Algebra, functions and mathematical modeling
Build and solve equations, inequalities and systems, interpret quadratic shape, and use exponential/logarithmic models within a stated domain.
Choose any lesson or try the project first. Shared lessons retain the same saved work wherever you enter them. Completing a lesson records participation; practice, transfer checks and independent reasoning remain separate.
Recommended preparation and ways to catch up
- Review fractions and signed-number arithmetic when needed; all lessons remain directly accessible.
- Before solving: substitution means replacing a symbol by a known equal value or expression.
- Before curves and inverse growth: a function assigns an output to each permitted input; a graph displays those input-output pairs.
Find a foundation course · Open contextual refreshers. Each investigation includes a short recap; preparation never locks access.
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Your units and lessons
Choose a unit to see its lesson sequence. Every lesson opens on its own page.
From situations to linear rules
Define inputs, outputs, slope, intercept and the domain where a rule is meaningful.
Use a function as an input–output rule
Substitute values, follow the order of operations and check the permitted inputs.
Separate a starting value from a rate
Change slope and intercept independently and calculate a rate from two points.
Solve and combine constraints
Solve equations and inequalities with degenerate cases, then satisfy two rules simultaneously.
Balance an equation, bound a decision
What changes when you divide an inequality by a negative number?
Satisfy two rules at once
When do two linear requirements agree?
Compare two options at the right scale
Find where costs match and decide which option is cheaper for an allowed input.
Quadratic and exponential relationships
Interpret vertices and roots, model compounding, and reverse exponential growth with logarithms.
Read a quadratic from its shape
When does a curved model reach zero?
Follow growth one period at a time
Why do repeated percentages differ from repeated fixed additions?
Find the exponent that reaches a target
How do you solve a growth equation when time is unknown?
Make the algebra serve a decision
Distinguish mathematical solutions from feasible whole-number choices and omitted real conditions.
Allocate a constrained budget
Which combinations fit after reserving a safety margin?
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.
Build from lesson evidence, compare alternatives, write an artifact, and tackle unfamiliar numerical cases. Use the rubric with a teacher, peer or colleague to assess the quality of your reasoning.
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