Description

HIGH SCHOOL (9-12) Mathematics, Physics & Chemistry

MATHEMATICS

Algebra I & II

• Linear equations, inequalities
• Systems of equations
• Polynomials and factorization
• Quadratic functions and equations
• Exponentials, logarithms

Geometry

• Euclidean geometry
• Similarities, congruences
• Trigonometry in triangles
• Analytic geometry : lines, circles, parabolas

Trigonometry

• Unit circle, radians, cosine, sine
• Trigonometric identities
• Trigonometric equations
• Trigonometric functions, graphs, transformations

Pre-calculus

• Functions
• Limits (intuitive)
• Sequences, series
• Exponentials and logarithms

Introduction to calculus

• Limits
• Derivatives, variation, tangent lines
• Convexity
• Basic optimization and interpolation
• Introduction to integrals, area

PHYSICS

Kinematics

• Simple motion
• Velocity and acceleration
• Free fall and projectile motion

Dynamics

• Newton’s laws
• Free-body diagrams
• Friction (basics)
• Circular motion

Energy

• Work and energy, power
• Kinetic and potential energy
• Conservation laws
• Work-Energy theorem
• Linear momentum

Waves and optics

• Wave motion, basic notions : wavelength, frequency, velocity
• Reflection, refraction
• Interference, double-slit experiment
• Thin lenses, ray tracing, telescopes

Electricity

• Electric circuits, Ohm’s law, Kirchhoff laws
• Electric charge, basic electric fields

CHEMISTRY

Atoms and molecules

• Atomic structure, subatomic particles, isotopes
• Electron configuration, periodic trends
• Periodic table, group and periods, reactivity
• Covalent bonds, Lewis structures
• VSEPR theory, molecular geometry, polarity

Stoichiometry, reactions, solutions

• Mole concept
• Chemical equations, limiting reagents, reaction yields
• Solution concentration, dilution, solubility
• Colligative properties (basics)

Thermochemistry

• Ideal gas law, phase diagrams
• Enthalpy
• Calorimetry
• Exothermic and endothermic reactions

Kinetics

• Reaction rates, first order reactions
• Differential equation, half-life
• Dynamic equilibrium, kinetic factors
• Activation energy

Acids, bases

• pH, half-reactions, conjugate acids and bases
• Strong and weak acids
• Acido-basic reactions, acid dissociation constant

Redox reactions

• Oxidizer and reducer, electron exchange
• Redox reactions
• Electrochemical cells