This course features comprehensive, full-length lectures and is driven by conceptual understanding.

 

Overview: IB Mathematics: Analysis and Approaches is designed for students who enjoy rigorous mathematical thinking and wish to pursue mathematics, engineering, physical sciences, or economics at university.

Objectives:

• Develop a deep understanding of mathematical principles.
• Enhance problem-solving skills through rigorous analysis.
• Prepare for advanced studies in mathematics and related fields.

Course Content:

1. Number and Algebra:

   • Sequences and series
   • Exponents and logarithms
   • Complex numbers
   • Proof by induction

2. Functions:

   • Types of functions and their properties
   • Transformations of functions
   • Polynomial, rational, exponential, and logarithmic functions
   • Trigonometric functions

3. Geometry and Trigonometry:

   • Vectors in two and three dimensions
   • Geometric transformations
   • Trigonometric identities and equations
   • Circular functions and their applications

4. Calculus:

   • Limits and continuity
   • Differentiation and its applications
   • Integration and its applications
   • Differential equations

5. Statistics and Probability:

   • Descriptive statistics
   • Probability distributions
   • Statistical inference
   • Hypothesis testing

Assessment:

• Internal Assessment (20%): A mathematical exploration project.
• External Assessment (80%):
  • Paper 1: Non-calculator (30%)
  • Paper 2: Calculator allowed (30%)
  • Paper 3: Problem-solving and investigative techniques (20%)

Skills Developed:

• Analytical and critical thinking
• Advanced problem-solving
• Mathematical reasoning and communication
• Application of mathematics in real-world scenarios

Prerequisites: A strong foundation in mathematics, ideally with prior coursework equivalent to IB Mathematics: Applications and Interpretation SL or HL.

Target Audience: Students passionate about mathematics and aiming for careers in engineering, physics, computer science, economics, or advanced mathematics.

Course Format: Delivered through lectures, discussions, problem-solving sessions, and projects, with access to textbooks, online platforms, and mathematical software.

Expectations: Active engagement, timely completion of assignments, and a willingness to explore challenging mathematical concepts. Regular attendance and participation are crucial for success.