Mathematics — 3rd year, BCS track

🎯 Course goals

This course covers the complete official Mathematics program for 3rd-year post-fundamental students (BCS track — Biology, Chemistry, Earth Sciences) in Burundi. It builds the full toolkit of real analysis, calculus, complex numbers, and analytic geometry needed for further scientific study, with worked examples and real-world applications throughout.

📘 Detailed syllabus — Palier 1: Real functions, differentials and integrals

1. Review of numerical functions & Reciprocal functions (general theorems)
2. Circular reciprocal functions (arcsin, arccos, arctan, arccotan) and their derivatives
3. Natural logarithm and logarithm of base a
4. Exponential functions
5. Differentials & Introduction to antiderivatives
6. Integration by parts & rational functions
7. Antiderivatives of irrational and trigonometric functions
8. Antiderivatives (continued): recurrence formulas
9. Definite integrals: fundamental theorem of calculus
10. Integration situation: Bacteria culture (exponential growth model)
11. Integration situation: A city's population (exponential growth model)

📘 Detailed syllabus — Palier 2: Advanced calculus, series, complex numbers, progressions

1. Definite integral calculation techniques
2. Applications of integral calculus: plane areas
3. Volumes of solids of revolution & Taylor and Mac Laurin series
4. Complex numbers: algebraic form
5. Complex numbers: trigonometric and exponential form
6. Complex numbers: roots and equations
7. Arithmetic and geometric progressions & Summation formulas
8. Integration situation: The reward (arithmetic vs. geometric payment plans)
9. Integration situation: Preparing a wedding celebration

📘 Detailed syllabus — Palier 3: Analytic geometry and probability

1. The line in the affine plane
2. The line (continued) & The circle in an orthonormal frame
3. The circle and the line: intersections, tangents, radical axis
4. Conics: definition and graphical representation (parabola, ellipse, hyperbola)
5. Conics (continued): foci, directrix, eccentricity, tangents
6. Combinatorial analysis & Random phenomena (introduction)
7. Random phenomena (continued): probability
8. Integration situation: Karakura's field (triangular plot, analytic geometry)
9. Integration situation: At the Kijana bar-restaurant (probability, combinatorics)

🎓 Learning Format

• 📖 Full online course on our Moodle academy platform, accessible anytime
• ✅ Interactive quizzes for every week of content, with instant feedback
• 💬 Discussion forum, live chat, and private messaging with your teacher and classmates
• ♾️ Unlimited access and unlimited quiz attempts — learn at your own pace

💡 Why this course

Mathematics for BCS students is often treated as secondary to the biology/chemistry/earth science core — but a solid grasp of calculus, complex numbers, and analytic geometry directly supports quantitative reasoning in every science course, from population growth models to statistics. This course closes that gap with the complete official program, worked examples grounded in real Burundian contexts, and full exam-style graded situations matching the national curriculum.