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Mathematics required course 1

1.set

(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 i.

(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. )/kloc-For those who have played an important role in the development of mathematics around the 0/7th century, or some examples of functions in real life, write an article about the formation, development or application of the concept of functions in the form of group cooperation and communicate in class. See the requirements of mathematical culture for specific requirements.

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Mathematics compulsory 2

A preliminary study on 1. solid geometry

(about 18 class hours)

(1) space geometry

① Using physical models and computer software to observe a large number of spatial graphics, we can understand the structural characteristics of columns, cones, platforms, balls and their simple combinations, and can use these characteristics to describe the structure of simple objects in real life.

(2) Can draw three views of simple space graphics (simple combination of cuboid, sphere, cylinder, cone, prism, etc.). ), can identify the three-dimensional model represented by the above three views, can make models with materials (such as cardboard), and can draw their own front views by oblique double-sided method.

③ By observing the views and straight views drawn by two methods (parallel projection and central projection), we can understand the different representations of spatial graphics.

(4) Complete the internship, such as drawing some views and front views of buildings (the requirements for size and lines are not strict without affecting the graphic characteristics).

⑤ Understand the formulas for calculating the surface area and volume of spheres, prisms, pyramids and platforms (no need to memorize formulas).

(2) the positional relationship between points, lines and surfaces

(1) With the help of the cuboid model, on the basis of intuitive knowledge and understanding of the positional relationship between points, lines and surfaces in space, the definition of the positional relationship between lines and surfaces in space is abstracted, and the following axioms and theorems that can be used as the basis of reasoning are understood.

Axiom 1: If two points on a straight line are on a plane, then the straight line is on this plane.

Axiom 2: When three points that are not on a straight line intersect, there is one and only one plane.

Axiom 3: If two non-coincident planes have a common point, then they have one and only one common straight line passing through the point.

Axiom 4: Two lines parallel to the same line are parallel.

Theorem: If the two sides of two angles in space are parallel, then the two angles are equal or complementary.

② Based on the above-mentioned definitions, axioms and theorems of solid geometry, we can know and understand the related properties and judgments of parallelism and verticality of straight lines and planes in space through intuitive perception, operational confirmation and speculative argumentation.

Operation confirmation, summed up the following judgment theorem.

◆ If the straight line out of the plane is parallel to the straight line in the plane, the straight line is parallel to the plane.

◆ Two intersecting straight lines in one plane are parallel to another plane, so the two planes are parallel.

◆ If a straight line is perpendicular to two intersecting straight lines in the plane, the straight line is perpendicular to the plane.

◆ If one plane intersects the perpendicular of another plane, the two planes are perpendicular.

The operation is confirmed, and the following property theorems are summarized and proved.

◆ If a straight line is parallel to a plane, the intersection line between any plane passing through the straight line and the plane is parallel to the straight line.

◆ If two planes are parallel, the intersection lines obtained by the intersection of any plane and these two planes are parallel to each other.

◆ Two straight lines perpendicular to the same plane are parallel.

◆ If two planes are perpendicular, the straight line perpendicular to the intersection line in one plane is perpendicular to the other plane.

③ We can use the conclusions to prove some simple propositions of spatial relationship.

2. Analysis of Plane Analytic Geometry

(about 18 class hours)

(1) row sum equation

(1) In the plane rectangular coordinate system, combined with specific graphics, the geometric characteristics of determining the position of a straight line are explored.

② Understand the concepts of inclination angle and slope of a straight line, experience the process of describing the slope of a straight line by algebraic method, and master the calculation formula of the slope of a straight line passing through two points.

③ Two straight lines can be judged to be parallel or vertical according to their slopes.

(4) According to the geometric characteristics of determining the position of a straight line, explore and master several forms of linear equation (point oblique, two points, general), and understand the relationship between oblique line and linear function.

⑤ The coordinates of the intersection of two straight lines can be obtained by solving the equation.

⑥ Explore and master the distance formula between two points and the distance formula from point to straight line, and find the distance between two parallel straight lines.

(2) Circle sum equation

(1) review and determine the geometric characteristics of the circle, explore and master the standard equation and general equation of the circle in the plane rectangular coordinate system.

② According to the given equation of straight line and circle, we can judge the positional relationship between straight line and circle and between them.

③ Some simple problems can be solved by equations of straight lines and circles.

(3) During the initial study of plane analytic geometry, I realized the idea of using algebraic method to deal with geometric problems.

(4) Spatial Cartesian coordinate system

(1) Through specific situations, feel the necessity of establishing a spatial rectangular coordinate system, understand the spatial rectangular coordinate system, and describe the position of points by using the spatial rectangular coordinate system.

