Learn Use rates, geometry and constraints to test everyday decisions.
Start with everyday situations, predict an outcome, and test your ideas. You need basic arithmetic, percentages and graph reading; explanations introduce additional ideas where needed. No coding or account is required. Every investigation has school, college and workplace extensions—you can choose any of them.
Translate a situation into rates, constraints, probability, matrix operations and optimization; test the assumptions against numerical evidence.
Open any topic directly. Review functions and graphs whenever useful.
The original two-investigation starter remains available. Choosing the full course adds its published lessons to your selected scope; your earlier work stays saved. Skipping does not count as completion or understanding.
Free exploration: no completion scope selected yet. Project reports and independent evidence are tracked separately.
Choose a unit, then open a lesson on its own page. This outline lists the sequence; it does not combine the full lessons into one page.
Separate fixed and variable terms, enforce feasibility and distinguish additive from multiplicative change.
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How much time can faster travel actually save?
Plan a synthetic journey with a fixed distance, constant moving speed and fixed delays. This is a mathematical model, not a driving recommendation.
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Which combinations fit after reserving a safety margin?
An original synthetic project buys A units for 4 credits and B units for 6. Choose a reserve and A quantity, then calculate the maximum whole B quantity.
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Why do repeated percentages differ from repeated fixed additions?
An invented stock begins at a chosen number of units and changes by a constant annual percentage. Compare compounding with changes computed from the original base.
Use conditional branches and matrix rows to connect inputs to outcomes with correct dimensions.
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Does being late mean it probably rained?
An original synthetic travel model supplies rain probability and different late-arrival rates for rainy and dry days. Use mutually exclusive branches rather than guessing.
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How can one table calculate several resource totals?
Original synthetic production: a small kit uses 2 kg material and 1 labor hour; a large kit uses 5 kg and 2 hours. Matrix rows represent resources.
Find constrained optima, use local slopes and evaluate a forecast on later observations.
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Which rectangle gives the most space for a fixed fence?
Design a rectangular garden using a fixed amount of fencing for all four sides. Allocate part of the half-perimeter to its width.
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When does following the downhill direction overshoot?
Minimize the original synthetic squared-error function (x − 2)². A derivative gives its local slope; step size controls how far to move.
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How do smoothing and trend assumptions change a forecast?
Original synthetic demand history begins 10,12,14,16. A held-out pair 18,20 is used only to evaluate the displayed predictions; it becomes exposed practice after inspection.
Build a fictional resource plan with a budget and at least two products or activities. Use a matrix to calculate needs, test one growth forecast, and compare feasible alternatives. Explain where uncertainty or a nonlinear relationship changes your decision.
Save a report, compare captured evidence, and attempt three new cases. A completed report records submitted work; the rubric supports a separate human review of its quality.
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