The Best AP® Calculus AB-BC Review Guides

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The Best AP® Calculus AB-BC Review:Topic Summaries, Examples, and Free Practice

Welcome to Albert’s collection of science topic reviews for teaching and reviewing AP® Calculus AB-BC. Teachers and students can explore our easy-to-follow guides below for use at home or in the classroom.

Explore Albert's AP® Calculus AB-BC Practice

Contents:

Overview and Scoring
Study and Test Prep
Unit 1: Limits and Continuity
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
Unit 6: Integration and Accumulation of Change
Unit 7: Differential Equations
Unit 8: Applications of Integration
Unit 9: Parametric Equations, Polar Coordinates, and Vector- Valued Functions (BC)
Unit 10: Infinite Sequences and Series (BC)

Overview and Scoring

What is on the AP® Calculus exam? How is it scored?

Explore the structure and topics of the AP® Calculus AB and BC exams. Understand scoring criteria, key concepts, and strategies to maximize your score.

The Best AP® Calculus AB Review Guide for 2025 Review topic AP® Calculus AB FAQ: Everything You Need to Know for 2024 Review topic Is AP® Calculus Hard? Review topic AP® Calculus AB Score Calculator Review topic AP® Calculus BC Score Calculator Review topic

Study and Test Prep

How can I ace the AP® Calculus AB or BC exam? What are the must-know strategies and study tips?

These articles offer key advice for mastering the AP® Calculus AB and BC exams. Learn effective study techniques, review strategies, and exam tips to strengthen your understanding and boost your score.

One Month AP® Calculus Study Guide Review topic How to Study for AP® Calculus Review topic The Ultimate List of AP® Calculus Tips Review topic

Unit 1: Limits and Continuity

How to solve limits to infinity? How to do average rate of change? How to tell if a function is continuos

Build a rock‑solid limits foundation for the AP® Calculus AB/BC exam in one place. These bite‑size reviews cover every limits and continuity skill—average rate of change, formal limit laws, rational and infinite limits, discontinuities, asymptotes, and the IVT—paired with fast practice to sharpen speed and accuracy.

1.1 Introducing Calculus: Can Change Occur at an Instant? Review topic 1.2 Defining Limits and Using Limit Notation Review topic 1.3 Estimating Limit Values from Graphs Review topic 1.4 Estimating Limit Values from Tables Review topic 1.5 Determining Limits Using Algebraic Properties of Limits Review topic 1.6 Determining Limits Using Algebraic Manipulation Review topic 1.7 Selecting Procedures for Determining Limits Review topic 1.8 Determining Limits Using the Squeeze Theorem Review topic 1.9 Connecting Multiple Representations of Limits Review topic 1.10 Exploring Types of Discontinuities Review topic 1.11 Defining Continuity at a Point Review topic 1.12 Confirming Continuity over an Interval Review topic 1.13 Removing Discontinuities Review topic 1.14 Connecting Infinite Limits and Vertical Asymptotes Review topic 1.15 Connecting Limits at Infinity and Horizontal Asymptotes Review topic 1.16 Working with the Intermediate Value Theorem (IVT) Review topic

Unit 2: Differentiation: Definition and Fundamental Properties

How to find the instantaneous rate of change? What is the quotient rule? When does a derivative not exist?

Master derivatives fast: start with the difference quotient, notation, and slope estimates, learn when derivatives fail, then apply the power, product, quotient, and trig rules to any polynomial or trig function. These bite‑size AP® Calculus AB/BC guides pair clear rules with quick practice so you can differentiate accurately under test pressure.

2.1 Defining Average and Instantaneous Rates of Change at a Point Review topic 2.2 Defining the Derivative of a Function and Using Derivative Notation Review topic 2.3 Estimating Derivatives of a Function at a Point Review topic 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Review topic 2.5 Applying the Power Rule Review topic 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple Review topic 2.7 Derivatives of cos(x), sin(x), e^x, and ln(x) Review topic 2.8 The Product Rule Review topic 2.9 The Quotient Rule Review topic 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions Review topic

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

When to use the chain rule? What is implicit differentiation? How to find the derivative of an inverse function?

Expand your AP® Calculus derivative arsenal with concise guides on the Chain Rule, implicit differentiation, and derivatives of inverse and inverse trig functions—plus higher‑order derivatives. Bite‑size explanations and targeted practice problems ensure you can apply every rule quickly and accurately on exam day.