② By representing the coordinates of the vertices of a special cuboid (each side is parallel to the coordinate axis), the distance formula between two points in space is explored.

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Mathematics compulsory course 3

1. Preliminary algorithm

(about 12 class hours)

The meaning of (1) algorithm, program block diagram.

(1) by analyzing the process and steps to solve specific problems (such as solving binary linear equations, etc.). ), we can understand the idea and significance of the algorithm.

② Through imitation, operation and exploration, experience the process of expressing and solving problems by designing program block diagram. In the process of solving specific problems (such as solving ternary linear equations, etc. ), understand the three basic logical structures of program block diagram: sequence, conditional branch and loop.

(2) Basic algorithm statements: Through the process of transforming the program block diagram of specific problems into program statements, we can understand several basic algorithm statements-input statements, output statements, assignment statements, conditional statements and loop statements, and further understand the basic idea of the algorithm.

(3) By reading the algorithm cases in ancient mathematics in China, we can understand the contribution of ancient mathematics in China to the development of mathematics in the world.

2. Statistics

(about 16 class hours)

(1) random sampling

(1) can raise some valuable statistical questions from real life or other disciplines.

② Understand the necessity and importance of random sampling in combination with specific practical problem situations.

③ In the process of solving statistical problems, learn to use simple random sampling method to extract samples from the population; Through case study, we can understand the methods of stratified sampling and systematic sampling.

④ Data can be collected through experiments, consulting materials and designing questionnaires.

(2) estimate the population with samples

① Understand the significance and function of distribution through examples. In the process of representing sample data, learn to list the frequency distribution table, draw the frequency distribution histogram, frequency line diagram and stem leaf diagram (see example 1), and understand their respective characteristics.

② Understand the significance and function of standard deviation of sample data through examples, and learn to calculate the standard deviation of data.

③ We can reasonably select samples according to the needs of practical problems, extract basic numerical features (such as mean and standard deviation) from sample data, and make reasonable explanations.

④ In the process of solving statistical problems, we will further understand the idea of estimating the population with samples. We will estimate the population distribution with the frequency distribution of samples and estimate the basic digital characteristics of the population with the basic digital characteristics of samples. Understand the randomness and numerical characteristics of sample frequency distribution.

⑤ We will use the basic method of random sampling and the idea of sample estimation to solve some simple practical problems; Through the analysis of data, we can provide some basis for rational decision-making, understand the role of statistics and understand the difference between statistical thinking and deterministic thinking.

⑥ Form a preliminary evaluation consciousness of data processing.

(3) Correlation of variables

① Make a scatter plot by collecting the data of two related variables in the real question, and use the scatter plot to intuitively understand the correlation between variables.

② Experiencing the process of describing the linear correlation of two variables with different estimation methods. Knowing the idea of least square method, we can establish a linear regression equation according to the given coefficient formula of linear regression equation (see Example 2).

3. Possibility

(about 8 class hours)

(1) Understand the uncertainty and frequency stability of random events in specific situations, and further understand the meaning of probability and the difference between frequency and probability.

(2) Understand two mutually exclusive events's probability addition formulas through examples.

(3) Through examples, we can understand the classical probability and its probability calculation formula, and use enumeration method to calculate the number of basic events and the probability of some random events.

(4) Knowing the meaning of random numbers, we can use simulation methods (including random numbers generated by calculators for simulation) to estimate the probability and get a preliminary understanding of the meaning of geometric probability (see Example 3).

(5) By reading the materials, we can understand the cognitive process of human beings to random phenomena.

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Mathematics compulsory 4

1. trigonometric function

(about 16 class hours)

(1) Any angle and radian

Understand the concept of arbitrary angle and radian system, and realize the conversion between radian and angle.

(2) Trigonometric function

① Understand the definition of trigonometric functions (sine, cosine and tangent) with the help of the unit circle.

② Derive inductive formulas (sine, cosine and tangent) with the help of trigonometric function lines in the unit circle, and draw pictures to understand the periodicity of trigonometric functions.

③ Understand the properties of sine function, cosine function and tangent function (such as monotonicity, maximum and minimum value, image intersecting with X axis, etc.). ) with the help of images.

④ Understand the basic relationship of trigonometric functions with the same angle:

⑤ Understand the practical significance with concrete examples; With the help of the image drawn by calculator or computer, we can observe the influence of parameters a and ω on the change of function image.

⑥ trigonometric function can be used to solve some simple practical problems, and it is recognized that trigonometric function is an important function model to describe periodic changes.

