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Barron's Sat Subject Test Math Level 1 BARRON’S SAT* SUBJECT TEST MATH LEVEL 1 4TH EDITION Ira K. Wolf, Ph.D. President, PowerPrep, Inc. Former High School Math Teacher, College Professor of Mathematics, and University Director of Teacher Preparation * SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. About the Author Dr. Ira Wolf has had a long career in math education. In addition to teaching math at the high school level for several years, he was a professor of mathematics at Brooklyn College and the Director of the Mathematics Teacher Preparation program at SUNY Stony Brook. Dr. Wolf has been helping students prepare for the PSAT, SAT, and SAT Subject Tests in Math for 35 years. He is the founder and president of PowerPrep, a test preparation company on Long Island that currently works with more than 1,000 high school students each year. © Copyright 2012, 2010, 2008 by Barron’s Educational Series, Inc. Previous edition © Copyright 2005 under the title How to Prepare for the SAT II: Math Level 1C. All rights reserved. No part of this work may be reproduced or distributed in any form or by any means without the written permission of the copyright owner. All inquiries should be addressed to: Barron’s Educational Series, Inc. 250 Wireless Boulevard Hauppauge, New York 11788 www.barronseduc.com eISBN: 978-1-4380-8376-6 Second eBook publication: August, 2012 Contents What You Need to Know About SAT Subject Tests What You Need to Know About the SAT Subject Test in Math Level 1 TEST-TAKING STRATEGIES 1 Important Tactics An Important Symbol Used in This Book Calculator Tips The Inside Scoop for Solving Problems TOPICS IN ARITHMETIC 2 Basic Arithmetic The Number Line Absolute Value Addition, Subtraction, Multiplication, Division Integers Exponents and Roots Squares and Square Roots Logarithms PEMDAS Exercises Answers Explained 3 Fractions, Decimals, and Percents Fractions Arithmetic Operations with Fractions Arithmetic Operations with Mixed Numbers Complex Fractions Percents Percent Increase and Decrease Exercises Answers Explained 4 Ratios and Proportions Ratios Proportions Exercises Answers Explained ALGEBRA 5 Polynomials Polynomials Algebraic Fractions Exercises Answers Explained 6 Equations and Inequalities First-Degree Equations and Inequalities Absolute Value, Radical, and Fractional Equations and Inequalities Quadratic Equations Exponential Equations Systems of Linear Equations The Addition Method The Substitution Method The Graphing Method Solving Linear-Quadratic Systems Exercises Answers Explained 7 Word Problems Rate Problems Age Problems Percent Problems Integer Problems A Few Miscellaneous Problems Exercises Answers Explained PLANE GEOMETRY 8 Lines and Angles Angles Perpendicular and Parallel Lines Exercises Answers Explained 9 Triangles Sides and Angles of a Triangle Right Triangles Special Right Triangles Perimeter and Area Similar Triangles Exercises Answers Explained 10 Quadrilaterals and Other Polygons The Angles of a Polygon Special Quadrilaterals Perimeter and Area of Quadrilaterals Exercises Answers Explained 11 Circles Circumference and Area Tangents to a Circle Exercises Answers Explained SOLID AND COORDINATE GEOMETRY 12 Solid Geometry Rectangular Solids Cylinders Prisms Cones Pyramids Spheres Exercises Answers Explained 13 Coordinate Geometry Distance Between Two Points The Midpoint of a Segment Slope Equations of Lines Circles and Parabolas Exercises Answers Explained TRIGONOMETRY 14 Basic Trigonometry Sine, Cosine, and Tangent What You Don’t Need to Know Exercises Answers Explained FUNCTIONS 15 Functions and Graphs Relations Functions Combining Functions Composition of Functions Inverse Functions Exercises Answers Explained STATISTICS, COUNTING, AND PROBABILITY 16 Basic Concepts of Statistics, Counting, and Probability Statistics Counting Probability Exercises Answers Explained MISCELLANEOUS TOPICS 17 Imaginary and Complex Numbers Imaginary Numbers Complex Numbers Exercises Answers Explained 18 Sequences Repeating Sequences Arithmetic Sequences Geometric Sequences Exercises Answers Explained 19 Logic Statements Negations Conditional Statements Exercises Answers Explained MODEL TESTS Guidelines and Scoring 20 Model Test 1 21 Model Test 2 22 Model Test 3 What You Need to Know About SAT Subject Tests *The importance of the College Board’s Score Choice policy* • What Are SAT Subject Tests? • How Many SAT Subject Tests Should You Take? • How Are SAT Subject Tests Scored? • How Do You Register for an SAT Subject Test? This e-Book contains hyperlinks that will help you navigate through content, bring you to helpful resources, and allow you to click between exam questions + answers. *Please Note: This e-Book may appear differently depending on which device you are using. Please adjust accordingly. Since you are reading this book, it is likely that you have