MATHEMATICS CURRICULUM

INTRODUCTION

GENERAL OBJECTIVES

TABLE OF DISTRIBUTION OF PERIODS PER WEEK/YEAR

bASIC Education

ELEMENTARY LEVEL

SCOPE AND SEQUENCE – First Cycle

SCOPE AND SEQUENCE – Second Cycle

SCOPE AND SEQUENCE – Intermediate Level

ELEMENTARY LEVEL - First Cycle

OBJECTIVES

SYLLABUS

First Year Second Year Third Year

ELEMENTARY LEVEL - Second Cycle

OBJECTIVES

SYLLABUS

Fourth Year Fifth Year Sixth Year

INTERMEDIATE LEVEL

OBJECTIVES

SYLLABUS

Seventh Year Eighth Year Ninth Year

Secondary EDUCATION

Literature and Humanities Section

OBJECTIVES

SCOPE AND SEQUENCE

Sociology and Economics Section

OBJECTIVES

SCOPE AND SEQUENCE

General Sciences Section

OBJECTIVES

SCOPE AND SEQUENCE

Life Sciences Section

OBJECTIVES

SCOPE AND SEQUENCE

SYLLABUS

First Secondary Second Secondary – Humanities Section Second Secondary – Sciences Section Third Secondary – Literature and Humanities Section Third Secondary – Sociology and Economics Section Third Secondary – General Sciences Section Third Secondary – Life Sciences Section

INTRODUCTION

Mathematics constitute an activity of the mind which takes the dimensions of a big human adventure. It is a fertile field for the development of critical thinking, for the formation of the habit of scientific honesty, for objectivity, for rigor and for precision. It offers to students the necessary knowledge for the social life and efficient means to understand and explore the real world whatever the domain is: physical, chemical, biological, astronomical, social, psychological, computer, etc.

The flashing advancement in science and technology has deeply marked modern society. We speak today of the era of “information” like we spoke, a quarter of a century ago, of the industrial era. Now, everybody agrees on the fact that this development could not have been accomplished but by the mathematical tool whose use has allowed to substitute the qualitative description of reality by its quantification and its operational modeling. Today, more than ever, Mathematics proves to be an ineluctable necessity to the life of societies and to their development. This science can no longer remain the property of a specialized elite, but many of its results and means must be acquired by a more considerable number of citizens.

This extension of Mathematics to all the reality, and the increasing demand for its learning have, without doubt, modified the spirit and the use. The reform of its teaching is to be operated in three axes: a new formulation of the objectives, a remodeling of contents and a suitable choice of methods.

1. Formulation of objectives: The fundamental objectives concerning the mental activities and the formation of mathematical reasoning, continue to figure, the stress is mainly on the individual construction of Mathematics; it no longer consists of teaching already made Mathematics but of making it by oneself. Starting with real-life situations in which the learner raises questions, lays down problems, formulates hypotheses and verifies them, the very spirit of science is implanted and rooted.

Our intention is also to form the students to the communication: reading a mathematical text, understanding it, interpreting it, using symbols, graphs, tables etc..., writing a demonstration, explaining a situation, etc... remain essential objectives of the teaching.

2. Remodeling contents: The subjects are not judged according to their theoretical interest but according to their practical interest. They must be accessible to all the students and respond to their need of formation and to their cultural development. Every theoretical overuse was abolished, every virtuosity in the accomplishment of the tasks was omitted. This allowed a significant reduction in the programs which aim to form “well made heads”. The introduction to the calculator and the possibility of using the computer are two technological novelties which will have benefits on the formation. Other subjects which deal with the treatment of information, such as Statistics, allow the new generations to adapt better to socio-economic problems.

3. Method of teaching: The teaching of Mathematics must be organized in such a way as to demythicize it and make it accessible to a larger public. The recommended method consists of starting from real-life situations, lived or familiar, to show that there is no divorce between Mathematics and everyday life. This practice of Mathematics will lead students to the intelligence of conceptual models whose effectiveness will be understood by the transfer of successful teachings.

That was the context in which this new program has been prepared. Our essential aim is to form a citizen capable of critical thinking and intellectual autonomy.

GENERAL OBJECTIVES

The present curriculum, through the acquisition of adequate mathematical knowledge, aims to achieve the following general objectives.

1. Training in the construction of arguments and evaluating them, developing critical thinking, and emphasizing MATHEMATICAL REASONING. These are the major goals of this curriculum. Toward this end, student will be given the chance to observe, analyse, abstract, doubt, foresee, conjecture, generalize, synthesize, interpret and demonstrate

2. SOLVING MATHEMATICAL PROBLEMS is perhaps the most significant activity in the teaching of mathematics. On the one hand, every new mathematical knowledge must start from a real-life problem. On the other hand, students must learn to use various strategies to tackle difficulties in solving a problem. Toward this end, he must be able to serialize, classify, quantify, discover mathematical methods, manipulate simulation techniques, construct and use algorithms, take decisions, verify, apply, measure, use ad hoc techniques and manipulate information.

3. Modern society has a greater need for highly qualified workers and researchers in all areas. The Mathematics curriculum responds to these demands by offering the student an opportunity of practicing the scientific approach, developing the scientific spirit, improving skills in research, establishing relations between mathematics and the surrounding reality in all its dimensions and valuing the role of Mathematics in technological, economical and cultural development.

4. Our intention is to train the student to COMMUNICATE MATHEMATICALLY. To achieve this, he must learn to encode and decode messages, formulate, express information orally, in writing and/ or with the help of mathematicals tools.

5. Aside from being a utilitarian science, Mathematics is also an art. The curriculum gives the student a chance to VALUE Mathematics by helping him to acquire confidence in mathematical methods, to appreciate precision, rigor, order and harmony of mathematical theories, to develop intuition, imagination and creativity, to find pleasure in intellectual activities and persevere at work.

TABLE OF DISTRIBUTION OF PERIODS PER WEEK/YEAR

level	Basic Education									Secondary Education
	Elementary Level						Intermediate Level
	First			Second						First	Second		Third
Class	First	Second	Third	Fourth	Fifth	Sixth	Seventh	Eighth	Ninth		Humanities	Sciences	Literature and Humanities	Sociology and Economics	General Sciences	Life Sciences
Number of periods per week	5	5	5	5	5	5	5	5	5	5	4	6	2	4	10	5
Number of periods per year	150	150	150	150	150	150	150	150	150	150	120	180	60	120	300	150

BASIC EDUCATION

SCOPE AND SEQUENCE - FIRST CYCLE

ARITHMETIC AND ALGEBRA

Grade Level	First Year	Second Year	Third Year
Subject
1. NUMBERS	n NATURAL INTEGERS (60 h) - Numbers less than 100. - Reading, writing in standard form. - Comparison. - Grouping by 10.	n NATURAL INTEGERS (25 h) - Numbers less than 1 000. - Reading and writing in words numbers less than 100. - Order; signs < and >; representation on a straight line. - Expanded writing.	n NATURAL INTEGERS (15 h) - Numbers less than 100 000. - Reading and writing in standard form and in words. - Compatibility of the order with addition, subtraction and multiplication. n FRACTIONS (5 h) - Fractions .
2. OPERATIONS	n ADDITION (50h) - Addition of whole numbers. - Function "add n". - Tables of addition: construction (up to 9). - Computational technique with trading. - Decomposition of a whole number. n SUBTRACTION (10 h) - Initiation.	n ADDITION (30 h) - Memorization of tables of addition. - Mastering the computational technique. n SUBTRACTION (30 h) - Inverse operation of addition. - Function "subtract n". - Computational technique: with trading. n MULTIPLICATION (30 h) - Repeated addition. - Table of multiplication: construction (up to 9). - Multiplication by a one-digit factor. n DIVISION (5 h) - Initiation: sharing, distribution.	n ADDITION (10 h) - Properties: commutativity and associativity. n SUBTRACTION (20 h) - Mastering the computational technique n MULTIPLICATION (30 h) - Function "multiply by n". - Multiplication by 10 and by a multiple of 10. - Distributivity of multiplication over addition. - Memorization of multiplication tables. - Computational technique: two-digit factors. n DIVISION (30 h) - Exact division and Euclidean division. - Computational technique.

GEOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. LOCATION	n Domain. n Displacement. n Position in space.	n Locating a point.	n Midpoint of a segment. n Perpendicular straight lines.
	(10 h)	(5 h)	(5 h)
2. SOLID FIGURES	n Rectangular prism. Cube. Sphere. Cylinder. Cone.	n Description of solid figures: vertices, edges and faces.	n Construction of a cube and of a rectangular prism.
	(5 h)	(5 h)	(7 h)
3. PLANE FIGURES	n Lines. n Square. Rectangle. Triangle. Disc.	n Segment. n Description of plane figures: vertices and sides.	n Right angle. Application to the rectangle and the square.
	(5 h)	(5 h)	(3 h)
4. TRANSFORMATIONS	n Axis of symmetry.	n Figures having an axis of symmetry.	n Reflection.
	(5 h)	(5 h)	(5 h)

MEASUREMENT

Grade Level	First Year	Second Year	Third Year
Subject
1. LENGTH	n Comparison of lengths.	n Mesurement of length: meter, centimeter.	n Units of length: kilometer, meter, centimeter, millimeter. n Distance between two points. n Length of a polygonal line. Perimeter.
	(5 h)	(5 h)	(10 h)
2. MASS		n Comparison of masses.	n Kilogram, gram.
		(5 h)	(5 h)
3. TIME AND DURATION			n Telling time. n Duration of an event. n Units of time: hour, minute, second.
			(5 h)

