【People's Education Press】High School Mathematics Compulsory Volume 2 (Version A)

This textbook covers five major chapters: plane vectors and their applications, complex numbers, introductory solid geometry, statistics, and probability. It aims to cultivate core mathematical competencies—logical reasoning, mathematical modeling, and data analysis—by integrating "numbers" with "shapes."

Master core mathematical thinking and explore the deep integration of vectors, complex numbers, and geometry.

Author: Zhang Jianyue, Li Zenghu

Acknowledgments: This textbook has been reviewed and approved by the Expert Committee of the National Textbook Committee (2019); related funding and copyright belong to People's Education Press.

1. Understand the physical background of vectors, grasp fundamental concepts such as vectors, equal vectors, and collinear vectors, along with their geometric representations.
2. Master vector addition, subtraction, scalar multiplication, and their geometric meanings, and apply coordinate-based linear operations proficiently.
3. Understand the definition, properties, and concept of projection vectors for the dot product of vectors, and comprehend its physical significance (e.g., work).
4. Understand the algebraic representation of complex numbers z = a+bi, conjugate complex numbers, and the concept of modulus.
5. Master the algebraic operations of complex numbers—addition, subtraction, multiplication, and division—and use conjugate complex numbers to handle division.
6. Be able to transform complex number operations into vector operations in the complex plane (parallelogram rule, triangle rule), and apply the geometric meaning of modulus to solve distance and locus problems.
7. Accurately identify structural characteristics of prisms, pyramids, frustums, and solids of revolution, and recognize simple composite solids.
8. Master surface area and volume formulas for cylinders, cones, frustums, and spheres, and understand the role of Zu Geng's Principle in deriving volumes.
9. Master the theorems for determining and properties of spatial parallelism and perpendicularity, and apply axiomatic methods for rigorous geometric proofs.
10. Students can distinguish between and implement simple random sampling and stratified random sampling, and select appropriate data collection methods based on context.