2. Plane vector

(about 12 class hours)

The Practical Background and Basic Concepts of (1) Plane Vector

Through the analysis of force and other examples, we can understand the actual background of vector, the meaning of plane vector and vector equality, and the geometric representation of vector.

(2) Linear operation of vectors

① Master the operation of vector addition and subtraction and understand its geometric meaning.

(2) Master the operation of vector multiplication and understand its geometric meaning and the meaning of two vector lines.

③ Understand the linear operation properties of vectors and their geometric significance.

(3) The basic theorem and coordinate representation of plane vector.

① Understand the basic theorem of plane vector and its significance.

② Master the orthogonal decomposition of plane vector and its coordinate representation.

③ Coordinates will be used to represent the addition, subtraction and multiplication of plane vectors.

(4) understand the condition that the plane vector * * * straight line is represented by coordinates.

(4) the product of plane vectors

① Understand the meaning and physical meaning of the product of plane vectors through examples such as "work" in physics.

② Understand the relationship between the product of plane vector and vector projection.

(3) Grasp the coordinate expression of the product of quantity, and carry out the product operation of plane vector.

(4) The included angle between two vectors can be expressed by the product of quantities, and the vertical relationship between two plane vectors can be judged by the product of quantities.

(5) Application of carrier

Through the process of solving some simple plane geometric problems, mechanical problems and other practical problems with vector method, I realize that vector is a tool to deal with geometric and physical problems and cultivate the ability to calculate and solve practical problems.

3. Trigonometric identity transformation

(about 8 class hours)

(1) experienced the process of deriving the cosine formula of the difference between two angles by using the product of vectors, and further realized the function of vector method.

(2) Sine, cosine and tangent formulas of sum and difference of two angles and sine, cosine and tangent formulas of two angles can be derived from cosine formula of difference of two angles, so as to understand their internal relations.

(3) We can use the above formula to carry out simple identity transformation (including guiding and deducing product sum and difference, product sum and difference, and half-angle formula, but we don't need to remember).

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Mathematics compulsory 5

1. Solving triangles

(about 8 class hours)

(1) By exploring the relationship between the sides and angles of any triangle, we can master the sine theorem and cosine theorem and solve some simple triangle measurement problems.

(2) Be able to use knowledge and methods such as sine theorem and cosine theorem to solve some practical problems related to measurement and geometric calculation.

Step 2: Order

(about 12 class hours)

The Concept and Simple Representation of (1) Sequence

Understand the concept of sequence and several simple expressions (list, image, general formula), and understand that sequence is a special function.

(2) arithmetic progression and geometric progression

(1) Understand the concepts of arithmetic progression and geometric progression.

② Explore and master the general formula of arithmetic progression and geometric progression and the formula of the sum of the first n items.

(3) In specific problem situations, we can find the arithmetic relationship or proportional relationship of the sequence, and use relevant knowledge to solve corresponding problems (see example 1).

④ Understand the relationship between arithmetic progression and geometric progression and between linear function and exponential function.

3. Inequality

(about 16 class hours)

(1) inequality relation

Feel a lot of unequal relations in the real world and daily life, and understand the actual background (group) of inequality.

(2) One-dimensional quadratic inequality

① Experience the process of abstracting a quadratic inequality model from the actual situation.

(2) Understand the relationship between unary quadratic inequality and corresponding functions and equations through function images.

(3) Can solve the unary quadratic inequality, and try to design the program block diagram for the given unary quadratic inequality.

(3) Binary linear inequalities and simple linear programming problems.

① A set of binary linear inequalities is abstracted from the actual situation.

(2) To understand the geometric meaning of binary linear inequality, we can express binary linear inequality by plane region (see Example 2).

③ Some simple binary linear programming problems are abstracted from the actual situation and can be solved (see Example 3).

(4) Basic inequality:

① Explore and understand the process of proving basic inequalities.

② The basic inequality will be used to solve the simple maximum (minimum) problem (see Example 4).

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Mathematics elective course

Elective course 2- 1

1. Common logical terms (about 8 class hours)

(1) proposition and its relationship

① Understand the inverse proposition, negative proposition and negative proposition of a proposition.

② Understand the meanings of necessary conditions, sufficient conditions and necessary and sufficient conditions, and analyze the relationship among the four propositions.

(2) Simple logical connectives

Understand the meaning of logical conjunction "or" and "not".

(3) Full name quantifiers and existential quantifiers

① Understand the meaning of universal quantifiers and existential quantifiers.

② Propositions containing quantifiers can be correctly denied.

