# AP Calculus BC tutor: live classes, unit by unit

Source: https://tutix.ai/programs/ap-calculus-bc  
Updated: 2026-10-21

**The short answer.** AP Calculus BC on Tutix is a ready-made series of live classes with an AI tutor. It covers all 10 units and 111 topics, in five levels from 5 hours to the full 86.2. It ends with 2 full practice papers (48 questions each). You can start on the free plan.

- Follows the College Board AP course description
- 10 units and 111 topics, taught in 15-minute lessons
- Five levels, 5 to 86.2 hours of teaching
- 2 full practice papers, 96 marks each
- Starts on the free plan (45 live minutes a month)

## What AP Calculus BC covers

AP Calculus BC develops students’ understanding of limits, differentiation, integration, and their applications. It also covers differential equations, parametric and polar functions, vector-valued functions, and infinite series.

AP Calculus BC is a College Board course that covers the Calculus AB material and adds parametric equations, polar coordinates and vector-valued functions, and infinite sequences and series.

### Unit 1: Limits and Continuity (5–10%)

Topics: Introducing Calculus: Can Change Occur at an Instant?; Defining Limits and Using Limit Notation; Estimating Limit Values from Graphs; Estimating Limit Values from Tables; Determining Limits Using Algebraic Properties of Limits; Determining Limits Using Algebraic Manipulation; Selecting Procedures for Determining Limits; Determining Limits Using the Squeeze Theorem; Connecting Multiple Representations of Limits; Exploring Types of Discontinuities; Defining Continuity at a Point; Confirming Continuity over an Interval; Removing Discontinuities; Connecting Infinite Limits and Vertical Asymptotes; Connecting Limits at Infinity and Horizontal Asymptotes; Working with the Intermediate Value Theorem (IVT).

### Unit 2: Differentiation: Definition and Fundamental Properties (5–10%)

Topics: Defining Average and Instantaneous Rates of Change at a Point; Defining the Derivative of a Function and Using Derivative Notation; Estimating Derivatives of a Function at a Point; Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist; Applying the Power Rule; Derivative Rules: Constant, Sum, Difference, and Constant Multiple; Derivatives of cos x, sin x, ex, and ln x; The Product Rule; The Quotient Rule; Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions.

### Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (5–10%)

Topics: The Chain Rule; Implicit Differentiation; Differentiating Inverse Functions; Differentiating Inverse Trigonometric Functions; Selecting Procedures for Calculating Derivatives; Calculating Higher - Order Derivatives.

### Unit 4: Contextual Applications of Differentiation (5–10%)

Topics: Interpreting the Meaning of the Derivative in Context; Straight-Line Motion: Connecting Position, Velocity, and Acceleration; Rates of Change in Applied Contexts Other Than Motion; Introduction to Related Rates; Solving Related Rates Problems; Approximating Values of a Function Using Local Linearity and Linearization; Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms.

### Unit 5: Analytical Applications of Differentiation (10–15%)

Topics: Using the Mean Value Theorem; Extreme Value Theorem, Global Versus Local Extrema, and Critical Points; Determining Intervals on Which a Function Is Increasing or Decreasing; Using the First Derivative Test to Determine Relative (Local) Extrema; Using the Candidates Test to Determine Absolute (Global) Extrema; Determining Concavity of Functions over Their Domains; Using the Second Derivative Test to Determine Extrema; Sketching Graphs of Functions and Their Derivatives; Connecting a Function, Its First Derivative, and Its Second Derivative; Introduction to Optimization Problems; Solving Optimization Problems; Exploring Behaviors of Implicit Relations.

### Unit 6: Integration and Accumulation of Change (15–20%)

Topics: Exploring Accumulations of Change; Approximating Areas with Riemann Sums; Riemann Sums, Summation Notation, and Definite Integral Notation; The Fundamental Theorem of Calculus and Accumulation Functions; Interpreting the Behavior of Accumulation Functions Involving Area; Applying Properties of Definite Integrals; The Fundamental Theorem of Calculus and Definite Integrals; Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation; Integrating Using Substitution; Integrating Functions Using Long Division and Completing the Square; Integrating Using Integration by Parts; Integrating Using Linear Partial Fractions; Evaluating Improper Integrals; Selecting Techniques for Antidifferentiation.

### Unit 7: Differential Equations (5–10%)

Topics: Modeling Situations with Differential Equations; Verifying Solutions for Differential Equations; Sketching Slope Fields; Reasoning Using Slope Fields; Approximating Solutions Using Euler’s Method; Finding General Solutions Using Separation of Variables; Finding Particular Solutions Using Initial Conditions and Separation of Variables; Exponential Models with Differential Equations; Logistic Models with Differential Equations.

