Mathematics
Explore the H1, H2, and H3 Mathematics programmes at ACJC, designed to build strong foundations for university studies in sciences, engineering, and the social sciences.
H1 MATHEMATICS (SYLLABUS 8865)
Aims
Mathematics at ACJC aims to provide students with enriching opportunities to acquire clear conceptual understanding of Mathematics, its processes and applications. The H1 syllabus provides a foundation in Mathematics for students that will support their business or social sciences studies at university. It is particularly appropriate for students without an Additional Mathematics background because it offers an opportunity for them to learn important mathematics concepts and skills in algebra and calculus that were taught in Additional Mathematics. Students will also learn basic statistical methods that are necessary for studies in business and social sciences.
The teaching programme is designed to enable students to:
acquire mathematical concepts and skills to support their tertiary studies in business and the social sciences;
develop thinking, reasoning, communication and modelling skills through a mathematical approach to problem-solving;
connect ideas within mathematics and apply mathematics in the context of business and social sciences;
experience and appreciate the value of mathematics in life and other disciplines.
Approach
At ACJC, H1 Mathematics is taught using differentiated instruction using tutorial-based lessons. Students will be banded according to their Additional Mathematics grade at ‘O’ level, with students without Additional Mathematics at ‘O’ level placed in a separate class. Differentiated teaching materials and instruction will be used to deliver lessons.
As students’ capacity in H1 Mathematics has to be developed from their knowledge and skills at the ‘O’ level to reach the advanced level expected at ‘A’ levels, 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 examinations for independent study by students. Students are required to be regular and consistent in handing in assigned work throughout their two years. Consultations and remedial sessions are conducted by teachers to meet the needs of individual students.
Programme
There are no prerequisites to offer H1 Mathematics.
The topics covered in H1 Mathematics include Functions and Graphs, Equations and Inequalities, Calculus, Permutations and Combinations, Probability, Statistical Distributions, Sampling Theory, Hypothesis Testing, and Correlation and Linear Regression.
The A Level Examination for H1 Mathematics comprises one 3 hour paper with about 11 to 13 questions. There will be one question on the application of mathematics in real-world contexts, including those from business and the social sciences. This question will carry at least 12 marks and may require concepts and skills from more than one topic. Candidates will be expected to answer all questions.
The syllabus document for the 2025 H1 Mathematics syllabus is available on the SEAB website here (opens in new tab) along with a specimen paper (opens in new tab).
H2 MATHEMATICS (SYLLABUS 9758)
Aims
The H2 syllabus is designed to prepare students for a range of university courses, including Mathematics, Sciences, Engineering and related courses, where a good foundation in mathematics is required. It develops mathematical thinking and reasoning skills that are essential for further learning of mathematics. Through applications of mathematics, students also develop an appreciation of mathematics and its connections to other disciplines and to the real world.
The teaching programme is designed to enable students to:
acquire mathematical concepts and skills to prepare for their tertiary studies in Mathematics, Sciences, Engineering, and other related disciplines;
develop thinking, reasoning, communication and modelling skills through a mathematical approach to problem-solving;
connect ideas within mathematics and apply mathematics in the contexts of Sciences, Engineering, and other related disciplines;
experience and appreciate the nature and beauty of mathematics and its value in life and other disciplines.
Approach
As students’ capacity in Mathematics has to be developed from their knowledge and skills at the ‘O’ level to reach the advanced level expected at ‘A’ levels, 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 two years. Consultations and remedial sessions are conducted by teachers to meet the needs of individual students.
Programme
Students are recommended to have a minimum B4 grade in ‘O’ Level Additional Mathematics.
The topics covered in H2 Mathematics include Functions and Graphs, Sequences and Series, Vectors, Complex Numbers, Calculus, Permutations and Combinations, Probability and Random Variables, Statistical Distributions, Sampling Theory, Hypothesis Testing, and Correlation and Linear Regression.
The A Level Examination for H2 Mathematics comprises two 3 hour papers with about 10 to 13 questions each. In each paper, there will be one question on the application of Mathematics in real-world contexts, including those from sciences and engineering. This question will carry at least 12 marks and may require concepts and skills from more than one topic. Candidates will be expected to answer all questions.
The syllabus document for the 2025 H2 Mathematics syllabus is available on the SEAB website here (opens in new tab) along with specimen papers 1 (opens in new tab) and 2 (opens in new tab).
H3 MATHEMATICS (SYLLABUS 9820)
Aims
The H3 syllabus provides students who intend to pursue mathematics in 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 non-routine 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.
Approach
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.
Programme
H3 Mathematics is offered only in the JC2 year. Students with excellent results in H2 Mathematics and good results overall will be invited to offer H3 Mathematics.
Students will be introduced to writing mathematical statements and proofs, and will also learn to use problem solving heuristics to solve mathematical problems. They will also learn mathematical reasoning principles, including methods of formal proof, to develop and critically evaluate mathematical arguments, and mathematical language to communicate ideas. Finally, they will learn to read mathematical texts and make mathematical investigations, including formulating conjectures, forming generalisations, and critiquing solutions. The A Level Examination for H3 Mathematics comprises one 3 hour paper with 6 questions of differing lengths. The paper will be marked out of 80; questions 1 to 5 will be worth 10 to 14 marks each. Question 6 will be worth 16 to 20 marks and will require students to read and respond to a short mathematical text. Candidates will be expected to answer all questions. The syllabus document for the 2025 A Level Examinations is available on the SEAB webpage here (opens in new tab) along with a specimen paper (opens in new tab).