12th Grade, Scientific section



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Overview:

A clearly decisive year in the students' life.
2 main goals:
• the "baccalauréat": coefficient 7 or 9 ("Spécialité).
• be prepared for after high school studies!!

Students will go in depths in the study of functions, especially through infinitesimal calculus and integration.
We will also extend our set of fundamental functions: exponential, logarithms, trigonometric functions.
Also students will discover complex numbers, vector and cartesian space geometry and finally continuous laws of probabilities.

A vast and ambitious curriculum … Be ready! Go …


Contents:
Sequences are fundamental in calculus. This year is supposed to give the students the necessary formal basis for science studies.

Students will go through:

• reasoning by induction

• convergence:

◊ Formal definition

◊ Computing limits

◊ Monotony and convergence

Sequences will give plenty of opportunity to study algorithms.
Still the largest part of the curriculum. It will be about:

• Limits of function: formal definition, computing

• Composing functions

• Differential calculus

• Continuity and intermediate value theorem

• New functions: sine, cosine, exponential and logarithm

• Integrals
A new set of numbers:

• Definitions

• Operations

• Solving quadratics

• Exponential form

• A bit of complex geometry
Bringing vectors to space :

• Parallelism, orthogonality, positions of lines and planes

• Vectors in space

• Axes & coordinates in space

• Dot product

• Cartesian equations of planes and spheres, intersections of surfaces
2 approaches:

• Discrete probabilities: getting formal introducing conditional probability.

• Continuous probabilities:
    • Principles
    • uniform law
    • exponential law
    • normal law
    • Using the normal law for decision.
There won’t be any course of algorithmic. Students will be trained at any possible opportunity.

They should be able to write an simple algorithm when needed or appropriate.

No programming langage in particular will be taught.



Advices:
• For the "baccalauréat"
The "baccalauréat" is to assess the knowledge of the students.
It mostly consist in classical exercises.
Students should have obtained the meaning and the basic rules of the notions and concepts, in order to recognize and manipulate them.
They need to work on acquiring precise knowledges and rigorous methods of reasoning. Even though sometimes intuition looks like sufficient to give the answer, students will be evaluated on their abilities to use the correct tools and reasoning.

• Give yourself a goal
The curriculum aims to give you a consistent level in maths such that you can follow nicely primarily scientific studies in Colleges and universities.
The actual world is complex.
Some of you will need precise knowledges in order to read and understand theories that apply to real life situations.
Some of you will need precise knowledges in order to develop and imagine theories that modelize real life situations.
The curriculum should give you the tools that permits you to find your way in.


Enjoy the school year.


Note that these informations are not exhaustive nor lessons plans.

It’s just a overview of the curriculum.