Mathematics

Group 5 subjects

Overview of Mathematics in the IBDP

There are two Mathematics courses within the IB Diploma Programme.

• Mathematics: Analysis and Approaches

• Mathematics: Applications and Interpretation

Both courses are offered at Higher Level (HL) and Standard Level (SL). The courses are designed for different types of students: those who wish to study mathematics as a subject in its own right or to pursue their interest in areas related to mathematics, and those who wish to gain understanding and competence in how mathematics relates to the real world and to other subjects. These courses are designed to meet the needs of students with differing abilities and different requirements for higher education.

In making this selection, consideration should be taken of the following factors:

• a student’s ability in mathematics and the type of mathematics they can be successful in

• a student’s interest in mathematics and those particular areas of the subject that hold the most interest for them

• other subject choices within the framework of the Diploma Programme

Skills developed (all Mathematics courses)

Problem-solving is central to learning Mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems. Having followed a DP Mathematics course, students will be expected 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 abstract and real-world 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 standardised notation; use appropriate notation and terminology

• 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 from the real-world, involving organising and analysing information, making conjectures, drawing conclusions, and testing their validity

University courses and careers

Mathematics: Analysis and Approaches: This subject is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or economics.

Mathematics: Applications and Interpretation: This subject is aimed at students who will go on to study subjects such as social sciences, natural sciences, statistics, business, some economics, psychology, and design.

Mathematics: Analysis and Approaches (HL and SL)

Mathematics: Analysis and Approaches at SL and HL is appropriate 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 the use of technology. Students who take Mathematics: Analysis and Approaches will be those who enjoy the thrill of mathematical problem solving and generalisation. This subject is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or economics, for example.

Course content

Both courses at HL and SL share the same common core of 120 hours. HL then takes each topic and adds more depth of analysis, adding an extra 90 hours in total. Both SL and HL courses are also allocated 30 hours to write up and develop the skills needed for internally assessed coursework—The Mathematical exploration. This focuses on investigative, problem-solving and modelling skills development leading to individual exploration. The exploration is a piece of written work that involves investigating an area of Mathematics.

Course outline

This course has an emphasis on generalisation, proof and calculus. There will be more time spent on the units of Number, Algebra, Geometry, Trigonometry and Calculus.

• Topic 1: Number and Algebra

• Topic 2: Functions

• Topic 3: Geometry and trigonometry

• Topic 4: Statistics and probability

• Topic 5: Calculus

• The toolkit and Mathematical exploration:

Investigative, problem-solving and modelling skills development leading to individual exploration. The exploration is a piece of written work that involves investigating an area of mathematics.

For Mathematics: Analysis and Approaches syllabus, click here.

Assessment

SL: two written papers – 80%

(section A short questions; section B long questions)

• paper 1 (1 hour 30 minutes) – 40%

will be without the use of technology

• paper 2 (1 hour 30 minutes) – 40%

will allow the use of a graphical calculator

HL: three written papers – 80%

(section A short questions; section B long questions)

• paper 1 (2 hours) – 30%

will be without the use of technology

• paper 2 (2 hours) – 30%

will allow the use of a graphical calculator

• paper 3 (1 hour) – 20%

problem-solving paper; will allow the use of a graphical calculator; two extended questions leading to generalisations or interpretations (same weightings as current papers)

SL/HL mathematical exploration – 20%

This component is internally assessed by the teacher and externally moderated by the IB at the end of the course; this is a piece of written work that gives students the opportunity to appreciate a wider range of mathematics, as well as applying mathematical concepts to real life situations.

Mathematics: Applications and Interpretation (HL and SL)

Mathematics: Applications and Interpretation SL and HL is appropriate for students who are interested in developing their Mathematics for describing our world and solving practical problems. They will also be interested in harnessing the power of technology alongside exploring mathematical models. Students who take Mathematics: Applications and Interpretation will be those who enjoy Mathematics best when seen in a practical context. This subject is aimed at students who will go on to study subjects such as social sciences, natural sciences, statistics, business, some economics, psychology, and design, for example.

Course content

Both courses at HL and SL share the same common core of 120 hours. HL then takes each topic and adds more depth of analysis, adding an extra 90 hours in total. Both SL and HL courses are also allocated 30 hours to write up and develop the skills needed for internally assessed coursework—The Mathematical exploration. This focuses on investigative, problem-solving and modelling skills development leading to an individual exploration. The exploration is a piece of written work that involves investigating an area of Mathematics.

Course outline

This course has an emphasis on technology, practical problem solving, statistics and modelling. There will be more time spent on the units of Functions and Statistics and Probability.

• Topic 1: Number and Algebra

• Topic 2: Functions

• Topic 3: Geometry and trigonometry

• Topic 4: Statistics and probability

• Topic 5: Calculus

• The toolkit and Mathematical exploration:

Investigative, problem-solving and modelling skills development leading to individual exploration. The exploration is a piece of written work that involves investigating an area of Mathematics.

For Mathematics: Applications and Interpretation, click here.

Assessment

SL: two written papers – 80%

(all papers with graphical calculator)

• paper 1 (1 hour 30 minutes) short questions – 40%

• paper 2 (1 hour 30 minutes) long questions – 40%

HL: three written papers – 80%

(all papers with graphical calculator)

• paper 1 (2 hours) short questions – 30%

• paper 2 (2 hours) long questions – 30%

• paper 3 (1 hour) – 20%

problem-solving paper; two extended questions leading to generalisations or interpretations.

SL/HL Mathematical exploration – 20%

This component is internally assessed by the teacher and externally moderated by the IB at the end of the course; this is a piece of written work that gives students the opportunity to appreciate a wider range of Mathematics, as well as applying mathematical concepts to real life situations