79 free lessons · A guided path
Calculus
Understand a changing world.
Make sense of rates and accumulation, then explore series, differential equations, and several variables.
Explore the path ↓Find a comfortable starting point
One subject. Many levels of understanding.
Start with a familiar idea and move forward when the reasoning feels clear. Each lesson states its prerequisites. Grade is your first guide; the stages below describe the challenge within this subject, rather than a single school year. Extension lessons introduce selected advanced topics.
Foundations
Build intuition, name the quantities, and explain the basic idea.
1 lessons
Developing
Connect familiar ideas and choose a useful representation for a problem.
2 lessons
Intermediate
Combine methods, compare approaches, and justify the steps you take.
3 lessons
Advanced
Use deeper tools and check the assumptions behind a model or argument.
56 lessons
Extension
Meet selected university and research ideas after reviewing their prerequisites.
17 lessons
Your calculus lesson library
Choose the idea you want to explore.
Filter by grade or topic difficulty, or search for a particular skill. The collection includes every calculus lesson, with 12 shown at a time so you can browse at your own pace.
Showing 12 of 79 matching lessons · All free
CalculusGrade 12 · Advanced 15 min
Diagnose a jump through unequal one-sided limits
Separate a function's assigned value from its nearby behavior.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Control an oscillation by bounding its amplitude
Use two converging bounds when a factor oscillates without a limit.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Derive a power derivative from the difference quotient
Cancel a nonzero increment before taking its limit.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Differentiate a product with two changing factors
Include one contribution for the change in each factor.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Differentiate a normalized ratio
Apply the quotient rule and inspect its retained domain.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Differentiate a relation without solving it into one global function
Use the chain rule when both coordinates vary along a curve.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Relate the sensitivity of a function to that of its inverse
Differentiate an inverse composition at matching input-output points.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Differentiate when the base and exponent both vary
Use a logarithm to turn a variable power into a product.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Connect volume change to a changing height
Use geometric similarity before differentiating a related-rates model.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Guarantee a horizontal tangent between equal endpoint heights
Check Rolle's theorem and find its interior point.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Recognize a horizontal tangent without a maximum or minimum
Use sign changes of derivatives to classify a stationary inflection.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Minimize squared distance to avoid a square root
Find all closest points using symmetry and a nonnegative remainder.
Read, practice, and reflectGive the idea a shape.
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