Perfect 800: SAT Math, Advanced Strategies for Top Performance

386 Pages·2021·6.821 MB·English

by  Dan Celenti

800
Perfect

SAT

Math

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4th Edition
800
Perfect

SAT

Advanced
Strategies
for Top
Performance
Math

Dan Celenti, Ph.D.
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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
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The value of an education . . . is not the learning of many
facts but the training of the mind to think.
—Albert Einstein
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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
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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
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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
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