Math - Super Candidate - Preparing for the Gaokao Second Round Review (2007 Gaokao Essential)

Author: Kong Feng
Publisher:
Publish Date: 2006-10-01
Features: The second round of senior high school mathematics review focuses on knowledge and method review, emphasizing the clarification of college entrance examination requirements, establishing a comprehensive knowledge system, understanding question-setting patterns, mastering problem-solving techniques, and improving problem-solving abilities. This is a process of deepening and improving, and it is the key to achieving high scores in the college entrance examination. To better assist students in their second round of mathematics review, outstanding senior and advanced teachers from key high schools in Hubei Province and Wuhan City, as well as college entrance examination research experts, have meticulously compiled this book. The content reflects the authors' successful experience in college entrance examination tutoring and the latest achievements in question-setting research, characterized by accurate of the examination trends, timely and comprehensive information, novel materials, flexible methods, thorough explanations, precise guidance, emphasis on analysis, and focus on improvement. The entire book is guided by the principle of improving abilities and achieving better results. On one hand, it is grounded in fundamentals, highlights key points, and emphasizes analysis, meaning that during the process of solving problems, it reveals the essential structure of questions, analyzes difficulties, points out doubts, provides examples for generalization, and enhances abilities. On the other hand, it clarifies, refines, and summarizes college entrance examination knowledge points, analyzes question-setting trends, and aims to improve performance. The purpose of this book is to guide and assist students in reviewing with maximum efficiency within limited time, enabling significant improvements in mathematical abilities and breakthroughs in college entrance examination scores.
The book is divided into four major sections:
Section 1: Knowledge Topics – Focuses on the flexible and comprehensive application of chapter knowledge.
Section 2: Mathematical Thinking and Methods Topics – Aims to permeate mathematical thinking, cultivate mathematical thinking qualities, and enhance mathematical abilities.
Section 3: Comprehensive Topics at the Intersection of Knowledge and Methods – Specifically designed because recent college entrance examination requirements emphasize the creation of comprehensive questions at the intersection of knowledge and method networks.
Section 4: Exam Strategies Topics – Helps students master exam techniques and improve problem-solving efficiency to achieve high scores successfully.
Throughout these sections, the following main themes are:
(1) Analyzing college entrance examination key points, especially those prone to errors, and their countermeasures.
(2) Revealing hotspots, difficulties, and trends in college entrance examination question-setting.
(3) Emphasizing the mastery and application of fundamental mathematical thinking and methods, such as mathematical induction, proof by contradiction, substitution, the method of undetermined coefficients, and the method of completing the square, as well as ideas like the function and equation mindset, the number-shape combination mindset, the equivalence transformation mindset, and the classification discussion mindset.
(4) Improving problem-solving techniques and flexible adaptability.
To facilitate ease of use for students and teachers, each topic is divided into the following sections:
Key Point Analysis – Primarily analyzes the requirements of the College Entrance Examination Syllabus for each chapter's knowledge points in the exam, summarizes the key knowledge of the chapter, and outlines the main methods for mastering it, providing a comprehensive grasp of the chapter.
Exemplary Explanations – Selects recent national and provincial major examination or joint examination questions, while also incorporating classic examples, reflecting practicality and relevance. Each topic includes eight examples, with the first six presented only as questions for teacher explanation, and the last two provided with solutions and analysis or comments, primarily to facilitate student reading and flexible teacher handling, as well as to improve standardized writing during exams.
Exam Question Solutions – Focuses on questions set by independent-proposing provinces and cities in 2005, 2006, and 2007, as well as those set by the National Examination Center in recent years. Four examples are selected, all with detailed answers and comments, helping students grasp the question-setting characteristics and trends of recent college entrance examinations in each chapter, and better understand the exam's detailed requirements.
Ability Practice – Tailored to students with different mathematical abilities, two sets of practice questions are provided. Set A follows the 4+2+2 model, primarily to further reinforce the consolidation of mathematical fundamentals. Set B follows the 2+2+4 model, playing a crucial role in enhancing students' abilities. Students can choose one set based on their learning characteristics.
With a commitment to being earnestly responsible to our readers and striving for excellence, we closely monitor the latest trends in college entrance examinations and maintain close ties with teaching practices, striving to make this book even better. Although we have been extremely rigorous in our writing and have implemented multi-level review processes to ensure perfection, it is inevitable that some omissions may remain. We sincerely welcome readers to point out any errors and hope that this book will be loved and welcomed by more readers.