BASIC EDUCATION

SCOPE AND SEQUENCE - SECOND CYCLE

ARITHMETIC AND ALGEBRA

Grade Level	Fourth Year	Fifth Year	Sixth Year
Subject
1. NUMBERS	n NATURAL INTEGERS (15 h) - Numbers greater than 100 000. - Multiples of a whole number. - Criteria for the divisibility by 2, 5 and 10. - Sexagesimal numeration. n FRACTIONS (15 h) - Fractions ( a b). - Comparison of fractions. n DECIMALS (10 h) - Decimal numbers.	n NATURAL INTEGERS (20 h) - Criteria for divisibility by 3, 4 and 9. - Common multiples of two whole numbers. - Divisors of a whole number. - Common divisors of two whole numbers. - System of decimal numeration. n FRACTIONS (10 h) - Equality and simplification of fractions. - Mixed numbers. n DECIMALS (10 h) - Comparison and representation of decimal numbers	n NATURAL INTEGERS (15 h) - Expanding a natural integer according to the powers of 10. - G.C.F. and L.C.M. of two natural integers. - Relatively prime numbers. n FRACTIONS (10 h) - Irreducible fractions. - Decimal fractions. n DECIMALS (10 h) - Fractional writing of a decimal number. - Expanding a decimal number according to the powers of 10 and of . n INTEGERS (15 h) - Positive numbers and negative numbers. - Representation on the numerical axis. - Comparison. n NOMBRES RELATIFS (15 h) - Nombres positifs et nombres négatifs. - Représentation sur l'axe numérique. - Comparaison.
2. OPERATIONS	n ADDITION (15 h) - Addition of decimals. - Addition of fractions having the same denominator. - Addition of duration and time. n SUBTRACTION (15 h) - Subtraction of decimals. - Subtraction of fractions having the same denominator. - Subtraction of duration and time. n MULTIPLICATION (10 h) - Multiplication of a decimal by a whole number. - Properties: commutativity and associativity. - Distributivity of multiplication over addition and substraction. n DIVISION (30 h) - Computational technique on whole numbers: divisors having two or more digits, whole number quotient. - Function "diviser par n".	n ADDITION (15 h) - Addition of fractions. - Addition of decimals with several decimal places. n SUBTRACTION (15 h) - Subtraction of fractions. - Subtraction of decimals with several decimal places. n MULTIPLICATION (20 h) - Multiplication of decimals. - Function "multiply by ". - Product of duration by a whole number. n DIVISION (10 h) - Decimal quotient of a division.	n ADDITION (5 h) - Addition of integers. n SUBTRACTION (5 h) - Subtraction of integers. n MULTIPLICATION (10 h) - Multiplication of fractions. - Powers of exponents 2 and 3. - Powers of 10. n DIVISION (10 h) - Division of fractions. - Quotient and ratio. - Division of duration by a whole number.
3. PROPORTIONALITY			n Percentage. Rates. n Proportional sequences. n Scale.
			(20 h)
4. ALGEBRAIC EXPRESSIONS			n Order of operations. n Calculation on literal expressions. n Numerical value of a literal expression.
			(10 h)

GEOMETRY

Grade Level	Fourth Year	Fifth Year	Sixth Year
Subject
1. LOCATION	n Distance from a point to a straight line. n Localization of a point on a squared grid.	n Distance of two parallel lines.	n Relative positions of two straight lines in a plane. n Relative positions of a straight line and a circle.
	(5 h)	(3 h)	(2 h)
2. SOLID FIGURES	n Building models.	n Development of solids.	n Patterns of solids.
	(5 h)	(7 h)	(3 h)
3. PLANE FIGURES	n Intersecting straight lines. Parallel straight lines. n Classification of quadrilaterals according to the sides. n Circle. Disc.	n Angle. n Diagonals of a polygon. n Classification of quadrilaterals according to the diagonals. n Diameter of a circle.	n Adjacent angles, vertically opposite angles. n Bisector of an angle. n Perpendicular bisector of a segment. n Triangle: particular triangles; particular straight lines in a triangle; sum of angles of a triangle.
	(5 h)	(10 h)	(10 h)
4. TRANSFORMATIONS	n Drawing the symmetric of a figure with respect to an axis.	n Homothecy.	n Central symmetry. n Study of figures from their elements of symmetry.
	(5 h)	(5 h)	(10 h)

MEASUREMENT

Grade Level	Fourth Year	Fifth Year	Sixth Year
Subject
1. LENGTH	n Metric units of length.	n Length of a circle.
	(6 h)	(3 h)
2. MASS	n Metric units of mass.
	(3 h)
3. AREA	n Comparison of areas.	n Area of a square, rectangle, right triangle, disc.	n Area of a parallelogram, of a triangle. n Metric units of area.
	(3 h)	(10 h)	(8 h)
4. ANGLE		n Measure of an angle in degrees.	n Complementary angles; supplementary angles.
		(2 h)	(2 h)
5. CAPACITY	n Litre and submultiples.	n Metric units of capacity.
	(3 h)	(5 h)
6. VOLUME			n Calculation of volume: cube, rectangular prism, right circular cylinder, ball. n Metric units of volume.
			(10 h)

STATISTIQUE

Grade Level	Fourth Year	Fifth Year	Sixth Year
Subject
HANDLING DATA	n Collecting and organizing data.	n Recording data: pictographs, bar graphs, tile graphs.	n Interpreting data: circular diagram.
	(5 h)	(5 h)	(5 h)

BASIC EDUCATION

SCOPE AND SEQUENCE - INTERMEDIATE LEVEL

ARITHMETIC AND ALGEBRA

Grade Level	Seventh Year	Eighth Year	Ninth Year
Subject
1. NUMBERS	n NATURAL INTEGERS (10 h) - Prime numbers. - Decomposition of a whole number into factors. n FRACTIONS (10 h) - Reducing fractions. n DECIMALS (5 h) - Decimal writing of a fraction.	n NATURAL INTEGERS (5 h) - G.C.F. and L.C.M. of several whole numbers. n FRACTIONS (5 h) - Literal fractions. - Composite fractions. n DECIMALS (5 h) - Compatibility of the order of operations. n SQUARE ROOTS (10 h) - Square roots of a positive number.	n REAL NUMBERS (5 h) - Rational and irrational numbers.
2. OPERATIONS	n Subtraction and multiplication of integers. n Powers of a positive number having positive integer exponent. n Common factor. Factorization.	n Powers of a positive number having positive integer exponent. n Powers of a negative integer exponent of 10.	n Rationalizing the denominator of a numerical fraction. n Calculation on real numbers.
	(30 h)	(5 h)	(10 h)
3. PROPORTIONALITY	n Directly proportional magnitudes.	n Grandeurs inversement proportionnelles.	n Linear functions and proportionality.
	(10 h)	(5 h)	(5 h)
4. ALGEBRAIC EXPRESSIONS	n Calculation on algebraic expressions.	n Identités remarquables. n Expressions littérales sous forme fractionnaire.	n Algebraic expressions having radicals. n Polynomial in one variable.
	(15 h)	(20 h)	(10 h)
5. EQUATIONS AND INEQUATIONS	n Equations reduced to ax = b.	n Equations du type: (ax + b) (cx + d) = 0. n Equations et inéquations du premier degré à une inconnue.	n Equations of the form: . n Systems of equations of the first degree in two unknowns. n Systems of inequations of the first degree in one unknown.
	(10 h)	(15 h)	(40 h)

GEOMETRY

Grade Level	Seventh Year	Eighth Year	Ninth Year
Subject
1. LOCATION	n Geometric locii and constructions. n Orthogonal system and coordinates of a point in a plane.	n Relative positions of two circles. n Geometric locii and constructions. n Coordinates of the midpoint of a segment.	n Tangents and circles. n Geometric locii and constructions. n Graphic representation of a straight line. n Analytical properties of two parallel and of two orthogonal straight lines. n Length of a segment in an orthonormal system. n Solving graphically a system of linear equations in two unknowns.
	(10 h)	(15 h)	(35 h)
2. SOLID GEOMETRY	n Plane representation of a cube and a rectangular prism.	n Plane representation of a cylinder, a pyramid, a cone and a sphere. n Relative positions of straight lines and of planes.	n Intersection of a straight line and a common solid. n Intersection of a plane and a common solid.
	(5 h)	(10 h)	(5 h)
3. PLANE FIGURES	n Cases of congruent triangles. n Angles formed by two parallel straight lines cut by a transversal. n Characteristic properties of the perpendicular bisector of a segment. n Characteristic properties of the bisector of an angle.	n Pythagoras’ theorem. n Theorem of midpoints in a triangle, in a trapezoid. n Characteristic properties of a parallelogram. n Central angle in a circle, inscribed angle in a circle. Area of a circular sector.	n Cyclic quadrilaterals. n Thales’ theorem. n Similar triangles.
	(35 h)	(40 h)	(20 h)
4. TRANSFORMATIONS AND VECTORS	n Translation.	n Vector and translation.	n Vector in a plane.
	(5 h)	(5 h)	(5 h)
5. TRIGONOMETRY			n Sine, cosine and tangent of an acute angle in a right triangle.
			(5 h)

STATISTICS

Grade Level	Seventh Year	Eighth Year	Ninth Year
Subject
HANDLING DATA	n Relative frequencies. n Representation of data: bar graph, frequency polygon.	n Cumulative exact values and frequencies. n Representation of data: circular diagram, cumulative frequency polygon.	n Distribution in one discrete variable: different representations. n Mean and weighted mean.
	(5 h)	(10 h)	(10 h)

BASIC EDUCATION – ELEMENTARY LEVEL - FIRST CYCLE

OBJECTIVES :

The Mathematics curriculum must, in the following domains, make the student able to:

A. MATHEMATICAL REASONING

- Recognize tendencies or relations in sequences of simple facts.

- Justify an answer.

B. PROBLEM SOLVING

- Take initiatives.

- Use appropriate mathematical techniques in solving concrete problems of daily life.

- Use ad-hoc means to find a result.

C. COMMUNICATION

- Use pictorial or symbolic representations.

- Express himself correctly, both orally and/or in writing.

- Ask and answer questions.

