About the Authors Richard Ku has been teaching secondary mathematics, including Algebra and 2, Geometry, Precalculus, AP Calculus, and AP Statistics, for almost 30 years He has coached math teams for 15 years and has also read AP Calculus exams for years and began reading AP Statistics exams in 2007 Howard P Dodge spent 40 years teaching math in independent schools before retiring Acknowledgments I would like to dedicate this book to my wonderful wife, Doreen I would also like to thank Barron’s editor Pat Hunter for guiding me through the preparation of this new edition R.K © Copyright 2012, 2010, 2008 by Barron’s Educational Series, Inc Previous edition © Copyright 2003, 1998 under the title How to Prepare for the SAT II: Math Level IIC Prior editions © Copyright 1994 under the title How to Prepare for the SAT II: Mathematics Level IIC and © Copyright 1991, 1987, 1984, 1979 under the title How to Prepare for the College Board Achievement Test—Math Level II by Barron’s Educational Series, Inc 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 e-ISBN: 978-1-4380-8377-3 e-Book revision: August, 2012 Contents Introduction PART DIAGNOSTIC TEST Diagnostic Test Answer Key Answers Explained Self-Evaluation Chart for Diagnostic Test PART REVIEW OF MAJOR TOPICS Functions 1.1 Overview Definitions Exercises Combining Functions Exercises Inverses Exercises Odd and Even Functions Exercises Answers and Explanations 1.2 Polynomial Functions Linear Functions Exercises Quadratic Functions Exercises Higher-Degree Polynomial Functions Exercises Inequalities Exercises Answers and Explanations 1.3 Trigonometric Functions and Their Inverses Definitions Exercises Arcs and Angles Exercises Special Angles Exercises Graphs Exercises Identities, Equations, and Inequalities Exercises Inverse Trig Functions Exercises Triangles Exercises Answers and Explanations 1.4 Exponential and Logarithmic Functions Exercises Answers and Explanations 1.5 Rational Functions and Limits Exercises Answers and Explanations 1.6 Miscellaneous Functions Parametric Equations Exercises Piecewise Functions Exercises Answers and Explanations Geometry and Measurement 2.1 Coordinate Geometry Transformations and Symmetry Exercises Conic Sections Exercises Polar Coordinates Exercises Answers and Explanations 2.2 Three-Dimensional Geometry Surface Area and Volume Exercises Coordinates in Three Dimensions Exercises Answers and Explanations Numbers and Operations 3.1 Counting Venn Diagrams Exercise Multiplication Rule Exercises Factorial, Permutations, Combinations Exercises Answers and Explanations 3.2 Complex Numbers Imaginary Numbers Exercise Complex Number Arithmetic Exercises Graphing Complex Numbers Exercises Answers and Explanations 3.3 Matrices Addition, Subtraction, and Scalar Multiplication Exercises Matrix Multiplication Exercises Determinants and Inverses of Square Matrices Exercises Solving Systems of Equations Exercises Answers and Explanations 3.4 Sequences and Series Recursive Sequences Arithmetic Sequences Geometric Sequences Series Exercises for Sequences and Series Answers and Explanations 3.5 Vectors Exercises Answers and Explanations Data Analysis, Statistics, and Probability 4.1 Data Analysis and Statistics Measures and Regression Exercises Answers and Explanations 4.2 Probability Independent Events Mutually Exclusive Events Exercises Answers and Explanations PART MODEL TESTS Model Test Answer Key Answers Explained Self-Evaluation Chart Model Test Answer Key Answers Explained Self-Evaluation Chart Model Test Answer Key Answers Explained Self-Evaluation Chart Model Test Answer Key Answers Explained Self-Evaluation Chart Model Test Answer Key Answers Explained Self-Evaluation Chart Model Test Answer Key Answers Explained Self-Evaluation Chart Summary of Formulas 47 * (B) Temperature increases by 3.4°F for each additional chirp Therefore, additional chirps indicate an increase of 5(3.4) = 17.0°F [1.2] 48 * (C) Complete the square on the ellipse formula, and put the equation in standard form: x2 – 4x + + 4(y2 + 2y – 1) = 28 + + This leads to the length of the major axis: 12 Therefore, the radius of the circle is 6, and the area = 36π [2.1] = 113 49 (C) Since the velocity of a 45-mile-per-hour wind is times that of a 15mile-per-hour wind and the force on the sail is proportional to the square of the wind velocity, the force on the sail of a 45-mile-per-hour wind is times that of a 15-mile-per-hour wind: · 45 = 405 [algebra] 50 * (B) Total horizontal distance traveled = (4)(8) = 32 Total vertical distance traveled = (5)(6) = 30 If a coordinate system is superimposed on the diagram with A at (0,0), then B is at (32,30) Use the program on your calculator to find the distance between two points to compute the correct answer choice [2.1] Self-Evaluation Chart for Model Test Evaluate Your Performance Model Test Rating Excellent