Integrated Mathematics

{"examination": "CAPE Integrated Mathematics", "syllabus_topics": {"School-Based Assessment (SBA)": ["Paper 031 - Research Project: a compulsory project requiring candidates to demonstrate the practical application of Mathematics in everyday life [20]. Candidates must choose one of two options: Project A, which is theory-based and involves the solution or proof of a mathematical problem, or Project B, which is experiment-based and requires the collection and analysis of data [20].", "Assessment Criteria: projects are evaluated on the candidate's ability to clearly state a project title and problem statement, identify important mathematical elements, provide a logical solution, and discuss the findings using appropriate mathematical language and tools [21]."], "Unit 1: Integrated Mathematics": ["Module 1 - Foundations of Mathematics: focusing on algebraic techniques including functions (injective, surjective, bijective), inverse functions, and composite functions [1, 2]. It covers solving linear and quadratic inequalities, exponents, logarithms, and the Remainder and Factor Theorems for polynomials [2, 3]. Additionally, it addresses sequences and series (arithmetic and geometric progressions), binomial expansion, matrices, systems of linear equations, and complex numbers [3-5].", "Module 2 - Statistics: addressing data collection through various sampling techniques such as random and stratified sampling [6]. It explores data representation using histograms, stem-and-leaf plots, and box-and-whisker plots [7]. Key topics include calculating measures of central tendency and dispersion (mean, standard deviation), understanding probability (permutations, combinations, expected values), and analyzing relationships through regression and correlation [7-9].", "Module 3 - Calculus: focusing on the concepts of limits and continuity, including the identification of points of discontinuity [10, 11]. It covers differentiation techniques such as the power, product, quotient, and chain rules, and their application to rates of change and finding stationary points [12-15]. The module also details integration as the reverse of differentiation, calculating indefinite and definite integrals, and applying these to determine areas under curves and volumes of revolution [16-19]."]}}