D. SPACIAL

- Find directions with the help of a map.

- Recognize solid figures and plane figures.

E. NUMERICAL

- Recognize natural integers, use Indo-Arabic numeration.

- Recognize the four arithmetic operations.

- Master the computational techniques of addition and substraction.

- Get training in the computational techniques of multiplication and division.

- Apply relations among numbers in well-thought out calculations.

- Use simple fractions to indicate parts of a whole.

F. MEASUREMENT

- Measure length, mass and duration.

- Tell time.

BASIC EDUCATION – ELEMENTARY LEVEL

First Cycle: First Year

SYLLABUS
ARITHMETIC AND ALGEBRA (120 h) 1. LOCATION (10 h) · Domain. · Displacement. · Position in space. 2. SOLID FIGURES (5 h) · Rectangular prism. Cube. Sphere. Cylinder. Cone. 3. PLANE FIGURES (5 h) · Lines. · Square. Rectangle. Triangle. Disc. 4. TRANSFORMATIONS (5 h) · Axis of symmetry.	GEOMETRY (25 h) 1. LOCATION (10 h) · Domain. · Displacement. · Position in space. 2. SOLID FIGURES (5 h) · Rectangular prism. Cube. Sphere. Cylinder. Cone. 3. PLANE FIGURES (5 h) · Lines. · Square. Rectangle. Triangle. Disc. 4. TRANSFORMATIONS (5 h) · Axis of symmetry. MEASUREMENT (5 h) 1. LENGTH (5 h) · Comparison of lengths.

BASIC EDUCATION – ELEMENTARY LEVEL

First Cycle: Second Year

SYLLABUS

ARITHMETIC AND ALGEBRA (120 h) 1. NATURAL INTEGERS (25 h) · Numbers less than 1 000. · Reading and writing in words numbers less than 100. · Order; signs < and >; representation on a straight line. · Expanded writing. 2. ADDITION (30 h) · Memorization of tables of addition. · Mastering computational technique. 3. SUBTRACTION (30 h) · Inverse operation of addition. · Function "subtract n". · Computational technique: with trading. 4. MULTIPLICATION (30 h) · Repeated addition. · Table of multiplication: construction (up to 9). · Multiplication by a one-digit factor. 5. DIVISION (5 h) · Initiation: sharing, distribution.

GEOMETRY (20 h) 1. LOCATION (5 h) · Locating a point. 2. SOLID FIGURES (5 h) · Description of solid figures: vertices, edges and faces. 3. PLANE FIGURES (5 h) · Segment. · Description of plane figures: vertices and sides. 4. TRANSFORMATIONS (5 h) · Figures having an axis of symmetry. MEASUREMENT (10 h) 1. LENGTH (5 h) · Mesurement of length: meter, centimeter. 2. MASS (5 h) · Comparison of masses.

BASIC EDUCATION – ELEMENTARY LEVEL

First Cycle: Third Year

SYLLABUS

ARITHMETIC AND ALGEBRA (110 h) 1. NATURAL INTEGERS (15 h) · Numbers less than 100 000. · Reading and writing in standard form and in words. · Compatibility of order with addition, subtraction and multiplication. 2. FRACTIONS (5 h) · Fractions . 3. ADDITION (10 h) · Properties: commutativity and associativity. 4. SUBTRACTION (20 h) · Mastering the computational technique. 5. MULTIPLICATION (30 h) · Function "multiply by n". · Multiplication by 10 and by a multiple of 10. · Distributivity of multiplication over addition. · Memorization of tables of multiplication. · Computational technique: two-digit factors. 6. DIVISION (30 h) · Exact division and Euclidean division. · Computational technique.

GEOMETRY (20 h) 1. LOCATION (5 h) · Midpoint of a segment. · Perpendicular straight lines. 2. SOLID FIGURES (7 h) · Construction of a cube and a rectangular prism. 3. PLANE FIGURES (3 h) · Right angle. Application to the rectangle and the square. 4. TRANSFORMATIONS (5 h) · Reflection. MEASUREMENT (20 h) 1. LENGTH (10 h) · Units of length: kilometer, meter, centimeter, millimeter. · Distance between two points. · Length of a polygonal line. Perimeter. 2. MASS (5 h) · Kilogram, gram. 3. TIME AND DURATION (5 h) · Telling time. · Duration of an event. · Units of time: hour, minute, second.

ELEMENTARY LEVEL - SECOND CYCLE

OBJECTIVES:

The curriculum assures the students who finish this cycle a necessary and durable formation, so that if they have to leave school at 12 years of age to take part in production, they would have enough aptitude not to return to the state of mathematical illiteracy. Thus, in the following domains, students must be able to:

A. MATHEMATICAL REASONING

- Find tendencies in a sequence of results and generalize them.

- Extract general statements out of specific contexts.

- Establish procedures.

- Argue by analogy, giving examples and counterexamples.

B. PROBLEM SOLVING

- Visualize situations and handle information.

- Use and apply Mathematics in various domains, especially in technology and other branches of learning.

- Verify the results.

- Use mini-calculators to carry out the four operations.

C. COMMUNICATION

- Read, understand and interpret a mathematical text by translating it into figures, representations or equations .

- Translate a given mathematical relation into spoken language.

D. SPACIAL

- Represent locations on a map.

- Characterize various plane figures and use geometric instruments to represent them.

- Develop the understanding of some solid figures.

E. NUMERICAL

- Master the Indo-Arabic system of numeration.

- Recognize decimal numbers.

- Master all types of calculation; computational, mental and with a mini-calculator (integers and decimals).

- Perform simple operations with fractions.

- Estimate a result.

F. MEASUREMENT

- Measure perimeters, areas, capacity and angles.

- Use metroic units.

G. STATISTICS

- Collect and interpret data.

BASIC EDUCATION – ELEMENTARY LEVEL

Second Cycle: Fourth Year

SYLLABUS

ARITHMETIC AND ALGEBRA (110 h) 1. NATURAL INTEGERS (15 h) · Numbers greater than 100 000. · Multiples of a whole number. · Criteria for the divisibility by 2, 5 and 10. · Sexagesimal numeration. 2. FRACTIONS (15 h) · Fractions ( a b). · Comparison of fractions. 3. DECIMALS (10 h) · Decimal numbers. 4. ADDITION (15 h) · Addition of decimals. · Addition of fractions having the same denominator. · Addition of duration and time. 5. SUBTRACTION (15 h) · Subtraction of decimals. · Subtraction of fractions having the same denominator. · Subtraction of duration and time. 6. MULTIPLICATION (10 h) · Multiplication of a decimal by a whole number. · Multiplication of several whole numbers. · Distributivity of multiplication over addition and substraction. 7. DIVISION (30 h) · Computational technique on whole numbers: divisors having two or more digits, whole number quotient. · Function "divide by n".

GEOMETRY (20 h) 1. LOCATION (5 h) · Distance from a point to a straight line. · Localization of a point on a square grid. 2. SOLID FIGURES (5 h) · Building models. 3. PLANE FIGURES (5 h) · Intersecting straight lines. Parallel straight lines. · Classification of quadrilaterals according to the sides. · Circle. Disc. 4. TRANSFORMATIONS (5 h) · Drawing of the symmetric of a figure with respect to an axis. MEASUREMENT (15 h) 1. LENGTH (6 h) · Metric units of length. 2. MASS (3 h) · Metric units of mass. 3. AREA (3 h) · Comparison of areas. 4. CAPACITY (3 h) · Litre and submultiples. STATISTICS (5 h) 1. HANDLING DATA (5 h) · Collecting and organizing data.

BASIC EDUCATION – ELEMENTARY LEVEL

Second Cycle: Fifth Year

SYLLABUS

ARITHMETIC AND ALGEBRA (110 h) 1. NATURAL INTEGERS (20 h) · Criteria for divisibility by 3, 4 and 9. · Common multiples of two whole numbers. · Divisors of a whole number. · Common divisors of two whole numbers. · System of decimal numeration. 2. FRACTIONS (10 h) · Equality and simplification of fractions. · Mixed numbers. 3. DECIMALS (10 h) · Comparison and representation of decimal numbers. 4. ADDITION (15 h) · Addition of fractions. · Addition of decimals with several decimal places. 5. SUBTRACTION (15 h) · Subtraction of fractions. · Subtraction of decimals with several decimal places. 6. MULTIPLICATION (20 h) · Multiplication of decimals. · Function "multiply by ". · Product of duration by a whole number. 7. DIVISION (10 h) · Decimal quotient of a division.

GEOMETRY (25 h) 1. LOCATION (3 h) · Distance of two parallel lines. 2. SOLID FIGURES (7 h) · Development of solids. 3. PLANE FIGURES (10 h) · Angle. · Diagonals of a polygon. · Classification of quadrilaterals according to diagonals. · Diameter of a circle. 4. TRANSFORMATIONS (5 h) · Homothecy. MEASUREMENT (20 h) 1. LENGTH (3 h) · Length of a circle. 2. AREA (10 h) · Area of a square, rectangle, right triangle, disc. 3. ANGLE (2 h) · Measure of an angle in degrees. 4. CAPACITY (5 h) · Metric units of capacity. STATISTICS (5 h) 1. HANDLING DATA (5 h) · Recording data: pictographs, bar graphs, tile graphs.

BASIC EDUCATION – ELEMENTARY LEVEL

Second Cycle: Sixth Year

SYLLABUS

ARITHMETIC AND ALGEBRA (110 h) 1. NATURAL INTEGERS (15 h) · Expanding a natural integer according to the powers of 10. · G.C.F. and L.C.M. of two natural integers. · Relatively prime numbers. 2. FRACTIONS (10 h) · Irreducible fractions. · Decimal fractions. 3. DECIMALS (10 h) · Fractional writing of a decimal number. · Expanding a decimal number according to the powers of 10 and of . 4. INTEGERS (15 h) · Positive and negative numbers. · Representation on the numerical axis. · Comparison. 5. ADDITION (5 h) · Addition of integers. 6. SUBTRACTION (5 h) · Subtraction of integers. 7. MULTIPLICATION (10 h) · Multiplication of fractions. · Powers of exponents 2 and 3. · Powers of 10. 8. DIVISION (10 h) · Division of fractions. · Quotient and ratio. · Division of duration by a whole number. 9. PROPORTIONALITY (20 h) · Percentage. Rates. · Proportional sequences. · Scale. 10. ALGEBRAIC EXPRESSIONS (10 h) · Order of operations. · Calculation on literal expressions. · Numerical value of a literal expression.

