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AP Calculus AB/BC Study Guide & Review

AP Calculus AB/BC covers 10 units, from Limits and Continuity to Infinite Sequences and Series (BC Only). Use this hub for unit study guides, topic review, FRQs, key terms, cheatsheets, score calculators, and exam prep.

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Study guides125 guides FRQ practice137 FRQs Key terms159 terms Cheatsheets Score calculator

AP Calculus AB/BC at a glance

10 course unitskey terms

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Get the big picture: what AP Calculus AB/BC covers, how it is scored, and how the units connect.

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What is AP Calculus AB/BC?

What students review in AP Calculus AB/BC

Evaluate limits and confirm continuity using graphs, tables, and algebraic methods
Apply the power, product, quotient, and chain rules plus implicit and inverse differentiation
Solve related rates, optimization, and motion problems in real contexts
Use the Fundamental Theorem of Calculus to evaluate definite integrals and accumulation functions
Model and solve differential equations and compute areas and volumes
For BC, analyze parametric and polar curves and test infinite series for convergence

AP Calculus AB/BC units & exam weights

The course is organized into 10 units. The percentages below are the College Board exam weights, so you can see which units carry the most multiple-choice points. Open each unit for its study guide, topic pages, key terms, and practice questions.

Unit 1 – Limits and Continuity

AP Calculus Unit 1, Limits and Continuity, makes up 10-12% of the AP exam and builds the single idea everything else in calculus rests on.

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 Calc)

10–12%exam weight

Unit 2 – Fundamentals of Differentiation

AP Calculus Unit 2, Fundamentals of Differentiation, is where you formally define the derivative as a limit of a difference quotient and learn the core rules for computing it, including the Power Rule, Product Rule, Quotient Rule, and the derivatives of sin x, cos x, e^x, and ln x.

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, sinx, e^x, and ln x The Product Rule The Quotient Rule Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

10–12%exam weight

Unit 3 – Composite, Implicit, and Inverse Functions

AP Calculus Unit 3 is about one rule and everything it unlocks.

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

9–13%exam weight

Unit 4 – Contextual Applications of Differentiation

AP Calculus Unit 4, Contextual Applications of Differentiation, is where derivatives stop being abstract slope machines and start answering real questions, like how fast a ladder slides down a wall or what a population's growth rate means.

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 Intro to Related Rates Solving Related Rates Problems Approximating Values of a Function Using Local Linearity and Linearization Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

10–15%exam weight

Unit 5 – Analytical Applications of Differentiation

AP Calculus Unit 5, Analytical Applications of Differentiation, is where derivatives stop being a computation and start being evidence.

Using the Mean Value Theorem Extreme Value Theorem, Global vs 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 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

15–18%exam weight

Unit 6 – Integration and Accumulation of Change

AP Calculus Unit 6, Integration and Accumulation of Change, is where the second half of calculus begins.

Integration and Accumulation 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 (AB)

17–20%exam weight

Unit 7 – Differential Equations

AP Calculus Unit 7 covers differential equations, which are equations that relate a function to its own derivative, like dy/dx = ky.

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

6–12%exam weight

Unit 8 – Applications of Integration

AP Calculus Unit 8, Applications of Integration, is where the definite integral stops being an abstract area calculation and starts answering real geometric questions, like the average value of a function, how far a particle travels, the area trapped between two curves, and the volume of a 3D solid.

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

10–15%exam weight

Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only)

AP Calculus BC Unit 9 extends everything you know about derivatives and integrals to curves that can't be written as y = f(x), using parametric equations, vector-valued functions, and polar coordinates.

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

11–12%exam weight

Unit 10 – Infinite Sequences and Series (BC Only)

Unit 10 is the BC-only unit on infinite series, and its single biggest idea is that adding up infinitely many numbers can produce a finite answer.

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

17–18%exam weight

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AP Calculus AB/BC by the numbers

These trends come from real Fiveable practice data, so you can see what students are reviewing, which topics need extra attention, and how written practice can improve over time.

Topics with the highest MCQ miss rate

57,139 MCQs

6.12 Using Linear Partial Fractions

59%

8.12 Volume with Washer Method

57%

6.11 Integrating Using Integration by Parts

55%

6.10 Integrating Functions Using Long Division and Completing the Square

55%

Miss rate is based on high-volume AP Calculus AB/BC multiple-choice practice.

More MCQ practice lines up with stronger accuracy

+5 pts

accuracyMCQs practiced

Average MCQ accuracy by student practice volume across 2,534 AP Calculus AB/BC students.

