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Perfect 800: SAT Math, Advanced Strategies for Top Performance PDF

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800 Perfect SAT Math PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd.. TTeexxtt..iinnddbb 11 0033--0088--22002211 1177::4477::5577 4th Edition 800 Perfect SAT Advanced Strategies for Top Performance Math Dan Celenti, Ph.D. PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd--11..iinndddd 33 0066--0088--22002211 1122::3300::0011 First published by Prufrock Press Inc. Published 2021 by Routledge 605 Third Avenue, New York, NY 10017 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business Copyright ©Taylor & Francis All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Notice: Product or corporate names may be trademarks or registered trademarks and are used only for identifcation and explanation without intent to infringe. Library of Congress Control Number: 2021939311 Cover design by Shelby Charette and layout design by Allegra Denbo ISBN: 978-1-03214-499-3 (hbk) ISBN: 978-1-64632-104-9 (pbk) ISBN: 978-1-00323-711-2 (ebk) DOI: 10.4324/9781003237112 PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd--11..iinndddd 44 0066--0088--22002211 1177::2277::4411 The value of an education . . . is not the learning of many facts but the training of the mind to think. —Albert Einstein PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd.. TTeexxtt..iinnddbb 55 0033--0088--22002211 1177::4477::5577 vii Contents Acknowledgements xi Foreword to the Fourth Edition xiii Introduction: Why Another SAT Book 1 This Book’s Approach 3 PART I: GENERAL TEST-TAKING ADVICE AND STRATEGIES Chapter 1: What Is Math and Why Do I Need to Study It? 1 1 Why You Should Never Say “I Hate Math!” .........................12 Chapter 2: Test Preparation Strategies and Advice 1 3 How Too Much “Strategy” Can Be Hazardous to Your Performance......13 An Approach to Test Preparation .................................17 Do Calculators Really Help? .....................................18 Too Much Memorization?........................................21 Ubiquitous Algebra.............................................22 Problem Solving and Data Analysis ...............................24 Fast Math ....................................................25 Reading Comprehension ........................................32 PSAT Versus SAT..............................................32 SAT Versus ACT...............................................34 Final Tips for Better Learning....................................38 PART II: SPECIFIC MATH TOPICS, TIPS FOR PROBLEM SOLVING, AND SAMPLE PROBLEMS Chapter 3: Arithmetic Concepts 4 3 3.1: Integer ...................................................43 3.2: Odd/Even Numbers.........................................44 3.3: Consecutive Integers........................................44 3.4: Number Line ..............................................45 3.5: Reciprocal (of a Number).....................................48 3.6: Factors (of a Number) .......................................48 3.7: Common Factors ...........................................49 3.8: Greatest Common Factor (GCF)...............................49 3.9: Common Multiples (of Two or More Numbers) ...................50 3.10: Least Common Multiple (LCM) ..............................51 3.11: Greatest Common Divisor (GCD).............................51 3.12: Prime Numbers ...........................................52 3.13: Ratio....................................................54 3.14: Percent..................................................55 3.15: Proportion ...............................................60 PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd.. TTeexxtt..iinnddbb 77 0033--0088--22002211 1177::4477::5577 viii PERFECT 800: SAT MATH 3.16: Directly Proportional Quantities .............................60 3.17: Inversely Proportional Quantities ............................61 3.18: Sequence.................................................62 3.19: Arithmetic Sequence .......................................63 3.20: Geometric Sequence .......................................66 3.21: Set......................................................68 3.22: Union ...................................................69 3.23: Intersection ..............................................69 3.24: Venn Diagram ............................................70 3.25: Factorials ................................................71 3.26: The Fundamental Counting Principle .........................72 3.27: Permutation..............................................75 3.28: Combination..............................................76 3.29: Distinguishable Permutations ...............................78 3.30: Absolute Value............................................79 Chapter 4: Algebra 8 3 4.1: Monomial.................................................83 4.2: Coeffcient ................................................84 4.3: Polynomial................................................85 4.4: Term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85 4.5: Like Terms................................................86 4.6: Exponents.................................................87 4.7: Function..................................................88 4.8: Quadratic Function.........................................91 4.9: Domain...................................................93 4.10: Range ...................................................95 4.11: Interpreting and Solving Equations/Inequalities ................96 4.12: Cartesian Coordinate System................................97 4.13: Straight Line .............................................98 4.14: Slope....................................................99 4.15: Distance................................................100 4.16: Midpoint................................................100 4.17: Graphical Representation of Inequalities .....................104 4.18: Complex Numbers........................................105 Chapter 5: Geometry 1 09 5.1: Angles...................................................109 5.2: Vertex...................................................109 5.3: Acute Angles..............................................110 5.4: Obtuse Angles ............................................110 5.5: Vertical Angles............................................112 5.6: Supplementary Angles .....................................112 5.7: Complementary Angles.....................................114 5.8: Straight Angles ...........................................114 5.9: Right Angles..............................................115 5.10: Exterior Angles ..........................................116 5.11: Polygon.................................................117 PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd.. TTeexxtt..iinnddbb 88 0033--0088--22002211 1177::4477::5577 CONTENTS ix 5.12: Diagonal................................................119 5.13: Triangle ................................................120 5.14: Acute Triangle ...........................................121 5.15: Obtuse Triangle..........................................121 5.16: Right Triangle ...........................................121 5.17: Equilateral Triangle ......................................122 5.18: Isosceles Triangle.........................................122 5.19: Hypotenuse .............................................127 5.20: Congruent Triangles ......................................128 5.21: Similar Triangles.........................................133 5.22: Altitude.................................................135 5.23: Quadrilaterals ...........................................137 5.24: Parallelograms...........................................139 5.25: Rectangles ..............................................139 5.26: Squares.................................................140 5.27: Perimeter...............................................142 5.28: Regular Polygon..........................................142 5.29: Circle ..................................................143 5.30: Diameter ...............................................145 5.31: Radius..................................................146 5.32: Arc.....................................................147 5.33: Tangent Line ............................................148 5.34: Tangent to a Circle........................................148 5.35: Circumference ...........................................150 5.36: Central Angle............................................150 5.37: Area of a Sector and Arc Length.............................151 5.38: Solid Geometry ..........................................154 Chapter 6: Trigonometry 1 55 6.1: Right Triangle ............................................155 6.2: Unit Circle ...............................................156 6.3: Degrees to Radians Conversion ..............................156 6.4: Trigonometric Functions....................................156 6.5: Miscellaneous Identities ....................................157 6.6: Pythagorean Identities .....................................157 Chapter 7: Miscellaneous Topics 1 61 7.1: Average/Arithmetic Mean...................................161 7.2: Median..................................................162 7.3: Mode....................................................163 7.4: Weighted Average .........................................165 7.5: Probability ...............................................165 7.6: Probability and Compound Events............................168 7.7: Elements of Statistics ......................................173 PPeerrffeecctt 880000 SSAATT MMaatthh,, 44tthh eedd.. TTeexxtt..iinnddbb 99 0033--0088--22002211 1177::4477::5577

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