IB Diploma Programme Mathematics: Analysis and Approaches: Subject Overview

Individual students have different needs, aspirations, interests and abilities. For this reason the IB Diploma Programme offers two mathematics subjects – Mathematics: Analysis and Approaches, and Mathematics: Applications and Interpretation – each designed to meet the needs of a particular group of students. Both are offered at SL and HL, and share 60 hours of common SL content, so the choice between them is genuinely about which style of mathematical thinking suits a given student, not about one course being a harder or easier version of the other.

What this course emphasizes

Mathematics: Analysis and Approaches recognizes the need for analytical expertise in a world where innovation increasingly depends on a deep understanding of mathematics. The focus is on developing important mathematical concepts in a comprehensible, coherent and rigorous way. Students apply their mathematical knowledge to solve abstract problems as well as those set in meaningful contexts, with a strong emphasis on constructing, communicating and justifying correct mathematical arguments. Students develop insight into mathematical form and structure, and are equipped to appreciate the links between concepts in different topic areas. An internally assessed exploration allows students to develop independence in mathematical learning.

Aims

The aims of all DP mathematics courses, including this one, are to enable students to:

• 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 instil 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.

How it’s assessed

Mathematics: Analysis and Approaches is assessed through written papers plus an internally assessed exploration, with different weightings and paper counts at SL and HL. At SL, Paper 1 (1.5 hours, no calculator or other technology permitted) and Paper 2 (1.5 hours, technology allowed) are each worth 40% of the final grade. At HL, both papers run for 2 hours and are each worth 30%, and HL students additionally sit Paper 3 (1 hour 15 minutes, technology allowed: two extended-response problem-solving questions), worth 20%. The distinguishing feature of Analysis and Approaches, compared with Applications and Interpretation, is that Paper 1 is sat without a calculator or other technology, directly testing algebraic manipulation and proof.

The current course described here runs to its final examination session in November 2028. Its successor, first assessed in 2029, shortens HL Paper 3 to 1 hour – a change that applies only from that first assessment onward, not to the course described in this guide.

In both SL and HL, the internally assessed mathematical exploration is worth the remaining 20% of the final grade: a written piece of independent mathematical investigation into a topic of the student’s choosing, structured identically to its counterpart in Applications and Interpretation.

The five content strands

The syllabus is organised into five strands. Number and algebra covers sequences and series, financial applications such as compound interest, exponents and logarithms, the binomial theorem, and, at HL, further algebraic techniques such as complex numbers and proof by induction – the smallest strand at SL relative to the others, but the one that expands the most, proportionally, at HL (more than doubling from 19 to 39 hours). Functions covers the concept of a function, graphing and transforming functions, and solving equations, forming the algebraic and graphical toolkit that the Calculus strand later depends on heavily. Geometry and trigonometry covers geometry in two and three dimensions, trigonometric identities and equations, and, at HL, vectors in more depth – its proportional SL-to-HL jump is close behind Number and algebra’s, reflecting substantial HL-only content in vectors and further trigonometry. Statistics and probability covers descriptive statistics, probability and distributions, including bivariate data, correlation and regression, and grows only modestly from SL to HL since much of the statistical toolkit is shared between both levels. Calculus, covering differentiation, integration and their applications, completes the five strands and carries the largest number of teaching hours at both levels, and the largest absolute increase in hours from SL to HL.

How this course differs from Applications and Interpretation

Both DP mathematics courses share 60 hours of common SL content and the same assessment objectives, but distribute their remaining hours very differently across the same five strand names, reflecting a real difference in emphasis: Analysis and Approaches leans towards rigorous, proof-oriented technique, most visibly in its calculator-free Paper 1, while Applications and Interpretation leans towards modelling and technology-driven interpretation, permitting technology throughout every paper. A student deciding between the two courses is really choosing between these two styles of mathematical work, since the internally assessed exploration is structured identically in both courses and so offers no real basis for choosing one over the other.

Why Paper 1’s calculator-free format matters

The distinguishing practical feature of Analysis and Approaches, set against Applications and Interpretation, is that Paper 1 is sat without a calculator or other technology, directly testing algebraic manipulation and proof rather than allowing technology to carry part of the computational load. This has a direct consequence for preparation: fluency in manipulating expressions, solving equations and constructing an argument by hand needs to be genuinely automatic by the time of the exam, since there is no calculator available to check or complete a calculation partway through a question, unlike Paper 2 or Paper 3, where technology is permitted throughout.

Source

International Baccalaureate Organization, Mathematics: Analysis and Approaches subject brief (Diploma Programme), 2019.