High School Mathematics (Selected Compulsory Volume 1, A Edition) | People's Education Press

📚 Content Summary

This textbook aligns with the Curriculum Standards for Ordinary High School Mathematics (2017 Edition), focusing on core content including spatial vectors and solid geometry, equations of lines and circles, and equations of conic sections. By integrating numerical and geometric thinking with vector methods, the course aims to enhance students’ core competencies in mathematical modeling, logical reasoning, and intuitive visualization.

Master vector tools and analytic geometry to unlock the door to spatial mathematical thinking.

Author: People's Education Press Curriculum and Textbook Research Institute, Center for Research and Development of Secondary School Mathematics Curriculum and Textbooks

Acknowledgments: Approved by the National Textbook Committee Expert Review Panel (2019)

🎯 Learning Objectives

1. Understand and master the concept of spatial vectors, linear operations, and necessary and sufficient conditions for collinearity and coplanarity.
2. Grasp the fundamental theorem of spatial vectors and be proficient in establishing a spatial rectangular coordinate system for coordinate operations of vectors.
3. Use direction vectors and normal vectors of spatial vectors to determine positional relationships—parallelism and perpendicularity—between lines and planes in space.
4. Master algebraic representations of lines: deeply understand the concepts of inclination angle and slope, and skillfully apply point-slope form, general form, and parametric equations to describe lines.
5. Quantify geometric relationships and distances: master the conditions for parallelism and perpendicularity between two lines, and be proficient in using distance formulas for points, point-to-line, and between parallel lines.
6. Construct mathematical models of circles: determine standard and general equations of circles given specific conditions, and analyze positional relationships among points, lines, and circles, as well as between two circles.
7. Master standard equations: derive standard equations of ellipses, hyperbolas, and parabolas based on given conditions, and conduct case analysis according to focus positions.
8. Analyze geometric properties: skillfully identify and compute vertices, foci, major/minor axes (real/imaginary axes), eccentricity of conic sections, asymptotes of hyperbolas, and directrices of parabolas.
9. Solve positional relationships: learn to use the discriminant method to address problems involving common points between lines and ellipses, and master techniques for computing chord length and finding midpoints' loci.