Further Mathematics Higher Level is a step further from Mathematics HL. The course began in 2014 i.e. their first assessment was held in 2014. However, the course ended in 2020. This course is usually taken by students who have a very strong background in mathematics and students who wish to pursue this in their university as a degree. The student would be required to have a high degree of competence in a range of analytical and technical skills. Studying mathematics at such a high level means the students delve into a variety of branches of mathematics in depth while appreciating their practical applications. This course is particularly for students who also wish to pursue courses in physics, engineering, or technology. While they follow this degree, they will simultaneously be satisfying the group 5 aims which include applying and transferring skills to other areas of knowledge and future developments. Some other aims are shown below:

- 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.

Further mathematics allows the students to indulge themselves and appreciate the diversity of the subject. This curriculum makes sure that the student enjoys learning the subject and develops an understanding of the principles of the subject.

**The curriculum consists of 6 topics:**

- 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

As for the assessment, students are graded based on two written papers. Paper 1 consists of short to medium-length questions. The graphical calculator is allowed for this paper. Paper 2, on the contrary, has medium to extended-length questions. The GDC is required for this paper as well. Both papers carry a 50% weightage each.

In mathematics the art of proposing a question must be held of higher value than solving it. – Georg Cantor

**Also Read **– Comparison of all Mathematics

## Assessment Model**: **

Having followed the further mathematics HL course, students will be ex- pected 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 analyzing information, making conjectures, drawing conclusions and testing their validity.

As for the difficulty between Mathematics HL and Further Mathematics, Math HL requires the student to study all the core topics plus one option. These courses are considered to be a first year university-level course. On the contrary, Further Math requires the students to study all the options in addition to the core topics. Therefore, the major difference would be in terms of the amount of concepts one has to learn but not the depth covered in each of the topics.

https://www.ibo.org/globalassets/publications/recognition/5_furthermathhl.pdf

https://www.spps.org/cms/lib/MN01910242/Centricity/Domain/853/IBFurtherMathGuide2014.pdf