Focus the object
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
Topics 626 to 650 with explanations, methods, course and equipment guidance.
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.
Select an idea. Titles and areas are starting points, not finished research questions.
Check A and C. These codes give an initial indication of assessment type, course and level.
Read P, M and S. They show possible independent direction, tools, and safety or data-protection needs.
| 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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
3 | 6 | 1467811 | 359131620 | 2 |
No topic ideas match this combination.
The table stays narrow on a phone by replacing long descriptions with numeric codes. Entries may contain several P and M codes.
The table is designed to speed up the first step. The actual research question emerges through focus, mathematical choice and critical checking.
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
Decide which models, proofs, statistical procedures or optimisation steps can genuinely answer the question.
Use your own data, comparisons, modelling choices, extensions or proof ideas rather than reproducing a standard procedure.
Examine assumptions, sources of error, data quality, model limitations, safety and possible improvements.
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 requirementsNo. 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.
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.
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.
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.
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 same 900 entries are available as plain text and bilingual JSON for search, accessibility and AI systems.
The catalogue complements the PreLearning explanations. Current official IB documents and the school's instructions remain authoritative.