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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