BPM MATH0 – Syllabus
Mathematics 0 – Syllabus (10 weeks)
Course Goals
This preparatory course is designed for first-year economics students to review and reinforce
essential secondary-school mathematics. The course provides a strong foundation
for university-level quantitative subjects.
Structure
ˆ Duration: 10 weeks (9 instructional weeks + 1 revision week)
ˆ Sessions: 100 minutes weekly (seminar)
ˆ Language of instruction: English
Weekly Topics
Week 1: Algebraic expressions and basic equations
ˆ Simplifying powers, roots, and rational expressions
ˆ Factoring, expanding, and algebraic manipulation
ˆ Linear and basic quadratic equations
Week 2: Absolute value and inequalities
ˆ Properties and graphs of absolute value functions
ˆ Linear and quadratic inequalities
ˆ Absolute value equations and their geometric meaning
Week 3: Rational expressions and equations
ˆ Domain restrictions, simplifying rational expressions
ˆ Solving equations and inequalities with rational terms
Week 4: Radical expressions and equations
ˆ Simplifying and manipulating roots and powers
ˆ Solving radical equations and interpreting solutions
Week 5: Functions I – polynomials and power functions
ˆ Definitions and properties of functions
ˆ Linear, quadratic and higher-order polynomial functions
ˆ Domain, range, and basic graphing
BPM MATH0 – Syllabus
Week 6: Functions II – exponential and logarithmic functions
ˆ Exponential growth and decay
ˆ Logarithms: definition, rules, and applications
ˆ Graphs and transformations
Week 7: Equations with exponents and logarithms
ˆ Solving exponential and logarithmic equations and inequalities
ˆ Applications and nested expressions
Week 8: Composite and inverse functions; graph transformations
ˆ Function composition and inverse functions
ˆ Shifts, reflections, stretching/compressing of graphs
Week 9: Piecewise functions and mixed review
ˆ Graphs and interpretation of piecewise-defined functions
ˆ Review of challenging types of problems
ˆ Preparation for the final practice test
Week 10: Final review and practice test
ˆ Simulated final test with group discussion
ˆ Summary of key concepts and student feedback
Assessment
A final test