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Objectives

1.1.   Binary relations.

1. Recognize a binary relation.
2. Recognize an equivalence relation.
3. Recognize an order relation.

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Objectives

1.1. Binary relations.

1. Identify a binary relation on a set.
2. List the elements of the graph of a binary relation on a finite set.
3. Identify an equivalence relation.
4. List the members of the equivalence class of an element.
5. Determine the partition associated with an equivalence relation.
6. Identify an order relation.

3.1. System of linear equations (3 ´ 3). Linear programming.

1. Translate the constraints of a linear programming problem into the form of a system of linear inequalities and an economic function.
2. Find graphically the optimal solution of a problem of linear programming.

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Objectives

4.1. Euclidean division of a polynomial by another.

1. Perform the Euclidean division of a polynomial by another.

Under the title:

4.2. “Factorization. Simplification of rational fractions”, we eliminate:

1. Use factorization to simplify a rational fraction.

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Objectives

1.2. Projections in space.

1. Characterize the projections of a point and a plane figure on a plane parallel to a given direction.
2. Characterize the projections of a point and a vector on a line parallel to a given plane.
3. Deduce the properties of orthogonal projection on a plane and a line.

1.3. Solids.

1. Recognize a prism, a pyramid, a cone, a cylinder and a sphere.
2. Know the expression of the lateral area and the volume of each of these solids.
3. Determine the intersection of a cone and a cylinder with a plane parallel to the base.
4. Study the relative position of a plane.

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Objectives

1.1. Binary operation.

1. Identify a binary operation.
2. Recognize the properties of a binary operation.
3. Recognize certain particular elements.

1.2. Structure of group.

1. Define a group.

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Objectives

1.3  Exponential growth and exponential function.

1. Calculate a^x for a real positive number a in the two cases a > 1 and 0 < a < 1.
2. Know and use the properties:

  a^x . a^y = a^x+y.

.

Content

Objectives

1.1. Binary operation.

1. Identify a binary operation.
2. Recognize the properties of a binary operation.
3. Recognize certain particular elements.

1.2. Structure of group.

1. Define a group.

3.1. Systems of linear equations (m ´ n): definition, elementary operations on the equations, Gauss’ method.

1. Identify a linear system (m ´ n).
2. Spread out a linear system (m ´ n) by successive applications of elementary operations.
3. Solve a linear system (m ´ n) by the Gauss’ method.

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Objectives

Under the title:

1.3. “Natural (Napierian) logarithmic function. Logarithmic function to the base a”, we eliminate:

1. Know the relation which links the function ln to the logarithmic function to base a (a > 0 and a ¹ 1) and deduce the properties of the latter.

Under the title:

1.4. “Exponential functions”, we eliminate:

1. Study and represent graphically the exponential function to base a.
2. Study the power function x® x^a.
3. Compare the increase of the functions ln, x ® e^x et x ® x^a.

Under the title:

2.2. “Second derivative”, we eliminate

• Calculate the second derivative of the reciprocal function at a point.

4.1. Differential equations

       (Definition).

1. Identify a differential equation and determine its order.

4.2. Equations of separable variables.

1. Identify and solve an equation of separable variables.

4.3. Linear first order equations with constant coefficients.

1. Identify and solve a linear differential equation of the first order with constant coefficients.

4.4. Finite differences equations.

1. Identify and solve a finite differences equation with constant coefficients of the first order.
2. Solve some finite differences equations with constant coefficients of the second order.

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Objectives

1.1. Binary operation.

1. Identify a law of binary operation.
2. Recognize the properties of a binary operation.
3. Recognize certain particular elements.

1.2. Structure of group.

1. Define a group and give examples of groups.

3.1. Systems of linear equations (m ´ n): definition, elementary operations on the equations, Gauss’ method.

1. Identify a linear system (m ´ n).
2. Reduce a linear system (m ´ n) by successively applying elementary operations.
3. Solve a linear system (m ´ n) by the Gauss’ method.

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Objectives

2.1. Level curves  (mod p or 2p).

1. Determine the level  (mod p or 2p) and characterize the cocyclicity of four points.

Under the title:

2.2. “Vector equation of a straight line, of a plane, of a sphere”, we eliminate:

1. Vectorially characterize of a sphere.

3.6. Equation of a sphere.

1. Determine the equation of a sphere defined by its center and its radius or by a diameter in an orthonormal system.
2. Link the position of a point with respect to a sphere to the power of this point relative to this sphere.