### Unit 8: Applications of Integration (5–10%)

Topics: Finding the Average Value of a Function on an Interval; Connecting Position, Velocity, and Acceleration of Functions Using Integrals; Using Accumulation Functions and Definite Integrals in Applied Contexts; Finding the Area Between Curves Expressed as Functions of x; Finding the Area Between Curves Expressed as Functions of y; Finding the Area Between Curves That Intersect at More Than Two Points; Volumes with Cross Sections: Squares and Rectangles; Volumes with Cross Sections: Triangles and Semicircles; Volume with Disc Method: Revolving Around the x- or y-Axis; Volume with Disc Method: Revolving Around Other Axes; Volume with Washer Method: Revolving Around the x- or y-Axis; Volume with Washer Method: Revolving Around Other Axes; The Arc Length of a Smooth, Planar Curve and Distance Traveled.

### Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (10–15%)

Topics: Defining and Differentiating Parametric Equations; Second Derivatives of Parametric Equations; Finding Arc Lengths of Curves Given by Parametric Equations; Defining and Differentiating Vector-Valued Functions; Integrating Vector- Valued Functions; Solving Motion Problems Using Parametric and Vector-Valued Functions; Defining Polar Coordinates and Differentiating in Polar Form; Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve; Finding the Area of the Region Bounded by Two Polar Curves.

### Unit 10: Infinite Sequences and Series (15–20%)

Topics: Defining Convergent and Divergent Infinite Series; Working with Geometric Series; The nth Term Test for Divergence; Integral Test for Convergence; Harmonic Series and p-Series; Comparison Tests for Convergence; Alternating Series Test for Convergence; Ratio Test for Convergence; Determining Absolute or Conditional Convergence; Alternating Series Error Bound; Finding Taylor Polynomial Approximations of Functions; Lagrange Error Bound; Radius and Interval of Convergence of Power Series; Finding Taylor or Maclaurin Series for a Function; Representing Functions as Power Series.

## A class in AP Calculus BC, opened

Every class works like this. The tutor asks, you answer in your own words, and it reads what you wrote while you are still in the room, then tells you what is missing and asks you to try again.

A class, opened. A sample written to show how a class sounds (not a real learner); the scores show how the exam would credit each answer.

> **Unit 10 · Convergence of series.** Question: Does the series Σ 1/n^2 converge?
> The student wrote: Yes, because the terms 1/n^2 go to 0. (the exam would credit 1 of 3)
> The tutor: The conclusion is right, but the terms going to 0 cannot prove it: the terms of Σ 1/n go to 0 too, and that series diverges. Which test settles this one?
> The student then wrote: Yes. It is a p-series with p = 2, which is greater than 1, so it converges. (the exam would credit 3 of 3)

## How the AP Calculus BC exam is built

The 2027 exam is on Monday, May 10, in the morning session, with the same shape as AB: 42 multiple-choice questions in 100 minutes and 6 free-response questions in 90 minutes, each section worth half of the score. A graphing calculator is required for part of each section.

| Exam section | Detail |
| --- | --- |
| Section I, Part A: multiple choice, no calculator | 29 questions · 62 min · 35% of the score; No calculator |
| Section I, Part B: multiple choice, calculator required | 13 questions · 38 min · 15% of the score; Calculator |
| Section II, Part A: free response, calculator required | 2 questions · 30 min · 17% of the score; Calculator |
| Section II, Part B: free response, no calculator | 4 questions · 60 min · 33% of the score; No calculator |

## How students score on AP Calculus BC

How students scored in 2026 (share of students at each AP score):

| Score | Share of students |
| --- | --- |
| 5 | 46% |
| 4 | 22% |
| 3 | 14% |
| 2 | 14% |
| 1 | 4% |

The share of students scoring 3 or higher on AP Calculus BC was 75.2% in 2021 and 82% in 2026. The College Board reviews each exam's score standards every five to ten years, so a change from one year to the next can reflect a new standard as well as how students did. AP pass rates for every exam shows the whole table.

| Year | 5 | 4 | 3 | 2 | 1 | 3 or higher | Students | Mean score |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 2026 | 46% | 22% | 14% | 14% | 4% | 82% | n/a | n/a |
| 2025 | 44.0% | 21.9% | 12.8% | 15.2% | 6.2% | 78.6% | 160,436 | 3.82 |
| 2024 | 47.7% | 21.1% | 12.1% | 13.9% | 5.2% | 80.9% | 148,191 | 3.92 |
| 2023 | 43.5% | 15.9% | 19.0% | 15.2% | 6.3% | 78.5% | 135,458 | 3.75 |
| 2022 | 41.2% | 15.6% | 20.1% | 16.4% | 6.8% | 76.9% | 120,238 | 3.68 |
| 2021 | 38.3% | 16.5% | 20.4% | 18.2% | 6.6% | 75.2% | 124,599 | 3.62 |

