Historical syllabus archive, rebuilt in 2026. This page was first published in 2015 for the former IB Diploma Mathematics Standard Level course. That course architecture is no longer current. Since August 2019, IB Diploma mathematics has been organised as Mathematics: Analysis and Approaches (AA) and Mathematics: Applications and Interpretation (AI), each available at Standard Level and Higher Level.
Quick Read
The old “Mathematics SL” name belongs to a retired IB Diploma structure. Students in 2026 should not use the 2015 topic list below as a current syllabus checklist. The useful historical value is seeing how much mathematical continuity remains: algebra, functions, geometry, trigonometry, calculus, statistics and probability still matter, but IB now organises the subject through the AA and AI pathways.
Current IB route: International Baccalaureate — Mathematics in the Diploma Programme.
What replaced the old Mathematics SL course?
From August 2019, with first assessment in May 2021, IB offered four Diploma Programme mathematics options:
- Mathematics: Analysis and Approaches SL;
- Mathematics: Analysis and Approaches HL;
- Mathematics: Applications and Interpretation SL;
- Mathematics: Applications and Interpretation HL.
Students take one mathematics course as part of the Diploma Programme.
AA and AI are not simply “hard maths” and “easy maths”
A useful distinction is about mathematical emphasis rather than status.
| Course family | Typical emphasis |
|---|---|
| Analysis and Approaches | Algebraic reasoning, mathematical argument, symbolic manipulation, functions, calculus and analytical techniques. |
| Applications and Interpretation | Mathematical modelling, statistics, technology-supported exploration, interpretation of data and mathematics in real contexts. |
Both require mathematical thinking. The right course depends on the learner’s strengths, intended university pathway and the requirements of future programmes.
The next IB mathematics update is already announced
IB has announced updated AA and AI courses for first teaching in August 2027 and first assessment in May 2029. IB describes the redevelopment as a refinement of the current courses rather than a complete reinvention.
This is why old syllabus pages should be preserved as archives rather than silently rewritten as if the historical labels were still current.
Historical 2015 Mathematics SL topic map
The original eduKate page grouped the former Mathematics SL material into four large families. The exact course structure is historical, but the underlying mathematical ideas remain useful for comparison.
Algebra, Functions and Equations
- quadratic functions and equations;
- exponents and logarithms;
- algebraic manipulation;
- function notation, domain and range;
- composite and inverse functions;
- transformations of graphs;
- sequences and series;
- binomial expansion.
Geometry and Trigonometry
- radian measure;
- sine, cosine and tangent functions;
- trigonometric equations and identities;
- sine and cosine rules;
- triangle and circle geometry;
- three-dimensional trigonometry;
- vectors and vector equations.
Calculus
- differentiation and interpretation of derivatives;
- tangents and normals;
- stationary points;
- optimisation;
- indefinite and definite integration;
- areas under and between curves;
- chain, product and quotient rules;
- integration by substitution;
- kinematics and volumes of revolution.
Statistics and Probability
- measures of centre and spread;
- frequency tables and grouped data;
- cumulative frequency and histograms;
- correlation;
- theoretical and empirical probability;
- Venn and tree diagrams;
- conditional probability;
- random variables;
- binomial and normal distributions.
What survives across syllabus changes?
Course names and assessment structures change. Mathematical capability is more durable.
A student should still become able to:
- represent a problem mathematically;
- move between symbolic, graphical, numerical and verbal forms;
- choose an appropriate method;
- use technology responsibly;
- interpret a result in context;
- justify a conclusion;
- recognise limitations of a model;
- communicate mathematical reasoning clearly.
Those are safer long-term targets than memorising a syllabus table without understanding the mathematics underneath it.
AA-style thinking: structure before calculation
Students leaning toward Analysis and Approaches need strong symbolic control and comfort with abstraction. A useful learning sequence is:
definition → relationship → representation → algebraic method → proof or justification → transfer.
Formula recall is not enough. The student needs to understand why the mathematical object behaves as it does.
AI-style thinking: model, compute, interpret, question
Applications and Interpretation places greater emphasis on mathematics interacting with data, technology and real situations.
A useful loop is:
real situation → mathematical model → technological or analytical solution → interpretation → limitation check → revised model.
The calculator or software can produce an output. The learner still has to decide whether the model and result make sense.
Technology is part of the mathematics, not an escape from it
IB mathematics expects students to become competent with technology, including graphical-display calculators in the current course architecture. But technological fluency should not hide mathematical weakness.
Students should know:
- what quantity is being entered;
- what mathematical operation the tool is performing;
- what output is being returned;
- whether the answer has a plausible scale;
- what assumptions sit behind the result;
- when an exact form is more informative than a decimal approximation.
The tool should extend capability, not erase understanding.
Choosing AA or AI
Students should not choose from reputation alone. A sensible decision checks:
- current mathematical strengths;
- comfort with symbolic manipulation and proof-style reasoning;
- comfort with data, modelling and technology;
- intended university courses;
- specific admissions requirements;
- whether SL or HL is appropriate for the intended pathway.
University requirements can be specific and can change. Students should verify the requirements of the actual institutions and programmes they intend to apply to rather than relying on forum advice or old school notes.
How to use this archive safely
- Use the historical topic list to understand how the former Mathematics SL course was organised.
- Do not use it as a 2026 examination checklist.
- Use the current IB subject briefs for present-day course content and assessment.
- Check the 2027/2029 update if planning for future cohorts.
- Keep the underlying mathematical concepts, but update the course architecture around them.
The deeper principle
A syllabus is a temporary map of a subject. Mathematics is larger than the map.
Students who learn only the current list can become fragile when the list changes. Students who understand functions, models, representations, proof, uncertainty and mathematical communication can move across syllabus generations much more easily.
Archive note: first published 27 April 2015 as “Mathematics SL Maths IB Diploma Syllabus”. Rebuilt in 2026 to preserve the retired course as history, document the current AA/AI architecture and point future cohorts toward the 2027/2029 IB curriculum update. This URL is intentionally noindexed because its slug names an obsolete syllabus.