3.7. Intersection of a sphere with a straight line, a plane or a sphere.

1. Determine the relative positions of a sphere with respect to a line, a plane or a sphere and determine the elements of intersection where they exist.

4.1. Displacement in the plane.

1. Characterize a displacement in the plane.
2. Study the effect of a displacement on the plane geometric figures.
3. Distinguish the isometries which are displacements and those which are not.

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Objectives

Under the title:

1.5. “Exponential functions. Power functions”, we eliminate:

1. Study and represent graphically the exponential function to base a.
2. Study the power function x ® x^a.
3. Compare the increases of the functions ln, x ® e^x and x ® x^a.

1.7. Parametric curves.

1. Study simple curves defined parametrically.

3.3. Mean value theorem for definite integrals. Max-Min inequality.

1. Demonstrate and use the mean value theorem.

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Objectives

2.1. Solving simple trigonometric equations.

1. Solve simple trigonometric equations.

Content

Objectives

1.1. Binary operation.

1. Identify a binary operation.
2. Recognize the properties of a binary operation.
3. Recognize certain particular elements.

1.2. Structure of group.

1. Define a group and give examples of groups.

3.1. Systems of linear equations (m ´ n): definition, elementary operations on the rows, Gauss’ method.

1. Identify a linear system (m ´ n).
2. Reduce a linear system (m ´ n) by successively applications of elementary operations.
3. Solve a linear system (m ´ n) by the Gauss method.

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Objectives

1.2. Inverse trigonometric functions.

1. Study the functions Arcsin, Arccos and Arctan.

Under the title:

1.4. “Exponential functions”, we eliminate:

1. Study and represent graphically the exponential function to base a.
2. Study the power function x ® x^a.
3. Compare the increases of the functions functions ln, x ® e^x and x ® x^a.

Under the title:

2.4. “Second derivative. Successive derivatives”, we eliminate:

1.           Successive derivatives of a function.

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Objectives

2.4. Bernoulli variable.

1. Recognize a Bernoulli variable during a trial.

2.5. Binomial law.

1. Recognize a binomial law and determine its parameters characteristics.

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Objectifs

1.1. Pgcd et ppcm de plusieurs entiers.

1. Calculer le pgcd et le ppcm de deux ou plusieurs entiers.

Contenu

Objectifs

2.2. Positions relatives de droites et de plans.

1. Reconnaître les positions relatives de deux droites, de deux plans, d’une droite et d’un plan.

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objectifs

5.3. systèmes d’inéquations du premier degré à une inconnue.

1. résoudre un système d’inéquations du premier degré à une inconnue à cœfficients numériques.
2. organiser les données d’un problème, les traduire par un système de deux inéquations du premier degré à une inconnue, résoudre ce système et trouver les solutions.

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objectifs

2.1. intersection d’une droite et d’un solide usuel.

1. dessiner l’intersection d’une droite et d’un solide usuel.

2.2. intersection d’un plan et d’un solide usuel.

1. dessiner l’intersection d’un plan et d’un solide usuel.

3.1. quadrilatères inscriptibles.

1. connaître et utiliser les conditions nécessaires et suffisantes pour qu’un quadrilatère soit inscriptible.

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objectifs

1.2. produit cartésien.

1.   ecrire en extension le produit cartésien de deux ensembles finis.

1.3. application, bijection.

1. identifier une application.
2. identifier une bijection.

sous le titre:

2.4. “encadrement. approximation”, on éliminera:

1. identifier une approximation d’un nombre réel.
2. interpréter en termes de valeur absolue le fait qu’un réel a est une approximation à e près d’un réel x. cas où e = 10^-n.

sous le titre:

3.1. “equation du premier degré”, on éliminera:

• discuter et résoudre une équation paramétrée du premier degré à une inconnue.

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objectifs

2.2. projection dans le plan.

1. définir les projetés d’un point, d’un vecteur sur une droite parallèlement à une direction donnée et en dégager les propriétés essentielles.