Model a changing quantity
How well can a linear, quadratic, exponential, or sinusoidal function describe a real dataset?Collect or source appropriate data, compare models, justify a choice, interpret parameters, and discuss limitations.
Projects and investigations
Math projects and investigations
Use a prompt, requirements, marking criteria, and submission checklist. Your teacher’s instructions remain authoritative.
Investigate a fair decision
How can probability and expected value help evaluate a game, policy, or repeated choice?Define outcomes, build a probability model, calculate expected results, test with simulation or data, and qualify the conclusion.
Optimize a design
Which dimensions maximize or minimize a meaningful geometric quantity under a fixed constraint?Define variables and restrictions, build the objective function, analyze candidates, interpret units, and test feasibility.
Study a financial choice
How do interest rate, payment timing, and compounding change a savings or borrowing scenario?State assumptions, compare at least two models, show formulas, use consistent time periods, and discuss what the model omits.
Project requirements
Show the full line of reasoning.
- Focused questionSpecific, answerable, and mathematically meaningful.
- Sources and assumptionsIdentify data origin, units, restrictions, and simplifying choices.
- Mathematical developmentShow formulas, substitutions, graphs, calculations, and reasons for each method.
- InterpretationExplain what results mean in context—not only what the calculator displayed.
- Limitations and reflectionIdentify uncertainty, model limits, and a reasonable next question.
Suggested marking criteria
Understanding · 25%
Concepts, notation, definitions, and conditions are accurate.
Process · 30%
Methods are appropriate, organized, justified, and reproducible.
Communication · 25%
Graphs, tables, units, labels, explanations, and sources are clear.
Interpretation · 20%
Conclusions answer the question and acknowledge limitations.
Submission checklist
- My name, course, date, title, and research question are visible.
- Every table and graph has a title, axis labels, units, and source.
- I showed formulas and representative calculations, not only outputs.
- I cited outside data, images, definitions, and ideas using the required style.
- I checked domain restrictions, rounding, units, and reasonableness.
- I followed the teacher’s file type, naming, length, and submission instructions.