Mandatory 1
The first chapter is the concept of set and function.
1. 1 set
1.2 function and its representation
Basic properties of 1.3 function
Chapter II Basic Elementary Functions (Ⅰ)
2. 1 exponential function
2.2 Logarithmic function
2.3 power function
Chapter III Functional Application
3. 1 functions and equations
3.2 Functional model and its application
compulsory 2
Chapter I Space Geometry
1. 1 spatial geometry
1.2 Three Views and Straight Views of Space Geometry
1.3 surface area and volume of space geometry
Chapter II Positional Relations of Points, Lines and Surfaces
2. 1 The positional relationship among points, lines and surfaces in space
2.2 Determination of parallelism between straight line and plane and its properties
2.3 Determination and characteristics of vertical lines and planes
Chapter III Linear Sum Equation
3. 1 Angle and slope of straight line
3.2 linear equation
3.3 Formula for coordinates and distance of intersection points of straight lines
The fourth chapter circle sum equation
4. Equation of1circle
4.2 The positional relationship between straight line and circle
4.3 Spatial Cartesian Coordinate System
Compulsory 3
The first chapter is the preliminary algorithm.
1. 1 algorithm and program block diagram
1.2 basic algorithm statement
1.3 algorithm case
Chapter II Statistics
2. 1 random sampling
2.2 Using samples to estimate the population
2.3 Correlation between variables
Chapter III Probability
3. 1 Probability of random events
3.2 Classical probability
3.3 Geometric probability
Required 4
The first chapter trigonometric function
1. 1 arbitrary angle and arc system
1.2 trigonometric function at any angle
The inductive formula of 1.3 trigonometric function
Images and properties of 1.4 trigonometric function
1.5 function y=Asin(ωx+ψ)
Simple application of 1.6 trigonometric function model
Chapter II Plane Vector
2. The actual background and basic concepts of1plane vector
2.2 Linear Operation of Plane Vector
2.3 Basic Theorem and Coordinate Representation of Plane Vector
2.4 product of plane vectors
2.5 examples of plane vector application
Chapter III Triangular Identity Transformation
3. 1 sine, cosine and tangent sum difference formula
3.2 Simple trigonometric identity transformation
Elective course 5
Chapter 1 Solving Triangle
1. 1 sine theorem and cosine theorem
Application example of 1.2
1.3 Practice homework
Chapter II Sequence of Numbers
2. The concept and simple representation of1sequence
2.2 arithmetic progression
2.3 arithmetic progression's top n sums
2.4 geometric series
2.5 the sum of the first n terms in geometric series
Chapter III Inequality
3. 1 inequality relation and inequality
3.2 One-variable quadratic inequality and its solution
3.3 Binary Linear Inequalities (Groups) and Simple Linear Programming Problems
3.4 Basic inequality
Elective course 1- 1
Chapter 1 Common Logical Terms
1. 1 proposition and its relationship
The necessary and sufficient condition of 1.2
1.3 Simple logical connectives
1.4 Full name quantifier and existential quantifier
Chapter II Conic Curve and Equation
2. 1 ellipse
2.2 hyperbola
2.3 parabola
Chapter III Derivatives and Their Applications
3. 1 rate of change and derivative
3.2 Calculation of Derivative
3.3 Application of Derivative in Function Research
3.4 examples of optimization problems in life
Elective course 1-2
Chapter I Statistical Cases
The basic idea of 1. 1 regression analysis and its preliminary application
The basic idea of 1.2 independence test and its preliminary application
Chapter II Reasoning and Proof
2. 1 Reasonable Reasoning and Deductive Proof
2.2 Direct proof and indirect proof
Chapter 3: The extension of number system and the introduction of complex numbers.
3. Generalization of1number system and the concept of complex number
3.2 Four operations in complex algebraic form
Chapter IV Block Diagram
4. 1 Flowchart
4.2 Structure Diagram
Elective course 2- 1
Chapter 1 Common Logical Terms
1. 1 proposition and its relationship
The necessary and sufficient condition of 1.2
1.3 Simple logical connectives
1.4 Full name quantifier and existential quantifier
Chapter II Conic Curve and Equation
2. 1 curves and equations
2.2 ellipse
2.3 hyperbola
2.4 parabola
Elective course 2-2
Chapter 1 Derivative and Its Application
1. 1 rate of change and derivative
Calculation of 1.2 derivative
Application of 1.3 derivative in function research
1.4 examples of optimization problems in life
The concept of 1.5 definite integral
1.6 Fundamental Theorem of Calculus
Simple application of 1.7 definite integral
Chapter II Reasoning and Proof
2. 1 Rational reasoning and deductive reasoning
2.2 Direct proof and indirect proof
2.3 Mathematical induction
Chapter 3: The extension of number system and the introduction of complex numbers.
3. Generalization of1number system and the concept of complex number
3.2 Four operations in complex algebraic form
Elective 2-3
The first chapter is the counting principle
1. 1 classification addition counting principle and step multiplication counting principle
1.2 permutation and combination
1.3 binomial theorem
Chapter II Random Variables and Their Distribution
2. 1 Discrete Random Variable and its Distribution Table
2.2 binomial distribution and its application
2.3 mean and variance of discrete random variables
2.4 Normal distribution
Chapter III Statistical Cases
3. The basic idea of1regression analysis and its preliminary application
3.2 the basic idea of independence test and its preliminary application
Elective course 4- 1 geometric proof.
The first lecture on similar triangles's judgment and related properties
Equal division theorem of parallel lines
Proportional theorem of dividing two parallel lines into line segments
Judgement and nature of three similar triangles.
1. similar triangles's judgment
2. The nature of similar triangles
Projective Theorems of Four Right Triangles
The second lecture on the positional relationship between straight line and circle
Rounded corner theorem
Properties and Judgement Theorem of Quadrilateral Inscribed by Two Circles
Properties and Judgement Theorem of Tri-circle Tangent
Properties of Quadrant Tangent Angle
Five proportional line segments related to a circle.
The third lecture on the properties of conic curves
parallel projection
Secant between two planes and cylindrical surface
Secant lines of three planes and conical surfaces
Elective 4-4 coordinate system and parameter equation
The first lecture on coordinate system
rectangular coordinates/ cartesian coordinates
Bipolar coordinate system
Polar coordinate equations of three simple curves
Brief introduction of four-column coordinate system and spherical coordinate system
Lecture 2 parametric equation
Parametric equation of curve
Parametric equation of conic curve
Parametric equation of three straight lines
Four involute and cycloid
Lecture on inequality 4-5.
The first 1 lecture on inequality and absolute inequality
An inequality
Basic properties of 1. inequality
2. Basic inequality
3. Arithmetic geometric mean inequality of three positive numbers
Double absolute inequality
1. Absolute trigonometric inequality
2. The solution of absolute inequality
The second lecture explains the basic methods of inequality.
comparative law
Two synthetic methods and analytical methods
Three reduction to absurdity and scaling method
Lecture 3 Cauchy inequality and rank inequality
A two-dimensional Cauchy inequality
Two general forms of Cauchy inequality
Third-order inequality
The fourth lecture is about proving inequalities by mathematical induction.
complete induction
Second, prove the inequality by mathematical induction