Mathematics HL

**(NOTE: The syllabi for all subjects in group 5 have been revised for students starting the diploma period in 2012. This page will be updated with the new subject content has been released for publication by the IBO.)**

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.

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 other learning environments.

The internally assessed component, the portfolio, offers students a framework for developing independence in their mathematical learning through engaging in mathematical investigation and mathematical modelling. Students will be provided with opportunities to take a considered approach to these activities, and to explore different ways of approaching a problem. The portfolio also allows students to work without the time constraints of a written examination and to develop skills in communicating mathematical ideas.

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 other learning environments.

The internally assessed component, the portfolio, offers students a framework for developing independence in their mathematical learning through engaging in mathematical investigation and mathematical modelling. Students will be provided with opportunities to take a considered approach to these activities, and to explore different ways of approaching a problem. The portfolio also allows students to work without the time constraints of a written examination and to develop skills in communicating mathematical ideas.

Topic 1: Algebra

Topic 2: Functions and equations

Topic 3: Circular functions and trigonometry

Topic 4: Matrices

Topic 5: Vectors

Topic 6: Statistics and probability

Topic 7: Calculus

Topic 2: Functions and equations

Topic 3: Circular functions and trigonometry

Topic 4: Matrices

Topic 5: Vectors

Topic 6: Statistics and probability

Topic 7: Calculus

In addition, Mathematics HL students study __one__ of the options below:

Topic 8: Statistics and probability

Topic 9: Sets, relations and groups

Topic 10: Series and differential equations

Topic 11: Discrete mathematics

Topic 8: Statistics and probability

Topic 9: Sets, relations and groups

Topic 10: Series and differential equations

Topic 11: Discrete mathematics

The final assessment from the IB consists of the following components:

The internal assessment component is assessed by subject teacher and moderated externally by the IBO at the end of the course. This component makes up 20% of the final grade and consists of an individual portfolio with two tasks in mathematical modelling and investigation.

The external assessment component consists of three examinations at the end of the course.

Adapted from the IB Mathematics guide © International Baccalaureate Organization