The scope of knowledge involved in "National Senior High School Mathematics League (Trial)" does not exceed the full-time senior high school mathematics syllabus published by the Ministry of Education in 2000.

The National Senior High School Mathematics League (plus test) has expanded its knowledge and appropriately added some contents beyond the outline. Add the following:

1. Plane geometry

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

Imitation center, fermat point and Euler line of triangle;

Geometric inequality;

Geometric extremum problem;

Transformation in geometry: symmetry, translation and rotation;

Power and root axis of a circle:

Area method, complex number method, vector method, analytic geometry method.

2. Algebra

Periodic function, a function with absolute value;

Trigonometric formula, trigonometric identity, trigonometric equation, trigonometric inequality, inverse trigonometric function;

Recursion, recursive sequences and their properties, general formulas of first-order and second-order linear recursive sequences with constant coefficients;

Second mathematical induction;

Mean inequality, Cauchy inequality, rank inequality, Chebyshev inequality, one-dimensional convex function and their applications;

Complex number and its exponential form, triangular form, Euler formula, Dimov theorem, unit root;

Polynomial division theorem, factorization theorem, polynomial equality, rational root of integer coefficient polynomial *, polynomial interpolation formula *;

The number of roots of polynomials of degree n, the relationship between roots and coefficients, and the pairing theorem of imaginary roots of polynomials with real coefficients;

Function iteration, find n iterations *, simple function equation *.

3. Elementary number theory

Congruence, Euclid division, Peishu theorem, complete residue system, indefinite equations and equations, Gaussian function [x], Fermat's last theorem, lattice point and its properties, infinite descent method *, euler theorem *, Sun Tzu's theorem *.

4. Combination problem

Cyclic permutation, permutation and combination of repeated elements, combinatorial identity;

Combinatorial counting, combinatorial geometry;

Pigeon cage principle;

Exclusion principle;

Extreme principle;

Graph theory problems;

Division of sets;

Coverage;

Planar convex set, convex hull and their applications.

(The content marked with * will not be tested in the additional test for the time being, but it may be tested in the winter camp. ) The executive summary of China Physics Olympiad revised in February 2006.

First, the theoretical basis

Force research

1, kinematics

Frame of reference. Displacement and distance, velocity and acceleration of particle motion. Relative speed.

Vector and scalar. Composition and decomposition of vectors. Scalar product and vector product of vectors

Uniform linear motion and its image. The composition of sports. Projectile motion. Circular motion.

Translation and rotation of a rigid body around a fixed axis.

2. Newton's law of motion

Several common forces in mechanics

Newton's first, second and third laws of motion. The concept of inertial reference system. Friction.

Elastic force. Hooke's law. The concept of inertial force.

The law of universal gravitation. The gravitational formula of uniform spherical shell to particles inside and outside the shell (no derivation is needed).

Kepler's law. The motion of planets and satellites.

3. Balance of objects

* * * The balance of objects under the action of point force. Moment balance of rigid body. The type of center of gravity of object balance.

4. Momentum effect

Impulse Momentum theorems of particles and particle groups.

Law of conservation of momentum. The center of mass, the motion theorem of the center of mass. Recoil movement and rocket.

5. Pulse distance

Angular momentum. Angular momentum theorem of particles and particle groups (without introducing moment of inertia).

Law of conservation of angular momentum.

6, mechanical energy

Work and power. Kinetic energy and kinetic energy theorem.

Gravity potential energy. The gravitational potential energy formula of internal and external gravitational and potential energy of particle and uniform spherical shell (without deduction).

Elastic potential energy of a spring. Functional principle. Law of conservation of mechanical energy. Collision. Recovery coefficient.

7. Hydrostatics

Pressure in a still fluid. buoyancy

8. Vibration

Simple wiping vibration [x=Acos(ωt α)]. Amplitude. Frequency and period. Stage. Vibrating images.

Reference circle. Vibration speed nu =-asin (ω t α)] and acceleration.

The frequency and energy of simple harmonic vibration are determined by dynamic equations.

Synthesis of simple harmonic vibration in the same direction and frequency.

Damping vibration. Forced vibration and * * * vibration (qualitative understanding).

9. Wave harmony

Shear wave and longitudinal wave. Relationship among wavelength, frequency and wave velocity. Images of waves.

The expression of plane harmonic y = acos (t-x/v)

Interference and diffraction of waves (qualitative). Standing waves, sound waves. Loudness, pitch and tone of sound.

* * * voice. Music and noise. Doppler effect.

thermology

1, molecular dynamics theory

The order of magnitude of atoms and molecules.

Thermal motion of molecules. Brownian motion. The microscopic significance of temperature.

Molecular force kinetic energy of molecules and intermolecular potential energy. The internal energy of an object.

2, the first law of thermodynamics

The first law of thermodynamics.

3. The second law of thermodynamics

The second law of thermodynamics. Reversible process and irreversible process.

4, the nature of gas

Thermodynamic temperature scale.

Equation of state of ideal gas. Universal gas constant.

Microscopic interpretation of the equation of state of ideal gas (qualitative).

Internal energy of ideal gas.

Constant volume, constant pressure, constant temperature and adiabatic process of ideal gas (without calculus operation).

5. Properties of liquid

Characteristics of fluid molecular motion.

Surface tension coefficient. Seepage phenomenon and capillary phenomenon (qualitative).

6, the nature of the solid

Crystalline and amorphous. Spatial lattice.

Characteristics of solid molecular motion.

7. Changes in the state of matter

Melting and solidification. Melting point heat of fusion.

Evaporation and condensation. Saturation pressure of water vapor. Boiling and boiling point. Heat of vaporization. Critical temperature.

Sublimation of solids. Air humidity and hygrometer. dew point

8. Mode of heat transfer

Conduction, convection and radiation.

