Brilliant teaches calculus across three courses. Calculus is the complete one: 42 lessons that run the whole subject, from the derivative through integrals, limits, continuity, and infinite series. Limits and Derivatives are newer and much slower, and they are still being built — between them they cover sequences, convergence, and the derivative at a point in 43 lessons, which is more careful groundwork than any textbook chapter gives you. All three build calculus as ideas rather than procedures: what a limit is, why a derivative is a rate of change, where the Fundamental Theorem comes from. Coverage is deep on the concepts and thin on technique, so it works best alongside a class or textbook.
One scoping note: Common Core has no calculus strand, so there is no Common Core map to measure calculus against. The College Board's Course and Exam Description for AP Calculus AB and BC is the closest thing to a shared syllabus for the class most students are taking, so that is the framework this page uses. Brilliant is not an AP course and does not prepare you for the exam's free-response section.
Which Brilliant course covers which part of calculus?
| Course | What it covers for calculus | Where to start |
|---|---|---|
| Calculus (42 lessons) | The derivative and its uses, the differentiation rules, integrals and the Fundamental Theorem, volumes and surface areas, function limits and continuity, sequences and series, Taylor series | Rate Of Change |
| Derivatives (23 lessons) | Average rate of change, net change and velocity, difference quotients, local linearity, the tangent line, the limit definition of the derivative, linear approximation | Visualizing Change |
| Limits (20 lessons) | Sequences on a number line and as graphs, recursive and explicit formulas, arithmetic and geometric sequences, boundedness, convergence to a limit | Sequences |
Limits and Derivatives are partly built. Limits has 3 of its 14 levels written and Derivatives 4 of 11; the remaining level titles are listed on each course page as coming soon. Everything below describes lessons that exist today.
Where Brilliant is strongest: the derivative, built slowly
If you want to understand where the derivative comes from rather than be handed it, Derivatives is the best reason to use Brilliant. It takes four levels to reach a result most textbooks state on the first page, and that patience is the point.
It opens on rate of change as something you can see. Visualizing Change and Constant Rate of Change work on graphs before any formula appears; Variable Rate of Change breaks the constant-rate assumption, and Average Rate of Change and Secant Lines make the average rate a chord slope. The second level adds sign and motion — Net Change, Displacement, Velocity — and ends by assembling the object itself in Difference Quotients.
Only then does the limit arrive. Local Linearity zooms in until a curve looks straight, The Tangent Line and The Derivative at a Point name what that gives you, and The Limit Definition of Derivative writes it down. The fourth level computes derivatives from that definition rather than from rules — Computing Derivatives for f(x) = x², Derivatives of Linear Functions, Derivatives of Exponential Functions, Derivative of the Square Root Function — and closes on Linear Approximation.
What it does not yet have is the differentiation rules. The power, product, and chain rules, related rates, and curve sketching are announced as coming levels but are not written. For those, use Calculus, which covers them in its third level: Constant Multiples, Sums, Products and Powers, Chain Rule, and Quotients.
Limits, and what "limit" means before functions
Limits is a sequences course today. That is not a gap so much as a different route in: it builds the limit concept on sequences, where the definition is easiest to see, before functions complicate it.
The first two levels are the sequence mechanics — Sequences, The Index, Recursive Sequences, Increasing or Decreasing, and Bounded, then the same objects on a graph in Sequences as Functions, Arithmetic Sequences, and Geometric Sequences. Decimal Expansions and Approximating a Number quietly set up why anyone would want a limit at all.
The third level is the payoff, and it is the epsilon definition without the notation. Hitting the Target asks whether a sequence can be made to land inside a target band, Any Target Size asks whether it can do so for every target, and The Limit names the answer. Comparing Powers and Comparing Coefficients turn it into something you can compute.
Function limits, one-sided limits, limits at infinity, and continuity are announced as coming levels of this course but are not written yet. Today they live in Calculus, in Function Limits, Limit Theorems, Continuity, and Smooth Functions, which builds the differentiability-versus-continuity distinction that trips up a lot of students, plus Intermediate Value Theorem and Extreme Value Theorem.
Integrals, and the idea that ties the subject together
Integration is only in Calculus, and it is the part of that course worth the most to a student who has already sat through a class. The Area Problem and The Integral build the definite integral as an accumulation, and The Fundamental Theorem explains why differentiation and integration are inverses. If your class introduced antiderivatives as a procedure and the connection never clicked, this is a short, targeted fix. Antiderivatives and Apply: Falling objects follow, and the next level applies integrals to Volume With Integrals and Surface Area via Integrals.
The applications of the derivative are here too, rather than in Derivatives: Maxima And Minima and Critical Points, then Identifying Extremes, Test Limitations, and Higher-Order Derivatives.
Series, if you are in BC
What is an Infinite Sum?, Geometric Sums, and Harmonic Sum build convergence intuitively, and Quadratic Approximations and Taylor Series explain what a Taylor series is for before you memorize the standard ones. Sine and Cosine and The Exponential Function derive the series for the functions you will be asked to recognize.