Very good Above average Average Below average Calculating Your Score Number Right 41–50 33–40 25–32 15–24 Below 15 Raw score R = number right – (number wrong), rounded = Approximate scaled score S = 800 – 10(44 – R) = If R 44, S = 800 Summary of Formulas CHAPTER 1: FUNCTIONS 1.2 Polynomial Functions Linear Functions General form of the equation: Ax + By + C = Slope-intercept form: y = mx + b, where m represents the slope and b the yintercept Point-slope form: y – y1 = m(x – x1), where m represents the slope and (x1,y1) are the coordinates of some point on the line Slope: , where (x1,y1) and (x2,y2) are the coordinates of two points Parallel lines have equal slopes Perpendicular lines have slopes that are negative reciprocals If m1 and m2 are the slopes of two perpendicular lines, m1 · m2 = –1 Distance between two points with coordinates (x1,y1) and ( x2 , y2 ) = Coordinates of the midpoint between two points = Distance between a point with coordinates (x1,y1) and a line Ax + By + C = = If is the angle between two lines, tan slopes of the two lines Quadratic Functions General quadratic equation: ax2 + bx + c = General quadratic formula: General quadratic function: y = ax2 + bx + c Coordinates of vertex: Axis of symmetry equation: Sum of zeros (roots) = Product of zeros (roots) = Nature of zeros (roots): If b2 – 4ac < 0, two complex numbers If b2 – 4ac = 0, two equal real numbers If b2 – 4ac > 0, two unequal real numbers , where m1 and m2 are the 1.3 Trigonometric Functions and Their Inverses Length of arc in circle of radius r and central angle is given by Area of sector of circle of radius r and central angle is given by Trigonometric Reduction Formulas In any ABC: Law of sines: Law of cosines: Area = 1.4 Exponential and Logarithmic Functions Exponents Logarithms LogbN = x if and only if bx = N 1.6 Miscellaneous Functions Absolute Value If x 0, then |x| = x If x < 0, then |x| = –x Greatest Integer Function [x] = i, where i is an integer and i x[...]... Mathematics Subject Test in June after you complete a precalculus course You can register for SAT Subject Tests at the College Board’s web site, www.collegeboard.com; by calling (866) 756-7346, if you previously registered for an SAT Reasoning Test or Subject Test; or by completing registration forms in the SAT Registration Booklet, which can be obtained in your high school guidance office You may register...Introduction The purpose of this book is to help you prepare for the SAT Level 2 Mathematics Subject Test This book can be used as a self-study guide or as a textbook in a test preparation course It is a self-contained resource for those who want to achieve their best possible score Because the SAT Subject Tests cover specific content, they should be taken as soon as possible after... sitting Important Reminder Be sure to check the official College Board web site for the most accurate information about how to register for the test and what documentation to bring on test day Colleges use SAT Subject Tests to help them make both admission and placement decisions Because the Subject Tests are not tied to specific curricula, grading procedures, or instructional methods, they provide uniform... way, colleges can use Subject Test results to compare the achievement of students who come from varying backgrounds and schools You can consult college catalogs and web sites to determine which, if any, SAT Subject Tests are required as part of an admissions package Many “competitive” colleges require the Level 1 Mathematics Test If you intend to apply for admission to a college program in mathematics,... e-Book contains hyperlinks to help you navigate through content, bring you to helpful resources, and click between test questions and their answer explanations OVERVIEW OF THE LEVEL 2 SUBJECT TEST The SAT Mathematics Level 2 Subject Test is one hour in length and consists of 50 multiple-choice questions, each with five answer choices The test is aimed at students who have had two years of algebra, one... multiple-choice problem-solving technique called back-solving, where answer choices are entered into the problem to see which works In problems where decimal answer choices are rounded, none of the choices may work satisfactorily Be careful not to overuse this technique The College Board has established rules governing the use of calculators on the Mathematics Subject Tests: • You may bring extra batteries or a backup... graph in the figure above? I y = sin 4x II III (A) only I (B) only I and II (C) only II and III (D) only II (E) I, II, and III 41 If 2 sin2x – 3 = 3 cos x and 90° < x < 270°, the number of values that satisfy the equation is (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 42 If A = tan–1 and A + B = 315°, then B = (A) 278.13° (B) 351.87° (C) –8.13° (D) 171.87° (E) 233.13° 43 Observers at locations due north and due south