IB Mathematics · Complete topic list

900 topic ideas – page 26 of 36.

Topics 626 to 650 with explanations, methods, course and equipment guidance.

Mathematics and applications

Compare 900 ideas clearly.

The list mixes calculus, statistics, modelling, geometry, number theory, computer science, sport, environmental topics and other areas. Each entry includes a short explanation and visible methods such as differential calculus, integral calculus, statistics or regression.

Planning guidance, not official topic approvalThe IA, EE, AA, Math AI, SL and HL classifications are editorial guidance. The current subject guide, assessment session, mathematical depth, focus and school approval remain decisive.
1

Select an idea. Titles and areas are starting points, not finished research questions.

2

Check A and C. These codes give an initial indication of assessment type, course and level.

3

Read P, M and S. They show possible independent direction, tools, and safety or data-protection needs.

Work
Course
Level

Showing 25 of 25 topic ideas

Mixed topic list for the Mathematics IA and Mathematics Extended Essay
No. Topic idea A C P M S
626 Mobile reception, Wi-Fi, and radio attenuationLine of sight, corners, and walls

Compare direct line of sight, one building corner, and several intervening walls at similar distances. Develop an additive attenuation model.

Functions & modelling
3 9 121112 120 1
627 Mobile reception, Wi-Fi, and radio attenuation2.4 GHz versus 5 GHz

Measure both frequency bands at the same positions and behind the same materials. Compare range, attenuation, and data rate.

Trigonometry
3 9 11112 6 1
628 Mobile reception, Wi-Fi, and radio attenuationSignal strength, throughput, and packet loss

At many positions, record RSSI, throughput, latency, and packet loss. Search for thresholds or piecewise relationships.

Functions & modellingTrigonometryGeometry
3 9 11112 3617 1
629 Rubik’s Cube, graph theory, and optimizationScramble length and minimum solution distance

Generate 2×2×2 scrambles of different lengths and determine the optimal solution using exhaustive search. Investigate the saturation effect.

Functions & modellingDifferential calculusGraph theoryGeometryOptimisation
3 9 1381112 1111316 0
630 Rubik’s Cube, graph theory, and optimizationDistribution of optimal solution distances

Analyse all or a large sample of 2×2×2 states. Determine the distribution, mean, and variance of minimum solution length.

Functions & modellingDifferential calculusStatistics & probabilityGraph theoryOptimisation
3 9 1381112 1111316 0
631 Rubik’s Cube, graph theory, and optimizationPractice time and solving speed

Measure one person’s solving time over many standardized practice sessions. Compare exponential, logarithmic, and power learning curves.

Functions & modellingDifferential calculusGraph theoryAlgebraOptimisation
3 9 13481112 3611121316 0
632 Rubik’s Cube, graph theory, and optimizationComparing solving methods

Compare beginner, CFOP, and computer-assisted methods in terms of move count, time, and variation. Create a Pareto analysis of speed and efficiency.

Functions & modellingDifferential calculusGraph theoryOptimisation
3 9 1381112 611121316 1
633 Rubik’s Cube, graph theory, and optimizationHeuristic quality and computational effort

Vary heuristic strength in A\* or IDA\* search. Measure explored states, memory use, runtime, and solution quality.

Functions & modellingDifferential calculusGraph theoryGeometrySimulation & algorithmsOptimisation
3 9 13781112 611131617 0
634 Rubik’s Cube, graph theory, and optimizationHalf-turn and quarter-turn metrics

Solve the same states using both move definitions. Investigate the distribution and ratio of the resulting minimum solution distances.

Functions & modellingDifferential calculusStatistics & probabilityGraph theoryOptimisation
3 9 1381112 1111316 0
635 Experiments with artificial intelligencePrompt specificity and answer quality

Present the same task with different levels of precise detail. Measure correctness, completeness, and number of unmet requirements.

Geometry
3 9 1381112 13 0
636 Experiments with artificial intelligenceZero-shot versus few-shot prompting

Give the model zero, one, three, or five solved examples. Investigate how the number of examples changes accuracy.

