1. setting; 2. subset; 3. supplement;

4. Intersection; 5. Trade unions; 6. Logical connector;

7. Four propositions; 8. Necessary and sufficient conditions.

Second, the function (30 class hours, 12)

1. mapping; 2. Function; 3. Monotonicity of the function;

4. Inverse function; 5. The relationship between function images of reciprocal function; 6. Extension of the concept of index;

7. Operation of rational exponential power; 8. Exponential function; 9. Logarithm;

10. Operational properties of logarithm; 1 1. logarithmic function. 12. An application example of the function.

III. Series (12 class hours, 5)

1. sequence; 2. arithmetic progression and its general formula; 3. arithmetic progression's first N terms and formulas;

4. Geometric series and its topping formula; 5. The first n terms and formulas of geometric series.

Fourth, trigonometric function (46 class hours 17)

The generalization of the concept of 1. angle; 2. Curvature system; 3. Trigonometric function at any angle;

4. The trigonometric function line in the unit circle; 5. Basic relations of trigonometric functions with the same angle;

6. Inductive formulas of sine and cosine. Sine, cosine and tangent of sum and difference of two angles;

8. Sine, cosine and tangent of double angles; 9. Images and properties of sine function and cosine function;

10. Periodic function; The parity of 1 1. function; 12. Image of the function;

13. Images and properties of tangent function; 14. Find the angle with the known trigonometric function value; 15. Sine theorem;

16 cosine theorem; 17 example of oblique triangle solution.

V. Plane Vector (12 8 class hours)

1 .vector 2. Addition and subtraction of vectors 3. Product of real number and vector;

4. Coordinate representation of plane vector; 5. The demarcation point of the line segment; 6. The product of plane vectors;

7. The distance between two points on the plane; 8. Translation.

Inequalities of intransitive verbs (22 class hours, 5)

1. Inequality; 2. Basic properties of inequality; 3. Proof of inequality;

4. Solving inequality; 5. Inequalities with absolute values.

VII. Equation of Line and Circle (22 class hours, 12)

1. Angle and slope of straight line; 2. Point-oblique and two-point linear equations; 3. General formula of linear equation;

4. Conditions for two straight lines to be parallel and vertical; 5. Angle of intersection of two straight lines; 6. Distance from point to straight line;

7. The plane area is expressed by binary linear inequality; 8. Simple linear programming problem. 9. Concepts of curves and equations;

10. The curve equation is listed by known conditions; Standard equation and general equation of 1 1. circle; 12. The parametric equation of the circle.

VIII. Conic Curve (18 7 class hours)

1 ellipse and its standard equation; 2. Simple geometric properties of ellipse; 3. Parametric equation of ellipse;

4. Hyperbola and its standard equation; 5. Simple geometric properties of hyperbola; 6. Parabola and its standard equation;

7. Simple geometric properties of parabola.

Nine, (2) straight line, plane, simple (36 hours, 28 hours)

1. plane and its basic properties; 2. Intuitive drawing of plane graphics; 3. Plane straight line;

4. Determination and nature of parallelism between straight line and plane: 5. Determination of perpendicularity between straight line and plane;

6. Three vertical theorems and their inverse theorems; 7. The positional relationship between two planes;

8. Space vector and its addition, subtraction, multiplication and division; 9. Coordinate representation of space vector;

10. the product of space vectors; 1 1. The direction vector of the straight line; 12. angles formed by straight lines on different planes;

13. Common perpendicular of straight lines on different planes; 14 straight line distance in different planes; 15. Verticality of straight line and plane;

16. The normal vector of the plane; 17. Distance from point to plane; 18. The angle formed by a straight line and a plane;

19. The projection of the vector on the plane; 20. The nature that the plane is parallel to the plane; 2 1. Distance between parallel planes;

22. dihedral angle and its plane angle; 23. Determination and nature of verticality of two planes; 24. Polyhedron;

25. Prism; 26. pyramids; 27. Regular polyhedron; 28. Ball.

Ten, permutation, combination, binomial theorem (18 class, 8)

1. Classification counting principle and step-by-step counting principle. 2. Arrangement; 3. Formula of permutation number

4. combination; 5. Combination number formula; 6. Two properties of combination number:

7. binomial theorem; 8. The nature of binomial expansion.

