**Head of Faculty: Mr Ian Bengey**

**Email:**ian.bengey@wis.edu.hk

**Aims**

The aims of all courses in group 5 are to enable students:

- To appreciate the multicultural and historical perspectives of all group 5 courses
- To enjoy the courses and develop an appreciation of the elegance, power and usefulness of the subjects
- To develop logical, critical and creative thinking
- To develop an understanding of the principles and nature of the subject
- To employ and refine their powers of abstraction and generalisation
- To develop patience and persistence in problem solving
- To appreciate the consequences arising from technological developments
- To transfer skills to alternative situations and to future developments
- To communicate clearly and confidently in a variety of contexts

**Overview**

Because individual students have different needs, interests and abilities, there are three IB Maths courses offered at West Island School. These courses are designed for different types of students: those who wish to study mathematics in depth, either as a subject in its own right or to pursue their interests in areas related to mathematics; those who wish to gain a degree of understanding and competence better to understand their approach to other subjects; and those who may not as yet be aware how mathematics may be relevant to their studies and in their daily lives. Each course is designed to meet the needs of a particular group of students. Therefore, great care should be taken to select the course that is most appropriate for an individual student.

In making this selection, individual students should be advised to take account of the following factors:

- Their academic plans, in particular the subjects they wish to study in future
- Their choice of career
- Their own abilities in mathematics and the type of mathematics in which they can be successful
- Their own interest in mathematics and those particular areas of the subject that may hold the most interest for them
- Their other choices of subjects within the framework of the diploma

Mathematical Studies SL |
Suitable for students who have completed Edexcel or CIE IGCSE with a grade C or higher and who do not need advanced Maths skills for their future studies. |

Mathematics SL |
Suitable for students who have completed CIE Extended course with a grade B or higher and who need Mathematics for their future university studies. |

Mathematics HL |
Suitable for students who have completed CIE IGCSE with a grade A* and have genuine passion for the subject. Students taking HL are likely to study mathematics, engineering or economics at university. |

**Mathematical Studies SL or Mathematics SL?**

Why take Mathematics SL when Mathematical Studies SL is easier and both are SL options? Students take Maths SL instead of Maths Studies SL for one of two reasons:

- Their university course specifically requires Maths SL not Maths Studies – for example to study science, medicine and some business courses.
**YOU MUST CHECK THIS BEFORE CHOOSING OPTIONS!** - Maths SL is the appropriate level of academic challenge for the individual and they enjoy mathematics.

It should be noted that Mathematics SL is a rigorous course which is at a similar academically challenging level as A-Level mathematics. Students should consider their choice of SL course very carefully – a number of students in international schools around the world choose unwisely and have to transfer from mathematics SL to Mathematics Studies after a period of time.

**MATHEMATICAL STUDIES (SL ONLY)**

**Course Objectives**

This course is available at standard level (SL) only. It caters for students with varied backgrounds and abilities. More specifically, it is designed to build confidence and encourage an appreciation of mathematics in students who do not anticipate a need for mathematics in their future studies. Students taking this course need to be already equipped with fundamental skills and a rudimentary knowledge of basic processes. They should have obtained a grade C in IGCSE Maths.

The course concentrates on mathematics that can be applied to contexts related as far as possible to other subjects being studied, to common real-world occurrences and to topics that relate to home, work and leisure situations. The course includes project work, in which students must produce a piece of written work based on personal research, guided and supervised by the teacher. The project provides an opportunity for students to carry out a mathematical investigation in the context of another course being studied, a hobby or interest of their choice using skills learned before and during the course. This process allows students to ask their own questions about mathematics and to take responsibility for a part of their own course of studies in mathematics.

The students most likely to select this course are those whose main interests lie outside the field of mathematics, and for many students this course will be their final experience of being taught formal mathematics. All parts of the syllabus have therefore been carefully selected to ensure that an approach starting with first principles can be used. As a consequence, students can use their own inherent, logical thinking skills and do not need to rely on standard algorithms and remembered formulae. Students likely to need mathematics for the achievement of further qualifications should be advised to consider an alternative mathematics course.

Because of the nature of Mathematical Studies, teachers may find that traditional methods of teaching are inappropriate and that less formal, shared learning techniques can be more stimulating and rewarding for students. Lessons that use an inquiry-based approach, starting with practical investigations where possible, followed by analysis of results, leading to the understanding of a mathematical principle and its formulation into mathematical language, are often most successful in engaging the interest of students. Furthermore, this type of approach is likely to assist students in their understanding of mathematics by providing a meaningful context and by leading them to understand more fully how to structure their work for the project.

**Course Outline**

The Mathematical Studies SL programme consists of the study of seven core topics.

Core Topics:

- Number and algebra
- Sets and logic
- Geometry and trigonometry

- Statistics and probability
- Functions
- Financial mathematics
- Differentiations

**Course Assessment**

The final assessment is based on the performance in two terminal examination papers and a project completed during the course.

**Paper 1 (40%)**: A one and a half hour paper comprising short-response questions on the core syllabus content. A graphical display calculator is required.

**Paper 2 (40%)**: A one and a half hour paper requires extended-response questions on the core content to be answered. A graphical display calculator is required.

**Project (20%)**: The project is an individual piece of work involving the collection and/or generation of data and the analysis and evaluation of that data. Projects may take the form of mathematical modelling, investigations, applications, statistical surveys and the like.

MATHEMATICS SL

MATHEMATICS SL

**Course Objectives**

This course caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematical background as they prepare for future studies in subjects such as chemistry, medicine, economics, psychology and business administration. The course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way, rather than insisting on mathematical rigour. Students should wherever possible apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context.