Functions & modellingStatistics & probability
3 6 181112 320 0
637 Experiments with artificial intelligenceGerman and English prompts

Translate a fixed set of tasks as equivalently as possible. Compare correctness, response length, and consistency between languages.

Proof
3 2 18101112 1 0
638 Experiments with artificial intelligenceIrrelevant information in prompts

Gradually add irrelevant or distracting information to tasks. Measure at what amount performance begins to decline.

Geometry
3 9 181112 3 0
639 Experiments with artificial intelligenceTypographical and linguistic noise

Introduce controlled letter swaps, missing spaces, or punctuation errors. Model accuracy as a function of noise level.

Functions & modellingStatistics & probabilityProofAlgebra
3 2 138101112 1120 0
640 Experiments with artificial intelligenceRepeatability of identical AI queries

Ask the same question in many independent runs. Determine agreement rate, response entropy, and variation in numerical results.

Numerical methods
3 9 1381112 13 0
641 Experiments with artificial intelligenceFree response versus fixed output format

Request free text in one condition and a fixed table or JSON-like schema in another. Compare formatting and content errors separately.

Geometry
3 9 181112 13 0
642 Experiments with artificial intelligenceSource requirements and verifiable claims

Compare responses without a source requirement with responses requiring verifiable evidence. Independently check every cited source.

Functions & modelling
3 9 1381112 13 0
643 Experiments with artificial intelligencePosition bias in multiple-choice questions

Systematically change the order of answer options for identical questions. Test whether particular positions are selected disproportionately.

Sequences & series
3 9 1381112 3 0
644 Experiments with artificial intelligenceRobustness to small numerical changes

Slightly change numerical values in a mathematics problem without changing its structure. Investigate sudden errors and local answer stability.

Numerical methods
3 9 13681112 1013 0
645 Experiments with artificial intelligenceImage brightness and classification accuracy

Create graded versions of the same images with different brightness and contrast. Determine accuracy and confidence.

Statistics & probability
3 6 1481112 7 0
646 Experiments with artificial intelligenceRotation and partial occlusion

Rotate images through fixed angles or cover a controlled proportion of each image. Model recognition rate as a function of angle or occlusion.

Functions & modellingTrigonometryGeometryAlgebra
3 9 181112 13720 0
647 Experiments with artificial intelligenceTraining-set size and model accuracy

Train the same small classification model using increasing amounts of data. Create learning curves for training and test error.

Functions & modellingStatistics & probabilityProof
3 2 148101112 1220 0
648 Experiments with artificial intelligenceClass imbalance and evaluation metrics

Change the class proportions in the training dataset. Compare accuracy, precision, recall, F1 score, and confusion matrices.

Statistics & probabilityMatricesProof
3 2 148101112 31213 0
649 Experiments with artificial intelligenceModel size, accuracy, and speed

Compare models or compression levels on the same task. Create a Pareto frontier using accuracy, runtime, memory use, and energy consumption.

Functions & modellingStatistics & probabilityOptimisation
3 6 1381112 61220 0
650 Experiments with artificial intelligenceClassical regression versus AI models

Use your own water, CO₂, battery, or sound data. Compare linear or polynomial regression with a machine-learning model using unseen test data.

Functions & modellingRegressionSimulation & algorithmsAlgebra
3 6 1467811 359131620 2
Code legend

What A, C, P, M and S mean.

The table stays narrow on a phone by replacing long descriptions with numeric codes. Entries may contain several P and M codes.