9, thermal expansion

Thermal expansion and coefficient of expansion.

electrotherapy

1, electrostatic field

Coulomb's law, law of conservation of charge.

Electric field intensity. Principle of electric field line field strength and field strength superposition of point charge. Formula of internal and external field strength of uniformly charged spherical shell (no demand derivative). Uniform electric field.

Conductor in electric field. Electrostatic shielding.

Potential and potential difference. The formula of equipotential surface potential of point charge electric field (without deduction). Principle of potential superposition. Formula of potential inside and outside the shell of a uniformly charged spherical shell (without deduction).

Capacitance. Connection of capacitors. Capacitance formula of parallel plate capacitor (without deduction).

The electric energy after the capacitor is charged. Polarization of dielectric. Dielectric constant.

2. Constant current

Ohm's law relation between resistivity and temperature.

Electricity and electricity. Series and parallel connection of resistors.

Ohm's law of electromotive force in closed circuit.

Ohm's law with power supply circuit. Kirchhoff's law

Ammeter. Voltmeter. Ohmmeter.

Wheatstone bridge, compensation circuit.

3. Conductivity of materials

Electric current in metals. Microscopic interpretation of ohm's law.

The current in a liquid. Faraday's law of electrolysis.

The current in the gas. Stimulated discharge and self-excited discharge (qualitative).

The current in a vacuum. oscilloscope

Conductive properties of semiconductors. P-type semiconductor and n-type semiconductor.

Unilateral conductivity of crystal diode. Transistor amplification (no mechanism required).

Superconducting phenomenon.

4. Magnetic field

The magnetic field of current. Magnetic induction intensity. Magnetic induction line uniform magnetic field. Current and magnetic field in long straight wires.

Ampere. Lorentz force. Determination of electron charge-mass ratio. Mass spectrometer. Cyclotron.

5, electromagnetic induction

Faraday's law of electromagnetic induction. Lenz's law induced electric field (eddy current electric field)

Self-inductance coefficient. Mutual inductance and transformer.

6. alternating current

Principle of alternator. Maximum effective value of alternating current.

Pure resistance, pure inductance and pure capacitance circuits.

Rectification, filtering and voltage stabilization.

Three-phase alternating current and its connection method. Principle of induction motor.

7, electromagnetic oscillation and electromagnetic waves

Electromagnetic oscillation. Oscillating circuit and oscillating frequency.

Electromagnetic fields and electromagnetic waves. Wave velocity of electromagnetic wave, Hertz experiment.

Emission and modulation of electromagnetic waves. Receive, tune and detect electromagnetic waves.

optics

1, geometric optics

Direct light, reflection and refraction. Total reflection.

Scattering of light. Relationship between refractive index and light speed.

Plane mirror imaging. Imaging formula and drawing method of spherical mirror. Imaging formula and drawing method of thin lens.

Eyes. Magnifier. Microscope. Telescope.

2. Wave optics

Optical path, interference and diffraction of light (qualitative), double-slit interference, single-slit diffraction.

Spectrum and spectral analysis. Electromagnetic spectrum.

Atoms and nuclei

1, the essence of light

Photoelectric effect. Historical development of light theory. Einstein equation. Energy and momentum of wave-particle duality photons.

2. Atomic structure

Rutherford experiment. The nuclear structure of atoms.

Bohr model interpretation of hydrogen spectrum. Limitations of bohr model.

Stimulated radiation of atoms. Laser.

3. Core

The order of magnitude of the nucleus.

Natural radiation phenomenon. Detection of radiation.

The discovery of protons. The discovery of neutrons. The composition of the nucleus.

Nuclear reaction equation. Mass and energy equations. Fission and fusion. Elementary particles. Quark model.

4. Wave-particle duality of uncertain physical particles.

5. Special Relativity Einstein assumed the relativistic effect of time and length.

6. Preliminary knowledge of solar system, galactic universe and black holes.

foundations of mathematics

1, all elementary mathematics (including analytic geometry) in middle school.

2. Synthesis and decomposition of vectors. Basic concepts of limit, infinity and infinitesimal.

3. Calculus is not needed for derivation or operation.

Second, the experimental basis

1, it is required to master the experiments of all students in the "Full-time Middle School Physics Teaching Outline" formulated by the State Education Commission.

2. It is required to correctly use the following instruments and appliances (including selection): meter ruler. Vernier caliper. Screw micrometer. Balance. Stop the watch. Thermometer. Calorimeter. Ammeter. Voltmeter. Ohmmeter. Multimeter. Batteries. Resistance box. Variable resistor. Capacitor. Transformers. Electric key. Diode. Optical bench (including plane mirror, spherical mirror, prism, lens and other optical elements).

3. Some instruments that have never been seen before. It is required to use the instrument correctly according to the given instructions. For example: bridge, potentiometer, oscilloscope, regulated power supply, signal generator, etc.

4. In addition to the students' experiments stipulated in the "Full-time Middle School Physics Teaching Syllabus" formulated by the State Education Commission, other experiments can be arranged to examine students' experimental ability, but the principles and methods involved in these experiments shall not exceed the first part (theoretical basis) of this abstract, and the instruments used are within the range pointed out in the above 2 and 3.

5. For data processing, besides calculation, it is also required to be used as a graphic method. As for the error, only effective digital bridge PM6306 and error are needed; The calculation results are valid: digital bridge PM6306 (not strictly required); Analysis of main system error sources.

Third, other aspects.

Part of the content of physics competition should be extended to the knowledge gained after class. Mainly includes the following three aspects:

1, the application of physical knowledge in various aspects. Explanation of some physical phenomena in nature, production and daily life.

2. Some important achievements in modern physics and some important information in modern times.

3. The names of some physicists who have made important contributions and their main contributions.