Group 5

Mathematics – Analysis and Approaches

This course is designed for students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. They will also be fascinated by exploring real and abstract applications of these ideas, with and without technology. Students who take Mathematics: analysis and approaches will be those who enjoy the thrill of mathematical problem solving and generalization.

This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL.

The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of choice of course. However, Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

Distinction between SL and HL

Students who choose Mathematics: analysis and approaches at SL or HL should be comfortable in the manipulation of algebraic expressions and enjoy the recognition of patterns and understand the mathematical generalization of these patterns.

Students who wish to take Mathematics: analysis and approaches at higher level will have strong algebraic skills and the ability to understand simple proof. They will be students who enjoy spending time with problems and get pleasure and satisfaction from solving challenging problems.


  1. The aims of all DP mathematics courses are to enable students to:
  2. develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power.
  3. develop an understanding of the concepts, principles and nature of mathematics.
  4. communicate mathematics clearly, concisely and confidently in a variety of contexts.
  5. develop logical and creative thinking, and patience and persistence in problem solving to instil confidence in using mathematics.
  6. employ and refine their powers of abstraction and generalization.
  7. take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments in their local and global communities.
  8. appreciate how developments in technology and mathematics influence each other.
  9. appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics.
  10. appreciate the universality of mathematics and it’s multicultural, international and historical perspectives.
  11. appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course
  12. develop the ability to reflect critically upon their own work and the work of others
  13. independently and collaboratively extend their understanding of mathematics.

Course Structure

All topics are compulsory. Students must study all the sub-topics in each of the topics in the detailed syllabus guide.

Topic 1: Number and Algebra

Topic 2: Functions

Topic 3: Geometry and trigonometry

Topic 4: Statistics and probability

Topic 5: Calculus

Mathematical exploration: Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics.

Assessment at Standard Level

Assessment component Weighting
External assessment
Paper 1 (1 hour 30 minutes) No calculator allowed. 40%
Paper 2 (1 hour 30 minutes) Graphic display calculator required. 40%
Internal assessment
Mathematical exploration 20%

Assessment at Higher Level

Assessment component Weighting
External assessment
Paper 1 (2 hours) No calculator allowed 30%
Paper 2 (2 hours) Graphic display calculator required. 30%
Paper 3 (1 hour) Graphic display calculator required. 20%
Internal assessment
Mathematical exploration 20%