basic knowledge

1. vector

2. Addition and subtraction of vectors

3. Representation method of plane vector

4. Coordinate operation of plane vector

5. Product of real number and vector

6. The product of plane vectors

7. Vectors and real numbers

8. Properties of vectors

9. Angle formula of vector and its application

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The demarcation point of 1 1. line segment

12. The distance between two points on the plane

13. Translation

14. Basic exercises

Classification of college entrance examination questions

Linear operation of 1. vector

2. Vector multiplication

3. The positional relationship of vectors

4. Geometric operations of vectors

5. Directed line segment and fraction ratio

6. Proportional comprehensive calculation

College entrance examination comprehensive questions

Application of 1. Vector Equilibrium Property

2. Triangulation of vectors

Chapter II Set and Simple Logic

basic knowledge

1.set

2. Subsets and proper subset

Step 3: Supplement

4. Intersection

5. Alliance

6. Wayne Diagram and Morgan's Law

7. Four propositions

8. Logical connectors

9. Common mathematical logic symbols

10. Sufficient and necessary conditions

1 1. Basic exercises

Classification of college entrance examination questions

1. Logical symbolic expression

2. Application of set attributes

3. The problem of set definition

4. Judgment of set equality

5. Application of set graph method

6. The solution of the union of pairwise intersecting sets.

7. Propositions and negative propositions

8. Necessary and sufficient conditions

College entrance examination comprehensive questions

Comparison of sets.

2. Set and permutation combination

Chapter III Functions

basic knowledge

1 ... mapping and one-to-one mapping

2. Coordinate system and quadrant

3. Functions and inverse functions

4. Monotonicity and parity of functions

5. Symmetry of functions

6. Self-symmetry of functions

7. Definition domain and value domain

8. Function translation and coordinate system translation

9. Exponents and Logarithms

10. Power function, exponential function and logarithmic function

Properties of 1 1. unary quadratic function

12. Basic exercises

Classification of college entrance examination questions

1. Functional areas and scope

2. Application of function image

3. Conversion between function and inverse function

4. The application of functional symmetry

5. Application of function translation and coordinate system translation

6. Dividing and multiplying quadrants

7. Comprehensive application of monotonicity and parity of functions

8. Properties and images of power function, exponential function and logarithmic function

9. Composite function

10. One-variable quadratic equation and application of Vieta theorem.

Monotonicity of 1 1. piecewise function

College entrance examination comprehensive questions

Extension of symmetry of 1. function

2. Functions and fixed points

3. Comprehensive application of functions

4. Information definition

Chapter IV Inequality

basic knowledge

1. The basis of inequality

2. Basic properties of inequality

3. Proof of inequality

4. Several important formulas

5. Solution of inequality

6. Absolute inequality

7. The solution of absolute inequality

8. Binary linear inequalities and inequality regions

9. Inequality region of curve

10. Basic exercises

Classification of college entrance examination questions

Application of inequality formula.

2. How to find the maximum value of several kinds of inequalities?

3. Reduction to absurdity and mathematical induction

4. Application of inequality region

5. Solve inequality equations

6. The solution of piecewise function inequality

7. Inequalities and quadratic equations in one variable

8 Synthesis of inequality equations and functions

9. The application of absolute value equations and absolute inequality.

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College entrance examination comprehensive questions

1.

