Gaokao (China National College Entrance) 1-Day Intensive

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.

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.

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.