Lebanon: Description of the Advanced Mathematics Programs and Curriculum
At Grade 12, students receive a solid mathematical foundation with the aim of preparing them to pursue their studies as teachers, engineers, and researchers. The mathematics competencies students must have in each domain are provided in the table below.
| Domain | Competencies |
|---|---|
| Mathematical Reasoning |
Recognize the difference between a mathematical explanation and 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 |
| 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 information given in 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 obtained solutions |
| Communication |
Give a summary of a mathematical document
Take notes on a mathematical lecture Critique a mathematical presentation Write a proof correctly |
| Spatial |
Prove and apply the properties of solid figures and conics
Characterize plane or space figures using vector notation Study geometric problems analytically Determine the effect of transformations on plane figures |
| Numbers and Algebra |
Analyze the extensions of the sets of numbers (natural numbers, integers, rational numbers, real numbers, complex numbers)
Study the properties of complex numbers and their use in geometry and trigonometry Generalize fundamental mathematical notions (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 inequalities |
| Calculus |
Acquire the fundamental concepts of limit, continuity, and differentiability, and use them graphically
Analyze the graphs of polynomial, rational, irrational, trigonometric, logarithmic, and exponential functions Integrate functions and solve simple differential equations |
| 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 |