Solving problems and upgrading high school mathematics

Author: Zhao Xiaoling, Editor-in-Chief
Publisher:
Publish Date: 2005-06-01
Features:
This series of books is characterized by:
Comprehensive Analysis and Solutions: Fully analyze and solve typical problems related to knowledge points, key points, difficulties, and examination points, providing thinking angles for problem-solving approaches, demonstrating the solution process, and indicating scientific problem-solving methods!
Training Package: Based on the examination points involved in the examples, set up targeted training for knowledge extension and expansion, allowing for learning by analogy!
Gas Station: Emphasizes important formulas, patterns, and problem-solving approaches to boost problem-solving skills!
Detailed Answers and Explanations: The answers to the training package are detailed, revealing problem-solving approaches or providing analysis!
This book comprehensively analyzes and solves typical problems related to knowledge points, key points, difficulties, and examination points, serving as an educational aid with the nature of a problem-solving dictionary. However, it surpasses a traditional problem-solving dictionary by not only demonstrating the solution process but also providing a more detailed explanation of the thinking process and the selection of entry points, making its function of teaching methods and guiding thinking even stronger.
Students must meet two conditions to improve their problem-solving skills: first, to build a solid foundation, and second, to apply acquired knowledge to analyze and solve problems. This book explains knowledge points, key points, difficulties, and examination points through example analysis while providing the thinking process for problem-solving. It activates abilities while building a foundation and consolidates basic knowledge through practical problem-solving. Additionally, the training package set up based on examples serves as a model for learning by analogy. Once these examples and exercises are mastered, similar problems can be solved effortlessly. Therefore, this book perfectly fulfills the role of improving problem-solving skills.
This book is organized by chapter order according to curriculum standards and teaching progress, with examples and training questions set according to the examination guidelines for the junior high school entrance examination. Examples are arranged in the order of basic questions, ability-based questions, and comprehensive questions, fully aligning with students' in-class learning rhythm and can be used anytime to solve problem-solving issues students encounter. Each example mainly includes three content sections: analysis, solution, and notes, just like a teacher's lecture: first, it provides the thinking process for analysis, then solves the problem, and for difficult or easily mistaken questions, it highlights important points, correct methods, and error diagnosis. It is extremely easy to master.
The example analysis in this book has the following functions:
1. Links the knowledge system;
2. Explains knowledge points and examination points;
3. Interprets key points and difficulties;
4. Teaches methods and guides thinking;
5. Covers all types of questions;
6. Allows for learning by analogy.
Specifically, the examples in this book are set according to three principles:
1. Examples can explain knowledge points and examination points, meaning the number of examples is equal to the number of knowledge points and examination points;
2. Comprehensive question types, including traditional classic question types as well as new question types such as reading questions and situational questions that have appeared in recent years in junior high school entrance examinations;
3. Examples are typical in question types and content, serving as a model for learning by analogy.
The examples in this book are closely related to exams. First, all examination points in the textbook are accompanied by example analysis. Second, the examples emphasize the purpose of ability, increasing application-based and ability-based question types, aligning with the trend of exam reform in junior high school entrance examinations.