The internally assessed component, the portfolio, offers students a framework for developing independence in their mathematical learning by engaging in a mathematical exploration. Students will select a topic for their exploration based on their academic interests. This process allows students to ask their own questions about mathematics and to take responsibility for a part of their own course of studies in mathematics.

This course does not have the depth found in the Mathematics HL course. Students wishing to study subjects with a high degree of mathematical content should therefore opt for the Mathematics HL course rather than the Mathematics SL course.

Although this is a Standard Level course, the content is more demanding than that of Mathematical Studies SL. It is recommended that a prospective student should have obtained at least a grade B or higher at CIE IGCSE.

**Course Outline**

Core Topics:

- Number and algebra
- Functions and equations

- Circular functions and trigonometry
- Vector geometry

- Statistics and probability
- Calculus

**Course Assessment**

The final assessment is based on the performance in two terminal examination papers and an exploration completed during the course.

**Paper 1 (40%)**: A one and a half hour paper comprising short-response and extended response questions on the core syllabus content. Calculator not allowed.

**Paper 2 (40%)**: A one and a half hour paper comprising short-response and extended response questions on the core syllabus content. Graphical Display Calculator mandatory.

**Exploration (20%)**: This will be a written report on a mathematical topic of the student’s choice.

**MATHEMATICS HL**

**Course Objectives**

This course caters for students with a good background in mathematics who are competent in a range of analytical and technical skills.

**The majority of these students will be expecting to include mathematics as a major component of their university studies**, either as a subject in its own right or within courses such as physics, engineering and technology. Others may take this subject because they have a strong interest in mathematics and enjoy meeting its challenges and engaging with its problems. Students should have obtained a grade A* at CIE IGCSE Mathematics.

The nature of the subject is such that it focuses on developing important mathematical concepts in a comprehensible, coherent and rigorous way. This is achieved by means of a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solving problems set in a variety of meaningful contexts. Development of each topic should feature justification and proof of results. Students embarking on this course should expect to develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. They should also be encouraged to develop the skills needed to continue their mathematical growth in bother learning environments.

The internally assessed component, the portfolio, offers students a framework for developing independence in their mathematical learning by engaging in a mathematical exploration. Students will select a topic for their exploration based on their academic interests. This process allows students to ask their own questions about mathematics and to take responsibility for a part of their own course of studies in mathematics.

This course is a demanding one, requiring students to study a broad range of mathematical topics through a number of different approaches and to varying degrees of depth. Students wishing to study mathematics in a less rigorous environment should therefore opt for one of the standard level courses, Mathematics SL or Mathematical Studies SL. This is a Higher Level course that contains all of the material in the Mathematics SL course and more. This course is only recommended for those who have an intense interest in the subject and those who need mathematics for proposed university studies.

**Course Outline**

The course covers all of the topics listed in the Mathematics SL course (most to a greater depth) and in addition introduces includes an option component for greater mathematical analysis. The option topic is chosen by the class teacher in consultation with the head of faculty.

**Options:**

• Statistics

• Sets and groups

• Discrete mathematics

• Differential equations

**Course Assessment**

The final assessment is based on the performance in three terminal examination papers and a portfolio of two pieces of work completed during the course.

**Paper 1 (30%)**: A two hour paper comprising short-response and extended response questions on the core syllabus content. Calculator not allowed.

**Paper 2 (30%)**: A two hour paper comprising short-response and extended response questions on the core syllabus content. Graphical Display Calculator mandatory.

**Paper 3 (20%)**: A one hour paper on one of the option topics. Graphical Display Calculator mandatory.

**Exploration (20%)**: This will be a written report on a mathematical topic of the student’s choice.

**Further Mathematics HL**

**Course Objectives**

This course is available only at higher level. It caters for students with a very strong background in mathematics who have attained a high degree of competence in a range of analytical and technical skills, and who display considerable interest in the subject. Most of these students will expect to study mathematics at university, either as a subject in its own right or as a major component of a related subject. The course is designed specifically to allow students to learn about a variety of branches of mathematics in depth and also to appreciate practical applications. It is expected that students taking this course will also be taking mathematics HL.

Note: Mathematics HL is an ideal course for students expecting to include mathematics as a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering or technology. It should not be regarded as necessary for such students to study further mathematics HL. Rather, further mathematics HL is an optional course for students with a particular aptitude and interest in mathematics, enabling them to study some wider and deeper aspects of mathematics, but is by no means a necessary qualification to study for a degree in mathematics.

Please note that students taking HL Further mathematics will usually attend additional classes either at another ESF school or ESF Centre, joining with students form other schools.

***Further mathematics HL must be taken in addition to Maths HL, either replacing Group 6 or as a 7th subject.*****Course Outline**

All topics are compulsory. Students must study all the sub-topics in each of the topics in the syllabus as listed in this guide. Students are also required to be familiar with all of the core topics in mathematics HL.

Topic 1 Linear algebra

Topic 2 Geometry

Topic 3 Statistics and probability

Topic 4 Sets, relations and groups

Topic 5 Calculus

Topic 6 Discrete mathematics

**Note: One of topics 3–6 will be taught as part of the mathematics HL course.**

**Course Assessment**

The final assessment is based on the performance in two external examination papers.

**Paper 1 (50%)**: A 2 hours 30 minutes exam. Graphic display calculator required. Compulsory short- to medium-response questions based on the whole syllabus.

**Paper 2 (50%)**: A 2 hours 30 minutes exam. Graphic display calculator required. Compulsory medium- to extended-response questions based on the whole syllabus.