GEOMETRY (25 h) 1. LOCATION (2 h) · Relative positions of two straight lines in a plane. · Relative positions of a straight line and a circle. 2. SOLID FIGURES (3 h) · Patterns of solids. 3. PLANE FIGURES (10 h) · Adjacent angles, vertically opposite angles. · Bisector of an angle. · Perpendicular bisector of a segment. · Triangle: particular triangles; particular straight lines in a triangle; sum of angles of a triangle. 4. TRANSFORMATIONS (10 h) · Central symmetry. · Study of figures from their elements of symmetry MEASUREMENT (20 h) 1. AREA (8 h) · Area of a parallelogram, of a triangle. · Metric units of area. 2. ANGLE (2 h) · Complementary angles; supplementary angles 3. VOLUME (10 h) · Calculation of volume: cube, rectangular prism, right circular cylinder, ball. · Metric units of volume. STATISTICS (5 h) 1. HANDLING DATA (5 h) · Interpreting data: circular diagram.

BASIC EDUCATION - INTERMEDIATE LEVEL

OBJECTIVES:

The curriculum proposes, in the following domains, that students should be able to:

A. MATHEMATICAL REASONING

- Find connections between the real world and mathematical models, and between these models and concepts.

- Induce the general term of a sequence of results duly constructed.

- Distinguish between a general statement and a particular one.

- Carry out simple proofs.

- Recognize a false proof.

B. PROBLEM SOLVING

- Analyze a situation and deduce the relevant elements.

- Look for necessary information to clarify an incomplete given.

- Construct a mathematical model associated with a situation.

- Choose a strategy to find the solution.

- Decompose a problem into simpler tasks, and conversely, combine necessary facts to reach a conclusion.

- Use calculating machines with memory.

C. COMMUNICATION

- Read, understand and use mathematical notations and language.

- Present their work orally or in writing, with clarity and rigor, with particular care to writing a proof.

D. SPACIAL

- Construct geometric figures based on given.

- Represent solid figures.

- Prove and apply the properties of plane figures.

- Perform affine transformations on figures.

E. NUMERICAL

- Find and use relations among numbers.

- Extend computational techniques to literal expressions.

- Find approximate values of a result.

F. MEASUREMENT

- Measure areas and volumes.

G. STATISTICS

- Make representations of statistical problems and read them.

- Calculate the mean of a statistical distribution.

BASIC EDUCATION

Intermediate Level: Seventh Year

SYLLABUS

ARITHMETIC AND ALGEBRA (90 h) 1. NATURAL INTEGERS (10 h) · Prime numbers. · Decomposition of a whole number into factors. 2. FRACTIONS (10 h) · Reducing fractions. 3. DECIMALS (5 h) · Decimal writing of a fraction. 4. OPERATIONS (30 h) · Subtraction and multiplication of integers. · Powers of a positive number having a positive integer exponent. · Common factor. Factorization. 5. PROPORTIONALITY (10 h) · Directly proportional magnitudes. 6. ALGEBRAIC EXPRESSIONS (15 h) · Calculation on algebraic expressions. 7. EQUATIONS AND INEQUATIONS (10 h) · Equations reduced to ax = b.

GEOMETRY (55 h) 1. LOCATION (10 h) · Geometric locii and constructions. · Orthogonal system and coordinates of a point in a plane. 2. SOLID GEOMETRY (5 h) · Plane representation of a cube, and a rectangular prism. 3. PLANE FIGURES (35 h) · Cases of congruent triangles. · Angles formed by two parallel straight lines cut by a transversal. · Characteristic properties of the perpendicular bisector of a segment. · Characteristic properties of the bisector of an angle. 4. TRANSFORMATIONS AND VECTORS (5 h) · Translation. STATISTICS (5 h) 1. HANDLING DATA (5 h) · Relative frequencies. · Representation of data: bar graph, frequency polygon.

BASIC EDUCATION

Intermediate Level: Eighth Year

SYLLABUS

ARITHMETIC AND ALGEBRA (70 h) 1. NATURAL INTEGERS (5 h) · G.C.F. and L.C.M. of several whole numbers. 2. FRACTIONS (5 h) · Literal fractions. · Composite fractions. 3. DECIMALS (5 h) · Compatibility of the order of operations. 4. SQUARE ROOTS (10 h) · Square roots of a positive number. 5. OPERATIONS (5 h) · Powers of a positive number having a positive integer exponent. · Powers of a negative integer exponent of 10. 6. PROPORTIONALITY (5 h) · Inversely proportional magnitudes. 7. ALGEBRAIC EXPRESSIONS (20 h) · Remarkable identities. · Literal expressions in fractional form. 8. EQUATIONS AND INEQUATIONS (15 h) · Equations of the form: (ax + b)(cx + d) = 0. · First degree equations and inequations in one unknown.

GEOMETRY(70 h) 1. LOCATION (15 h) · Relative positions of two circles. · Geometric locii and constructions. · Coordinates of the midpoint of a segment. 2. SOLID GEOMETRY (10 h) · Plane representation of a cylinder, a pyramid, a cone and a sphere. · Relative positions of straight lines and of planes. 3. PLANE FIGURES (40 h) · Pythagoras’ theorem. · Theorem of midpoints in a triangle, in a trapezoid. · Characteristic properties of a parallelogram. · Central angle in a circle, inscribed angle in a circle. Area of a circular sector. 4. TRANSFORMATIONS AND VECTORS (5 h) · Vector and translation. STATISTICS (10 h) 1. HANDLING DATA (10 h) · Cumulative exact values and frequencies. · Representation of data: circular diagram, cumulative frequency polygon.

BASIC EDUCATION

Intermediate Level: Ninth Year

SYLLABUS

ARITHMETIC AND ALGEBRA (70 h) 1. NATURAL INTEGERS (5 h) · Rational and irrational numbers. 2. OPERATIONS (10 h) · Rationalizing the denominator of a numerical fraction. · Calculation on real numbers. 3. PROPORTIONALITY (5 h) · Linear functions and proportionality. 4. ALGEBRAIC EXPRESSIONS (10 h) · Algebraic expressions having radicals. · Polynomial in one variable. 5. EQUATIONS AND INEQUATIONS (40 h) · Equations of the form: . · Systems of equations of the first degree in two unknowns. · Systems of inequations of the first degree in one unknown.

GEOMETRY(70 h) 1. LOCATION (35 h) · Tangents and circles. · Geometric locii and constructions. · Graphic representation of a straight line. · Analytical properties of two parallel and of two orthogonal straight lines. · Length of a segment in an orthonormal system. · Solving graphically a system of linear equations in two unknowns. 2. SOLID GEOMETRY (5 h) · Intersection of a straight line and a common solid. · Intersection of a plane and a common solid. 3. PLANE FIGURES (20 h) · Cyclic quadrilaterals. · Thales’ theorem. · Similar triangles. 4. TRANSFORMATIONS AND VECTORS (5 h) · Vector in a plane. 5. TRIGONOMETRY (5 h) · Sine, cosine and tangent of an acute angle in a right triangle. STATISTICS (10 h) 1. HANDLING DATA (10 h) · Distribution in one discrete variable: different representations. · Mean and weighted mean.

SECONDARY EDUCATION – LITERATURE AND HUMANITIES SECTION

OBJECTIVES:

In this section, students learn to appreciate Mathematics as a basic activity of the intellect and to use the results to study information obtained from Humanities. This is why, in the following domains, they must be able to:

A. MATHEMATICAL REASONING

- Recognize various forms of mathematical reasoning.

B. . PROBLEM SOLVING

- Use an adequate mathematical interpretation to represent the given of a problem.

- Find the solution of a problem following a given algorithm.

C. COMMUNICATION

- Get the formulas and relations out of a mathematical text.

- Do their work with precision.

D. SPACIAL

- Represent solid figures.

E. NUMERICAL AND ALGEBRAIC

- Analyze the extensions of the sets of numbers: N Ì Z Ì Q Ì R.

- Generalize basic notions already used: set, relation, binary operation and propositional calculation.

- Acquire the notion of the structure of group.

- Solve simple problems in one or two unknowns.

F. CALCULUS

- Study and represent simple functions.

- Relate exponential growth to the exponential function.

- Calculate simple and compounded interests.

G. STATISTICS AND PROBABILITY

- Organize information and represent it graphically.

- Study the characteristics of a statistical series in one variable.

- Solve simple probability problems mainly in discrete cases where the events are equally likely.

