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IB MYP Y4–5 Extended Phase 1 Course Description This 30-lesson course is designed for students pursuing the IB MYP Year 4–5 Extended Level Mathematics, which goes beyond the Standard Level curriculum by incorporating deeper conceptual understanding and more challenging applications. This course emphasizes advanced problem-solving, rigorous mathematical reasoning, and preparation for future studies in higher-level mathematics. Students will engage with more complex concepts in Number, Algebra, Geometry and Trigonometry, Statistics and Probability, and Financial Mathematics, with a focus on analytical thinking and mathematical modelling in real-world contexts. Unit 1: Advanced Number and Operations (5 Lessons) Lesson 1: Diagnostic Assessment and Course Introduction ．Overview of the Extended Curriculum ．Prime factorization, least common multiple (LCM), and greatest common divisor (GCD) Lesson 2: Rational, Irrational, and Real Numbers ．Proofs and properties of irrational numbers ．Simplifying and approximating surds Lesson 3: Exponents and Radicals ．Fractional and negative exponents ．Simplifying expressions involving exponents and radicals Lesson 4: Standard Form and Significant Figures ．Real-world applications and advanced calculations ．Error margins and rounding strategies Lesson 5: Modular Arithmetic and Bases ．Concepts of congruence ．Introduction to number bases and applications Unit 2: Advanced Algebra (5 Lessons) Lesson 6: Simplifying Complex Algebraic Expressions ．Polynomial division ．Completing the square with complex coefficients Lesson 7: Quadratic Equations and Functions ．Solving quadratics using the quadratic formula ．Graphical analysis of parabolas (vertex, roots, axis of symmetry) Lesson 8: Cubic and Higher-Degree Polynomials ．Factor theorem and remainder theorem ．Sketching higher-degree polynomials Lesson 9: Simultaneous Equations ．Non-linear systems (quadratic-linear, quadratic-quadratic) Lesson 10: Inequalities ．Solving quadratic inequalities ．Graphical representation of inequalities in two dimensions