# IB DP- Further Mathematics (HL)

It is a requirement of the programme that students study at least one course in mathematics. Students can only study one course out of three in mathematics. All DP

mathematics courses serve to accommodate the range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations.

The aims of these courses are to enable students to:

- Develop mathematical knowledge, concepts and principles
- Develop logical, critical and creative thinking
- Employ and refine their powers of abstraction and generalization.

Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

In this article we will discuss **Further Mathematics**

The IB DP further mathematics higher level (HL) course 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. The nature of the subject is such that it focuses on different branches of mathematics to encourage students to appreciate the diversity of the subject. Students should be equipped at this stage in their mathematical progress to begin to form an overview of the characteristics that are common to all mathematical thinking, independent of topic or branch.

**Aims of the Course**

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

• Enjoy mathematics, and develop an appreciation of the elegance and power of mathematics

• Develop an understanding of the principles and nature of mathematics

• Communicate clearly and confidently in a variety of contexts

• Develop logical, critical and creative thinking, and patience and persistence in problem-solving

• Employ and refine their powers of abstraction and generalization

• Apply and transfer skills to alternative situations, to other areas of knowledge and to future developments

• Appreciate how developments in technology and mathematics have influenced each other

• Appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics

• Appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives

• Appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course.

**Curriculum Model Overview**

**Topic 1**

Linear algebra

Recommended teaching hours- 48

**Topic 2**

Geometry

Recommended teaching hours- 48

**Topic 3**

Statistics and probability

Recommended teaching hours- 48

**Topic 4**

Sets, relations and groups

Recommended teaching hours- 48

**Topic 5**

Calculus

Recommended teaching hours- 48

**Topic 6**

Discrete mathematics

Recommended teaching hours- 48

**Assessment Model**

Having followed the further mathematics HL course, the subject brief states that, students will be taught and learn to demonstrate the following-

• Knowledge and understanding: recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.

• Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in both real and abstract contexts to solve problems.

• Communication and interpretation: transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation.

• Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to solve problems.

• Reasoning: construct mathematical arguments through use of precise statements, logical deduction and inference, and by the manipulation of mathematical expressions.

• Inquiry approaches: investigate unfamiliar situations, both abstract and real-world, involving organizing and analysing information, making conjectures, drawing conclusions and testing their validity.

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