Limits, derivatives, and integrals: a learning progression
Use nearby behavior, rates of change, and accumulation to extend algebraic and graphical reasoning.
Before you begin
Be comfortable with functions, factoring, exponents, trigonometry, and graph interpretation.
Readiness depends on the ideas you can use, not only your age or grade. Start earlier in the sequence when an example feels unfamiliar.
How the skill develops
- Study limits using tables, graphs, substitution, and simplification.
- Connect derivatives to tangent slopes and instantaneous rates.
- Choose differentiation rules based on the structure of an expression.
- Connect integrals with accumulated change and check antiderivatives by differentiation.
What grade is this taught?
Our catalog includes this progression from grade 12 through grade 12. That is a map of the practice available here, not a rule that every school uses the same schedule. Earlier grades may introduce models that later grades formalize.
The sequence is our teaching organization, informed by the published curriculum reference. High-school courses and calculus enrollment vary; check your school’s syllabus for placement decisions.
Build your next practice steps
Mark skills you already feel comfortable with. We’ll suggest the next unchecked skills in this sequence. This is a self-selected path, not a test score.