Grade 8 - Junior High School Math Exam Guide Core Tutorial - (New Curriculum Standards)

Author: Wu Mingfeng
Publisher:
Publish Date: 2006-10-01
Features: The newly compiled "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series follows the requirements of the newly promulgated "Outline for Basic Education Curriculum Reform" and the "Full-time Compulsory Education Curriculum Standards," closely aligning with "new curriculum standards, new content, new characteristics, and new methods." The newly compiled "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series systematically explains the connotation and extension of mathematical formulas, rules, definitions, and theorems, emphasizing foundational knowledge and skills, innovative abilities, and comprehensive knowledge application, as well as practical and operational skills. The distinctive features of this series are:
1. Highlighting mathematical quality education, focusing on cultivating students' innovative spirit, and striving to develop their induction, reasoning, and judgment abilities during teaching.
2. Emphasizing the key and difficult points of the textbooks, closely integrating teaching with systematic and targeted explanations and exercises, focusing on cultivating students' analytical and problem-solving abilities.
3. Highlighting the understanding and application of mathematical methods, such as the method of completing the square, substitution, discriminant method, and the method of undetermined coefficients, etc.
4. Highlighting learning methods, closely integrating teaching with typical example analysis, focusing on familiarizing students with problem-solving strategies and methods (such as the principle of "first judge, then remove" for simplifying absolute values), which not only reduces students' learning burden but also improves learning efficiency.
5. Highlighting memory methods (e.g., the method of memorizing congruent right-angled triangles, which can be summarized as "two sides correspondingly equal, one side and one acute angle correspondingly equal"; the laws of exponent operations αm·αn=αm+n, αm÷n=αm-n, (αm)n=αmn, where the pattern of "keeping the base unchanged and reducing the operation level" is grasped, which helps students improve their memory skills).
6. Highlighting the classification of textbook examples and exercises (e.g., the solution methods of quadratic equations are actually summarized into two categories: the first is when the discriminant is a perfect square or a quadratic form, then the cross-multiplication method is used to find the roots of the equation; the second is when the discriminant is not a perfect square or quadratic form, then the quadratic formula method is used to find the roots of the equation, greatly improving students' learning efficiency).
7. Highlighting new types of questions that emphasize information acquisition and practical operations, cultivating students' abilities to obtain mathematical information and perform practical tasks.
8. Highlighting new types of questions that emphasize awareness of patterns, which helps students develop the ability to discover and generalize patterns.
9. Highlighting open-ended questions, which helps students develop the ability to explore and innovate knowledge.
10. Highlighting exam content and specialized topic tutoring, helping students review mathematical knowledge and skills comprehensively and systematically, and improving their exam performance.
The newly compiled "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series selects examples and exercises from the junior high school entrance exam papers and curriculum reform papers from provinces and cities such as Hubei, Beijing, Shanghai, Tianjin, Nanjing, Chongqing, Zhejiang, Guangdong, Heilongjiang, and Shanxi, with breadth, difficulty, and depth benchmarked against the most challenging questions from junior high school entrance exams across China.
In the newly compiled "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series, examples and exercises marked with "" are key content that must be mastered; those marked with "" are difficult examples and exercises, available for teachers and students to choose from; and those marked with "·" are for teachers and students using different versions of the new textbooks.
The newly compiled "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series is divided into three volumes: Volume 1 for Grade 7 (first year of junior high school); Volume 2 for Grade 8 (second year of junior high school); and Volume 3 for Grade 9 (third year of junior high school). This series is suitable for new textbooks such as the People's Education Press, Beijing Normal University Press, and East China Normal University Press.
The author compiled the "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series based on "new curriculum standards, new content, new characteristics, and new methods," making it suitable for use across all grades as synchronous tutoring and training, as well as for junior high school students in Grade 9 (third year of junior high school) for exam review. It can also serve as a teaching reference for junior high school mathematics teachers.
There are still shortcomings in the newly compiled "New Curriculum Standard · Junior High School Mathematics Entrance Exam Guide · Core Tutoring" series. I sincerely hope that the readers will not hesitate to offer advice, so that this series can be improved. Thank you!