【People's Education Press】High School Mathematics Compulsory Course First Volume (A Edition)

This textbook serves as an introductory resource for high school mathematics, covering core topics such as sets and common logical expressions, quadratic functions, equations, and inequalities, function concepts and properties, exponential and logarithmic functions, and trigonometric functions. It aims to develop students' mathematical core competencies, logical reasoning abilities, and awareness of mathematical modeling.

Open the door to high school mathematics—master core concepts and rigorous logical thinking.

Author: People's Education Press Curriculum & Textbook Research Institute, Center for High School Mathematics Curriculum and Textbook Research & Development

Acknowledgments: This textbook received the National Special Award for Outstanding Textbooks at the First National Textbook Construction Awards. It is developed based on the General Senior High School Mathematics Curriculum Standards (2017 Edition).

1. Accurately determine the definiteness, distinctness, and unordered nature of sets, and proficiently use enumeration and descriptive methods to represent sets.
2. Master the application of Venn diagrams and the formula for calculating the number of elements in a set: $ \text{card}(A \cup B) = \text{card}(A) + \text{card}(B) - \text{card}(A \cap B) $.
3. Understand and distinguish between sufficient conditions, necessary conditions, and necessary-and-sufficient conditions; apply logical language to describe geometric properties and criteria for determination.
4. Grasp the fundamental facts about comparing real numbers, and use inequality properties for algebraic proofs and size comparisons.
5. Understand the geometric background and applicability conditions (positive, fixed, equal) of basic inequalities, and solve simple extremum problems.
6. Master the solution flowchart for quadratic inequalities, comprehend the correspondence among the graph of a quadratic function, roots of equations, and solution sets of inequalities, and solve complex practical application problems.
7. Use set theory and mapping language to define functions, and understand the standard for identifying "identical functions" (same domain and correspondence).
8. Skillfully apply the three representation methods to describe variable relationships, with special emphasis on writing analytical expressions and drawing graphs of piecewise functions.
9. Strictly prove the monotonicity and even/odd nature of functions using definitions, and find extrema within given intervals.
10. Understand the concepts of nth roots and fractional exponents, and master their operational properties.