2. Mathematical inductive thinking

3. Comprehensive application of inequality

4. Comprehensive analysis of quadratic equation with one variable.

Chapter V Trigonometric Functions

basic knowledge

Degree and Curvature System of 1. Angle

2. The basic characteristics of triangle

3. Sine theorem and cosine theorem of triangle

IV. Trigonometric functions

5. Trigonometric functions and quadrants

6. Sine, cosine and tangent of sum and difference of two angles

VII. Sine, Cosine and Tangent of Double Angle

8. The properties of sine function and cosine function images

9. Properties of Tangent Function Images

10. Draw sine and cosine functions with five-point method.

1 1. Inverse trigonometric function

12. oblique triangle solution

13. Basic formula of trigonometric function

Supplementary formula of 14 ... trigonometric function

15. Basic exercises

Classification of college entrance examination questions

1. trigonometric function quadrant

2. Trigonometric functions and the nature of images

3. The periodicity and monotonicity of trigonometric functions

4. Simplified solution of trigonometric function

5. Trigonometric functions and vectors

6. Theorems of Triangle, Sine and Cosine

7. Solve the extreme value of trigonometric function

8. Solution of Oblique Triangle

College entrance examination comprehensive questions

1. Absolute value and trigonometric function

2. Comprehensive solution of trigonometric function

3. Construction method and trigonometric function solution

4. Solving the maximum value of trigonometric function

5. Comprehensive solution of triangle

6. Comprehensive application of oblique triangle

Chapter VI Sequence of Numbers

basic knowledge

1. order

2. Arithmetic series

3. Typical properties of arithmetic series

4. Equal ratio series

5. Typical properties of arithmetic series

6. Countdown series

7. Several typical recurrence relations of Sn → An

8. Several typical an+ 1→an recursive relations.

9. Several Typical an→n Recursive Relations

10. The form of sum or product of several typical sequences

1 1. Several typical Sn+ 1→Sn recurrence relations.

12. Basic exercises

Classification of college entrance examination questions

1. Basic application of arithmetic progression

2. Comprehensive application of arithmetic progression

3. The basic application of geometric series

4. Comprehensive application of geometric series.

5. The solution of reciprocal sequence

6. Sequences and equations

7. Algorithms and sequences

College entrance examination comprehensive questions

Comprehensive application of 1. arithmetic geometric series

2. Application of dislocation cancellation method

3. Complex definition of sequence analysis

4. Comprehensive application of sequence and inequality

5. Several complex recursive formulas of sequence.

Chapter VII Equations of Lines and Circles

basic knowledge

1. Distance between points

2. Slope and linear equation

3. Linear relationship and slope

4. Distance from point to straight line

5. The relationship between straight lines and curves

6. Curves and equations

7. The relationship between points and curves

8. The relationship between point and surface

9. Simple linear programming problem

10. Basic properties of circles

Typical characteristics of 1 1. circle

12. Typical problems of circles

13. Conditions of four-point * * * circle

14. Basic exercises

Classification of college entrance examination questions

The application of 1. linear equation

2. The application of point-line distance

3. Simple application of linear relationship

4. The properties of circle and the application of parameter equation.

5. The application of the relationship between straight line and circle

6. The application of the properties of circular missing chord

7. Proof problems related to circles and straight lines

College entrance examination comprehensive questions

Comprehensive application of 1. circle

2. The problem of rounding a fixed point

3. Extreme value problem of circle

Chapter VIII Conic Curve Equation

basic knowledge

Standard equation of ellipse.

2. Geometric properties of ellipse

3. Parametric equation of ellipse

4. Typical characteristics of ellipse

5. Physical properties of ellipse

6. Standard equation of hyperbola

7. Geometric properties of hyperbola

8. Physical properties of hyperbola

9. Standard equation of parabola

10. Geometric properties of parabola

Physical properties of 1 1. parabola

12. Typical characteristics of parabola

Classification database of college entrance examination questions

Application of 1. Elliptic Properties

2. Application of hyperbola.

3. Application of parabola.

4. Synthesis of conic curves and triangles

5. Synthesis of conic curves and circles

6. Conic curve and straight line equation

7. Correlation of three conic curves.

College entrance examination comprehensive questions

Comprehensive application of ellipse.