SECONDARY EDUCATION

Scope and Sequence - Literature and Humanities Section

ALGEBRA

Grade Level	First Year	Second Year	Third Year
Subject
1. FOUNDATIONS	n Sets. n Cartesian product. n Mapping, bijection.	n Binary relations.	n Binary operation. n Structure of group. n Propositional calculus.
	(7 h)	(10 h)	(10 h)
2. LITERAL AND NUMERICAL CALCULATIONS	n Square roots of a real number. Powers of a real number. n Order on R. Intervals. n Absolute value. n Framing. Approximation. n Counting.	n Arrangements and permutations.
	(23 h)	(10 h)
3. EQUATIONS AND INEQUATIONS	n Equation of the first degree. n Equation and inequation of the first degree involving absolute value. n System of linear equations (2 x 2). n Solving and interpreting graphically a system of linear inequations in two unknowns.	n Linear programming. n Solving a quadratic equation with real coefficients. n Sum and product of the roots of the quadratic trinomial.	n Situations-problems leading to the solution of equations and inequations.
	(15 h)	(15 h)	(10 h)
4. POLYNOMIALS	n Polynomials. n Root of a polynomial.	n Study of the sign of the quadratic trinomial.
	(8 h)	(5 h)
5. NUMBERS	n Sets of numbers: N, Z, Q, R.
	(2 h)

GEOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. CLASSICAL STUDY	n Plane representation of objects in space. n Intersection of a straight line or of a plane with common solids. n Straight lines and planes: relative positions, parallelism.
	(17 h)
2. VECTORIAL STUDY	n Vectors in the plane. n Projections in the plane. n Bases and reference frame in the plane.
	(20 h)
3. ANALYTICAL STUDY	n Equations of a straight line in the plane. n Scalar product.
	(18 h)

CALCULUS (NUMERICAL FUNCTIONS)

Grade Level	First Year	Second Year	Third Year
Subject
1. DEFINITIONS AND REPRESENTATION	n Functions. Graphical representation. n Solving graphically equations and inequations. n Study of functions.	n Limit of a function at a point. Limit at infinity. Vertical and horizontal asymptotes. n Calculation with limits. n Arithmetic sequences. Geometric sequences.	n Simple rational functions. n Graphical interpretation. n Exponential growth and exponential function.
	(20 h)	(15 h)	(15 h)
2. CONTINUITY AND DERIVATION		n Continuity of functions. n Derivative of a function at a point. n Derivative function. Derivatives of functions, differentiation rules. n Study of functions: polynomial functions, homographic functions.
		(25 h)
3. . INTEGRATION		n Primitives of a function continuous over an interval: calculation of primitives.
		(10 h)
4. MATHEMATICAL MODELS FOR ECONOMICS AND SOCIAL SCIENCES			n Simple interest, compounded interest.
			(10 h)

TRIGONOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. TRIGONOMETRIC LINES	n Trigonometric circle. Oriented arc. n Trigonometric lines of an arc.
	(10 h)

STATISTICS AND PROBABILITY

Grade Level	First Year	Second Year	Third Year
Subject
1. STATISTICS	n Statistics of vocabulary. n Graphical representation of a distribution of one discrete variable. n Frequencies and cumulative frequencies. n Measures of central tendancy, measures of variability.	n Continuous variable; distribution in classes. n Frequency distribution; histogram, polygons. n Cumulative frequency distribution; histogram, polygons.	n Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable.
	(10 h)	(15 h)	(10 h)
2. PROBABILITY		n Notion of probability. n Universe of possibilities. Cases of equally likely events. n Properties of probability. n Calculation of probabilities: event (A and B), event (A or B), incompatible events, opposite events.	n Conditional probability: definition, independence of two events.
		(15 h)	(5 h)

SECONDARY EDUCATION – SOCIOLOGY AND ECONOMICS SECTION

OBJECTIVES:

In this section, students learn to appreciate Mathematics as an indispensable tool for handling information in Economics and Social Sciences. Thus, in the following domains, students must be able to:

A. MATHEMATICAL REASONING

- Recognize the difference between a mathematical explanation and a concrete or experimental evidence.

- Make conjectures and discover means to test them.

B. PROBLEM SOLVING

- Formulate a problem in situations studied in Economics and Social Sciences.

- Use an adequate mathematical interpretation to represent the given of a problem.

- Apply their mathematical knowledge to find the solution of a problem following a convenient algorithm.

- Discuss the validity of obtained solutions.

C. COMMUNICATION

- Understand a consulted mathematical document and retain its main points.

- Take notes on a mathematical talk.

D. SPACIAL

- Prove and apply the properties of solid figures.

E. NUMERICAL AND ALGEBRAIC

- Analyze the extensions of the sets of numbers: N Ì Z Ì Q Ì R.

- Generalize basic notions already used: set, relation, binary operation.

- Acquire the notion of the structure of group.

- Develop mathematical tools for numerical calculations and for solutions of systems of equations and inequations.

F CALCULUS

- Use and interpret graphically the notions of limit, continuity, derivation in order to study numerical functions.

- Analyze the graphs of polynomial, rational, irrational, trigonometric, logarithmic and exponential functions.

- Intergrate a function and solve simple differential equations.

- Solve finite difference equations.

- Study functions encountered in Economics and Social Sciences.

- Solve problems in the financial Mathematics.

G. STATISTICS AND PROBABILITY

- Organize information and represent it graphically.

- Study the characteristics of a statistical distribution of one or two variables.

- Solve simple probability problems mainly in discrete cases where the events are equally likely.

SECONDARY EDUCATION

Scope and Sequence - Sociology and Economics Section

ALGEBRA

Grade Level	First Year	Second Year	Third Year
Subject
1. FOUNDATIONS	n Sets. n Cartesian product. n Mappings, bijection.	n Binary relations.	n Binary operation. n Structure of group.
	(7 h)	(10 h)	(8 h)
2. LITERAL AND NUMERICAL ALCULATIONS	n Square roots of a real number. Powers of a real number. n Order on R. Intervals. n Absolute value. n Framing. Approximation. n Counting.	n Arrangements and permutations.	n Combinations: definition, notation, binomial formula.
	(23 h)	(10 h)	(7 h)
3. EQUATIONS AND INEQUATIONS	n Equation of the first degree. n Equation and inequation of the first degree involving absolute value. n System of linear equations (2 x 2). n Solving and interpreting graphically a system of linear inequations in two unknowns.	n Linear programming. n Solving a quadratic equation with real coefficients. n Sum and product of the roots of the quadratic trinomial.	n System of linear equations (m x n): definition elementary operations on the rows, Gauss’ method.
	(15 h)	(15 h)	(10 h)
4. POLYNOMIALS	n Polynomials. n Root of a polynomial.	n Study of the sign of the quadratic trinomial.
	(8 h)	(5 h)
5. NUMBERS	n Sets of numbers: N, Z, Q, R
	(2 h)

GEOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. ETUDE CLASSIQUE	n Plane representation of objects in space. n Intersection of a straight line or of a plane with common solids. n Straight lines and planes: relative positions, parallelism.
	(17 h)
2. LITERAL AND NUMERICAL ALCULATIONS	n Vectors in the plane. n Projections in the plane. n Bases and reference frame in the plane.
	(20 h)
3. ANALYTICAL STUDY	n Equations of a straight line in the plane. n Scalar product.
	(18 h)

CALCULUS (NUMERICAL FUNCTIONS)

Grade Level	First Year	Second Year	Third Year
Subject
1. DEFINITIONS AND REPRESENTATION	n Functions. Graphical representation. n Solving graphically equations and inequations. n Study of functions.	n Limit of a function at a point. Limit at infinity. Vertical and horizontal asymptotes. n Calculation with limits. n Arithmetic sequences. Geometric sequences.	n Rational functions. n Inverse function. n Natural (Napierian) logarithmic function. Logarithmic function to the base a. n Exponential functions. n Numerical sequences. Geometric sequences: limits.
	(20 h)	(15 h)	(20 h)
2. CONTINUITY AND DERIVATION		n Continuity of functions. n Derivative of a function at a point. n Derivative function. Derivatives of functions, differentiation rules. n Study of functions: polynomial functions, homographic functions.	n Derivatives of composite functions. n Second derivative. n L’Hospital’s rule.
		(25 h)	(5 h)
3. INTEGRATION		n Primitives of a function continuous over an interval: calculation of primitives.	n Integral: definition, properties, calculation.
		(10 h)	(10 h)
4. DIFFERENTIAL EQUATIONS			n Definition. n Equations in separable variables. n Linear first order equations with constant coefficients. n Finite differences equations.
			(10 h)
5. MATHEMATICAL MODELS FOR ECONOMICS AND SOCIAL SCIENCES			n Functions of economics and social sciences. n Finance mathematics.
			(15 h)

TRIGONOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. TRIGONOMETRIC LINES	n Trigonometric circle. Oriented arc. n Trigonometric lines of an arc.
	(10 h)

STATISTICS AND PROBABILITY

Grade Level	First Year	Second Year	Third Year
Subject
1. STATISTICS	n Statistics vocabulary. n Graphical representation of a distribution of one discrete variable. n Frequencies and cumulative frequencies. n Measures of central tendancy, measures of variability.	n Continuous variable; distribution in classes. n Frequency distribution; histogram, polygons. n Cumulative frequency distribution; histogram, polygons.	n Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable. n Distribution of two variables: introduction, scatter plot, mean point. n Covariance of two variables, linear correlation coefficient. n Linear adjustment and regression lines.
	(10 h)	(15 h)	(15 h)
2. PROBABILITY		n Notion of probability. n Universe of possibilities. Cases of equally likely events. n Properties of probability. n Calculation of probabilities: event (A and B), event (A or B), incompatible events, opposite events.	n Conditional probability: definition, independence of two events. n Formula of total probabilities. n Random real variable, law of associated probability, distribution function. Characteristics.
		(15 h)	(20 h)

SECONDARY EDUCATION – GENERAL SCIENCES SECTION

OBJECTIVES:

This section gives students a solid mathematical formation with the aim of preparing them to pursue their studies as teachers, engineers and researchers. This is why, in the following domains, students must be able to:

A. MATHEMATICAL REASONING

- Recogize the difference between a mathematical explanation and a concrete or experimental evidence.

- Make conjectures and discover means to test them.

- Carry out proofs using various modes of reasoning.

- Analyze and prove a statement of necessary and sufficient conditions.

- Recognize a universal statement, a statement of existence and a statement of uniqueness.

- Evaluate a mathematical argument and criticize a proof.

- Carry out an inductive proof.

B. PROBLEM SOLVING

- Formulate a problem out of situations studied in Mathematics, in other sciences or encountered in real life.

