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# 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 develop:
• Understand and apply mathematical concepts and skills in a variety of contexts, including the manipulation of mathematical expressions and the use of graphic calculators
• Reason and communicate mathematically through writing mathematical explanations, arguments and proofs, and inferences
• Solve unfamiliar problems; translate common realistic contexts into mathematics; interpret and evaluate mathematical results, and use the results to make predictions, or comment on the context

## Difference between Mathematics at A level and O level

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, the 2016 A-level Mathematics Curriculum comprises an expanded suite of 5 syllabuses:

• H1 Mathematics;
• H2 Mathematics;
• H2 Further Mathematics; and
• H3 Mathematics (starting only in 2017 for JC2 students)

O-level Mathematics provides the assumed knowledge for H1 mathematics. H2 Mathematics assumes some of the content covered in Additional Mathematics. H2 Further Mathematics is an extension and expansion of H2 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, solve the mathematical problems, interpret and evaluate the mathematical solutions in the context of the problems and
• Reasoning and communicate 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.

### H2 Further Mathematics (9649)  Revised Syllabus for 2016

• For students who are mathematically-inclined and who wish to further expand and deepen their knowledge of mathematics and its applications.
• Students will develop advanced mathematical thinking and reasoning skills and learn a wider range of mathematical methods and tools. This will give a head-start to students who plan to study mathematics or mathematics-related university courses such as science and engineering in the form of a stronger and richer foundation in mathematics.
• H2 Further Mathematics is to be taken with H2 Mathematics as ‘double mathematics’.

## 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).
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)

### H2 Further Mathematics (9649)  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 – 50 marks)
- Section B (Statistics – 50 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

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. 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 rigorous 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

Programs available
• Students may pursue H3 Mathematics programs offered by NUS or MOE.

Assessment (MOE syllabus)
One 3-hour paper, marked out of 100.

Topic (Approximate Weighting)
• Functions and Graphs, Sequences and Series, Calculus 40%
• Combinatorics 25%
• Differential Equations and Mathematical Models 35%

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.

Should I do H2 Mathematics?
• Interested in science, strong in Mathematics and offers mathematics because it supports their future in science.
OR
• Generally strong in mathematics, but prefer a non-science-based course and intends to offer mathematics as a contrasting subject.

Should I do H1 Mathematics?
• Are more inclined towards the arts and humanities;
• Intend to offer Mathematics as a contrasting subject;
• Intend to pursue business and social sciences at the university;
• Have no Additional Maths background

Should I do H2 Further Mathematics?
• Interested and strong in Mathematics and intend to study mathematics or mathematics related university course
OR
• Interested in science, strong in Mathematics and offers mathematics because it supports their future in science.

What is the difference between H1 & H2 Mathematics?
The syllabus, emphasis, expectations and assessments are very different between the H1 and H2 Mathematics.

What is this Graphic Calculator?
Essentially, 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.

What are the prerequisites of studying H2 Further Mathematics

Students interested to study H2 Further Mathematics must meet all the criteria below:
• A1 in O-level Mathematics and at least A2 in Additional Mathematics;
• At least a pass in Pure Physics at O-level;
• To sit for selection test.
Take either one of six subject combinations offered by the college (You may also refer to the section on Subject Combinations):
• H2 Maths, H2 Further Maths, H2 Physics
• H2 Maths, H2 Further Maths, H2 Physics and H2 Economics
• H2 Maths, H2 Further Maths, H2 Physics and H2 Geography
• H2 Maths, H2 Further Maths, H2 Chemistry
• H2 Maths, H2 Further Maths, H2 Chemistry and H2 Economics
• H2 Maths, H2 Further Maths, H2 Chemistry and H2 Geography