AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
Fifty Lectures for
American Mathematics Competitions
Volume 2
Jane Chen
Sam Chen
http://www.mymathcounts.com/index.php
, AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
DEDICATION
This book is dedicated to Dr. Harold Reiter, who opened the door to the world of
mathematics for us, who has always been there for us, and who inspired us to write this
book.
ACKNOWLEDGEMENTS
We would like to thank the following math contests for their mathematical ideas. Many
problems in this book are modified or inspired from these tests. We also cited very few
problems directly from these tests for the purpose of comparison with our own solutions.
The AMC 10/12. An examination in secondary school mathematics containing problems
which can be understood and solved with precalculus concepts. Many problems in this
book are modified or inspired from AMC problems.
The AIME (American Invitational Mathematics Examination).
The ARML (American Regions Mathematics League). An annual high school
mathematics competition held simultaneously at five locations in the United States.
The China Middle School Math Competition.
The China High School Math Competition.
The China College Admission Exams.
Yongcheng Chen, Ph.D., Reviewer.
Guiling Chen, Owner, mymathcounts.com, Typesetter, Editor
Copyright © 2013 by mymathcounts.com. All rights reserved. Printed in the United
States of America. Reproduction of any portion of this book without the written
permission of the authors is strictly prohibited, except as may be expressly permitted by
the U.S. Copyright Act.
ISBN-13: 978-1470164300
ISBN-10: 1470164302
Please contact for suggestions, corrections, or clarifications.
, AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
Table of Contents
Chapter 13 Cubic Identities 1
Chapter 14 Arithmetic Sequence 15
Chapter 15 How to Use the Discriminant 43
Chapter 16 Completing the Square 61
Chapter 17 Analytic Geometry Distance and Lines 84
Chapter 18 Functional Equations 104
Chapter 19 Squeezing Method 122
Chapter 20 Nonegative Numbers 132
Chapter 21 Geometry Similar Triangles 148
Chapter 22 Geometry Angle Bisector And Median 169
Chapter 23 Geometry Eight More Methods To Draw Auxiliary Lines 191
Chapter 24 Trigonometry Identities 210
Chapter 25 AM-GM Inequality 231
, AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
This page is intentionally left blank
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
Fifty Lectures for
American Mathematics Competitions
Volume 2
Jane Chen
Sam Chen
http://www.mymathcounts.com/index.php
, AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
DEDICATION
This book is dedicated to Dr. Harold Reiter, who opened the door to the world of
mathematics for us, who has always been there for us, and who inspired us to write this
book.
ACKNOWLEDGEMENTS
We would like to thank the following math contests for their mathematical ideas. Many
problems in this book are modified or inspired from these tests. We also cited very few
problems directly from these tests for the purpose of comparison with our own solutions.
The AMC 10/12. An examination in secondary school mathematics containing problems
which can be understood and solved with precalculus concepts. Many problems in this
book are modified or inspired from AMC problems.
The AIME (American Invitational Mathematics Examination).
The ARML (American Regions Mathematics League). An annual high school
mathematics competition held simultaneously at five locations in the United States.
The China Middle School Math Competition.
The China High School Math Competition.
The China College Admission Exams.
Yongcheng Chen, Ph.D., Reviewer.
Guiling Chen, Owner, mymathcounts.com, Typesetter, Editor
Copyright © 2013 by mymathcounts.com. All rights reserved. Printed in the United
States of America. Reproduction of any portion of this book without the written
permission of the authors is strictly prohibited, except as may be expressly permitted by
the U.S. Copyright Act.
ISBN-13: 978-1470164300
ISBN-10: 1470164302
Please contact for suggestions, corrections, or clarifications.
, AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
Table of Contents
Chapter 13 Cubic Identities 1
Chapter 14 Arithmetic Sequence 15
Chapter 15 How to Use the Discriminant 43
Chapter 16 Completing the Square 61
Chapter 17 Analytic Geometry Distance and Lines 84
Chapter 18 Functional Equations 104
Chapter 19 Squeezing Method 122
Chapter 20 Nonegative Numbers 132
Chapter 21 Geometry Similar Triangles 148
Chapter 22 Geometry Angle Bisector And Median 169
Chapter 23 Geometry Eight More Methods To Draw Auxiliary Lines 191
Chapter 24 Trigonometry Identities 210
Chapter 25 AM-GM Inequality 231
, AMC10 Lectures Vol 2 Ch13-25 Fifty Lectures for
American Mathematics Competitions Volume 2 Jane
Chen Sam Chen
This page is intentionally left blank
