1. Numbers

COURSE DESCRIPTION

This course explores the foundational and advanced concepts of Number and Algebra within the IBDP Mathematics: Analysis and Approaches HL curriculum. The unit begins with essential numerical methods and algebraic operations, then progresses into more sophisticated topics such as sequences, series, complex numbers, and abstract proof techniques. Students will gain the skills to model real-world scenarios, manipulate mathematical expressions, and apply logical reasoning across pure and applied contexts.

LEARNING OUTCOMES

• Convert between numerical forms and express large/small numbers using standard form

• Solve and model problems involving arithmetic and geometric sequences and series

• Apply compound interest and depreciation models to financial contexts

• Understand and use laws of exponents and logarithms effectively

• Work with binomial expansions, including non-integer and negative indices

• Use and manipulate complex numbers in Cartesian, polar, and Euler form

• Solve higher-order polynomial equations using De Moivre’s theorem and understand conjugate root properties

• Demonstrate mathematical rigor through proof by induction, contradiction, and counterexamples

• Break down rational expressions using partial fractions

• Solve systems of linear equations using algebraic methods and matrix strategies

• Interpret algebraic and complex solutions through Argand diagrams and graphical representations

TOPICS COVERED

• SL 1.1–1.9: Standard form, sequences and series, financial applications, logarithmic laws, and binomial theorem
• AHL 1.10–1.16: Advanced binomial expansion, permutations and combinations, partial fractions, complex numbers (in Cartesian and polar form), and formal proof techniques