CJC > Education > Mathematics & Science > Mathematics

Mathematics

Purpose of studying Mathematics at A-Level.

Learning Mathematics is optional at the A-Level. However, it is offered by almost all students. The purpose of learning Mathematics, at the A-Level is two-fold. Firstly, it provides students, regardless of the intended course of study at the University, with a useful set of tools and analytical skills to support not just tertiary study but also to sharpen their problem solving skills. Secondly, learning Mathematics expose students to a way of thinking that complements other ways of thinking developed through the other disciplines.

Skills

The CJC Mathematics department aims to nurture effective problem solvers and critical thinkers based on the Singapore Mathematics Framework:
• Understanding and applying mathematical concepts and skills in a variety of contexts, including the manipulation of mathematical expressions and the use of graphic calculators
• Reasoning and communicating mathematically through writing mathematical explanations, arguments and proofs, and inferences
• Solving unfamiliar problems; translating common realistic contexts into mathematics; interpreting and evaluating mathematical results, and using the results to make predictions, or comment on the context

Difference between Mathematics at A- and O-Levels

In Secondary schools, all students learn O-Level Mathematics while students with an aptitude and interest in mathematics also offer Additional Mathematics. The learning of Mathematics at the A-Levels builds on students’ prior knowledge and skills in O-Level Mathematics and Additional Mathematics.

To cater to the diverse needs, interests and abilities of students, we offer the following 3 syllabuses:

• H1 Mathematics;
• H2 Mathematics and
• H3 Mathematics

O-Level Mathematics provides the assumed knowledge for H1 Mathematics while H2 Mathematics assumes some of the content covered in Additional Mathematics. H3 Mathematics is an extension of H2 Mathematics in terms of higher-order problem solving skills.

Assessment in the new Curriculum

Broadly speaking, students will be assessed on three levels:

• Understanding and applying mathematical or statistical concepts and skills in a variety of problems including those that may be set in unfamiliar context or require integration of concepts and skills from more than one topic;
• Formulating real-world problem mathematically, solving the mathematical problems, interpreting and evaluating the mathematical solutions in the context of the problems and
• Reasoning and communicating mathematically through making deductions and writing mathematical explanations, arguments of varying rigour and proofs.

Curriculum

H1 Mathematics (8865) Revised Syllabus for 2016

• To provide students with a foundation in mathematics and statistics.
• It is particularly appropriate for students without an Additional Mathematics background because it offers an opportunity for them to learn important mathematical concepts and skills in algebra and calculus that are covered in Additional Mathematics.

H2 Mathematics (9758) Revised Syllabus for 2016

• To prepare students for a range of university courses, including mathematics, sciences 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 the applications of mathematics, students also develop an appreciation of mathematics and its connections to other disciplines and to the real world.

H3 Mathematics (9820) Revised Syllabus for 2016

H3 Mathematics offers students who have a strong aptitude for and are passionate about Mathematics, an opportunity to further develop their mathematical modeling and reasoning skills. Students may pursue the H3 Mathematics programme jointly offered by NUS, MIE and MOE.

The syllabus aims to enable students who have an aptitude and passion for Mathematics to:

• Acquire advanced mathematical concepts and skills to deepen their understanding of Mathematics, and to widen the scope of applications of Mathematics
• Develop rigourous habits of mind through mathematical reasoning and proof, creative mathematical problem solving, and use of mathematical models
• Connect ideas within Mathematics at a higher level and between Mathematics and other disciplines through applications of Mathematics
• Appreciate the beauty, rigour, and abstraction of Mathematics through mathematical proof and applications

Topic Overview
• Numbers, e.g. primes, co-primes, divisbility, modulo arithmetic, greatest common divisor, division algorithm;
• Functions, e.g. graphs, symmetries, derivatives, integrals, differential equations, limiting behaviours, bounds;
• Sequences and series, e.g. general terms, sum, limiting behaviours, bounds;
• Inequalities, e.g. AM-GM inequality, Cauchy-Schwarz inequality, triangle inequality;
• Counting, e.g. distribution problems, Stirling numbers of the second kind, recurrence equations, bijection principle, principle of inclusion and exclusion.

H3 Mathematics is to be studied together with H2 Mathematics.

Students are selected for H3 Mathematics at the end of JC1, based on their performance throughout the year, including the end-of-year examination and possible selection tests.

Assessment

H1 Mathematics (8865) Revised Syllabus for 2016

• One 3-hour paper marked out of 100
- Section A (Pure Mathematics – 40 marks)
- Section B (Statistics – 60 marks).
Examination questions may integrate ideas from more than one topic, and topics may be tested in the contexts of problem solving and application of mathematics.
H2 Mathematics (9758) Revised Syllabus for 2016

• Two 3-hour papers, each carrying 50% of the total mark, and each marked out of 100.
• Paper 1 (3 hours) :
Only the Pure Mathematics section of the syllabus. (100 marks)
• Paper 2 (3 hours) :
- Section A (Pure Mathematics – 40 marks)
- Section B (Statistics – 60 marks)
Examination questions may integrate ideas from more than one topic, and topics may be tested in the contexts of problem solving and application of mathematics.

H3 Mathematics (9820) Revised Syllabus for 2016

• One 3-hour paper marked out of 100

1) Should I do H1 or H2 Mathematics?

You should consider H2 Mathematics if you are
• Interested in science, strong in Mathematics and offer Mathematics because it supports your future in science (excluding biological sciences).
OR
• Generally strong in Mathematics, but prefer a non-science-based course and intends to offer mathematics as a contrasting subject.

You should consider H1 Mathematics if you
• Are more inclined towards the arts and humanities;
• Intend to offer Mathematics as a contrasting subject;
• Intend to pursue business, social sciences or biological sciences at the university;
• Have no Additional Mathematics background

2) If I have no Additional Mathematics background, can I still take H2 Mathematics?

If you are very clear of the purpose of taking H2 Mathematics, you can still take H2 Mathematics provided you meet the college merit-based criteria (please refer to the subject combination section).

3) What is this Graphic Calculator?

A graphic calculator (GC) is a learning tool that is designed to help students visualize and better understand concepts in mathematics and science, and the use of a GC is expected for H1, H2 & H3 Mathematics. Examination papers will be set with the assumption that candidates will have access to a GC. The college uses the model by Texas Instruments.