Togo Collège (3ème) Curriculum - Mathematics

This information is based on the "Planning annuel du programme HPM" document, which appears to outline a mathematics curriculum for Togolese collèges. It is unclear whether this is the official government curriculum or a supplementary resource.

Third Year (3ème)

The curriculum is organized into trimesters, covering both geometric and numerical activities.

First Trimester:

• Geometry: Thales' Theorem (5 hours)
• Thales' theorem in a triangle (direct and reciprocal properties).
• Application of Thales' theorem.
• Similar triangles.
• Thales' theorem in the general case.
• Geometry: Right-Angled Triangles (8 hours)
• Review: Pythagorean theorem, circumscribed circle of a right-angled triangle.
• Other metric relations in a right-angled triangle.
• Trigonometry in a right-angled triangle (sine, cosine, tangent).
• Properties of trigonometric functions.
• Trigonometry of special angles.
• Calculations in a right-angled triangle using trigonometry.
• Use of numerical tables, coordinate systems, and calculators for trigonometric calculations.
• Geometry: Vectors (4 hours)
• Prerequisite: Understanding of vector addition.
• Product of a vector by a real number (definition and properties).
• Vectors and configurations (vectors with the same direction, collinear vectors, direction vectors of a line, orthogonal vectors).
• Numerical Activities: Literal Calculation (5 hours)
• Quotients.
• Powers with relative integer exponents.
• Expansion and simplification.
• Remarkable identities, factorization, null product.
• Examples of literal expressions (monomials, polynomials, rational fractions and simplification).
• Numerical Activities: Square Roots and Real Numbers (4 hours)
• Square root (definition).
• Introduction to real numbers.
• Comparison of real numbers.
• Operations and calculations with radicals.
• Numerical Activities: Numerical Calculation (8 hours)
• Absolute value (new inequalities, definition and properties of absolute value).
• Intervals in the set of real numbers.
• Comparison of real numbers.
• Approximation and bounds.
• Use of numerical tables and calculators for calculations (square roots).

Second Trimester:

• Geometry: Coordinates of a Vector (4 hours)
• Definition of vector coordinates.
• Coordinates of a sum of vectors.
• Coordinates of the product of a vector by a real number.
• Collinear and orthogonal vectors.
• Calculations in a coordinate system (calculating vector coordinates, midpoint of a segment, distance between two points, square of the norm of a vector).
• Geometry: Equations of Lines (3 hours)
• Cartesian equation of a line.
• Coordinates of a direction vector of a line.
• Slope of a line.
• Relative positions of two lines (parallel and perpendicular lines).
• Geometry: Inscribed Angles in a Circle (3 hours)
• Definition and vocabulary (central angle, inscribed angle, intercepted arc).
• Measure of an inscribed angle.
• Inscribed angles intercepting the same arc.
• Regular polygons (definition, regular polygons inscribed in a circle, construction of a pentagon inscribed in a given circle).
• Geometry: Symmetries and Translations (3 hours)
• Orthogonal symmetries, central symmetries, translations.
• Use of symmetries and translations for proofs and constructions.
• Successive orthogonal symmetries with parallel or perpendicular axes.
• Numerical Activities: Equations and Inequalities in the set of real numbers (6 hours)
• First-degree equations.
• Equations reducible to first-degree equations.
• First-degree inequalities.
• Systems of inequalities.
• First-degree problems.
• Numerical Activities: Equations and Inequalities with One Variable (6 hours)
• First-degree equations (systems of first-degree equations).
• First-degree inequalities (systems of first-degree inequalities).
• Systems of first-degree inequalities.
• Numerical Activities: Affine Applications (4 hours)
• Notion of affine applications.
• Graphical representation.
• Direction of variation.
• Linear applications (definition and representation, proportionality table and linear application).
• Examples of affine applications by intervals (graphical resolution).

Third Trimester:

• Geometry: Homothety (3 hours)
• Definitions.
• Properties.
• Image of simple figures.
• Geometry: Pyramids and Cones (refer to details in the linked document)
• Pyramids (observation, description, vocabulary, properties, regular pyramids, constructing a net, calculating volumes and areas, section of a pyramid by a plane parallel to the base, truncated pyramid, calculating volumes and areas of a truncated pyramid).
• Cones of revolution (similar topics as pyramids).
• Numerical Activities: Statistics (4 hours)
• Prerequisite: Understanding of qualitative and quantitative character studies.
• Example of grouping into classes (equal amplitudes).
• Histograms.
• Revisions and Preparation for the BEPC Exam.

This curriculum outlines the topics and allocated hours for each. It emphasizes a move away from rote learning towards a more active, problem-solving approach. It encourages teachers to use concrete examples and activities to introduce definitions and properties. Regular assessment through short, frequent exercises is also recommended.