Ⅰ.
1st year of middle school

1_ Calculating Cleverly/ 16
Practice Problem 1-1/ 21
Practice Problems 1-2/ 25
Practice Problems 1-3/ 30
2_ Divisibility properties of integers/ 32
Practice Problem 2/ 37
3_ Problems about absolute values/ 40
Practice Problem 3/ 45
4_ Linear equations and inequalities with one unknown variable/ 46
Practice Problem 4/ 53
5_ Linear Systems of Equations with Two Unknown Variables and Applications/ 56
Practice Problem 5/ 62
6_ Formal calculation/ 64
Practice Problem 6/ 72
7_ Factorization (1)/ 74
Practice Problem 7/80
8_ Calculating Fractions/ 82
Practice Problem 8/ 89
9_ Divisibility of integers/ 90
Practice Problem 9/103
10_ Odd, Even, and Simple Idiosyncratic Problems/ 104
Practice Problem 10/113
11_Solution to First-Order Indeterminate Equations/ 116
Practice Problem 11/124
12_Regarding the solution to the answer selection problem (1)/ 126
Practice Problem 12/132
13_Various Problems/ 136
Practice Problem 13/144

Ⅱ.
2nd year of middle school

14_ Mistake/ 150
Practice Problem 14/ 161
15_ Power Root Formula and Exponent/ 162
Practice Problem 15/ 172
16_ Elementary Applications of the Discriminant of Quadratic Equations with One Unknown Variable and Viette's Theorem/ 174
Practice Problem 16/182
17_ Some Special Solutions to Quadratic Equations with One Unknown Variable/ 186
Practice Problem 17/ 195
18_ Higher-Order Equations and Special Equations/ 200
Practice Problem 18/210
19_ Factorization (2)/ 214
Practice Problem 19/220
20_ Identity transformation of algebraic expressions/ 222
Practice Problem 20/229
21_ Triangle/ 232
Practice Problem 21/ 243
22_ Properties and Applications of Axisymmetric and Point-Symmetry Figures/ 246
Practice Problem 22/253
23_ Undetermined coefficient method/ 256
Practice Problem 23/265
24_ Simple Drawer Principle (1)/ 268
Practice Problem 24/278
25_ Various problems regarding integers/ 280
Practice Problem 25/286

Ⅲ.
3rd year of middle school

26_ Functions and Their Graphs / 290
Practice Problem 26/300
27_ Solving Inequalities/ 304
Practice Problem 27/312
28_ The Law of Sines, the Law of Cosines, and Their Applications/ 314
Practice Problem 28/324
29_ Similar Figures/ 326
Practice Problem 29/340
30_ Won (1) - Basic Summary / 344
Practice Problem 30/352
31_ Circle (2) - Four points on a circle/ 356
Practice Problem 31/ 365
32_ Won (3) - Bangmyeok's theorem/ 368
Practice Problem 32/380
33_ Circle (4) - Positional Relationship of Circles/ 384
Practice Problem 33/396
34_ Four Propositions and Basic Traces/ 398
Practice Problem 34/405
35_ Application of Equivalent Transformation/ 408
Practice Problem 35/414
36_ A Brief Introduction to the Law of Absurdity/ 416
Practice Problem 36/426
37_ On the solution to the answer selection problem (2)/ 428
Practice Problem 37/439

Practice problem answers and supplementary explanations

Part 1_Practice Problems Answers/ 2
Part II_Practice Problems and Answers/ 15
Part III_Practice Problems and Answers/ 35
Supplementary explanation of the practice problem answers/ 50

preface

'The Shortcut to Olympiad Mathematics (Intermediate)' is now available to readers.
In order to connect with the 'Shortcut to Olympiad Mathematics (Beginner)' for middle school students, this time it was called 'Shortcut to Olympiad Mathematics (Intermediate)'. The compilation criteria for 'Shortcut to Olympiad Mathematics (Intermediate)' are as follows.
The mathematics education project proposed by the Education Committee of the China Mathematical Society should implement the spirit of the 'education-centered and education-based improvement policy and the outline of the middle school mathematics competition', further promote the project of improving the quality of middle school mathematics teachers, and better satisfy the intellectual desire of students who have the capacity to study.
By overcoming the shortcomings of 'Shortcut to Olympiad Mathematics (Beginner)' and capitalizing on its strengths, 'Shortcut to Olympiad Mathematics (Intermediate)' has gained great applicability and practicality.

1.
It was compiled more strictly according to grade level.
In particular, Chapter 37 of the commercial book, in addition to partial specialized lectures for the first and second grades, mostly comes from textbooks, but by providing lectures at a higher level than the textbook, readers can study the basic knowledge of each part of middle school mathematics more deeply and flexibly.
If you master the contents of this section, you can get good scores on the 'Admission Test' and the first round of the competition.
The second volume focuses on specialized lectures for the competition, and supplements the textbook content and lectures, which are the improved portions of this book.

2.
Another feature of this book is that it starts from a relatively low point in terms of knowledge and gradually deepens, comprehensively and systematically explaining the key points of knowledge listed in the outline of the middle school mathematics Olympiad competition, and later reaches the level of the national mathematics Olympiad competition.
Therefore, I believe that this book, along with the partial specialized lectures in the second volume, will certainly satisfy the higher demands of students.

3.
It is necessary to provide guidance materials and teaching guidelines to students and teachers as basic teaching materials to prepare for the Mathematics Olympiad, and 'Shortcut to Mathematics Olympiad (Intermediate)' has been a large-scale project behind the scenes.
In addition to practice problems corresponding to each chapter, the second volume also includes 10 mock exams (for the first and second exams). These, along with the content of each chapter, comprehensively complement and enrich the content of this book. All practice problems and mock exams have answers.

4.
It has been made 'popular' in terms of language description to make it easy to understand and easy to study on one's own.
This feature will be better implemented in 'Shortcuts to Olympiad Mathematics (Intermediate)', which will greatly reduce the difficulties readers face when studying.

Nowadays, various Mathematical Olympiad activities are widely carried out in China and are receiving importance and support from relevant sectors at all levels.
Thanks to the teachers' dedicated spirit and practical content, this activity has received a good reputation from students and parents from all walks of life.
We believe that this textbook will definitely help these activities develop healthily.
Due to the limitations of the level, errors in compilation are inevitable.
I hope that readers will criticize and correct me here.

Sichuan University, China
Wei Yu Deok