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H3 Mathematics (Syllabus 9820)

Mathematics at ACJC aims to provide students with enriching opportunities to acquire clear conceptual understanding of Mathematics, its processes and applications. The H3 syllabus provides students, who intend to pursue mathematics at the university, with an insight into the practice of a mathematician. It equips students with the knowledge and skills to understand and write mathematical statements, proofs and solutions, and the techniques and results that come in helpful in their work. Students will develop these competencies through proving mathematical results and solving nonroutine mathematical problems in the course of the learning.

The teaching programme is designed to enable students to:
acquire advanced problems-solving skills and methods of proof by learning useful mathematical results and techniques to solve non-routine problems and prove statements;
develop rigour in mathematical argument and precision in the use of mathematical language through the writing and evaluation of mathematical proofs and solutions;
experience and appreciate the practice, value and rigour of mathematics as a discipline.

Requirements
Excellent results in H2 Mathematics and good results in other subjects at JC1 Promotional Examinations

As the H3 syllabus explores H2 topics as well as new content in substantial depth and rigour, student engagement in learning is a key factor. Students are expected to be disciplined and take responsibility for their own learning and improvement. On top of being prepared for all lectures and tutorials, timely revision materials are provided and solutions uploaded online, before tests and examination, for independent study by students. Students are required to be regular and consistent in handing in assigned work throughout their JC2 year.

Assessment comprises one 3 hour papers with 8 to 10 questions. Candidates will be expected to answer all questions.

Topics include Number Theory, Functions, Sequences and Series, Inequalities, and Combinatorics. Students will also learn to use problem solving heuristics to solve mathematical problems, mathematical reasoning principles, including methods of formal proof, to develop and critically evaluate mathematical arguments, and mathematical language to communicate ideas.