already decided to take the SAT Subject Test in Math Level 1; at the very least, you are seriously considering taking it. Therefore, you probably know something about the College Board and the tests it administers to high school students: PSAT, SAT, and SAT Subject Tests. In this short introductory chapter, you will learn the basic facts you need to know about the Subject Tests. In the next chapter, you will learn everything you need to know about the Math Level 1 test in particular. In 2009, the College Board instituted a Score Choice policy for all SAT Subject Tests, as well as for the SAT. What this means is that at any point in your high school career you can take (or even retake) any Subject Tests you want, receive your scores, and then choose whether or not the colleges to which you eventually apply will ever see those scores. In fact, you don’t have to make that choice until your senior year when you are actually sending in your college applications. Suppose, for example, that you take the Biology test one year and the Chemistry test the following year. If you earn very good scores on both exams, then, of course, you can send the colleges both scores; if, however, your Chemistry score is much better than your Biology score, you can send the colleges only your Chemistry score and the colleges won’t even know that you took the Biology test. Similarly, if you take the Math Level 1 test in June and retake it in November, you can send the colleges just your higher score and they will never know that you took it twice. WHAT ARE SAT SUBJECT TESTS? Each SAT Subject Test is an hour-long exam designed to test your knowledge of one specific course that you studied in high school. The following chart lists all the SAT Subject Tests that the College Board offers. Subject Tests English Literature Social Studies World History United States History Mathematics Math Level 1 Math Level 2 Science Biology Chemistry Physics Foreign Language French German Hebrew Italian Latin Spanish Chinese Japanese Korean Each of these tests consists entirely of multiple-choice questions. The number of questions ranges from 50 on the Math 1 and Math 2 tests to 95 on World History. Why Should You Take SAT Subject Tests? Not every college and university requires you to submit SAT Subject Test scores as part of the admissions process. So if you knew with certainty that you were applying only to schools that do not require their applicants to take Subject Tests, you would not have to take any. However, when you are in ninth-, tenth-, or even eleventh-grade, it is impossible for you to know exactly which schools you will be applying to in the fall of your senior year. Also colleges and universities that don’t currently insist that applicants submit scores from SAT Subject Tests may change their policy. In the past few years, many colleges that previously had not required applicants to take Subject Tests have begun requiring them. Therefore, most students—and certainly all good students — should plan on taking some Subject Tests. Another reason for taking SAT Subject Tests is that even colleges that do not require them for admissions may use them for placement purposes. Often, if you have a good score on a Subject Test, you may be exempted from taking an introductory course in that area and be able to take a more interesting elective. Finally, remember that because of Score Choice, you are at no risk. If you take a Subject Test and don’t get a score you are happy with, you never have to submit it. How Many SAT Subject Tests Should You Take? No college requires applicants to submit scores from more than three SAT Subject Tests, but many schools—including almost all of the most competitive ones—do ask for two or three. Consequently, most students should plan to take at least two Subject Tests and very strong students should take at least three. You should know, however, that many students take more than three, some as many as six or seven. They do this because the Score Choice policy allows them to send whichever scores they like. So they can pick their best two or three scores from among all the tests they have taken. Or, if they have really good scores on more than three tests, they can try to really impress the admissions officers by submitting scores from four, or five, or even more tests. A good guideline is that you should take an SAT Subject Test in any subject in which you feel you can earn a high score. On any test date, you may take one, two, or three Subject Tests, but you may not take any in the month you take the SAT. When Should You Take SAT Subject Tests? Most SAT Subject Tests are given six times per year: in January, May, June, October, November, and December. By far the most common month in which to take a Subject Test is June, at the end of the year in which you study the subject on that test.
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