Khan Academy
Start here for short explanations and free interactive practice. Each link in the table leads to the relevant current Calculus 1 unit.
Calculus II readiness
A focused Calculus I review
Calculus II relies on a small set of Calc I skills being easy to use. This guide highlights those skills and gives you a free practice path for each one.
What this review covers
This is intentionally not a complete Calc I course. It emphasizes limits, derivatives, antiderivatives, the Fundamental Theorem of Calculus, and u-substitution—the tools that prepare you most directly for Calc II. Related rates and optimization are omitted because they are less central to the techniques ahead.
Choose the resource that fits how you learn
Paul’s Online Math Notes
Use these detailed written notes and worked examples when you want another explanation or a slower reference.
Your Purdue lecture videos can be an excellent optional third resource for current students, but they should not be the only link because they require a Purdue account. When added, label them “Purdue students: course video” alongside—not instead of—the free options.
Calc I skills that matter most in Calc II
| Skill | Why it matters now | Practice with Khan Academy | Read with Paul’s Notes |
|---|---|---|---|
| Limits & continuity | |||
| Evaluating limits algebraically | Factoring, rationalizing, and simplifying limits keep reappearing in derivative and integration work. | Limits & continuity | Computing limits |
| One-sided, infinite & limit-at-infinity behavior | These ideas support improper integrals and interpreting asymptotes later in the course. | Limits & continuity | Calc I limits topics |
| Continuity | Continuity is part of the hypotheses behind key calculus theorems and helps you reason about functions before applying a technique. | Limits & continuity | Calc I continuity topics |
| Derivatives | |||
| Derivative meaning & basic rules | You need derivatives to recognize reverse chain-rule patterns and later to use L’Hôpital’s Rule appropriately. | Derivatives: definition & basic rules | Derivative introduction |
| Product & quotient rules | These rules help you differentiate the inner functions that appear in substitutions and support later applications. | Derivatives: definition & basic rules | Product & quotient rules |
| Chain rule | The chain rule is the derivative-side pattern behind u-substitution. | Chain rule & advanced derivatives | Chain rule |
| Trig, exponential & logarithmic derivatives | Calc II integration techniques depend on recognizing these functions and their derivatives quickly. | Chain rule & advanced derivatives | Trig derivatives · exponential & log derivatives |
| Implicit differentiation | This is useful background for later curve work and reinforces careful chain-rule thinking. | Chain rule & advanced derivatives | Implicit differentiation |
| Integration & the Fundamental Theorem | |||
| Basic antiderivatives | Integration techniques build on knowing common antiderivatives without having to derive each one from scratch. | Integrals | Indefinite integrals |
| Definite integrals & net change | These ideas return in applications and help distinguish a function from its accumulated change. | Integrals | Definite integrals |
| Fundamental Theorem of Calculus | You will repeatedly connect an accumulation function, its derivative, and a definite integral. | Integrals | Fundamental Theorem of Calculus |
| u-substitution: choosing u | Recognize a composite function and the matching derivative factor before starting a substitution. | Integrals — u-substitution | u-substitution: indefinite integrals |
| u-substitution: completing the change | Rewrite the entire integrand and either change the bounds or back-substitute correctly. | Practice u-substitution | u-substitution: definite integrals |
| Targeted prerequisites | |||
| Trig values & basic identities | These become essential for trig integrals and simplification; review only the parts that slow you down. | Trigonometry practice | Trig integrals reference |
| Exponential & logarithmic rules | Exponentials and logs appear in integration techniques and differential equations. | Exponential & log practice | Exponential & log functions |
| Algebraic simplification of integrands | Factoring, rational expressions, and correct cancellation often determine whether an integration technique works. | Algebra & precalculus refresher | Calc I algebra review |
A practical review plan
Begin with u-substitution and the supporting chain rule. If those feel comfortable, review basic antiderivatives and the Fundamental Theorem of Calculus. Return to limits or targeted algebra/trig only when they are creating friction in a problem.