready to get studying, flip to whatever chapter discusses the topic you need help with most. Chapters 4 through 12 provide a thorough review of the specific math skills that the ACT covers. You can focus on these chapters until you feel ready to take one of the practice tests in Part V. Alternatively, you can take a practice test first to find out which types of questions you can answer easily and which hang you up.
Part I
Getting into the Act: An Overview of ACT Math Basics
In this part. . .
In Part I, you get an overview of the types of math problems you can expect on the ACT. I outline the math skills you need most, show you some helpful test-taking skills, and discuss some useful problem-solving strategies.
Chapter 1
Reviewing ACT Math Basics
In This Chapter
Beginning with an overview of ACT math
Identifying four important steps to success
Studying the six math topics tested on the ACT
Figuring out what’s not tested
All across the United States — and especially in the Midwest, South, and Rocky Mountain states — high school juniors and seniors prepare for one of the most action-packed Saturdays of their lives. No, I don’t mean the prom, graduation day, or a really excellent date with someone their parents don’t know about and wouldn’t approve of if they did. No, they’re preparing for something even more fun than that: the ACT.
And if you believe any of this fun business, you’re in for a real treat: I also have a fortune in gold from the prince of a country whose name you can’t pronounce all ready to deposit into your bank account. Yeah, right.
Well, okay, some of this is true: You will be taking the ACT (which I figured out the moment you picked up this book). In this chapter, I begin the work of helping you get ready for the most fun part of all, the 60-minute math test.
I start this chapter with a look at what’s on the math portion of the ACT. Then I provide a bit of advice about four general ways to improve your score. Finally, I list the six math topics that the ACT tests you on, including a breakdown of the specific skills within each topic that you should focus on to do well.
The chapter ends with a sigh of relief as you discover the math that you don’t need to worry about on the ACT. (However, the teacher of your current math class may still want you to know something about it, so don’t flush it from your memory just yet!)
Getting an Overview of ACT Math
The ACT contains five separate tests, which are always presented in this order:
1. English
2. Mathematics
3. Reading
4. Science
5. Writing (optional)
This book focuses exclusively on the second test, the ACT mathematics test. This math portion lasts for 60 fun-filled minutes and contains 60 questions. Generally speaking, questions appear roughly in order of difficulty.
The test is scored on a scale of 1 (lowest) to 36 (highest). Additionally, you receive three subscores in the following three separate areas
Pre-algebra and elementary algebra
Intermediate algebra and coordinate geometry
Plane geometry and trigonometry
Subscores are tallied on a scale of 1 (lowest) to 18 (highest). Note that, flying in the face of common sense, your three subscores will not add up to your math score.
On the ACT, test graders don’t take off points for wrong answers — that is, you won’t be penalized for guessing. So keep an eye on the time and, just before your time is up, fill in answers to all 60 questions. Make as many educated guesses as you can, of course. But even wild guessing won’t hurt your score, so fill in those answers before time’s up!
Taking Four Key Steps to ACT Success
I like to give the following four important pieces of advice to those students who want to improve their ACT math scores:
Sharpen your basic math skills.
Get comfortable using your calculator.
Solidify your ACT-math-specific skills.
Take practice tests under timed conditions.
In this section, I give you an overview of these four steps. The rest of the book is devoted, one way or another, to working on them.
Sharpening your basic math skills
By the basics, I mean the math calculations that precede pre-algebra. For example:
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Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
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Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
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Lesen Sie weiter in der vollständigen Ausgabe!