FRQ scores often grow after another attempt

62 retries

41%first attempt

→

61%latest attempt

63%improved after retrying

2.5attempts per retried response

+20point average gain

Among AP Calculus AB/BC FRQ responses that students retried on Fiveable, average scores rose from 41% on the first attempt to 61% on the latest attempt.

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Big ideas & exam guides

These guides collect important exam skills, big ideas, essay tasks, and other subject-specific resources.

AP Calculus AB/BC Exams

3 guides

Multiple-Choice Questions (MCQ)Free Response Questions (FRQ)Is AP Calculus Hard? AP Calc AB vs BC Difficulty and Worth It Guide

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Mathematical Practices

4 guides

Practice 1 - Implementing Mathematical Processes Practice 2 - Connecting Representations Practice 3 - Justification Practice 4 - Communication and Notation

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Big Ideas

3 guides

Modeling Change Approximation and Limits Analysis of Functions

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How to study for AP Calculus AB/BC

Work through the material unit by unit and practice problems by hand every day, since reading examples feels productive but only solving builds the skill. Calculus is cumulative, so review earlier units as you go to keep limits and derivative rules sharp. Do problems on both calculator and no-calculator sections, because the exam tests both. Pull free-response questions from past exams to see exactly how reasoning is expected, and practice writing organized work that earns partial credit. Target your weak spots, whether that is related rates, integration techniques, or series, instead of redoing what you already know.

Build the foundation in Units 1 through 3: limits, continuity, and core derivative rules
Practice contextual and analytical derivative applications from Units 4 and 5, including related rates and optimization
Drill integration in Unit 6 with Riemann sums, the Fundamental Theorem, and substitution
Work differential equations and integration applications in Units 7 and 8, including volumes
For BC, add parametric, polar, and series work from Units 9 and 10
Take timed mixed multiple-choice sets and full FRQ practice, then review every mistake

AP Calculus AB/BC FRQ practice

Use the question types below to plan written-response practice and connect exam guides to timed FRQs.

Question	Focus	Details	% of Score
FRQs 1-2	Part A (Calculator)	30 min	16%
FRQs 3-6	Part B (No Calculator)	60 min	32%

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AP Calculus AB/BC study tools

FRQ practice

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Key terms

Review vocabulary, definitions, and exam language.

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Cheatsheets

Use printable review sheets and final-week summaries.

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Score calculator

Estimate your score and plan where extra points matter.

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Unit 9: Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only)

9.1Defining and Differentiating Parametric Equations 9.2Second Derivatives of Parametric Equations 9.3Finding Arc Lengths of Curves Given by Parametric Equations 9.4Defining and Differentiating Vector-Valued Functions 9.5Integrating Vector-Valued Functions 9.6Solving Motion Problems Using Parametric and Vector-Valued Functions 9.7Defining Polar Coordinates and Differentiating in Polar Form 9.8Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 9.9Finding the Area of the Region Bounded by Two Polar Curves

Unit 10: Infinite Sequences and Series (BC Only)

10.1Defining Convergent and Divergent Infinite Series 10.2Working with Geometric Series 10.3The nth Term Test for Divergence 10.4Integral Test for Convergence 10.5Harmonic Series and p-Series 10.6Comparison Tests for Convergence 10.7Alternating Series Test for Convergence 10.8Ratio Test for Convergence 10.9Determining Absolute or Conditional Convergence 10.10Alternating Series Error Bound 10.11Finding Taylor Polynomial Approximations of Functions 10.12Lagrange Error Bound 10.13Radius and Interval of Convergence of Power Series 10.14Finding Taylor or Maclaurin Series for a Function 10.15Representing Functions as Power Series

Frequently Asked Questions

What does AP Calculus AB/BC cover?

AP Calculus AB/BC covers limits, derivatives, integrals, applications of those ideas, and BC-only topics like series and advanced accumulation methods.

How should I use these AP Calculus study guides?

Review the main concept first, then work practice problems right away so the formulas and reasoning stick. Topic guides help most when you pair them with active problem-solving.

Where can I find AP Calculus FRQ practice?

Use Fiveable's AP Calculus FRQ practice for AP-style free-response questions with AI-supported scoring on setup, notation, calculator use, and mathematical reasoning.

Should I study by unit or by skill in AP Calculus?

Start by unit if you are following class material, and switch to skill-based review closer to the exam. That makes it easier to connect related ideas like derivatives, integrals, and their applications.

Ready to review?Start with the course overview, review the AP Calculus AB/BC course units, and use the linked guides when you are ready to plan final review.

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