XI。 Probability (12 class hours, 5)

1. Probability of random events; 2. The probability of this possible event; 3. mutually exclusive events has the probability of occurrence;

4. The probability of mutually independent events occurring simultaneously; 5. Repeat the test independently.

Elective 2 (24)

XII. Probability and Statistics (14 class hours, 6)

1. Distribution table of discrete random variables; 2. Expected value and variance of discrete random variables; 3. Sampling method;

4. Estimation of the overall distribution; 5. Normal distribution; 6. Linear regression.

Thirteen. Restrictions (12 class hours, 6)

1. Mathematical induction; 2. Examples of application of mathematical induction; 3. Limit of sequence;

4. Limit of function; 5. Four operations of limit; 6. Functional continuity.

Fourteen Derivative (18 class hour, 8)

The concept of 1. derivative; 2. Geometric meaning of derivative; 3. Derivatives of several common functions;

4. Derivative of sum, difference, product and quotient of two functions; 5. Derivative of composite function; 6. Basic derivative formula;

7. Using derivatives to study monotonicity and extremum of functions: the maximum and minimum of eight functions.

Fifteen, plural (4 class hours, 4)

The concept of 1. complex number; 2. Addition and subtraction of complex numbers; 3. Multiplication and division of complex numbers

Answer supplement

There are 130 knowledge points in high school mathematics. In the past, a test paper examined 90 knowledge points, and the coverage rate was about 70%, and this item was regarded as one of the criteria to measure the success of the test paper. This tradition has been broken in recent years, replaced by attaching importance to thinking, highlighting ability, and attaching importance to the examination of thinking methods and thinking ability.

Now, we are happier in math than before! ! Finally, I suggest you visit this website often, www.pep.com.cn, and I believe it will be helpful to your study. Wish you success!

Answer supplement

Just try it.

The outline of the preliminary test competition of the national senior high school mathematics league matches the teaching requirements and contents stipulated in the full-time middle school mathematics syllabus, that is, the knowledge scope and methods stipulated in the college entrance examination are slightly improved, and the preliminary test of probability and calculus is not taken.

Second division

1, plane geometry

Basic requirements: master all the contents determined by the outline of junior high school mathematics competition.

Supplementary requirements: area and area method.

Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem.

Several important extreme values: the point with the smallest sum of the distances to the three vertices of a triangle-fermat point. The center of gravity is the point where the sum of squares of the distances to the three vertices of a triangle is the smallest. The point where the distance product of three sides in a triangle is the largest is the center of gravity.

Geometric inequality.

Simple isoperimetric problem. Understand the following theorem:

In the set of N-polygons with a certain circumference, the area of the regular N-polygon is the largest.

In a set of simple closed curves with a certain perimeter, the area of the circle is the largest.

In a group of N-sided polygons with a certain area, the perimeter of the regular N-sided polygon is the smallest.

In a set of simple closed curves with a certain area, the circumference of a circle is the smallest.

Motion in geometry: reflection, translation and rotation.

Complex number method and vector method.

Planar convex set, convex hull and their applications.

Answer supplement

The second mathematical induction.

Recursion, first and second order recursion, characteristic equation method.

Function iteration, finding n iterations, simple function equation.

N-element mean inequality, Cauchy inequality, rank inequality and their applications.

Exponential form of complex number, Euler formula, Dimov theorem, unit root, application of unit root.

Cyclic permutation, repeated permutation and combination, simple combinatorial identity.

The number of roots of an unary n-degree equation (polynomial), the relationship between roots and coefficients, and the pairing theorem of imaginary roots of real coefficient equations.

Simple elementary number theory problems should include infinite descent method, congruence, Euclid division, nonnegative minimum complete residue class, Gaussian function, Fermat's last theorem, Euler function, Sun Tzu's theorem, lattice points and their properties.

3. Solid geometry

Polyhedral angle, properties of polyhedral angle. Basic properties of trihedral angle and straight trihedral angle.

Regular polyhedron, euler theorem.

Proof method of volume.

Sections, sections, and surface flat patterns will be made.

4. Plane analytic geometry

Normal formula of straight line, polar coordinate equation of straight line, straight line bundle and its application.

The region represented by binary linear inequality.

The area formula of triangle.

Tangents and normals of conic curves.

Power and root axis of a circle.