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A higher and better catalogue of high school mathematics ideas and methods
Chapter 1: Higher and better mathematical problem-solving strategies.

1. 1 Consolidate basic knowledge and strive for "going up the stairs"

1.2 to prevent mindset and realize "substitute flowers for trees"

1.3 Flexible use of strategies, trying to "attack jade with stones"

1.3. 1 inductive conjecture

1.3.2 simulated migration

1.3.3 mutual advance and retreat.

1.3.4 overall treatment

1.3.5.

1.4 pay attention to key issues and master "secret weapons"

1.4. 1 key rules

1.4.2 key issues

1.4.3 key methods

1.5 Improve the thinking process and achieve "conformity"

The second chapter is good at arming yourself with mathematical ideas

2. 1 function and equation ideas

2. 1. 1 explicit functional relationship

2. 1.2 transfer function relation

2. 1.3 constructor relation

2. 1.4 transformation equation form

2. 1.5 construction equation form

2. 1.6 Combinatorial Function and Equation Thought

2.2 Classification discussion ideas

2.2. 1 Counting problem and classification discussion in probability

2.2.2 Discussion on functional classification

2.2.3 Classification discussion series

2.2.4 Discussion on the Classification of Inequalities

2.2.5 Discussion on Classification in Analytic Geometry

2.3 Number-shape combination

2.3. Application of1number-shape combination in set

2.3.2 Application of the Combination of Numbers and Shapes in Functions

2.3.3 Application of the Combination of Numbers and Shapes in Inequalities

2.3.4 The application of the combination of numbers and shapes in the sequence of numbers

2.3.5 Application of Number-Shape Combination in Vector

2.3.6 Application of the Combination of Numbers and Shapes in Analytic Geometry

2.3.7 Application of the Combination of Numbers and Shapes in Solid Geometry

2.4 concept transformation and transformation

2.4. 1 variable and variable conversion

2.4.2 Transformation between High Dimension and Low Dimension

2.4.3 Transition from Special to General

2.4.4 Transformation of Part and Whole

2.4.5 Comprehensive application of transformation and transformation

2.5 Comprehensive use of mathematical ideas to solve problems

Select good questions and new questions (1)

The third chapter is the hot topic analysis of the college entrance examination finale.

3. 1 function synthesis problem

3. 1. 1 Quadratic Function Synthesis

3. 1.2 higher-order function synthesis

3. 1.3 fractional function synthesis

3. 1.4 synthesis of abstract functions

3. 1.5 function synthesis

Select Good Problems and New Problems (2)

3.2 derivative synthesis problem

Select good and new problems (3)

3.3 Series Synthesis Problem

3.3. 1 Series Attribute Synthesis

Function and sequence

Sequential inequality

3.3.4 Point by point problem

Select good problems and new problems (4)

3.4 Analytic Geometry Comprehensive Problems

3.4. 1 circle synthesis

Elliptic synthesis

Hyperbolic synthesis

Parabolic synthesis

Select good and new problems (5)

3.5 Novelty issues

Select Good Problems and New Problems (6)

The fourth chapter uses competitive strategy to optimize the problem-solving of college entrance examination.

4. 1 Familiar with recursive methods

4. 1. 1 cumulative multiplication

4. 1.2 undetermined coefficient method

4. 1.3 fixed-point method

4. 1.4 order difference method

4. 1.5 direct substitution method

4. 1.6 deformation transformation method

4. 1 _7 mathematical induction

Select good and new problems (7)

4.2 Understanding Extended Skills

4.2. 1 direct scaling

crack propagation

Zoom in and out

Strengthen flexibility

Select good and new problems (8)

4.3 Master important inequalities

4.3. 1 average inequality

4.3.2 Cauchy inequality

4.3.3 Uneven ranking

Select good and new problems (9)

4.4 Using parameters and parameter equation method

Select good questions and new questions (10)

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