Gaokao (China National College Entrance) 6-Month Plan

Domain and range, inverse functions, exponential and logarithmic functions, trigonometric functions and their inverses, and composite functions with applications in modeling.

Arithmetic and geometric sequences, recurrence relations, mathematical induction, limits of sequences, infinite series, convergence tests, and sum of infinite series.

Concept of limits, properties of limits, L'Hospital's rule, continuity and discontinuity, intermediate value theorem, and applications in calculus.

Differentiation rules, product, quotient, and chain rules, implicit differentiation, related rates, higher order derivatives, and applications to optimization problems.

Indefinite and definite integrals, integration techniques (substitution, parts, partial fractions), area under curves, volume of revolution, and improper integrals.

Formation and solution of first order differential equations, separable equations, linear differential equations, second order equations, and applications to physics and engineering.

Coordinate systems, straight lines, circles, ellipses, parabolas, hyperbolas, parametric equations, and polar coordinates with transformation techniques.

Vector operations in 2D and 3D, dot product, cross product, scalar triple product, vector equations of lines and planes, and applications in geometry and physics.

Kinematics in one and two dimensions, Newton's laws of motion, work-energy theorem, conservation of energy and momentum, rotational motion, angular momentum, and collision analysis.

Heat and temperature, calorimetry, heat transfer mechanisms, first and second laws of thermodynamics, entropy, Carnot cycle, and heat engine efficiency calculations.

Electric fields and potential, Gauss's law, capacitance, magnetic fields, Biot-Savart law, Ampere's law, electromagnetic induction, and Maxwell's equations overview.

Wave properties, superposition, interference, diffraction, polarization, reflection, refraction, lens systems, optical instruments, and interference experiments.

Special relativity, photoelectric effect, Bohr atom model, de Broglie hypothesis, wave-particle duality, Heisenberg uncertainty principle, and introduction to quantum mechanics.

Newton's law of universal gravitation, gravitational field and potential, Kepler's laws, orbital motion of satellites and planets, and escape velocity calculations.

Fluid statics, Pascal's principle, Archimedes' principle, Bernoulli's equation, fluid dynamics, viscosity, surface tension, and applications in engineering.

Simple harmonic motion, damped and forced oscillations, resonance, wave equation, sound waves, Doppler effect, and energy transfer in wave phenomena.

Quantum mechanical model, atomic orbitals, electron configuration, quantum numbers, periodic properties, and relationship between atomic structure and chemical behavior.

Ionic, covalent, and metallic bonding, VSEPR theory, hybridization of atomic orbitals, molecular geometry, bond polarity, and intermolecular forces.

Internal energy, enthalpy, Hess's law, bond energies, entropy, Gibbs free energy, spontaneity of reactions, and thermodynamic equilibrium analysis.

Reaction rates, rate laws, order of reactions, rate constants, activation energy, Arrhenius equation, reaction mechanisms, and catalysis.

Chemical equilibrium, equilibrium constants (Kp, Kc), Le Chatelier's principle, homogeneous and heterogeneous equilibria, and factors affecting equilibrium position.

Redox reactions, electrochemical cells, standard electrode potentials, Nernst equation, electrolysis, Faraday's laws, batteries, and corrosion.

Solution formation, concentration expressions, colligative properties, Raoult's law, boiling point elevation, freezing point depression, and osmotic pressure.

Hydrocarbons, functional groups, nomenclature, reaction mechanisms, stereochemistry, aromatic chemistry, polymers, and organic synthesis strategies.