René Cassin Highschool

Physical Signals

• Harmonic oscillator.
• Signal propagation.
• Geometric optics.
• Introduction to the quantum world.
• Electrical circuits within the QSA (Quasi-Static Approximation).
• First-order linear circuits.
• Damped oscillators.
• Linear filtering.

Mechanics 1

• Description and parameterization of a point's movement.
• Description of the movement of a solid in translation and rotation around a fixed axis.
• Linear momentum law.
• Energetic approach to the movement of a material point.
• Movement of charged particles in uniform and stationary electrical and magnetic fields.

Mechanics 2

• Angular momentum law.
• Energetic approach to the movement of a rotating solid around an oriented fixed axis in a Galilean reference frame.
• Kinetic energy law for a deformable system.
• Movement in a conservative central force field.
• Movement of charged particles in uniform and stationary electrical and magnetic fields.

Thermodynamics

• Microscopic and macroscopic description of a system at equilibrium.
• Energy exchanged by a system during a transformation.
• First principle. Energy balances.
• Second principle. Entropy balances.
• Thermal machines.

Fluid Statics

• Elements of fluid statics in a Galilean reference frame.

Induction and Laplace Forces

• Magnetic field.
• Action of a magnetic field.
• Linear momentum law.
• Laws of induction.
• Fixed circuit in a time-dependent magnetic field.
• Moving circuit in a stationary magnetic field.

Analysis (Fundamentals and Real Analysis)

• Fundamental techniques of differential and integral calculus.
  • Functions of a real variable with real or complex values.
  • Antiderivatives and linear differential equations.
• Real numbers and numerical sequences.
• Functions of a real variable: limits, continuity, and differentiability.
  • Limits and continuity.
  • Differentiability.
• Asymptotic analysis.
• Integration.
• Numerical series.
• Functions of two variables.

Algebra (Sets, Numbers and Linear Algebra)

• Set theory reasoning and vocabulary.
• Complements of algebraic calculus and trigonometry.
• Complex numbers.
• Polynomials.
• Matrix calculus and linear systems.
• Linear vector spaces.
  • Vector spaces.
  • Finite-dimensional spaces.
  • Linear maps.
• Matrices and determinants.
  • Matrices and linear maps.
  • Determinants.
• Real pre-Hilbert spaces.

Probability and Counting

• Counting.
• Probability.
  • Probability on a finite sample space, random variables, and distributions.
  • Expected value and variance.

Transformation of Matter

• Description and evolution of a system toward a final state during a chemical transformation.
  • Physico-chemical system.
  • Chemical transformation of a system.
• Temporal evolution of a system undergoing a chemical transformation.
  • Kinetics in a closed reactor with uniform composition.

Relations Between Chemical Entity Structure, Physical Properties, and Reactivity

• Structure of chemical entities.
  • Lewis model of the covalent bond.
  • Geometry and polarity of chemical entities.
  • Structure of organic chemical entities.
• Relations between entity structure and macroscopic physical properties.
  • Interactions between entities.
  • Phase changes.
  • Solubility, miscibility.
  • Amphiphilicity.
• Reactivity of organic species and initial applications in synthesis.
  • Reactivity of organic species and writing reaction mechanisms.
  • Organic synthesis in the laboratory.
  • Characteristic group modifications: example of haloalkanes.
  • Construction of the carbon skeleton: synthesis and use of Grignard reagents.

Transformations of Matter: Evolution of a System and Reaction Mechanism

• Microscopic modeling of a chemical transformation.
• Catalysis.

Microscopic Structures and Physical Properties of Solids

• Perfect crystal model.
• Metals and alloys.
• Covalent and molecular solids.
• Ionic solids.

Chemical Transformations in Aqueous Solution

• Acid-base and precipitation reactions.
  • Acid-base reactions.
  • Dissolution or precipitation reactions.
• Oxidation-reduction reactions.
  • Oxidants and reductants, redox reactions.
  • Potential-pH diagram.

Reactivity, Transformation in Organic Chemistry, and Synthesis Strategy

• Spectroscopic characterization techniques.
  • UV-visible and infrared absorption spectroscopies.
  • Proton nuclear magnetic resonance spectroscopy (1H NMR).
• Oxidation-reduction reactions in organic chemistry.
  • Oxidation level of organic species.
  • An example of interconversion between characteristic groups: from hydroxyalkyl group to carbonyl group and vice versa.
• Activation of characteristic groups.
  • Nucleophilic activation of alcohols and phenols.
  • Electrophilic activation of alcohols.
  • Electrophilic activation of the carbonyl group.
• Protection of characteristic groups and synthesis strategy.
  • Protection-deprotection.
  • Elementary approach to retrosynthetic analysis.
  • Electrophilic activation of the carbonyl group.

Analyze

• Analyze the need and requirements.
• Define the boundaries of the analysis.
• Analyze functional and structural organization.
• Analyze performances and deviations.

Model

• Choose physical quantities and characterize them.
• Propose a knowledge and behavior model.
• Validate a model.

Solve

• Propose a resolution process.
• Implement an analytical resolution process.
• Implement a numerical resolution process.

Experiment

• Set up and operate a system.
• Propose and justify an experimental protocol.
• Implement an experimental protocol.

Communicate

• Search for and process information.
• Produce and exchange information.

Design

• Design the architecture of an innovative system.
• Propose and choose technical solutions.