- Use various mathematical interpretations to represent the given of a problem, figure out a convenient strategy to solve it, and take various approaches to make this strategy work using mathematical knowledge.

- Discuss the validity of the obtained solutions.

C. COMMUNICATION

- Give an account of a consulted mathematical document.

- Take notes on a mathematical talk.

- Do a critique of a mathematical presentation.

- Write a proof correctly.

D. SPATIAL

- Prove and apply the properties of solid figures and conics.

- Characterize plane or space figures using vectorial notions.

- Study geometric problems analytically.

- Determine the effect of transformations on plane figures.

E. NUMERICAL AND ALGEBRAIC

- Analyze the extensions of the sets of numbers N Ì Z Ì Q Ì R Ì C.

- Study the properties of complex numbers and their use in Geometry and Trigonometry.

- Generalize the fundamental notions already used: set, relation, binary operation and propositional calculus.

- Acquire an example of structure.

- Develop mathematical tools for numerical calculations, and for solutions of systems of equations and inequations.

F. CALCULUS

- Acquire the fundamental concepts of limit, continuity, derivation, and use them to represent graphically the variations of any numerical function.

- Analyze the graphs of polynomial, rational, irrational, trigonometric, logarithmic and exponential functions.

- Integrate a function and solve simple differential equations.

G. STATISTIQUE ET PROBABILITE

- STATISTICS AND PROBABILITY

- Organize information and represent it graphically.

- Study the characteristics of a statistical distribution of one variable.

- Solve simple probability problems mainly in discrete cases where the events are equally likely.

SECONDARY EDUCATION

Scope and Sequence - General Sciences Section

ALGEBRA

Grade Level	First Year	Second Year	Third Year
Subject
1. FOUNDATIONS	n Sets. n Cartesian product. n Mappings, bijection.	n Binary relations	n Binary operation. n Structure of group. n Propositional calculus.
	(7 h)	(6 h)	(15 h)
2. LITERAL AND NUMERICAL CALCULATIONS	n Square roots of a real number. Powers of a real number. n Order on R. Intervals. n Absolute value. n Framing. Approximation. n Counting.	n Arrangements and permutations.	n Combinations: definition, notation, binomial formula, n Pascal’s triangle.
	(23 h)	(6 h)	(10 h)
3. EQUATIONS AND INEQUATIONS	n Equation of the first degree. n Equation and inequation of the first degree involving absolute value. n System of linear equations (2 x 2). n Solving and interpreting graphically a system of linear inequations in two unknowns.	n System of linear equations (3 x 3). Linear programming. n Polynomials, quadratic equations and inequations.	n System of linear equations (m x n): definition, elementary operations on the rows, Gauss’ method. n Quadratic equation with complex coefficients.
	(15 h)	(20 h)	(10 h)
4. POLYNOMIALS	n Polynomials. n Root of a polynomial	n Euclidean division of a polynomial by another. n Factorization. Simplification of rational fractions.
	(8 h)	(4 h)
5. NUMBERS	n Sets of numbers: N, Z, Q, R.	n Complex numbers: definition, algebraic form. n Operations on complex numbers. n Geometric representation of a complex number.	n Module and argument of a complex number. Properties. n Trigonometric and exponential forms of a complex number. n Geometric interpretation of addition, multiplication of complex numbers and the passing to the conjugate. n De Moivre’s formula. Applications. n N^th roots of a complex number, geometric representation of the n^th root of the unit. n Geometric interpretation of and of applications.
	(2 h)	(8 h)	(25 h)

GEOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. CLASSICAL STUDY	n Plane representation of objects in space. n Intersection of a straight line or of a plane with common solids. n Straight lines and planes: relative positions, parallelism.	n Orthogonality in space. n Projections in space. n Solids.	n Conics: definition, focii, directrix, eccentricity, focal axis. n Equation of a conic, vertices, center, elements of symmetry, reduced equation. n Quadratic curves.
	(17 h)	(18 h)	(20 h)
2. VECTORIAL STUDY	n Vectors in the plane. n Projections in the plane. n Bases and reference frame in the plane.	n Vectors and reference frame in space. n Barycenter. n Vector product.	n Level curves . n Vector equation of a straight line, of a plane, of a sphere.
	(20 h)	(16 h)	(5 h)
3. ANALYTICAL STUDY	n Equations of a straight line in the plane. n Scalar product.	n Equation of the circle. n Scalar product in space.	n Components of the vector product. Mixed product. n Equation of a plane and of a straight line in space. n Orthogonality of two straight lines, of a straight line and a plane; perpendicular planes. n Parallelism of straight lines and of planes. n Distance from a point to a plane, to a straight line. n Equation of a sphere. n Intersection of a sphere with a straight line, a plane or a sphere.
	(18 h)	(9 h)	(30 h)
4. TRANSFORMATIONS PLANES		n Isometry. Translation. n Plane rotation. n Reflection.	n Displacement in the plane. n Homothecy. n Complex form of plane transformation. n Direct plane similitudes: definition, complex form. n Transformations defined by and .
		(16 h)	(35 h)

CALCULUS (NUMERICAL FUNCTIONS)

Grade Level	First Year	Second Year	Third Year
Subject
1. DEFINITIONS AND REPRESENTATION	n Functions. Graphical representation. n Solving graphically equations and inequations. n Study of functions.	n Limit of a function. Asymptotes. n Numerical sequences. Arithmetic sequences. Geometric sequences.	n Irrational functions (simple cases). n Inverse function. n Inverse trigonometric functions. n Natural (Napierian) logarithmic function. Logarithmic function to the base a. n Exponential functions. Power functions. n Numerical sequences: limits, bounded sequences, convergent sequences. n Parametric curves.
	(20 h)	(14 h)	(40 h)
2. CONTINUITY AND DERIVATION		n Continuity. n Derivative of a function at a point. n Derivative function. n Study of functions: polynomial functions, rational functions	n Image of a closed interval by a continuous function. n Extension by continuity of a function. n Derivatives of composite functions. n Derivative of an inverse function. n Second derivative. Successive derivatives. n Rolle’s theorem. Mean value theorem. L’Hospital’s rule.
		(22 h)	(25 h)
3. INTEGRATION		n Primitives of a function continuous over an interval.	n Integral: definition, properties. n Rules of integration. n Mean value theorem for definite integrals. Max-Min inequality. n Applications of the integral calculation.
		(6 h)	(30 h)
4. DIFFERENTIAL EQUATIONS			n Definition. n Equations in separable variables. n Linear first order equations with constant coefficients. n Linear second order equations with constant coefficients.
			(10 h)

TRIGONOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. TRIGONOMETRIC LINES	n Trigonometric circle. Oriented arc. n Trigonometric lines of an arc.	n Oriented angle of two vectors. n Trigonometric formulas.	n Metric relations in a triangle. Calculation of areas.
	(10 h)	(4 h)	(5 h)
2. TRIGONOMETRIC EQUATIONS		n Solving equations of the form sinx = a, cosx = a, tanx = a.	n Solving simple trigonometric equations.
		(7 h)	(5 h)
3. CIRCULAR FUNCTIONS		n Study of circular functions.	n Study of circular functions of the form a cos (bx + c) and a sin (bx + c).
		(4 h)	(5 h)

STATISTICS AND PROBABILITY

Grade Level	First Year	Second Year	Third Year
Subject
1. STATISTICS	n Statistics vocabulary. n Graphical representation of a distribution of one discrete variable. n Frequencies and cumulative frequencies. n Measures of central tendancy, measures of variability.	n Continuous variable; distribution in classes. n Frequency distribution; histogram, polygons. n Cumulative frequency distribution; histogram, polygons.	n Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable.
	(10 h)	(8 h)	(10 h)
2. PROBABILITY		n Notion of probability. n Universe of possibilities. Cases of equally likely events. n Properties of probability. n Calculation of probabilities: event (A and B), event (A or B), incompatible events, opposite events.	n Conditional probability: definition, independence of two events. n Formula of total probabilities. n Random real variable, law of associated probability, distribution function. Characteristics.
		(12 h)	(20 h)

SECONDARY EDUCATION – LIFE SCIENCES SECTION

OBJECTIVES :

In this section, students receive a solid mathematical formation and acquire necessary knowledge to understand and treat problems encountered in experimental sciences and real life. This is why, in the following domains, they must be able to:

A. MATHEMATICAL REASONING

- Recognize the difference between a mathematical explanation and a concrete or experimental evidence.

- Make conjectures and discover means to test them.

- Carry out proofs using various modes of reasoning.

- Recognize a universal statement, a statement of existence and a statement of uniqueness.

B. PROBLEM SOLVING

- Formulate a problem based on situations studied in other sciences.

- Use adequate mathematical means to represent the given of a problem.

- Apply their knowledge to find the solution to a problem by following a convenient strategy.

C. COMMUNICATION

- Understand a consulted mathematical document and emphasize its essential points.

- Take notes on a mathematical talk.

- Write a proof correctly.

D. SPACIAL

- Prove and apply the properties of solid figures.

- Use vectorial notions as tools of study in various disciplines.

- Study a geometric problem analytically.

E. NUMERICAL AND ALGEBRAIC

- Analyze the extensions of the sets of numbers: N Ì Z Ì Q Ì R Ì C.

- Study the properties of complex numbers .

- Generalize the fundamental notions already used : set, relation, binary operation.

- Acquire the notion of the structure of group.

- Develop mathematical tools for numerical calculations and for solutions of systems of equations and inequations.

F. CALCULUS

- Acquire the fundamental concepts of limit, continuity, derivation, and use them to study graphically functional relations coming from other sciences.

- Analyze the graphs of polynomial, rational, irrational, trigonometric, logarithmic and exponential functions.

- Integrate a function and solve simple differential equations.

G. STATISTICS AND PROBABILITY

- Organize information and represent it graphically.

- Study the characteristics of a statistical distribution of one variable.

- Solve simple probability problems mainly especially in discrete cases where the events are equally likely.

