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Who can copy the outline of 20 13 national mathematics league?
Comparison of knowledge points between college entrance examination and Olympic outline

Orsay

National high school mathematics league exam outline

1.set

2. Exponential function

3. Logarithmic function

4. Vieta theorem

5. The relationship between root and coefficient

6. Characteristic equation method

7. Function iteration

8. Find n iterations

9. Simple function equation

10. Solution and proof of inequality

Average inequality of 1 1.n variables

12. Cauchy inequality

13. Ranking inequality and its application

14. Properties of sequences

15. Equal ratio series

16. Mathematical induction

17. The second mathematical induction method

18. Recursion (first and second order recursion)

19. Complex number operation

20. permutation and combination

Exponential form of 2 1. complex number

Euler formula

23. Demofo Theorem

24. Unit root

25. The application of unit root

26. The number of roots of an unary equation of degree n (polynomial)

27. Virtual Root Pairing Theorem of Real Coefficient Equation

28. The properties of trigonometric functions

29. The identity transformation of trigonometric functions

30. Triple angle formula

Some Simple Identities of 3 1. Triangle

32. Triangle inequality

33. Calculation of dihedral angle

34. The problem of rotating objects

35. Polyhedral problem

36. Batch certificate method

Part 37

38. Can make cross-section and surface development diagram.

39. Regular polyhedron

40. euler theorem

4 1. polygon

42. The properties of polyhedral angles

43. Three corners

44. The basic properties of straight trihedral angle

45. The distance formula between two points

46. The formula of dividing line segments into fixed ratios.

47. Linear equation

48. Equation of circle

49. The nature of the ellipse

50. The properties of hyperbola

Parametric equation of 5 1. conic curve

52. Vector operation

53. 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.

54. The center of gravity is the point where the product of the distances from a triangle to three sides is the largest.

55. Geometric inequalities

56. Ordinary line type

57. Polar coordinate equation of straight line

58. The region represented by binary linear inequality

59. Tangents and normals of conic curves

60. Several important theorems: Mené lios theorem, Seva theorem, Ptolemy theorem and siemsen theorem.

6 1. Several important extreme values: the point with the smallest sum of the distances to the three vertices of the triangle-fermat point.

62. Planar convex sets, convex hulls and their applications

63. Plane analytic geometry: straight line bundle and its application, power and root axis of circle.

64. Simple elementary number theory problems: infinite descent method, congruence, Euclidean division, nonnegative minimum complete residue class, divisibility, congruence, Gauss function of indefinite equation, Fermat theorem, Euler function, Sun Tzu theorem, lattice point and their properties.

65. Graph theory and combinatorial mathematics (pigeon hole principle, exclusion principle, extreme value principle, etc. ) set division, cyclic arrangement, repeated arrangement and combination, simple combination identity.

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