Grade 7 - Junior High School Math Exam Preparation Guide Core Tutorial - (New Curriculum Standards)

Author: Wu Mingfeng
Publisher:
Publish Date: 2006-10-01
Features: The newly compiled "New Curriculum·Junior High School Mathematics Exam Guide·Core Tutoring" series is designed in accordance with the requirements of the newly promulgated "Outline for Basic Education Curriculum Reform" and the "Full-time Compulsory Education Curriculum Standards" by the Ministry of Education, closely aligning with "New Curriculum, New Content, New Characteristics, and New Methods." The series systematically explains the connotation and extension of mathematical formulas, rules, definitions, and theorems, emphasizing foundational knowledge and skills, innovative ability, and comprehensive knowledge application, as well as practical and operational skills. The distinctive features of this series are as follows:
1. It highlights mathematical quality education, focusing on cultivating students' innovative spirit and developing their induction, reasoning, and judgment skills during teaching.
2. It emphasizes the key and difficult points of the curriculum, providing systematic and targeted instruction and practice closely linked to teaching, focusing on cultivating students' analytical and problem-solving abilities.
3. It highlights the understanding and application of mathematical methods, such as the method of completing the square, substitution, discriminant method, and the method of undetermined coefficients.
4. It emphasizes learning methods, offering in-depth analysis of typical examples closely tied to teaching, focusing on familiarizing students with problem-solving strategies and methods (e.g., the principle of simplifying absolute values with "first judge, then remove"), which reduces students' learning burden while improving efficiency.
5. It highlights memory methods, such as the method of memorizing congruent right triangles (which can be summarized as "corresponding two sides are equal, and one side and one acute angle are equal"), or the rules of exponent operations \(a^m \cdot a^n = a^{m+n}\), \(a^m \div a^n = a^{m-n}\), \((a^m)^n = a^{mn}\), where the pattern of "keeping the base unchanged and reducing the operation level" helps students enhance their memory skills.
6. It highlights the classification of textbook examples and exercises (e.g., solving quadratic equations, which are actually categorized into two types: the first type is when the discriminant is a perfect square or a quadratic form, where the cross-multiplication method is used to find the roots of the equation; the second type is when the discriminant is not a perfect square or quadratic form, where the quadratic formula is used to find the roots. This significantly improves students' learning efficiency).
7. It highlights new types of questions focusing on information acquisition and practical operations, cultivating students' ability to obtain mathematical information and perform hands-on tasks.
8. It highlights new types of questions emphasizing pattern awareness, which helps students develop the ability to discover and generalize patterns.
9. It highlights open-ended questions, fostering students' ability to explore and innovate knowledge.
10. It emphasizes exam content and specialized topic tutoring, assisting students in comprehensively reviewing mathematical knowledge and skills to improve their exam performance.
The newly compiled "New Curriculum·Junior High School Mathematics Exam Guide·Core Tutoring" series selects examples and exercises from the middle school exam papers and curriculum reform tests of Hubei, Beijing, Shanghai, Tianjin, Nanjing, Chongqing, Zhejiang, Guangdong, Heilongjiang, and Shanxi provinces, with their breadth, difficulty, and depth set as benchmarks for the most challenging questions in middle school exams across China.
In this series, content, examples, and exercises marked with "" are key points that must be mastered; those marked with "" are difficult examples and exercises for teacher and student selection; and those marked with a "·" are for teachers and students using different versions of the new curriculum textbooks.