AP® Calculus BC · free to start 2027 exam

AP®Calculus BC

AP® Calculus BC, all the way to series.

every AB topic, then series

Every AB topic and every BC topic, taught from scratch in framework order, then practice that grades typed answers, intervals and justifications.

Start the first lessonAll units

Series lab →

  • Every notes page free
  • Units 1 and 2 lessons free
  • Unit sheets free to print
  • Progress saved on your device

Made by Olivier Testa, an EMT who passed the NREMT studying with LevlPrep. Why I built it

In this course

Each unit's share of the BC exam, from the course framework. Every notes page is free; the lessons in Units 1 and 2 are free too. The units in framework order, then the math you need, each placed just before the topic that first needs it: functions, exponents, algebra for limits, trigonometry, logarithms, inverse functions and geometry, then parametric equations and vectors, polar coordinates, and sequences and sums. Pick a unit to open its lessons and practice.

  1. 01Limits and Continuity16 topics5 to 10%lessons free
  2. 02Differentiation: Definition and Fundamental Properties10 topics5 to 10%lessons free
  3. 03Differentiation: Composite, Implicit, and Inverse Functions6 topics5 to 10%of the exam
  4. 04Contextual Applications of Differentiation7 topics5 to 10%of the exam
  5. 05Analytical Applications of Differentiation12 topics10 to 15%of the exam
  6. 06Integration and Accumulation of Change14 topics15 to 20%of the exam
  7. 07Differential Equations9 topics5 to 10%of the exam
  8. 08Applications of Integration13 topics5 to 10%of the exam
  9. 09Parametric Equations, Polar Coordinates, and Vector-Valued Functions9 topics10 to 15%of the exam
  10. 10Infinite Sequences and Series15 topics15 to 20%of the exam
  11. S1Math you need10 topics, a skills trackSkillsalongside the units
AP® Calculus BC · The nth Term Test for Divergence

try one, it’s free

The terms of a series get closer and closer to 0 as n grows. What does the nth term test say about the series?

Choose one answer

pick one to see why

Nothing, either way.The nth term test can only show divergence: terms that do not approach 0 make a series diverge. Terms that do approach 0 decide nothing; the harmonic series has them and still diverges.

Open the free notes on series →

42 questions multiple choice · 100 minutes6 free response written answers · 90 minutes1,902 questions every option explainedFull length both sections, timed, one free

Sequence Starter

Level 1 · 0 XP · 0 / 100 XP to Level 2. One level and one streak count across every LevlPrep course.

Units0%Math you need0%
Start here

Functions and Their Graphs

Skills · Math you need. Units 1 and 2 lessons and every notes page are free.

Start the first lesson
Review queue

Missed questions come back

Anything you miss returns when you are about to forget it, not on a fixed date.

Open review →
Today’s goal

A little every day

Questions, cards and tool steps count toward a daily goal and a streak shared across every LevlPrep subject. 15 practice questions a day are free.

Practice now →

The lead

Open the notesFree forever A free notes page for every topic, in framework order, with a printable sheet for each unit and a glossary of every term.FlashcardsCram kitJustification trainerGlossary

How this course works

1

Learn a topic from scratch

Start with functions and their graphs, or jump to the BC units: each lesson checks what you need first, then walks it one step at a time. Start the first lesson →

2

Practice what you learned

Drill a unit, a topic or a mathematical practice, with graph and table sets. 15 a day are free. Practice now →

3

Sit a practice exam

Unit tests and full timed practice exams in the real four-part format. See the exams →

6free response questions on the examTry a free responseSection IIEvery recurring free-response type, with 9-point rubrics and sample answers. Unit tests and full timed practice exams in the real four-part format.

Tools

Series labFreePick the test, check its conditions, test both endpoints.Taylor labPremiumPolynomials that wrap the function, with the error bound as a band.Parametric motionPremiumA particle in the plane, its velocity and speed live.

All 6 tools →

Free

Everything to start

Start now, with no card.

Every notes page is free, and so are the lessons in Units 1 and 2 and the first three parametric topics. 15 practice questions a day are free too.

  • Every notes page, the glossary, the flashcards and the printable unit sheets
  • The cram-kit study plan outline, printable
  • Every lesson in Units 1 and 2, every "Math you need" lesson and the first three parametric lessons
  • 15 practice or review questions a day from any unit
  • One full practice exam
  • The series lab trainer
Start the first lesson
Premium · AP® Calculus BC

$17.50

Founding price, $25 from February 1, 2027. One pass, good through 30 June 2027, the end of the exam season.

  • Every interactive lesson
  • Unlimited practice and review from the whole question bank
  • Every BC trainer: Taylor polynomials, parametric motion, polar curves, integration methods, Euler and logistic
  • All free-response questions, unit tests and practice exams
  • The cram kit: a study plan fitted to your weakest units, and timed mixed sets
  • The full dashboard: mastery by unit, topic and mathematical practice
Unlock for $17.50

Full refund within 7 days · Never renews · Secure checkout by Polar

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Questions

What the course covers
10 units and 111 topics in the order of the course framework: the 81 Calculus AB topics and the 30 BC topics, each where the framework places it, plus 10 math topics placed where they are first needed. Each topic has an interactive lesson, a free notes page and exam-style practice, and each unit a printable unit sheet. Practice checks what the exam checks: answers you type as expressions, intervals of convergence with both endpoints, graphs and tables, calculator and no-calculator parts, and justifications that name the theorem or the test and check its conditions. Built on Calculus AB. Units 1 to 8 are the Calculus AB lessons, notes and questions, so a fix lands in both courses; Units 9 and 10 and the BC topics of Units 6 to 8 are new.
Four steps, every time you study.
Open your dashboard.
  • Read the lesson. It checks what you need first, then walks the cause and effect one step at a time, with a picture for every process.
  • Answer as you go. Anything you miss goes into your review queue and comes back when you are about to forget it.
  • Train the hard parts. Convergence tests and endpoints, Taylor polynomials and error bounds, parametric motion and polar area, each checked step by step.
  • Check your mastery. Your dashboard shows it by unit, topic and mathematical practice, and every miss links to its lesson.
What kinds of questions are there?
  • 1Read the situation
  • 2Pick the answer you would bet on
  • 3See the cause and effect behind it
Has this course been reviewed?
This course has not yet been reviewed by an AP® Calculus BC teacher. It follows the published course framework and open textbooks, listed on the Sources page. Spot a mistake? Report a problem.
Is this course free?
Every notes page is free, and so are the lessons in Units 1 and 2 and the first three parametric topics. 15 practice questions a day are free too.
Is LevlPrep affiliated with the exam?
AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this site.
Who makes LevlPrep?
An independent project, not a company or a training program. Premium is an optional one-time pass, and what is free is listed course by course. No ads.
How are the questions written?
Every question in every course is original, written for LevlPrep with an explanation on each one. Automated checks look for answer-position and length tells. Sources and checks.
How do I see what changed?
Corrected questions, new lessons and site fixes are listed, dated, on What’s new.
Start the first lesson