Courses / Mathematics / Algebra, functions and mathematical modeling / Project Build and defend your work Build and defend a model-based comparison Compare two fictional plans using linear costs or constraints, then add a nonlinear growth or quadratic relationship. Solve relevant boundaries, check them by substitution, and explain the domain where the model is useful.
Choose an audience, investigate alternatives, copy evidence from your experiments, and produce an artifact. You can open this project at any time. Reports, numerical transfer checks and human review are separate outcomes.
Your project workspace Choose the kind of work you want to produce School investigation College investigation Workplace application Compare two school-event fee plans and a changing quantity. Draw labeled graphs and test values on both sides of a boundary.
1. Collect and compare evidence Required experiment sources:
Include every source above and at least one pair with different inputs from the same experiment. Explain confounding changes yourself; the presence check does not judge your interpretation.
Open an experiment and change an input or capture a trial to make evidence available here.
2. Write and revise your report Situation and model contract Define variables, units, permitted inputs and the decision being supported. Explain why the chosen family of functions fits.
Solve and verify the constraints Show algebraic steps and substitute answers back into original equations. For inequalities, test values on each side.
Nonlinear mechanism Explain a quadratic vertex/root or exponential/logarithmic calculation with a numerical example and a graph.
Degenerate or infeasible case Capture a no-solution, infinite-solution, no-real-root or infeasible-budget example and interpret it.
Decision and model revision Choose a plan and state which input, uncertainty or omitted condition would make you revise it.
Your artifact: code, analysis, prototype or decision brief This field stores up to 12,000 characters of inert text. Code runs only through the explicit bounded editor in the relevant lessons; project attachments never execute.
Load a text artifact Review your work against the rubric Variables and domains are explicit; a plotted curve is not assumed valid everywhere. Equations are solved by valid operations, and negative inequality division reverses the direction. Reported solutions satisfy the original rules; exceptional cases are not represented as ordinary numeric answers. A nonlinear model is interpreted through its mechanism rather than extrapolated blindly. The recommendation distinguishes mathematical equality from real-world feasibility. 11 evidence requirements remain Capture evidence from Balance an equation, bound a decision. Capture evidence from Satisfy two rules at once. Capture evidence from Read a quadratic from its shape. Capture evidence from Find the exponent that reaches a target. Include two different input configurations from the same experiment to compare. Write your situation and model contract. Write your solve and verify the constraints. Write your nonlinear mechanism. Write your degenerate or infeasible case. Write your decision and model revision. Add your project artifact: code, analysis, prototype or decision brief. Record my report Download report and evidence Editing the report or evidence returns it to draft. Recording verifies field presence and input comparisons, not correctness of your reasoning or code.
3. Check transfer to unfamiliar cases These authored cases use different numbers or conditions from the lesson practice. They are public local checks, not secure certification. Each case permits three submissions. Opening, first responses and attempt counts survive imports; no reset creates fresh evidence.
Case alg-negative Open case alg-negative Case alg-system Open case alg-system Case alg-root Open case alg-root Case alg-log Open case alg-log
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