Brilliant teaches calculus across three topics, built as a sequence: Limits runs 49 lessons and Derivatives 44 so far, and Integrals is the newest. All three are still being built, and all three work the same way: they build calculus as ideas rather than procedures — what a limit is, why a derivative is a rate of change, how adding up rectangles becomes an integral — with more careful groundwork than any textbook chapter gives you. Between them they reach from sequences through limits of functions, the derivative of any polynomial, and the definite integral. Coverage is deep on the concepts it has reached and thin past them, 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 topic covers which part of calculus?
| Topic | What it covers for calculus | Where to start |
|---|---|---|
| Limits (49 lessons) | Sequences and their limits, convergence and divergence, one-sided limits, the limit of a function, the ways a limit can fail to exist, and limits at infinity | Sequences |
| Derivatives (44 lessons) | Average rate of change, net change and velocity, the limit definition of the derivative, linear approximation, graphing the derivative, and the first differentiation rules | Visualizing Change |
| Integrals | Area under a graph as a real quantity, signed area, Riemann sums, sigma notation, and the definite integral and its properties | Area Under a Graph |
All three topics are partly built. Limits has 8 of its 15 levels written, Derivatives 8 of 19, and Integrals 5 of 14; the remaining level titles are listed on each topic 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 name what that gives you, and the fourth level writes it down, in The Limit Definition of Derivative and Derivative Notation. The fifth 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.
The differentiation rules have now started to arrive. A level on Graphing the Derivative reads a derivative's graph off a function's and back, including spotting Local Extrema. Then The Power Rule, The Constant Multiple Rule, and The Sum Rule combine to differentiate any polynomial in Derivatives of Polynomials, and the eighth level derives The Derivative of Sine and The Derivative of Cosine from their graphs. The product and chain rules, related rates, and the second derivative are announced as coming levels but are not written; for those, use your class materials.
Limits, and what "limit" means before functions
Limits starts as a sequences topic, and that is still the route in: it builds the limit concept on sequences, where the definition is easiest to see, before functions complicate it. The function half has now begun to arrive.
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.
The fourth level turns the same machinery on sequences that never settle. Finitely Many Exceptions and Leaving the Target sharpen what the target test does and does not allow, The Limit Does Not Exist names the failure, and Goes To Infinity, Goes To Negative Infinity and Infinity on a Graph separate the ways a sequence can run away from one that merely has no limit. Comparing Geometric Sequences closes the level by ranking how fast two runaway sequences grow.
Function limits are now written, and they arrive the same way. One-Sided Limits and Piecewise Functions read a limit off a graph from each side, The Limit Definition and The One-Sided Definition carry the target test over from sequences to functions, and Limit vs Value separates what a function approaches from what it equals — the distinction most limit mistakes come down to. A level on the ways a limit can fail — Disagreeing Sides, Oscillations, To Infinity, sorted out in Classifying Limits — sets out the ways a limit can fail. The newest level asks the same question of unbounded inputs: Sweeping to Infinity follows a function as its input grows without bound, Converging at Infinity and Infinity at Infinity separate the case that settles from the case that runs away, Oscillations at Infinity covers the ones that never settle either way, and Limits at Negative Infinity runs it in the other direction. The limit laws, limit techniques, continuity, and the Intermediate Value Theorem are announced as coming levels but are not written yet.
Integrals, built from area up
Integration now has a topic of its own, and it takes the long way to the integral on purpose. Integrals opens by making area stand for something real — Area Under a Graph counts labor cost, energy, and distance out of graphs before any notation appears — and Negative Areas and Signed Area under Velocity Graphs add direction and sign. Riemann Sums and Left, Right, and Midpoint Sums approximate a curved region with rectangles and ask which way the estimate errs in Over and Underestimation; a level on Sigma Notation makes those sums precise. The Definite Integral then takes the limit in Infinitely Many Rectangles and establishes the integral's basic properties in Adding Intervals and Reversing the Bounds.
That is 5 of its 14 levels built; the other 9 are announced with no lessons yet. The announced half is the half a calculus class leans on hardest — the accumulation function, the Fundamental Theorem, antiderivatives, substitution, integration by parts, areas between curves, volumes, and improper integrals — so if the connection between derivatives and area is the thing you need explained, that part has not arrived. The topic's skills are now in Brilliant's standards mapping, so the unit-by-unit picture below does count it — but what it counts is the lessons that exist, not the announced ones.
Series, if you are in BC
Brilliant does not currently teach infinite series. The groundwork is in Limits — convergent and divergent sequences, and Comparing Geometric Sequences for how geometric growth behaves — but infinite sums, the convergence tests, and Taylor series are not on Brilliant today. For BC Unit 10, work from your textbook.
What you need before you start
Calculus assumes work these topics teach and a calculus class rarely reteaches.
| Topic | 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 (70 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:
- The Fundamental Theorem and integration technique. Antiderivatives, the Fundamental Theorem, substitution, integration by parts, and improper integrals are all announced levels of Integrals, not written ones. Brilliant currently builds what a definite integral is, then stops.
- Differential equations. Slope fields, separation of variables, and the full Unit 7 treatment. Exponential growth and decay models are covered, in Exponential Functions.
- Series. Infinite sums, the convergence tests, and Taylor series — all of BC Unit 10, as above.
- Contextual applications of the derivative. Related rates and optimization are announced levels of Derivatives, not written ones.
- 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 catalog, and the mapping is reviewed by Brilliant's curriculum team. The data here was pulled on November 6, 2026. Across AB and BC, the mapping now reaches something in all ten units, but unevenly: Units 1, 2, and 6 are where the direct coverage sits, Units 4, 5, and 8 are a single topic each, and Units 3, 7, and 9 are supported mostly by the prerequisites above. Units 1 and 2 — limits, and the definition and first rules of the derivative — are now the most directly covered of the ten; Unit 2 is mapped from average rate of change through the derivatives of sine and cosine, stopping before the product and quotient rules. That is the written Limits and Derivatives levels being tagged and mapped, not new lessons arriving. Unit 6, integration, follows, from the five written Integrals levels; its nine announced levels have nothing in them to map.
Frequently asked questions
Is Brilliant enough to pass the AP Calculus exam?
No. The three topics teach the ideas underneath the subject, not the exam — and they are still being built, with integration's second half and all of series yet to come. 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 what it is on: Limits if limits or convergence have not clicked, Derivatives if the derivative has not, Integrals once your class reaches area and accumulation. Starting from scratch and not in a hurry, Limits then Derivatives then Integrals is the intended order — each topic assumes the one before it.
Didn't Brilliant have a topic called Calculus?
It did — Calculus in a Nutshell, a 42-lesson tour of the whole subject. It has been retired from the catalog in favor of the dedicated Limits, Derivatives, and Integrals sequence, which rebuilds the same subject one idea at a time and in far more depth. The parts of the old topic the sequence has not reached yet — the Fundamental Theorem, applications of integrals, infinite series — are announced as coming levels rather than available lessons.
Does Brilliant cover AB, BC, or both?
The mapping touches all ten units of the AB and BC framework, though not evenly, and the deepest coverage — limits, the definition of the derivative, and the definite integral — sits in AB territory. On the BC side, the polar and vector work in the prerequisite topics supports Unit 9, but series are not yet taught. For the applications-heavy units in either course, 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 topic, then come back.
Is there a Brilliant topic 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 topic.
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 topics
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 "Integrals".
[4] Common Core State Standards Initiative, "Mathematics Standards".
[5] Brilliant curriculum team, AP Calculus skill mapping, pulled November 6, 2026.