## How long does AP Calculus BC take?

Every level covers the whole syllabus. A deeper level only adds classes, so you can go deeper later and keep everything you have done. Hours are hours of teaching, counted in classes of 45 or 60 minutes.

| Level | Hours | Classes of 45 min |
| --- | --- | --- |
| Short | 5 | 7 |
| Standard | 39.8 | 53 |
| In depth | 60.8 | 81 |
| Extended | 81.2 | 109 |
| Full syllabus | 86.2 | 115 |

The Programs page draws AP Calculus BC beside the other eleven programs on one hours scale, with what a pass costs at each level.

## Questions

**How many hours of teaching does AP Calculus BC take on Tutix?**

The Standard level takes 39.8 hours: 53 classes of 45 minutes, or 40 of 60. The Full syllabus level takes 86.2 hours (115 classes of 45 minutes). The Short level is 5 hours. Every level covers the whole syllabus; deeper levels add classes.

**What does the AP Calculus BC exam look like?**

As the board publishes it, the exam has these parts: Section I, Part A: multiple choice, no calculator (29 questions, 62 minutes); Section I, Part B: multiple choice, calculator required (13 questions, 38 minutes); Section II, Part A: free response, calculator required (2 questions, 30 minutes); Section II, Part B: free response, no calculator (4 questions, 60 minutes). Check your board's current specification for the exact format of the year you sit it.

**Which AP Calculus BC units carry the most weight?**

The heaviest units are Integration and Accumulation of Change (15–20%); Infinite Sequences and Series (15–20%); Analytical Applications of Differentiation (10–15%), measured as a share of the multiple-choice section.

**Are there practice papers for AP Calculus BC?**

Yes. The Full syllabus level includes 2 full practice papers written for Tutix in the style of the real exam (48 questions and 96 marks each). You can sit them as long homework, and a class can go over them afterwards.

**Is this an official College Board AP course?**

No. Tutix is not affiliated with College Board and its AP Calculus BC classes are not endorsed by College Board. The lessons and questions are Tutix's own, prepared to follow the published AP Calculus BC course description, and the real exam is set and marked by College Board.

**Can I try AP Calculus BC for free?**

Yes. The Free plan includes 45 live class minutes a month, about one class of the default length, and no card is needed. Pro is $15 a month for 360 live minutes (6 hours), and Pro+ is $30 a month for 900 live minutes.

**Is the AP Calculus BC tutor a person?**

No. The tutor is an AI. It talks with you in real time, teaches on a whiteboard, reads your answers and remembers what each earlier class covered. A parent can set up a child's classes and choose to get a recap after each one.

**When is the AP Calculus BC exam in 2027?**

AP Calculus BC is on Monday, May 10, 2027, in the morning session. The 2027 AP exam window runs from May 3 to May 7 and from May 10 to May 14, set by the College Board.

**What is a good AP Calculus BC score?**

The College Board calls a 5 extremely well qualified, a 4 very well qualified and a 3 qualified. In 2026, 82% of students who sat AP Calculus BC scored 3 or higher. What counts as good for you depends on the colleges you are aiming at.

**Does AP Calculus BC count for college credit?**

It depends on the college. The College Board says many US colleges grant credit or advanced placement for scores of 3 and above, and that each college makes its own decisions about which scores it accepts. Check each college's credit policy before you rely on a score.

## Sources

- College Board: [AP Calculus BC: the exam](https://apcentral.collegeboard.org/courses/ap-calculus-bc/exam) (accessed October 21, 2026)
- College Board: [AP Calculus BC: the course](https://apstudents.collegeboard.org/courses/ap-calculus-bc) (accessed October 21, 2026)
- College Board: [AP exam dates](https://apcentral.collegeboard.org/exam-administration-ordering-scores/exam-dates) (accessed October 21, 2026)
- College Board: [AP score distributions, 2026](https://apstudents.collegeboard.org/about-ap-scores/score-distributions) (2026 results)
- College Board: [The AP score scale](https://apstudents.collegeboard.org/about-ap-scores/ap-score-scale-table) (accessed October 21, 2026)
- College Board: [Getting credit and placement](https://apstudents.collegeboard.org/getting-credit-placement) (accessed October 21, 2026)
- College Board: [AP score distributions, by year (2021 to 2026)](https://apstudents.collegeboard.org/about-ap-scores/score-distributions) (2021 to 2026 results)

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