# Mathematics

### Programme Overview

At Tampines Junior College, we aim to nurture and motivate every student to realize his/her potential in Mathematics and help him/her achieve his/her personal best. Our instructional programme is targeted at students of different abilities and we organise enrichment activities every year for our students to bring them outside the confines of traditional classroom learning and to make their learning of Mathematics more enjoyable. These enrichment activities include:

- Singapore Mathematical Olympiad
- Australian Mathematics competition
- UNSW – ICAS Mathematics Assessment
- Singapore Kangaroo Math Contest
- Visits to NUS Mathematics Faculty
- Fastest Finger GC Competition
- Designing with GC Competition
- Statistics Poster Competition
- NUS Statistics Camp
- Overseas experiential learning trips

### Syllabus Outline

### Mathematics H1: 8865

This course provides students with a foundation in mathematics and statistics that will support their business or social sciences studies at the university. 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 were taught in Additional Mathematics. Students will also learn basic statistical methods that are necessary for studies in business and social sciences.

Topics covered include:

- Pure Mathematics: Functions and Graphs, Equations and Inequalities, Differentiation and Integration.
- Probability and Statistics: Probability, Binomial and Normal Distributions, Sampling, Hypothesis Testing, and Correlation and Linear Regression.

Knowledge of the content of O-Level Mathematics syllabus is assumed in this syllabus.

**Scheme of Examination Papers**

For the examination in H1 Mathematics, there will be one 3-hour paper marked out of 100 as follows:

Section A (Pure Mathematics－40 marks) will consist of about 5 questions of different lengths and marks based on the Pure Mathematics section of the syllabus.

Section B (Probability and Statistics－60 marks) will consist of 6 to 8 questions of different lengths and marks based on the Probability and Statistics section of the syllabus.

There will be at least two questions, with at least one in each section, on application of Mathematics in real-world contexts, including those from business and the social sciences. Each 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.

### Mathematics H2: 9758

This course is designed to prepare students for a range of university courses, such as 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 the applications of mathematics, students also develop an appreciation of mathematics and its connections to other disciplines and to the real world.

Topics covered include:

- Pure Mathematics: Functions and Graphs, Sequences and Series, Vectors, Complex Numbers, Calculus
- Probability and Statistics: Probability, Discrete Random Variables, Normal Distribution, Sampling, Hypothesis Testing, and Correlation and Linear Regression.

Knowledge of the content of O-Level Mathematics and part of Additional Mathematics is assumed in this syllabus.

**Scheme of Examination Papers**

For the examination in H2 Mathematics, there will be two 3-hour papers, each carrying 50% of the total mark, and each marked out of 100, as follows:

**Paper 1 (3 hours) **

A paper consisting of 10 to 12 questions of different lengths and marks based on the Pure Mathematics section of the syllabus.

There will be at least two questions on application of Mathematics in real-world contexts, including those from sciences and engineering. Each 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.

**Paper 2 (3 hours) **

A paper consisting of 2 sections, Sections A and B.

Section A (Pure Mathematics – 40 marks) will consist of 4 to 5 questions of different lengths and marks based on the Pure Mathematics section of the syllabus.

Section B (Probability and Statistics – 60 marks) will consist of 6 to 8 questions of different lengths and marks based on the Probability and Statistics section of the syllabus.

There will be at least two questions in Section B on application of Mathematics in real-world contexts, including those from sciences and engineering. Each 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.

### Mathematics H3: 9820

This course 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 this competencies through proving mathematical results and solving non-routine mathematical problems in the course of the learning.

Students will learn to prove properties and results, and solve non-routine problems involving:

- Numbers , e.g. primes, coprimes, divisibility, 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.

Knowledge of the content of H2 Mathematics is assumed.

**Scheme of Examination Papers**

For the examination in H3 Mathematics, there will be one 3-hour paper marked out of 100. The paper will consist of 8 to 10 questions of different lengths, and each question is worth 9 to 16 marks.

Candidates will be expected to answer all questions.

Updated as of 30 January 2018