Required part: required 1, required 2, required 3, required 4, required 5, optional 1- 1-2;

Elective courses: Elective courses 4- 1 (Selected lectures on geometry proof), Elective courses 4-2 (Matrix and Transformation), Elective courses 4-4 (Coordinate System and Parameter Equation), Elective courses 4-5 (Selected lectures on inequality).

Extended data:

compulsory course

1, setting

(about 4 class hours)

The Meaning and Representation of (1) Set

① Understand the meaning of set and the "subordinate" relationship between elements and set through examples.

② We can choose natural language, graphic language and assembly language (enumeration or description) to describe different specific problems and feel the significance and function of assembly language.

(2) the basic relationship between sets

① By understanding the meaning of inclusion and equality between sets, we can identify a subset of a given set.

② Understand the meaning of complete works and empty sets in specific situations.

(3) Basic operations of sets

① To understand the meaning of union and intersection of two sets, we require union and intersection of two simple sets.

② Understanding the meaning of the complement set of a subset in a given set will lead to the complement set of a given subset.

(3) venn diagram can be used to express the relations and operations of sets, and the role of intuitive graphs in understanding abstract concepts can be realized.

2. The concept of function and basic elementary function

(about 32 class hours)

(1) function

① Further understand that function is an important mathematical model to describe the dependence between variables, and on this basis, learn to describe functions with sets and corresponding languages, and understand the role of correspondence in describing the concept of functions; Knowing the elements that make up a function, we can find the definition and value range of some simple functions; Understand the concept of mapping.

② In actual situations, appropriate methods (such as image method, list method and analysis method) will be selected according to different needs to express functions.

③ Understand the simple piecewise function and apply it simply.

④ Understand the monotonicity, maximum (minimum) value and its geometric significance of the function through the learned function, especially the quadratic function; Understand the meaning of parity with specific functions.

⑤ Learn to use function images to understand and study the properties of functions (see example 1).

(2) Exponential function

(1) (cell division, the decay of archaeological C, the change of drug residues in human body, etc. ), and understand the actual background of exponential function model.

② Understand the meaning of rational exponential power, understand the meaning of real exponential power through concrete examples, and master the operation of power.

③ To understand the concept and significance of exponential function, we can draw the image of specific exponential function with the help of calculator or computer, and explore and understand the monotonicity and special points of exponential function.

④ In the process of solving simple practical problems, I realized that exponential function is an important function model (see Example 2).

(3) Logarithmic function

(1) Understand the concept of logarithm and its operational properties, and know that general logarithm can be converted into natural logarithm or ordinary logarithm by changing the base formula; By reading the materials, we can understand the history of logarithm and its role in simplifying operations.

② Through concrete examples, we can intuitively understand the quantitative relationship described by the logarithmic function model, preliminarily understand the concept of logarithmic function, and realize that logarithmic function is an important function model; With the help of calculator or computer, we can draw images of specific logarithmic functions and explore and understand the monotonicity and special points of logarithmic functions.

③ Know that exponential function and logarithmic function are reciprocal functions (A >；); 0，a≠ 1)。

(4) Power function

Understand the concept of power function through examples; Combine the images of functions to understand their changes.

(5) Functions and equations

① Combining the image of quadratic function, we can judge the existence and number of roots of quadratic equation in one variable, so as to understand the relationship between zero point of function and roots of equation.

(2) According to the image of a specific function, it is a common method to find the approximate solution of the corresponding equation by dichotomy with the help of a calculator.

(6) Function model and its application

① Compare the growth differences of exponential function, logarithmic function and power function with calculation tools; Combined with examples, we can understand the meaning of growth of different function types such as linear rise, exponential explosion and logarithmic growth.

② Collect some examples of function models (exponential function, logarithmic function, power function, piecewise function, etc. ) It is often used in social life to understand the wide application of functional models.

(7) Practice homework

According to a certain theme, collect some historical events and figures (Kepler, Galileo, Descartes, Newton, Leibniz, Euler, etc. ) Function examples that played an important role in the development of mathematics around17th century, or in real life.

Write an article about the formation, development or application of function concepts in the form of group cooperation, and communicate in class. See the requirements of mathematical culture for specific requirements.

Baidu encyclopedia-high school mathematics