2. Comprehensive application of hyperbola

3. Comprehensive application of parabola

4. Solve the extreme value of conic section

5. Comprehensive solution of conic curve

Chapter 9 Straight line and plane

basic knowledge

Basic properties of 1. plane

2. The intuitive drawing of plane graphics

3. Parallel straight lines

4. Straight lines in different planes

5. Lines and planes

6. Three Vertical Theorems and Their Inverse Theorems

7. The positional relationship between two planes

8. Application of reduction to absurdity in line-surface relationship

9. dihedral angle and its plane angle

10. Space vector

Angle formula of 1 1. space vector

12. Direction vector of straight line

13. Normal vector of plane

14. Application of space vector

Classification of college entrance examination questions

The relationship between straight lines in 1. space

2. The application of straight line and plane properties

3. Calculation of the relationship between straight line and plane

4. The relationship between triangle and plane in space

5. The nature of dihedral angle

6. Properties of space vectors

College entrance examination comprehensive questions

Comprehensive application of 1. line-plane included angle

2. Comprehensive application of dihedral angle

3. Comprehensive application of space vectors

Chapter 10 Simple Geometry

basic knowledge

1. Features of polygons;

2. Polyhedron, convex polyhedron and regular polyhedron

3. Prism

4. pyramids

5. The nature of the sphere

6. Regular tetrahedron and cube

7. Projections and views

8. Basic exercises

Classification of college entrance examination questions

Properties and Splitting of 1. Polyhedron

2. Cross-sectional shape of polyhedron

3. The problem of * * * surface on polyhedron

4. Solutions for pyramids and prisms

5. Cubes and regular tetrahedrons

6. Basic properties of sphere

7. inscribed polyhedron and circumscribed polyhedron of spherical surface

8. Regular triangles and circles, regular tetrahedrons and spheres

9. Application of View and Projection

10. Geometric proof of polyhedron

College entrance examination comprehensive questions

1. Comprehensive application of included angle between line and surface on polyhedron

Chapter 11 permutation, combination and binomial theorem

basic knowledge

1. Classification counting principle and step-by-step counting principle

2. Formula of permutation and permutation number

3. Combination and combination number formula

4. Two properties of combination number

5. Binomial Theorem

6. Problems and principles of permutation and combination

Classification of college entrance examination questions

Basic properties of 1. permutation and combination

2. Equivalence in permutation and combination

3. Inequalities in permutation and combination.

4. Application of the principle of special priority

5. The application of reverse thinking in permutation and combination.

6. The problem of adjacent permutation and combination

7. Application of tree diagram method in permutation and combination

8. The application of binomial expansion

9. The solution of power exponent

10. permutation and combination of simple geometric problems

College entrance examination comprehensive questions

Some Equations in 1. Binomial Formula

2. Combination mode of sum and limit

Chapter XII Probability and Statistics

basic knowledge

1. Random events and probabilities

2. The Independence Event and mutually exclusive events

3. The probability of mutually independent events happening at the same time

4. Completeness, purity and equality in probability calculation

5. Discrete random variables

6. Sampling

7. Variance and standard deviation

8. Basic exercises

Classification of college entrance examination questions

1. Application of Mean and Variance

2. Overall sampling and stratified sampling

3. The basic application of probability and mathematical expectation

4. Reverse thinking of probability application

5. Application of the standard formula PN (k) = CN KP K (1-P) (k)

6. Statistical application

College entrance examination comprehensive questions

Comprehensive application of 1. probability

2. Calculate the occurrence probability of events from the occurrence probability of opposing events.

3. Scheme comparison

Chapter XIII Derivatives

basic knowledge

The concept of 1. derivative

2. Sum, difference, product, quotient and derivative of two functions

3. Basic derivative formula

4. The application of derivative

5. Derivative and extreme value

Classification of college entrance examination questions

1. Derivative Function, Curve Slope and Tangent Equation

2. Derivative and monotonicity of functions

3. The application of derivative and extreme value

College entrance examination comprehensive questions

Comprehensive solution of 1. derivative

2. Derivative comparison function

3. The practical application of derivatives

Chapter XIV Complex Numbers

basic knowledge

The concept of 1. complex number

2. Addition and subtraction of complex numbers

3. Multiplication and division of complex numbers

4. Basic exercises

Classification of college entrance examination questions

Properties of 1. Complex Numbers

2. Basic operations of complex numbers

College entrance examination comprehensive questions

1. Complex operation skills

Chapter 15 Intellectual Interest in College Entrance Examination

Classification of test questions

1. Comparison problem

2. Binary analysis

3. Conceptual analysis

Solution induction

1. compromise method

2. Special value method

3. Comprehensive solution of coefficient sum

Comprehensive thinking on college entrance examination questions

1. Reverse thinking

2. Flexible thinking

3. Rule application thought

Observe your thoughts.

5. Split thinking

Step 6 compare ideas

Appendix Curriculum Reform Elective Content

1. polar coordinate system

2. Parametric equation

3. Geometric proof

4. Linear regression equation