2. Conic Curve and Equation (about 16 class hours)

(1) conic curve

① Understand the actual background of conic section and feel the function of conic section in depicting the real world and solving practical problems.

② Experience the process of abstracting ellipse and parabola models from specific situations, and master their definitions, standard equations, geometric figures and simple properties.

③ Understand the definition, geometry and standard equation of hyperbola, and know the related properties of hyperbola.

④ Coordinate method can be used to solve some simple geometric problems (the positional relationship between straight lines and conic curves) and practical problems related to conic curves.

⑤ Through the study of conic curve, we can further understand the idea of combining numbers with shapes.

(2) Curves and equations

Understand the corresponding relationship between curves and equations, and further feel the basic idea of the combination of numbers and shapes.

3. Space vector and solid geometry (about 12 class hours)

(1) space vector and its operation

(1) Experience vector and the process of its operation expanding from plane to space.

② Understand the concept, basic theorem and significance of space vector, and master the orthogonal decomposition and coordinate representation of space vector.

③ Master the linear operation of space vector and its coordinate representation.

(4) Master the quantity product of space vector and its coordinate representation, and use the quantity product of vector to judge the * * * line and vertical line of vector.

(2) Application of space vector

① Understand the direction vector of a straight line and the normal vector of a plane.

② The vertical and parallel relationships among lines, lines and planes can be expressed by vector language.

(3) Some theorems about the position relationship between a straight line and a plane (including the theorem of three perpendicular lines) can be proved by vector method (see Example 1, Example 2 and Example 3).

④ Using vector method can solve the problem of calculating the included angle between lines, lines and planes, and realize the function of vector method in studying geometric problems.

Reference case

Example 1. As we all know, in a straight triangular prism, ∠ ACB = 90, ∠ BAC = 30, and m is the midpoint of the edge. Prove:

Example 2. It is known that rectangular ABCD is perpendicular to rectangular ADEF, and AD is the same side, but not on the same plane. Points m and n are on diagonal lines BD and AE, respectively, and.

Proof: MN∑ plane CDE.

Example 3. Given the unit cube, e and f are the midpoint of the sum of edges, respectively. Try asking:

Angle with EF (1); (2) The angle between 2)AF and the plane; (3) The size of dihedral angle.

Elective course 2-2

1. derivative and its application (about 24 hours)

The Concept of (1) Derivative and Its Geometric Significance

(1) Through the analysis of a large number of examples and the transition from the average change rate to the instantaneous change rate, we can understand the actual background of the concept of derivative, know that the instantaneous change rate is a derivative, and understand the idea and connotation of derivative (see 1- 1 examples 2 and 3 in the elective case).

② Understand the geometric meaning of derivative intuitively through function images.

(2) the operation of derivative

① The derivative of a function can be found according to the definition of derivative.

② Using the derivative formula of basic elementary function and four arithmetic rules of derivative, we can find the derivative of simple function or simple compound function (only in form).

③ A derivative formula table can be used.

(3) The application of derivative in function research.

① Intuitively explore and understand the relationship between monotonicity and derivative of functions with the help of geometry (see Example 4 for the elective course 1- 1); The monotonicity of function can be studied by derivative, and the monotone interval of polynomial function with no more than three degrees can be found.

② Understand the necessary and sufficient conditions for the function to obtain the extreme value at a certain point by combining the image of the function; The derivative will be used to find the maximum and minimum values of polynomial functions with no more than cubic degree, and the maximum and minimum values of polynomial functions with no more than cubic degree in a closed interval; Understand the generality and effectiveness of derivative method in studying the properties of functions.

(4) Examples of optimization problems in life.

For example, by optimizing profit maximization, saving materials and achieving the highest efficiency, we can understand the role of derivatives in solving practical problems (see Example 5 for the case of taking 1- 1).

(5) Basic theorems of definite integral and calculus

① Understand the actual background of definite integral from the problem situation by calculating the area of curved trapezoid and doing work with variable force; With the help of geometry, we can intuitively understand the basic idea of definite integral and preliminarily understand the concept of definite integral.

② The significance of the basic theorem of calculus can be intuitively understood through the relationship between the speed and distance of a variable-speed moving object in a certain time (see example 1).

2. Reasoning and proof (about 8 class hours)

(1) Rational reasoning and deductive reasoning

① Understand the meaning of sensible reasoning, make simple reasoning through induction and analogy, and experience and understand the role of sensible reasoning in mathematical discovery (see Examples 2 and 3 in the elective course 1-2).

② Understand the importance of deductive reasoning, master the basic model of deductive reasoning and apply it to some simple reasoning.