- Construct a probability law in simple cases and explain its characteristics.

SECONDARY EDUCATION

Scope and Sequence - Life Sciences Section

ALGEBRA

Grade Level	First Year	Second Year	Third Year
Subject
1. FOUNDATIONS	n Sets. n Cartesian product. n Mappings, bijection.	n Binary relations	n Binary operation. n Structure of group.
	(7 h)	(6 h)	(8 h)
2. LITERAL AND NUMERICAL CALCULATIONS	n Square roots of a real number. Powers of a real number. n Order on R. Intervals. n Absolute value. n Framing. Approximation. n Counting.	n Arrangements and permutations	n Combinations: definition, notation, binomial formula, Pascal’s triangle.
	(23 h)	(6 h)	(10 h)
3. EQUATIONS AND INEQUATIONS	n Equation of the first degree. n Equation and inequation of the first degree involving absolute value. n System of linear equations (2 x 2). n Solving and interpreting graphically a system of linear inequations in two unknowns.	n System of linear equations (3 x 3). Linear programming. n Polynomials, quadratic equations and inequations.	n System of linear equations (m x n): definition, elememtary operations on the rows, Gauss’ method.
	(15 h)	(20 h)	(7 h)
4. POLYNOMIALS	n Polynomials. n Root of a polynomial.	n Euclidean division of a polynomial by another. n Factorization. Simplification of rational fractions.
	(8 h)	(4 h)
5. NUMBERS	n Sets of numbers: N, Z, Q, R.	n Complex numbers: definition, algebraic form. n Operations on complex numbers. n Geometric representation of a complex number.	n Module and argument of a complex number, properties. n Trigonometric and exponential forms of a complex number. n Geometric interpretation of addition and multiplication of complex numbers and the passing to the conjugate. n De Moivre’s formula, applications.
	(2 h)	(8 h)	(10 h)

GEOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. CLASSICAL STUDY	n Plane representation of objects in space. n Intersection of a straight line or of a plane with common solids. n Straight lines and planes: relative positions, parallelism.	n Orthogonality in space. n Projections in space. n Solids.
	(17 h)	(18 h)
2. VECTORIAL STUDY	n Vectors in the plane. n Projections in the plane. n Bases and reference frame in the plane.	n Vectors and frame reference in space. n Barycenter. n Vector product.
	(20 h)	(16 h)
3. ANALYTICAL STUDY	n Equations of a straight line in the plane. n Scalar product.	n Equation of the circle. n Scalar product in space.	n Components of the vector product. Mixed product. n Equation of a plane and of a straight line in space. n Orthogonality of two straight lines, of a straight line and a plane; perpendicular planes. n Parallelism of straight lines and of planes. n Distance from a point to a plane, to a straight line.
	(18 h)	(9 h)	(15 h)
4. TRANSFORMATIONS		n Isometry. Translation. n Plane rotation. n Reflection.
		(16 h)

CALCULUS (NUMERICAL FUNCTIONS)

Grade Level	First Year	Second Year	Third Year
Subject
1. DEFINITIONS AND REPRESENTATION	n Functions. Graphical representation. n Solving graphically equations and inequations. n Study of functions.	n Limit of a function. Asymptotes. n Numerical sequences. Arithmetic sequences. Geometric sequences.	n Inverse function. n Inverse trigonometric functions. n Natural (Napierian) logarithmic function. Logarithmic function to the base a. n Exponential functions.
	(20 h)	(14 h)	(25 h)
2. CONTINUITY AND DERIVATION		n Continuity. n Derivative of a function at a point. n Derivative function. n Study of functions: polynomial functions, rational functions.	n Image of a closed interval by a continuous function. n Derivation of composite functions. n Derivative of an inverse function. n Second derivative. Successive derivatives. n L’Hospital’s rule.
		(22 h)	(15 h)
3. INTEGRATION		n Primitives of a function continuous over an interval.	n Integral: definition, properties. n Rules of integration. n Applications of the integral calculation.
		(6 h)	(15 h)
4. DIFFERENTIAL EQUATIONS			n Definition. n Equations in separable variables. n Linear first order equations with constant coefficients. n Linear second order equations with constant coefficients.
			(10 h)

TRIGONOMETRY

Grade Level	First Year	Second Year	Third Year
Subject
1. TRIGONOMETRIC LINES	n Trigonometric circle. Oriented arc. n Trigonometric lines of an arc.	n Oriented angle of two vectors. n Trigonometric formulas.
	(10 h)	(4 h)
2. TRIGONOMETRIC EQUATIONS		n Solutions of equations of the form sinx = a, cosx = a, tanx = a
		(7 h)
3. CIRCULAR FUNCTIONS		n Study of circular functions.	n Study of the circular functions of the form a cos (bx + c) and a sin (bx + c).
		(4 h)	(5 h)

STATISTICS AND PROBABILITY

Grade Level	First Year	Second Year	Third Year
Subject
1. STATISTICS	n Statistics vocabulary. n Graphical representation of a distribution of one discrete variable. n Frequencies and cumulative frequencies. n Measures of central tendancy, measures of variability.	n Continuous variable; distribution in classes. n Frequency distribution; histogram, polygons. n Cumulative frequency distribution; histogram, polygons.	n Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable.
	(10 h)	(8 h)	(10 h)
2. PROBABILITY		n Notion of probability. n Universe of possibilities. Cases of equally likely events. n Properties of probability. n Calculation of probabilities: event (A and B), event (A or B), incompatible events, opposite events.	n Conditional probability: definition, independence of two events. n Formula of total probabilities. n Random real variable, law of associated probability, distribution function. Characteristics. n Bernoulli variable. n Binomial law.
		(12 h)	(20 h)

FIRST SECONDARY

SYLLABUS

ALGEBRA (55 h) 1. FOUNDATIONS (7 h) · Sets. · Cartesian product. · Mappings, bijection. 2. LITERAL AND NUMERICAL CALCULATIONS (23 h) · Square roots of a real number. Powers of a real number. · Order on R. Intervals. · Absolute value. · Framing. Approximation. · Counting. 3. EQUATIONS AND INEQUATIONS (15 h) · Equation of the first degree. · Equation and inequation of the first degree involving absolute value. · System of linear equations (2 x 2). · Solving and interpreting graphically a system of linear inequations in two unknowns. 4. POLYNOMIALS (8 h) · Polynomials. · Root of a polynomial. 5. NUMBERS (2 h) · Sets of numbers: N, Z, Q, R.

GEOMETRY (55 h) 1. CLASSICAL STUDY (17 h) · Plane representation of objects in space. · Intersection of a straight line or of a plane with common solids. · Straight lines and planes: relative positions, parallelism. 2. VECTORIAL STUDY (20 h) · Vectors in the plane. · Projections in the plane. · Bases and reference frame in the plane. 3. ANALYTICAL STUDY (18 h) · Equations of a straight line in the plane. · Scalar product. CALCULUS (NUMERICAL FUNCTIONS) (20 h) 1. DEFINITIONS AND REPRESENTATION (20 h) · Functions. Graphical representation. · Solving graphically equations and inequations. · Study of functions. TRIGONOMETRY(10 h) 1. TRIGONOMETRIC LINES (10 h) · Trigonometric circle. Oriented arc. · Trigonometric lines of an arc. STATISTICS (10 h) 1. STATISTICS (10 h) · Statistics vocabulary. · Graphical representation of a distribution of one discrete variable. · Frequencies and cumulative frequencies. · Measures of central tendancy, measures of variability.

Second Secondary - Humanities Section

SYLLABUS

ALGEBRA (40 h) 1. FOUNDATIONS (10 h) · Binary relations. 2. LITERAL AND NUMERICAL CALCULATIONS (10 h) · Arrangements and permutations. 3. EQUATIONS AND INEQUATIONS (15 h) · Linear programming. · Solving a quadratic equation with real coefficients. · Sum and product of the roots of the quadratic trinomial. 4. POLYNOMIALS (5 h) · Study of the sign of the quadratic trinomial. CALCULUS (NUMERICAL FUNCTIONS) (50 h) 1. DEFINITIONS AND REPRESENTATION) (15 h) · Limit of a function at a point. Limit at infinity. Vertical and horizontal asymptotes. · Calculation with limits. · Arithmetic sequences. Geometric sequences. 2. CONTINUITY AND DERIVATION (25 h) · Continuity of functions. · Derivative of a function at a point. · Derivative function. Derivatives of functions, differentiation rules. · Study of functions: polynomial functions, homographic functions. 3. INTEGRATION (10 h) · Primitives of a function continuous over an interval: calculation of primitives.

STATISTICS AND PROBABILITY (30h) 1. STATISTICS (15 h) · Continuous variable; distribution in classes. · Frequency distribution; histogram, polygons. · Cumulative frequency distribution; histogram, polygons. 2. PROBABILITY (15 h) · Notion of probability. · Universe of possibilities. Cases of equally likely events. · Properties of probability. · Calculation of probabilities: event (A and B), event (A or B), incompatible events, opposite events.

Second Secondary - Sciences Section

SYLLABUS

ALGEBRA (44 h) 1. FOUNDATIONS (6 h) · Binary relations. 2. LITERAL AND NUMERICAL CALCULATIONS (6 h) · Arrangements and permutations. 3. EQUATIONS AND INEQUATIONS (20 h) · System of linear equations (3 x 3). Linear programming. · Polynomials, quadratic equations and inequations. 4. POLYNOMIALS (4 h) · Euclidean division of a polynomial by another. · Factorization. Simplification of rational fractions. 5. NUMBERS (8 h) · Complex numbers: definition, algebraic form. · Operations on complex numbers. · Geometric representation of a complex number. GEOMETRY(59 h) 1. CLASSICAL STUDY (18 h) · Orthogonality in space. · Projections in space. · Solids. 2.VECTORIAL STUDY (16 h) · Vectors and frame reference in space. · Barycenter. · Vector product. 3. ANALYTICAL STUDY (9 h) · Equation of the circle. · Scalar product in space. 4. PLANE TRANSFORMATIONS (16 h) · Isometry. Translation. · Plane rotation. · Reflection.

