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Catalogue of high school mathematics elective textbooks

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