IB Diploma Programme Mathematics: Analysis and Approaches: Syllabus Guide

This guide covers the full syllabus structure of IB Diploma Programme Mathematics: Analysis and Approaches, first assessment 2021, for both Standard Level (SL) and Higher Level (HL) students. It complements the subject overview already on the site by setting out the five content strands and their teaching-hour balance – the actual shape of what is examined, not just the course’s aims and philosophy.

Analysis and Approaches shares 60 hours of common SL content with Mathematics: Applications and Interpretation, but the two courses distribute their teaching hours very differently across the same five strand names, reflecting a real difference in what each course emphasises – Analysis and Approaches leans towards rigorous, proof-oriented technique, while Applications and Interpretation leans towards modelling and technology-driven interpretation.

Both courses’ assessment objectives – knowledge and understanding, problem solving, communication and interpretation, technology, reasoning, and inquiry approaches – apply across all five strands, so a strand is never examined as pure recall in isolation from these wider skills.

Number and algebra (19 hours SL / 39 hours HL)

Covers sequences and series, financial applications of geometric sequences and series such as compound interest and annual depreciation, exponents and logarithms, the binomial theorem, and (at HL) further algebraic techniques such as complex numbers and proof by induction. This is the smallest strand at SL relative to the other four, but it expands the most of any strand, proportionally, at HL – from 19 to 39 hours, a factor of just over 2.05.

Functions (21 hours SL / 32 hours HL)

Covers the concept of a function, graphing and transforming functions, and solving equations – the algebraic and graphical toolkit that the Calculus strand later depends on heavily.

Geometry and trigonometry (25 hours SL / 51 hours HL)

Covers geometry in two and three dimensions, trigonometric identities and equations, and (at HL) vectors in more depth. This strand’s proportional jump from SL to HL (a factor of just over 2.04) is close behind, but second to, Number and algebra’s – reflecting substantial HL-only content in vectors and further trigonometry.

Statistics and probability (27 hours SL / 33 hours HL)

Covers descriptive statistics, probability, and distributions, including bivariate data, correlation and regression – content that grows only modestly from SL to HL, since much of the statistical toolkit is shared between both levels.

Calculus (28 hours SL / 55 hours HL)

Covers differentiation, integration and their applications. This is the largest strand at HL by absolute hours (55, versus 51 for Geometry and trigonometry), and along with Geometry and trigonometry accounts for most of the extra depth HL students study beyond the SL course – though Number and algebra shows the largest proportional increase of the five strands.

Together, the five content strands total 120 hours at SL and 210 hours at HL, with the remaining 30 hours at both levels given to the toolkit and the mathematical exploration together, as described below.

Toolkit and exploration (30 hours, both SL and HL)

The 30 hours at both SL and HL are shared between two components. The toolkit is time set aside within the taught hours for developing inquiry, modelling and technology skills – mathematical thinking techniques that transfer across strands – rather than being tied to any one strand’s content. Up to 15 of the 30 hours are for the exploration itself: an internally assessed mathematical investigation into a topic of the student’s own choosing, compulsory for both SL and HL, which develops independence in mathematical learning and lets students pursue a personal mathematical interest without the time constraints of a written exam.

Assessment structure

• Paper 1 (no technology, 40% SL / 30% HL) – Section A of compulsory short-response questions, Section B of compulsory extended-response questions, all based on the syllabus and requiring unaided algebraic fluency.
• Paper 2 (technology allowed, 40% SL / 30% HL) – the same short-response/extended-response structure as Paper 1, but with graphical display calculator use permitted throughout.
• Paper 3 (HL only, technology allowed, 20%) – two compulsory extended-response problem-solving questions, drawing on material across the whole syllabus rather than one strand at a time.
• Exploration (internal assessment, 20% SL / 20% HL) – the investigation described above.

The no-technology constraint on Paper 1 is the single most distinctive feature of this course’s assessment relative to Applications and Interpretation, where every external paper permits technology throughout – it is a direct reflection of Analysis and Approaches’ greater emphasis on manual algebraic and analytical technique.

How to approach it

Because Analysis and Approaches shares 60 hours of common content with Applications and Interpretation but distributes its remaining hours so differently – putting more weight on Calculus and Geometry and trigonometry, and comparatively less on Statistics and probability – students who transfer between the two courses, or who are choosing between them, should look closely at where their own strengths and interests actually lie: comfort with abstract algebraic manipulation and rigorous proof suits Analysis and Approaches, since Paper 1 (no technology allowed) tests exactly that kind of unaided algebraic fluency. HL roughly doubles the SL hours in three strands specifically – Number and algebra (19 to 39 hours), Geometry and trigonometry (25 to 51 hours), and, by absolute hours added, Calculus (28 to 55 hours) – so HL students should treat all three as the core of their extra study time, rather than the two that “roughly double” hours might suggest at a glance; Functions and Statistics and probability grow far less from SL to HL and warrant comparatively less additional study time, rather than spreading revision evenly across all five strands as if the SL/HL gap were uniform. For the exploration, choose a topic within a strand you are already comfortable with rather than an ambitious one outside your depth – since it is internally assessed on genuine mathematical understanding and communication, not novelty of topic, a well-executed exploration on familiar territory typically scores more reliably than an ambitious one that outruns the student’s technical control.

Both DP mathematics courses share a common set of assessment objectives – knowledge and understanding, problem solving, communication and interpretation, technology, reasoning, and inquiry approaches – so the underlying skills being tested are the same across Analysis and Approaches and Applications and Interpretation even though the content and the calculator policy differ. Choosing between the two courses is best made on genuine mathematical interest and aptitude rather than perceived ease, since both are assessed to an equally demanding standard.

Official syllabus

International Baccalaureate Organization, Diploma Programme Subject Brief – Mathematics: Analysis and Approaches, first assessment 2021, © 2019.