1- 1
Chapter 1 Common Logical Words
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
summary
Chapter II Conic Curve and Equation
2. 1 ellipse
Explore and find out why the section curve is elliptical.
Exploration point trajectory: ellipse
2.2 hyperbola
Explore and discover why it is a hyperbola.
Asymptotic line of
2.3 parabola
Reading and thinking about the optical properties of conic curve and its application
summary
Chapter III Derivatives and Their Applications
3. 1 rate of change and derivative
3.2 Calculation of Derivative
Exploring and Discovering Newton Method —— Finding Approximate Solution of Equation by Derivative Method
3.3 Application of Derivative in Function Research
Application and functional characteristics of information technology and graphic technology
3.4 examples of optimization problems in life
Practice homework into calculus
summary
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
Practice homework
summary
Chapter II Reasoning and Proof
2. 1 Rational reasoning and deductive reasoning
Reading and Thinking of Reasoning in Scientific Discovery
2.2 Direct proof and indirect proof
summary
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
summary
Chapter IV Block Diagram
4. 1 Flowchart
4.2 Structure Diagram
The application of information technology draws the flow chart with word2002.
summary
2- 1
Chapter 1 Common Logical Words
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
summary
Chapter II Conic Curve and Equation
2. 1 ellipse
Explore and find out why the section curve is elliptical.
Exploration point trajectory: ellipse
2.2 hyperbola
Explore and find out why it is the asymptote of hyperbola.
2.3 parabola
Why is the image of quadratic function a parabola?
2.4 The positional relationship between straight line and conic curve
Reading and thinking about the optical properties of conic curve and its application
2.5 curves and equations
Exploration and discovery of eccentricity and unified equation of conical curve
summary
Chapter III Space Vector and Solid Geometry
3. 1 space vector and its operation
Popularization and application of the concepts of reading and thinking vector
3.2 vector method in solid geometry
summary
2-2
Chapter 1 Derivative and Its Application
1. 1 rate of change and derivative
Calculation of 1.2 derivative
Exploring and Discovering Newton Method —— Finding Approximate Solution of Equation by Derivative Method
Application of 1.3 derivative in function research
Application and functional characteristics of information technology and graphic technology
1.4 examples of optimization problems in life
The concept of 1.5 definite integral
Information technology applications-Curved trapezoidal areas
1.6 Fundamental Theorem of Calculus
Simple application of 1.7 definite integral
Practice homework into calculus
Chapter II Reasoning and Proof
2. 1 Rational reasoning and deductive reasoning
Reading and Thinking about Cosine Theorem in Plane and Space
2.2 Direct proof and indirect proof
2.3 Mathematical induction
summary
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
Reading and thinking about the basic theorem of algebra
summary
2-3
The first chapter is the counting principle
1. 1 classification addition counting principle and division multiplication counting principle
How many subsets need to be explored and discovered?
1.2 permutation and combination
Exploring and discovering two properties of combination number
1.3 binomial theorem
summary
Chapter II Random Variables and Their Distribution
2. 1 Discrete Random Variable and its Distribution Table
2.2 binomial distribution and its application
Is it feasible to read and think about buying lottery tickets?
When exploring and discovering the values of random variables that obey binomial distribution, the probability is the greatest.
2.3 mean and variance of discrete random variables
2.4 Normal distribution
Information technology application? Influence of б on normal distribution
summary
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
Practice homework
summary
4- 1 Symposium on Geometry 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 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
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
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
Selected lectures on 4-5 inequalities
The first 1 lecture on inequality and absolute inequality
An inequality
Basic properties of inequality 1
2 Basic inequality
3 Arithmetic-Geometric Average Inequality of Three Positive Numbers
Double absolute inequality
1 absolute triangle inequality
2 absolute value inequality solution
The second lecture is about the basic method of proving inequality.
comparative law
Two synthetic methods and analytical methods
Three reduction to absurdity and scaling method
Lecture 3 Cauchy inequality and rank inequality
Cauchy inequality in two-dimensional form
Reading and thinking French scientist Cauchy
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