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 preuniversity 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 handheld 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.
Aims
 develop a curiosity and enjoyment of mathematics and appreciate its elegance and power.
 develop an understanding of the concepts, principles and nature of mathematics
 communicate mathematics clearly, concisely, and confidently in a variety of contexts.
 develop logical and creative thinking, and patience and persistence in problem solving to install confidence in using mathematics.
 employ and refine their powers of abstraction and generalization.
 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.
 appreciate how developments in technology and mathematics influence each other.
 appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics.
 appreciate the universality of mathematics and its multicultural, international and historical perspectives.
 appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course.
 develop the ability to reflect critically upon their own work and the work of others.
 independently and collaboratively extend their understanding of mathematics.
Assessment
Standard Level
Assessment component  Weighting 
External assessment (3 hours) Paper 1 (90 minutes) No technology allowed. (80 marks) Section A Compulsory shortresponse questions based on the syllabus. Section B Compulsory extendedresponse questions based on the syllabus.  80% 40% 
Paper 2 (90 minutes) Technology required. (80 marks) Section A Compulsory shortresponse questions based on the syllabus. Section B Compulsory extendedresponse questions based on the syllabus  40% 
Internal assessment This component is internally assessed by the teacher and externally moderated by the IB at the end of the course. Mathematical exploration Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)  20% 
Higher Level
Assessment component  Weighting 
External assessment (5 hours) Paper 1 (120 minutes) No technology allowed. (110 marks) Section A Compulsory shortresponse questions based on the syllabus. Section B Compulsory extendedresponse questions based on the syllabus.  80% 30% 
Paper 2 (120 minutes) Technology required. (110 marks) Section A Compulsory shortresponse questions based on the syllabus. Section B Compulsory extendedresponse questions based on the syllabus.  30% 
Paper 3 (60 minutes) Technology required. (55 marks) Two compulsory extended response problemsolving questions.  20% 
Internal assessment This component is internally assessed by the teacher and externally moderated by the IB at the end of the course. Mathematical exploration Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)  20% 
Syllabus
Syllabus component  Suggested teaching hours 

 SL  HL 
Topic 1—Number and algebra  19  39 
Topic 2—Functions  21  32 
Topic 3— Geometry and trigonometry  25  51 
Topic 4—Statistics and probability  27  33 
Topic 5 —Calculus  28  55 
The toolkit and the mathematical exploration Investigative, problemsolving and modelling skills development leading to an individual exploration. The exploration is a piece of written work that involves investigating an area of mathematics.  30  30 
Total teaching hours  150  240 
This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a datarich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a preuniversity mathematics course such as calculus and statistics.
The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.
Aims
 develop a curiosity and enjoyment of mathematics and appreciate its elegance and power.
 develop an understanding of the concepts, principles, and nature of mathematics.
 communicate mathematics clearly, concisely, and confidently in a variety of contexts.
 develop logical and creative thinking, and patience and persistence in problem solving to instill confidence in using mathematics.
 employ and refine their powers of abstraction and generalization.
 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.
 appreciate how developments in technology and mathematics influence each other.
 appreciate the moral, social, and ethical questions arising from the work of mathematicians and the applications of mathematics.
 appreciate the universality of mathematics and its multicultural, international, and historical perspectives.
 appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course.
 develop the ability to reflect critically upon their own work and the work of others.
 independently and collaboratively extend their understanding of mathematics.
