Grade 9 - Junior High School Math Exam Guide Core Tutorial - (New Curriculum Standards)

Author: Wu Mingfeng
Publisher:
Publishing Date: 2006-10-01
Features: The newly compiled "New Curriculum Standards · Junior High School Mathematics 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" issued by the Ministry of Education. It is compiled in line with the principles of "New Curriculum Standards, New Content, New Characteristics, and New Methods." The newly compiled "New Curriculum Standards · Junior High School Mathematics Exam Guide · Core Tutoring" series systematically elaborates on the connotation and extension of mathematical formulas, rules, definitions, and theorems, emphasizing foundational knowledge and skills, innovative abilities, and comprehensive knowledge application. It also focuses on 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 the teaching process.
2. It emphasizes key and difficult teaching materials, closely integrating systematic and targeted instruction and practice to cultivate students' analytical and problem-solving abilities.
3. It emphasizes 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. It emphasizes learning methods, closely integrating typical example analysis during teaching to familiarize students with problem-solving strategies and methods, such as the principle of simplifying absolute values with the "first judge, then remove" approach. This not only reduces students' learning burden but also enhances learning efficiency.
5. It emphasizes memory methods, such as the method of memorizing congruent right-angled triangles, which can be summarized as "corresponding two sides are equal, and one side and one acute angle are equal." For the laws of exponent operations, such as \(a^m \cdot a^n = a^{m+n}\), \(a^m \div a^n = a^{m-n}\), and \((a^m)^n = a^{mn}\), grasping the pattern of "keeping the base unchanged and reducing the operation level" helps students improve their memory skills.
6. It emphasizes the classification of examples and exercises in textbooks, such as the methods for solving quadratic equations, which can be summarized into two categories. The first category is when the discriminant is a perfect square or a quadratic form, in which case the cross-multiplication method is used to find the roots of the equation. The second category is when the discriminant is not a perfect square or quadratic form, in which case the quadratic formula is used to find the roots. This significantly improves students' learning efficiency.
7. It emphasizes new types of questions that involve information acquisition and practical operations, cultivating students' ability to obtain mathematical information and conduct experimental operations.
8. It emphasizes new types of questions that highlight pattern awareness, helping students develop the ability to discover and generalize patterns.
9. It emphasizes open-ended questions, fostering students' exploration and innovative awareness.
10. It emphasizes exam content and specialized topic tutoring, assisting students in comprehensively and systematically reviewing mathematical knowledge and skills to improve their exam performance.
The newly compiled "New Curriculum Standards · Junior High School Mathematics Exam Guide · Core Tutoring" series selects examples and exercises from junior high school exam questions and curriculum reform tests from provinces and cities such as Hubei, Beijing, Shanghai, Tianjin, Nanjing, Chongqing, Zhejiang, Guangdong, Heilongjiang, and Shanxi. Its breadth, difficulty, and depth are set as high as the top-level exam questions from various provinces and cities across the country.
In the newly compiled "New Curriculum Standards · Junior High School Mathematics Exam Guide · Core Tutoring" series, content, examples, and exercises marked with a "※" are key points that must be mastered. Examples and exercises marked with "※※" are difficult and are available for teachers and students to choose from. Content, examples, and exercises marked with a "·" are designed for teachers and students using different versions of the new textbooks.
The newly compiled "New Curriculum Standards · Junior High School Mathematics Exam Guide · Core Tutoring" series is divided into three volumes: the first volume is for seventh graders (first year of junior high school); the second volume is for eighth graders (second year of junior high school); and the third volume is for ninth graders (third year of junior high school). This series is suitable for use with new textbooks such as the "People's Education Press," "Beijing Normal University Press," and "East China Normal University Press."