【People's Education Press】Junior High School Mathematics Grade 9 Part 2

This is the final mathematics textbook for middle school, primarily covering four core modules: inverse proportion functions, similarity, trigonometric functions of acute angles, and projections and views. The course emphasizes understanding mathematical concepts through observation, exploration, and logical reasoning, and applying mathematical models to describe patterns, perform measurements, and solve spatial cognition problems in real-life contexts.

Explore the mysteries of functions and geometric logic—the concluding chapter in building core mathematical competencies for middle school.

Author: Lin Qun

Acknowledgments: This book was co-edited by Tian Zaijin, Xue Bin, and Li Haidong, with Zhang Jianyue as chief editor, and published by People's Education Press.

1. Understand concepts and expressions: Recognize inverse proportion functions, master the three forms y = \frac{k}{x}, y = kx^{-1}, and xy = k, and clearly identify the constraints k \neq 0 and x \neq 0.
2. Master graphs and properties: Accurately describe the quadrant distribution and monotonicity of inverse proportion function graphs, and understand the symmetry of hyperbolas.
3. Apply the method of undetermined coefficients: Use the method of undetermined coefficients to determine the expression of an inverse proportion function based on given point coordinates or graph information.
4. Understand and determine: Accurately define similar figures, identify the center of similarity by connecting corresponding points, and calculate the similarity ratio using side length ratios.
5. Coordinate operations: Master the coordinate transformation rules when the origin is the center of similarity (multiples of k or -k), and perform scaling operations (enlargement and reduction) of figures in the coordinate plane.
6. Comprehensive application: Skillfully apply the properties of similar polygons (equal corresponding angles, proportional side lengths) and triangle similarity criteria to solve problems involving height measurement, area calculation, and complex geometric proofs.
7. Master definitions and special values: Accurately understand and memorize the definitions of sine, cosine, and tangent, and fluently recall the trigonometric values for 30°, 45°, and 60° angles.
8. Develop problem-solving skills: Proficiently use scientific calculators to compute values, and apply the Pythagorean theorem and trigonometric relationships to solve right triangles.
9. Practical application ability: Identify and apply concepts such as elevation angle, depression angle, slope, and azimuth to solve real-world problems including height measurement, navigation avoidance of reefs, and engineering slope construction.
10. Understand the definitions of projection, parallel projection, central projection, and orthographic projection, and master the properties of points, lines, and planes under orthographic projection.