Assessment
Standard Level
Assessment component  Weighting 
External assessment (3 hours) Paper 1 (90 minutes) Technology required. (80 marks) Compulsory shortresponse questions based on the syllabus. (80 marks)  80% 40% 
Paper 2 (90 minutes) Technology required. (80 marks) Compulsory extendedresponse questions based on the syllabus. (80 marks)  40% 
Internal assessment This component is internally assessed by the teacher and externally moderated by the IB at the end of the course. Mathematical exploration Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)  20% 
Syllabus
Syllabus component  Suggested teaching hours—SL 
Topic 1—Number and algebra  16 
Topic 2—Functions  31 
Topic 3—Geometry and trigonometry  18 
Topic 4—Statistics and probability  36 
Topic 5—Calculus  19 
The “toolkit” and Mathematical exploration Investigative, problemsolving and modelling skills development leading to an individual exploration. The exploration is a piece of written work that involves investigating an area of mathematics.  30 
Total teaching hours  150 
The TOK course plays a special role in the DP by providing an opportunity for students to reflect on the nature, scope and limitations of knowledge and the process of knowing. In this way, the main focus of TOK is not on students acquiring new knowledge but on helping students to reflect on, and put into perspective, what they already know.
TOK underpins and helps to unite the subjects that students encounter in the rest of their DP studies. It engages students in explicit reflection on how knowledge is arrived at in different disciplines and areas of knowledge, on what these areas have in common and the differences between them. It is intended that through this holistic approach, discussions in one area will help to enrich and deepen discussions in other areas.
The course is an opportunity for teachers and students to engage in interesting conversations that cross the boundaries of individual disciplines and that help students to reflect on the knowledge they have acquired from both their academic studies and their lives outside the classroom. Students are encouraged to examine the evidence for claims and to consider, for example, how we distinguish fact from opinion, or how we evaluate the credibility of claims that we are exposed to in the media. They explore different methods and tools of inquiry and try to establish what it is about them that makes them effective, as well as considering their limitations.
The following 12 concepts have particular prominence within, and thread throughout, the TOK course: evidence, certainty, truth, interpretation, power, justification, explanation, objectivity, perspective, culture, values and responsibility. Exploration of the relationship between knowledge and these concepts can help students to deepen their understanding, as well as facilitating the transfer of their learning to new and different contexts.
The TOK course embraces the exploration of tensions, limitations and challenges relating to knowledge and knowing. However, it is also intended that TOK discussions will encourage students to appreciate and be inspired by the richness of human knowledge—and to consider the positive value of different kinds of knowledge. Consideration should be given to the benefits of this kind of reflection on knowledge and knowing; for example, in terms of its potential to help us think more subtly, to be more aware of our assumptions, or to overcome prejudice and promote intercultural understanding.
Aims
 to encourage students to reflect on the central question, “How do we know that?”, and to recognize the value of asking that question.
 to expose students to ambiguity, uncertainty, and questions with multiple plausible answers.
 to equip students to effectively navigate and make sense of the world and help prepare them to encounter novel and complex situations.
 to encourage students to be more aware of their own perspectives and to reflect critically on their own beliefs and assumptions.
 to engage students with multiple perspectives, foster openmindedness and develop intercultural understanding.
 to encourage students to make connections between academic disciplines by exploring underlying concepts and by identifying similarities and differences in the methods of inquiry used in different areas of knowledge.
 to prompt students to consider the importance of values, responsibilities and ethical concerns relating to the production, acquisition, application, and communication of knowledge.
Assessment
Assessment component  Weighting 
Internal assessment Theory of knowledge exhibition (10 marks) For this component, students are required to create an exhibition that explores how TOK manifests in the world around us. This component is internally assessed by the teacher and externally moderated by the IB at the end of the course.  1/3 (33%) 
External assessment TOK essay on a prescribed title (10 marks) For this component, students are required to write an essay in response to one of the six prescribed titles that are issued by the IB for each examination session. As an external assessment component, it is marked by IB examiners.  2/3 (67%) 
Syllabus
Course elements  Minimum teaching hours 
Core theme: Knowledge and the knower This theme provides an opportunity for students to reflect on themselves as knowers and thinkers, and on the different communities of knowers to which we belong.  32 
Optional themes Students are required to study two optional themes from the following five options.


Areas of knowledge Students are required to study the following five areas of knowledge.
 50 
Assessment Students are required to complete two assessment tasks.
 18 
Total minimum teaching hours  100 