③ Understand the connection and difference between perceptual reasoning and deductive reasoning through concrete examples.

(2) Direct proof and indirect proof

① Understand two basic methods of direct proof: analytical method and comprehensive method; Understand the thinking process and characteristics of analytical methods and comprehensive methods.

② Understand a basic method of indirect proof-reduction to absurdity; Understand the thinking process and characteristics of reduction to absurdity.

(3) Mathematical induction

Knowing the principle of mathematical induction, we can prove some simple mathematical propositions by mathematical induction.

(4) Mathematical culture

(1) through the introduction of examples (such as Euclid's Elements of Geometry, Marx's Das Kapital, Jefferson's Declaration of Independence, Newton's three laws), understand the axiomatic thought.

② Introduce the role of computer in the field of automatic reasoning and mathematical proof.

3. Extension of number system and introduction of complex numbers (about 4 class hours)

(1) Understand the expansion process of the number system in the problem situation, understand the role of the contradiction between actual needs and mathematics (the operation rules and equation theory of numbers) in the expansion process of the number system, and feel the role of human rational thinking and the connection between numbers and the real world.

(2) Understand the basic concepts of complex numbers and the necessary and sufficient conditions for the equality of complex numbers.

(3) Understand the algebraic representation of complex numbers and their geometric significance.

(4) Be able to perform four operations in the form of complex algebra and understand the geometric significance of addition and subtraction operations in the form of complex algebra. .

Reference case

Example 1. According to the law, an object moves in a straight line. We already know that its speed at a certain moment (that is, instantaneous speed or instantaneous rate of change) is the derivative of that moment, that is. Now consider the total position change between and. Let's divide the interval into n cells. We assume that the length between cells is equal, and its length is. For each cell, we assume that the rate of change is approximately constant, so we can say

Rate of change × time.

In the first cell, that is, from to, the change rate is assumed to be about 0, so there is

Similarly, for the second unit, from to, the change rate is assumed to be about 0, so there is

Wait a minute. Add all approximations of the position change obtained between all units to obtain

Total change of s

We can write the total position change between and. On the other hand, when the division is infinitely refined and n tends to infinity, the summation formula

The limit of is the definite integral or, that is, the total change of position between and. Therefore, we can draw the following conclusions:

That is to say, the definite integral of the change rate gives the total change.

Especially, when an object is moving at a uniform speed, that is,

When the object is uniformly accelerated, that is, (where is a constant),

Generally speaking, if it is a continuous function, then

This is the basic theorem of calculus. The proof given here is not very strict, but it reflects the basic idea of the basic theorem of calculus and the relationship between differential (derivative) and integral.

Elective 2-3

1. counting principle (about 14 class hours)

(1) classification addition counting principle and step-by-step multiplication counting principle

Summarize the principles of classified addition counting and step-by-step multiplication counting; According to the characteristics of specific problems, we can choose the principle of classified addition counting or step-by-step multiplication counting to solve some simple practical problems.

(2) permutation and combination

Understand the concepts of permutation and combination; The formulas of permutation number and combination number can be derived by using the counting principle, and simple practical problems can be solved.

(3) binomial theorem

Binomial theorem can be proved by counting principle (see example1); Will use binomial theorem to solve simple problems related to binomial expansion.

2. Statistics and Probability (about 22 class hours)

(1) probability

① In the analysis of specific problems, understand the concepts of finite discrete random variables and their distribution tables, and understand the importance of distribution tables in describing random phenomena.

② Understand the hypergeometric distribution and its derivation process through examples (such as lottery tickets), and simply apply it (see Example 2).

③ In specific situations, understand the concepts of conditional probability and independence of two events, understand the model and binomial distribution of n independent repeated trials, and solve some simple practical problems (see Example 3).

④ Understanding the concepts of mean and variance of finite discrete random variables can calculate the mean and variance of simple discrete random variables and solve some practical problems (see Example 4).

⑤ With the help of intuition (such as the histogram of practical problems), understand the characteristics of normal distribution curve and the meaning expressed by the curve.

(2) Statistical cases

① By exploring "Is lung cancer related to smoking?" Understand the basic idea, method and preliminary application of independence test (only 2×2 contingency table is needed).

② Through the exploration of "quality control" and "whether the new drug is effective", we can understand the basic ideas, methods and preliminary applications of the actual inference principle and hypothesis testing (see elective course 1-2 for example 1).

③ Understand the basic idea, method and preliminary application of cluster analysis through the exploration of "insect classification".

④ Understand the basic idea, method and preliminary application of regression by exploring the relationship between human body weight and height.