Description

ADVANCED PLACEMENT Mathematics, Physics & Chemistry

MATHEMATICS (AB & BC)

Limits and Continuity

• Formal approach
• Continuity
• Intermediate Value theorem and corollaries

Derivatives

• Rules of differentiation
• Implicit differentiation
• Linear approximation
• Taylor expansions
• Applications: optimization

Integrals

• Riemann sums
• Fundamental theorem of calculus
• Substitution
• Integration by parts
• Partial fractions
• Applications: areas and volumes, flow, arc length, physical applications

Differential equations

• First-order linear ODEs
• Separable equations
• Harmonic motion
• Application: exponential growth and decay

Series

• Taylor, MacLaurin
• Convergence tests
• Power series

Parametric equations

• Basic parametric equations, properties
• Polar coordinates
• Vector-valued functions

PHYSICS (1, 2, C)

Mechanics

• Kinematics
• Newtonian mechanics
• Work, Energy, Power
• Linear momentum
• Rotational dynamics
• Oscillations
• Gravitation (non-relativistic)

Electricity, Magnetism

• Electrostatics, electric fields and potentials
• Magnetostatics, magnetic fields and induction
• Capacitors
• DC circuits

Mathematical modeling

• Differential equations
• Harmonic oscillators
• Damped oscillators
• Energy-based methods

CHEMISTRY

Structure of Matter

• Quantum model of the atom
• Electron configuration
• Periodic table
• Lewis and VSEPR
• Hybridization
• Molecular orbital theory

Chemical reactions

• Reaction types
• Redox reactions
• Electrochemistry, Nernst laws, galvanic and electrolytic cells
• Equilibrium constant, Le Chatelier’s principle

Thermochemistry

• Enthalpy
• Hess’s law
• Entropy
• Gibbs free energy
• Spontaneity

Kinetics

• Reaction rates, first order reactions
• Rate laws
• Integrated rate laws
• Arrhenius equation
• Reaction mechanisms

Acids, bases

• Acid-base equilibria
• pH calculations
• Titrations