This course is intended for students with a strong 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, technology or economics. Others may take this subject because, irrespective of their plans for further study, they have a strong interest in mathematics and enjoy meeting its challenges and engaging with its problems.

The nature of mathematics can be summarized in a number of ways: it can be seen as a well-defined body of knowledge, as an abstract system of ideas, or as a useful tool. The Mathematics HL course provides students with in depth knowledge of the subject area. Mathematical concepts are developed in a comprehensible, coherent and rigorous way. Development of each topic will 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.

Aims of the course

• To develop an understanding of the principles and nature of the subject
• To develop logical, critical and creative thinking
• To develop an appreciation of the elegance, power and usefulness of mathematics
• To employ and refine students’ powers of abstraction and generalization
• To appreciate the multicultural and historical perspectives of mathematics
• To develop patience and persistence in problem-solving
• To appreciate the consequences arising from technological developments
• To transfer skills to alternative situations and to future developments
• To communicate clearly and confidently in a variety of contexts

Syllabus outline
The syllabus covers eight topics:

• Algebra
• Functions and equations
• Circular functions and trigonometry
• Matrices
• Vectors
• Statistics and probability
• Calculus
• HL Options

Differences between Mathematics HL and SL
The HL course in mathematics differs from the SL course in mathematics in terms of the:

• hours devoted to teaching (240 hours for HL compared to 150 hours for SL)
• extra depth and breadth required (HL Option topics)
• nature of the examination questions.

Assessment outline: Mathematics HL

This is a two-year course. In May 2012, students will sit three written papers:

• Paper 1 will assess topics 1-7 without the use of a calculator. The exam is for 2 hours and is worth 30% of the final mark.
• Paper 2 assesses topics 1-7 using a graphic display calculator. The exam lasts 2 hours and is worth 30% of the total mark
• Paper 3 assesses topic 8 – with a graphic display calculator. It lasts 1 hour and is worth 20% of total marks.

In addition, students submit a portfolio containing two pieces of work for internal assessment. The portfolio offers students a framework for developing independence in their mathematical learning through engaging in mathematical investigation and mathematical modeling. The portfolio allows students to work without the time constraints of a written examination and to develop skills in communicating mathematical ideas. The portfolio accounts for 20% of the total mark.

Prerequisites

This course is intended for students with a good background in mathematics who are competent in a range of analytical and technical skills.

This course is a demanding one, requiring students to study a broad range of mathematical topics through a number of different approaches and to varying degrees of depth. In making the selection, individual students are advised to take into account their own mathematical ability, their interest in mathematics, their choice of career and their other choices of subjects within the framework of the Diploma Program.

The IB specifies a long list of “presumed knowledge”, which can be found in the IB Subject Guide and which is also available upon request from Pamoja Education. The course will review a number of the topics, but students should be familiar with a majority of the topics prior to the start of the course.

This course requires that students have access to a graphic display calculator.

Adapted from the IB Mathematics HL Study Guide © International Baccalaureate Organization.