Pure Mathematics

{"examination": "CAPE Pure Mathematics", "syllabus_topics": {"School-Based Assessment (SBA)": ["Personal Research Project: involves a project (Paper 031) where candidates demonstrate the practical application of Mathematics in everyday life [30]. The project requires students to probe, describe, and explain a mathematical area of interest, communicating their findings through appropriate mathematical language and tools [30]."], "Unit 1: Algebra, Geometry and Calculus": ["Module 1 - Basic Algebra and Functions: covers reasoning and logic through simple and compound propositions, truth tables, and logical equivalence [19, 20]. It details the axioms of the real number system, including arithmetic operations and binary operations [20]. Other core areas include the concept of functions (injective, surjective), exponential and logarithmic functions, the Remainder and Factor Theorems for polynomials, and solving quadratic inequalities [19, 20].", "Module 2 - Trigonometry, Coordinate Geometry and Vectors: focuses on manipulating and describing the behavior of trigonometric functions, establishing identities, and solving trigonometric equations [19, 21]. It addresses coordinate geometry and the application of vectors in solving geometric problems [19, 22].", "Module 3 - Calculus I: introduces the fundamentals of calculus, specifically focusing on the techniques and concepts of differentiation and integration [19, 23]. Students learn to apply these tools to solve real-world problems through data analysis and creative presentations [23]."], "Unit 2: Complex Numbers, Analysis and Matrices": ["Module 1 - Complex Numbers and Calculus II: explores writing complex roots of quadratic equations and representing objects geometrically using complex numbers [19, 24]. It advances calculus studies with more complex techniques of differentiation and integration applied to modeling real-world scenarios [24].", "Module 2 - Sequences, Series and Approximations: defines sequences (periodic, oscillating, convergent, divergent) and uses recurrence relations [19, 25]. It addresses the binomial theorem, power series, and various approximation methods like linear interpolation and the use of the Intermediate Value Theorem for root finding [26, 27].", "Module 3 - Counting, Matrices and Differential Equations: covers the fundamental principles of counting and factorial notation [19, 28]. It details the algebra of matrices and solving systems of linear equations [28, 29]. Additionally, students develop skills to model real-world phenomena using differential equations and calculate solutions for these models [28]."]}}