What is missing is the convergence-test machinery — ratio test, integral test, alternating series, radius of convergence. Brilliant builds the intuition for convergence and then stops.
What you need before you start
Calculus assumes work these courses teach and a calculus class rarely reteaches.
| Course | What it gives a calculus student |
|---|---|
| Equations and Curves (61 lessons) | Asymptotes, removable discontinuities, and rational functions — the objects limit problems are about |
| Polynomials (52 lessons) | Factoring, roots, sign regions, and dominant terms — the algebra behind limit and extrema work |
| Exponential Functions (42 lessons) | Exponential models, the groundwork for growth and decay problems |
| Logarithms (29 lessons) | Logarithms as the inverse of exponentiation, and the log laws |
| Trigonometric Functions (62 lessons) | Radians, the unit circle, and periodicity, assumed throughout |
| Polar Coordinate Plane (35 lessons) | Polar coordinates and radian work needed before BC Unit 9 |
| Vectors (39 lessons) | Vector components, magnitude, and velocity — the setup for vector-valued functions |
What to supplement
These are standard parts of a calculus class. For them, use your textbook or teacher:
- Integration technique. Substitution, integration by parts, partial fractions, and improper integrals. Brilliant builds what an integral is, then stops short of how to evaluate hard ones.
- Differential equations. Slope fields, separation of variables, and the full Unit 7 treatment. Exponential growth and decay models are covered, in Exponential Functions.
- Convergence tests. The BC Unit 10 machinery, as above.
- Contextual applications of the derivative. Related rates and optimization problems in quantity. Apply: Optimization is one lesson, not a unit.
- The exam itself. There is no free-response practice, no scoring rubrics, no calculator-active sections, and no full-length timed exams anywhere on Brilliant.
Brilliant is a practice and explanation layer alongside your class: interactive problems and step-by-step reasoning for the parts it covers. It does not follow your syllabus or assess you.
How this mapping was made
Brilliant's skills are mapped topic by topic against the AP Calculus Course and Exam Description, working from the live course catalog, and the mapping is reviewed by Brilliant's curriculum team. The data here was pulled on September 30, 2026. Across AB and BC, Brilliant reaches something in all ten units, but unevenly: Units 1, 2, 6, and 10 are where it is strongest, Unit 4 is a single topic, and Units 3, 5, 7, 8, and 9 are supported mostly by the prerequisite courses above.
Frequently asked questions
Is Brilliant enough to pass the AP Calculus exam?
No. Three courses is more calculus than Brilliant used to carry, but they teach the ideas underneath the subject, not the exam — there is no free-response practice, no scoring rubrics, and no timed full-length sections. Treat Brilliant as a concept layer under a real course, not as a substitute for one.
Which of the three should I start with?
If you are in a class, match the topic: Derivatives if the derivative has not clicked, Limits if convergence has not, Calculus for everything else and for anything past the derivative. Starting from scratch and not in a hurry, Limits then Derivatives then Calculus is the intended order.
Why are Limits and Derivatives so much slower than Calculus?
They are a different kind of course. Calculus covers the whole subject in 42 lessons and moves quickly; Limits and Derivatives take one idea each and build it from the ground up. If you have already met the material once and it did not land, the slow courses are usually the better choice.
Does Brilliant cover AB, BC, or both?
Both, in the same way: the mapping touches all ten units of the AB and BC framework, though not evenly. The series material sits in BC territory, and the polar and vector work supports BC Unit 9. For the applications-heavy units in AB, lean on your class materials.
Can I use Brilliant if my class is Calculus but not AP?
Yes, and the fit is often better. A non-AP calculus class usually spends more time on the meaning of limits, derivatives, and integrals and less on exam-specific technique, which is exactly the part Brilliant teaches well.
What if calculus is already too fast?
If limits are hard because rational functions, asymptotes, logarithms, or radians are still shaky, the problem is upstream and calculus practice will not fix it. Start with Does Brilliant cover Precalculus? to find the right prerequisite course, then come back.
Is there a Brilliant course for multivariable calculus or differential equations?
No. Brilliant's calculus material is single-variable throughout. There is no multivariable calculus, linear algebra, or differential equations course.
Related resources
- Does Brilliant cover Precalculus?
- Does Brilliant cover Algebra 2?
- What math does Brilliant cover?
- Common Core math coverage: grade-by-grade Brilliant lesson mapping
- Explore Brilliant's courses
Sources
[1] College Board, "AP Calculus AB", Course and Exam Description.
[2] College Board, "AP Calculus BC", Course and Exam Description.
[3] Brilliant, "Limits", "Derivatives", and "Calculus".
[4] Common Core State Standards Initiative, "Mathematics Standards".
[5] Brilliant curriculum team, AP Calculus skill mapping, pulled September 30, 2026.