CALCULUS (NUMERICAL FUNCTIONS) (42 h) 1. DEFINITIONS AND REPRESENTATION (14 h) · Limit of a function. Asymptotes. · Numerical sequences. Arithmetic sequences. Geometric sequences. 2. CONTINUITY AND DERIVATION (22 h) · Continuity. · Derivative of a function at a point. · Derivative function. · Study of functions: polynomial functions, rational functions. 3. INTEGRATION (6 h) · Primitives of a function continuous over an interval. TRIGONOMETRY(15 h) 1. TRIGONOMETRIC LINES (4 h) · Oriented angle of two vectors. · Trigonometric formulas. 2. TRIGONOMETRIC EQUATIONS (7 h) · Solving equations of the form sinx = a, cosx = a, tanx = a. 3. CIRCULAR FUNCTIONS (4 h) · Study of circular functions. STATISTICS AND PROBABILITY (20 h) 1. STATISTICS · Continuous variable; distribution in classes. · Frequency distribution; histogram, polygons. · Cumulative frequency distribution; histogram, polygons. 2. PROBABILITY · Notion of probability. · Universe of possibilities. Cases of equally likely events. · Properties of probability. · Calculation of probabilities: event (A and B), event (A or B), incompatible events, opposite events.

Third Secondary - Literature and Humanities Section

SYLLABUS

ALGEBRA(20 h) 1. FOUNDATIONS (10 h) · Binary operation. · Structure of group. · Propositional calculus. 2. EQUATIONS AND INEQUATIONS (10 h) · Situations-problems leading to the solution of equations and inequations CALCULUS (NUMERICAL FUNCTIONS) (25) 1. DEFINITIONS AND REPRESENTATION (15 h) · Simple rational functions. · Graphical interpretation. · Exponential growth and exponential function. 2. MATHEMATICAL MODELS FOR ECONOMICS AND SOCIAL SCIENCES (10h) · Simple interest, compounded interest.

TATISTICS AND PROBABILITY ( (15 h) 1. STATISTICS (10 h) · Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable. 2. PROBABILITY (5 h) · Conditional probability: definition, independence of two events.

Third Secondary - Sociology and Economics Section

SYLLABUS

ALGEBRA(25 h) 1. FOUNDATIONS (8 h) · Binary operation. · Structure of group. 2. LITERAL AND NUMERICAL CALCULATIONS (7 h) · Combinations: definition, notation, binomial formula. 3. EQUATIONS AND INEQUATIONS (10 h) · System of linear equations (m x n): definition, elementary operations on the rows, Gauss’ method. CALCULUS (NUMERICAL FUNCTIONS) (60 h) 1. DEFINITIONS AND REPRESENTATION (20 h) · Rational functions. · Inverse function. · Natural (Napierian) logarithmic function. Logarithmic function to the base a. · Exponential functions. · Numerical sequences. Geometric sequences: limits. 2. CONTINUITY AND DERIVATION (5 h) · Derivatives of composite functions. · Second derivative. · L’Hospital’s rule. 3. INTEGRATION (10 h) · Integral: definition, properties, calculation. 4. DIFFERENTIAL EQUATIONS (10 h) · Definition. · Equations in separable variables. · Linear first order equations with constant coefficients. · Finite differences equations. 5. MATHEMATICAL MODELS FOR ECONOMICS AND SOCIAL SCIENCES (15 h) · Functions of economics and of social sciences. · Finance mathematics.

STATISTICS AND PROBABILITY (35 h) 1. STATISTICS (15 h) · Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable. · Distribution in two variables: introduction, scatter plot, mean point. · Covariance of two variables, linear correlation coefficient. · Linear adjustment and regression lines. 2. PROBABILITY (20 h) · Conditional probability: definition, independence of two events. · Formula of total probabilities. · Random real variable, law of associated probability, distribution function. Characteristics.

Third Secondary - General Sciences Section

SYLLABUS

ALGEBRA (60 h) 1. FOUNDATIONS (15 h) · Binary operation. · Structure of group. · Propositional calculus. 2. LITERAL AND NUMERICAL CALCULATIONS (10 h) · Combinations: definition, notation, binomial formula, Pascal’s triangle. 3. EQUATIONS AND INEQUATIONS (10 h) · System of linear equations (m x n): definition, elememtary operations on the rows, Gauss’ method. · Quadratic equation with complex coefficients. 4. NUMBERS (25 h) · Module and argument of a complex number. Properties. · Trigonometric and exponential forms of a complex number. · Geometric interpretation of addition, of multiplication of complex numbers and of the passing to the conjugate. · De Moivre’s formula. Applications. · Nth root of a complex number, geometric representation of the nth root of the unit. · Geometric interpretation of and of . Applications. GEOMETRY (90 h) 1. CLASSICAL STUDY (20 h) · Conics: definition, focii, directrix, eccentricity, focal axis. · Equation of a conic, vertices, center, elements of symmetry, reduced equation. · Quadratic curves. 2. VECTORIAL STUDY (5 h) · Level curves . · Vector equation of a straight line, of a plane, of a sphere. 3. ANALYTICAL STUDY (30 h) · Components of the vector product. Mixed product. · Equation of a plane and of a straight line in space. · Orthogonality of two straight lines, of a straight line and a plane; perpendicular planes. · Parallelism of straight lines and of planes. · Distance from a point to a plane, to a straight line. · Equation of a sphere. · Intersection of a sphere with a straight line, a plane or a sphere. 4. PLANE TRANSFORMATIONS (35 h) · Displacement in the plane. · Homothecy. · Complex form of a plane transformation. · Direct plane similitudes: definition, complex form. · Transformations defined by f(z) = az + b and .

CALCULUS (NUMERICAL FUNCTIONS) (105 h) 1. DEFINITIONS AND REPRESENTATION (40 h) · Irrational functions (simple cases). · Inverse function. · Inverse trigonometric functions. · Natural (Napierian) logarithmic function. Logarithmic function to the base a. · Exponential functions. Power functions. · Numerical sequences: limits, bounded sequences, convergent sequences. · Parametric curves. 2. CONTINUITY AND DERIVATION (25 h) · Image of a closed interval by a continuous function. · Extension by continuity of a function. · Derivatives of composite functions. · Derivative of an inverse function. · Second derivative. Successive derivatives. · Rolle’s theorem. Mean value theorem. L’Hospital’s rule. 3. INTEGRATION (25 h) · Integral: definition, properties. · Rules of integration. · Mean value theorem for definite integrals. Max-Min inequality. · Applications of the integral calculation. 4. DIFFERENTIAL EQUATIONS (10 h) · Definition. · Equations in separable variables. · Linear first order equations with constant coefficients. · Linear second order equations with constant coefficients. TRIGONOMETRY(15 h) 1. TRIGONOMETRIC LINES (5 h) · Metric relations in a triangle. Calculation of areas. 2. TRIGONOMETRIC EQUATIONS (5 h) · Solving simple trigonometric equations. 3. CIRCULAR FUNCTIONS (5 h) · Study of circular functions of the form a cos (bx + c) and a sin (bx + c). STATISTICS AND PROBABILITY (30 h) 1. STATISTICS (10 h) · Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable. 2. PROBABILITY (20 h) · Conditional probability: definition, independence of two events. · Formula of total probabilities. · Random real variable, law of associated probability, distribution function. Characteristics.

Third Secondary - Life Sciences Section

SYLLABUS

ALGEBRA(35 h) 1. FOUNDATIONS (8 h) · Binary operation. · Structure of group. 2. LITERAL AND NUMERICAL CALCULATIONS (10 h) · Combinations: definition, notation, binomial formula, Pascal’s triangle. 3. EQUATIONS AND INEQUATIONS (7 h) · System of linear equations (m x n): definition, elememtary operations on the rows, Gauss’ method. 4. NUMBERS (10 h) · Module and argument of a complex number, properties. · Trigonometric and exponential forms of a complex number. · Geometric interpretation of addition, of multiplication of complex numbers and of the passing to the conjugate. · De Moivre’s formula, applications. GEOMETRY (15 h) 1. CLASSICAL STUDY (15 h) · Components of the vector product. Mixed product. · Equation of a plane and of a straight line in space. · Orthogonality of two straight lines, of a straight line and a plane; perpendicular planes. · Parallelism of straight lines and of planes. · Distance from a point to a plane, to a straight line. CALCULUS (NUMERICAL FUNCTIONS) (65 h) 1. DEFINITIONS AND REPRESENTATION (25 h) · Inverse function. · Inverse trigonometric functions. · Natural (Napierian) logarithmic function. Logarithmic function to the base a. · Exponential functions. 2. CONTINUITY AND DERIVATION (15 h) · Image of a closed interval by a continuous function. · Derivatives of composite functions. · Derivative of an inverse function. · Second derivative. Successive derivatives. · L’Hospital’s rule. 3. INTEGRATION (15 h) · Integral: definition, properties. · Rules of integration. · Applications of the integral calculation. 4. DIFFERENTIAL EQUATIONS (10 h) · Definition. · Equations in separable variables. · Linear first order equations with constant coefficients. · Linear second order equations with constant coefficients.

TRIGONOMETRY (5 h) 1. CIRCULAR FUNCTIONS (5 h) · Study of the circular functions of the form a cos (bx + c) and a sin (bx + c). STATISTICS AND PROBABILITY (30 h) 1. STATISTICS (10 h) · Measures of central tendancy and measures of variability of a distribution of one (continuous or discrete) variable. 2. PROBABILITY (20 h) · Conditional probability: definition, independence of two events. · Formula of total probabilities. · Random real variable, law of associated probability, distribution function. Characteristics. · Bernoulli variable. · Binomial law.