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Calculus I — the complete course
The mathematics of change and accumulation: 71 lessons, 5 unit quizzes, and a 40-question final exam.
Your progress
Checking your progress…
Mark lessons as learned with the button on each formula page — quizzes count as attempted when you answer your first question.
What this course covers
Calculus I is the study of change (derivatives) and accumulation (integrals) — the two ideas that power physics, engineering, economics, and machine learning. The five units build on each other:
- Limits — what functions approach, continuity, and the infinite processes everything else rests on.
- Differentiation rules — the toolkit: computing derivatives of products, quotients, chains, trig, exponentials, and logs.
- Applications of derivatives — putting derivatives to work: motion, optimization, curve sketching, related rates.
- Integrals — undoing differentiation: areas, the Fundamental Theorem, substitution, and volumes of revolution.
- Exponential & log laws — the algebra behind ex and ln x that makes the transcendental functions manageable.
How to use this hub
- Learn a unit's lessons — every formula page teaches deeply (motivation, full derivation, worked examples) with a short quiz after each section.
- Take the unit quiz — 15 questions drawn from the whole unit. Retake until it feels easy.
- Sit the final exam — 40 questions across all five units. 32+/40 means the course is yours.
The final exam
40 questions sampled proportionally across all five units, in random order — limits through integrals, mixed together the way a real final mixes them. Every answer explains itself; missed questions tell you which lesson to revisit.
Study guide: how to pass a calculus final
- Do the units in order the first time — limits underpin derivatives, derivatives underpin integrals.
- Never skip a derivation. The steps are where the exam traps hide.
- Redo every worked example with the steps covered, then check.
- Use the unit quizzes as diagnostics: a miss means reread that lesson, not just retry the quiz.
- The night before, take the final exam twice. Sleep beats cramming.
Frequently asked questions
What does Calculus I cover?
This course covers all of single-variable Calculus I in five units: Limits, Differentiation rules, Applications of derivatives, Integrals, and Exponential & log laws — 71 formula lessons in total.
How should I use this course hub?
Work through one unit at a time: read each formula lesson (every section ends with a short quiz), then take the unit's 15-question quiz. When all five units feel solid, take the 40-question final exam.
How do the unit quizzes work?
Each unit quiz draws 15 questions at random from every lesson in that unit — about 1,500 questions feed the five units — so every attempt is different. Every answer explains itself, and you can retake as often as you like.
What is the final exam like?
40 questions sampled proportionally across all five units, in random order — a genuine exam simulation. Aim for 32+/40 before calling the course done.
Do I have to do the units in order?
Order is recommended — limits underpin derivatives, derivatives underpin integrals — but every lesson stands alone, so you can jump to whatever your class is covering this week.
Is this really free?
Yes. No account, no paywall, no sign-up. Everything runs in your browser.
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Questions or a bug to report? Email [email protected].