【People's Education Press】Junior High School Mathematics Grade 9 Part 1

This textbook is the standard mathematics curriculum for the first semester of Grade 9 in junior high school, covering five core modules: quadratic equations, quadratic functions, rotation, circles, and an introduction to probability. It aims to develop students’ logical thinking and mathematical modeling abilities.

Master the core logic of middle school mathematics and embark on an advanced exploration journey into functions and geometry.

Author: Lin Qun

Acknowledgments: Reviewed and approved by the Ministry of Education (2013), Second Prize for National Outstanding Textbooks at the First National Textbook Construction Award

1. Identify quadratic equations, proficiently convert equations into standard form, and accurately determine the coefficients of the quadratic term, linear term, and constant term.
2. Understand the meaning of roots of an equation and verify roots by substitution.
3. Formulate quadratic equations based on real-world contexts such as geometric area or quantitative relationships, and master solving simple quadratic equations using the definition of square roots (foundation of completing the square).
4. Understand and master the graphical characteristics of quadratic functions y=ax^2 and y=a(x-h)^2+k (opening direction, axis of symmetry, vertex).
5. Skillfully apply the translation rule “add to the left, subtract from the right; add to the top, subtract from the bottom” to transform function expressions.
6. Determine the expression of a quadratic function using the method of undetermined coefficients and explain the relationship between the x-axis intercepts of a parabola and the roots of the corresponding equation.
7. Understand and master the properties of rotation, and the concepts of central symmetry and centrally symmetric figures; identify and locate centers of symmetry.
8. Derive and memorize the coordinate characteristics of points symmetric about the origin, and perform basic rotational transformations of figures in the Cartesian coordinate system.
9. Apply knowledge of rotation and symmetry to pattern design, and understand the mathematical principles behind rotationally symmetric figures in real life.
10. Understand and master positional relationships: determine the position of a point relative to a circle or a line relative to a circle using numerical relationships (d and r).