AAssessment type
1
Internal Assessment (IA)
2
Mathematics Extended Essay (EE)
3
Potentially suitable for an IA or EE, depending on focus and mathematical depth
CCourse and level
1
Mathematics AA SL
2
Mathematics AA HL
3
Mathematics AA at SL or HL
4
Mathematics AI SL
5
Mathematics AI HL
6
Mathematics AI at SL or HL
7
Mathematics AA or AI at SL
8
Mathematics AA or AI at HL
9
Mathematics AA or AI at SL or HL
PWays to demonstrate independent direction and personal engagement
1
Own data, measurements, observations or experiment
2
Own photographs, drawings, constructions or models
3
Own sport, video, GPS or tracker context
4
Own school or class survey or observation
5
Own everyday, household, consumer or financial data
6
Local context: environment, buildings, traffic, climate or nature
7
Own programming, simulation or algorithm
8
Personal interest: music, art, games, design or another hobby
9
Public data selected, prepared and analysed independently
10
Own conjecture, proof idea, generalisation or theoretical comparison
11
Own modelling decision, construction, optimisation or adaptation
12
Critical comparison of assumptions, errors, limitations or ethical issues
MMeasuring instruments, tools or data access
0
No specialist physical instrument; a calculator, CAS, spreadsheet or open data may be sufficient
1
Ruler, tape measure, calliper or protractor
2
Balance or precision scale
3
Contact thermometer or temperature data logger
4
Infrared thermometer or thermal camera
5
Multimeter or another electrical measuring instrument
6
Stopwatch or timer
7
Camera or smartphone for photographic and video analysis
8
GPS device or fitness tracker
9
Microphone, sound-level meter or audio-analysis software
10
Light meter, light sensor or solar sensor
11
Conductivity, pH or salinity meter
12
Weather instruments, such as an anemometer or rain gauge
13
Computer, spreadsheet, CAS, GeoGebra, Desmos or Python
14
Survey form, data sheet or observation record
15
Force sensor or spring balance
16
Laboratory glassware, measuring cylinder or pipette
17
Telescope, binoculars or a suitable camera
18
Humidity or material-moisture sensor
19
Non-invasive physiology sensor, such as heart-rate or reaction-time measurement
20
Physical model, 3D printer or material samples
21
Specialist school laboratory equipment
SSafety and data protection
0
Likely to be low risk within normal school practice
1
Supervision recommended, for example for heat, electricity, sport or traffic observation
2
Carry out only in a school laboratory or with qualified supervision
3
Sensitive personal or health data: consent, anonymisation and preferably secondary data; no medical self-intervention
From heading to investigation

A topic becomes workable only through independent decisions.

The table is designed to speed up the first step. The actual research question emerges through focus, mathematical choice and critical checking.

Focus the object

Define the object, dataset, time period, variable or mathematical structure as precisely as possible.

Select the mathematics

Decide which models, proofs, statistical procedures or optimisation steps can genuinely answer the question.

Plan independent direction

Use your own data, comparisons, modelling choices, extensions or proof ideas rather than reproducing a standard procedure.

Reflect on limitations

Examine assumptions, sources of error, data quality, model limitations, safety and possible improvements.

Personal engagement and independent direction

A personal connection is more than one sentence in the introduction.

The P codes indicate possible ways to shape an investigation independently. Independent thinking becomes visible through justified decisions, appropriate data selection, personal model variants, meaningful comparisons and critical reflection. A code does not guarantee a particular mark.

Review the IA requirements
Frequently asked questions

Use the topic list correctly.

Are the titles finished research questions?

No. They name a possible direction. A question for assessed work must be focused more narrowly, matched to the course and level, and connected to a clear mathematical method.

What does A = 3 mean?

The broad direction could be developed as an IA or Mathematics EE, depending on focus and depth. An EE will normally require a substantially deeper mathematical argument and an appropriate research scope.

Is C an official IB classification?

No. C is editorial guidance for Mathematics AA or Math AI and SL or HL. Final suitability depends on the specific research question and the current requirements.

Do I need to own the listed instruments?

No. M indicates typical or possible tools. Many topics can use open data, a spreadsheet, CAS, GeoGebra, Desmos or Python. Adapt the topic to resources that are genuinely available.

How should topics involving health or personal data be handled?

Prefer anonymised or publicly available secondary data. Original data collection needs consent, data protection, school approval and a low-risk method. Diagnosis, medication changes and invasive self-experimentation do not belong in a Mathematics project.

The complete list is also machine-readable.

The same 900 entries are available as plain text and bilingual JSON for search, accessibility and AI systems.

Authoritative foundations

Check the current curriculum version before starting.

The catalogue complements the PreLearning explanations. Current official IB documents and the school's instructions remain authoritative.

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