3.1 The Chain Rule Review topic 3.2 Implicit Differentiation Review topic 3.3 Differentiating Inverse Functions Review topic 3.4 Differentiating Inverse Trigonometric Functions Review topic 3.5 Selecting Procedures for Calculating Derivatives Review topic 3.6 Calculating Higher-Order Derivatives Review topic

Unit 4: Contextual Applications of Differentiation

How to find instantaneous velocity? When is a particle at rest? What is an indeterminate form?

Turn derivative skills into real‑world power: learn to interpret rate of change, analyze particle motion, and solve classic related‑rates scenarios like expanding cones. Wrap up with linearization for quick approximations and L’Hospital’s Rule for indeterminate forms, giving you the applied‑calculus edge for AP® Calculus AB/BC.

4.1 Interpreting the Meaning of the Derivative in Context Review topic 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration Review topic 4.3 Rates of Change in Applied Contexts Other Than Motion Review topic 4.4 Introduction to Related Rates Review topic 4.5 Solving Related Rates Problems Review topic 4.6 Approximating Values of a Function Using Local Linearity and Linearization Review topic 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms Review topic

Unit 5: Analytical Applications of Differentiation

What is the mean value theorem? How to find relative extrema? How to find concavity?

Tackle AP® Calculus AB/BC graph analysis and optimization in one hub: use the Mean and Extreme Value Theorems plus first‑ and second‑derivative tests to pinpoint intervals, extrema, and concavity. Finish by sketching graphs, probing implicit relations, and solving classic optimization problems with confidence.

5.1 Using the Mean Value Theorem Review topic 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Review topic 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing Review topic 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema Review topic 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema Review topic 5.6 Determining Concavity of Functions over Their Domains Review topic 5.7 Using the Second Derivative Test to Determine Extrema Review topic 5.8 Sketching Graphs of Functions and Their Derivatives Review topic 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative Review topic 5.10 Introduction to Optimization Problems Review topic 5.11 Solving Optimization Problems Review topic 5.12 Exploring Behaviors of Implicit Relations Review topic

Unit 6: Integration and Accumulation of Change

How to do Riemann sums? What is the fundamental theorem of calculus? How to do u substitution?

Start with Riemann‑sum approximations and the Fundamental Theorem of Calculus to see how accumulation really works, then dive into definite‑integral properties and accumulation functions. Quick guides to u‑substitution, completing the square, integration by parts, partial fractions, and improper integrals give you every technique needed to ace AP® Calculus AB/BC integration problems.

6.1 Exploring Accumulations of Change Review topic 6.2 Approximating Areas with Riemann Sums Review topic 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation Review topic 6.4 The Fundamental Theorem of Calculus and Accumulation Functions Review topic 6.5 Interpreting the Behavior of Accumulation Functions Involving Area Review topic 6.6 Applying Properties of Definite Integrals Review topic 6.7 The Fundamental Theorem of Calculus and Definite Integrals Review topic 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation Review topic 6.9 Integrating Using Substitution Review topic 6.10 Integrating Functions Using Long Division and Completing the Square Review topic 6.11 Integrating Using Integration by Parts (BC) Review topic 6.12 Using Linear Partial Fractions (BC) Review topic 6.13 Evaluating Improper Integrals (BC) Review topic 6.14 Selecting Techniques for Antidifferentiation Review topic

Unit 7: Differential Equations

How to solve differential equations? How to sketch a slope field? What is Euler's method?

Master AP® Calculus AB/BC differential equations in one stop: see how slope fields, Euler’s Method, and separation of variables unlock exact and approximate solutions, from exponential to logistic growth models. Quick guides on verifying solutions, finding particulars, and interpreting slope‑field behavior give you the tools to tackle every DE question the exam throws your way.

7.1 Modeling Situations with Differential Equations Review topic 7.2 Verifying Solutions for Differential Equations Review topic 7.3 Sketching Slope Fields Review topic 7.4 Reasoning Using Slope Fields Review topic 7.5 Approximating Solutions Using Euler’s Method (BC) Review topic 7.6 Finding General Solutions Using Separation of Variables Review topic 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables Review topic 7.8 Exponential Models with Differential Equations Review topic 7.9 Logistic Models with Differential Equations (BC) Review topic

Unit 8: Applications of Integration

How to find average value of a function? How to find area between two curves? When to disk vs washer method?

Conquer geometric applications of integrals for AP® Calculus AB/BC: learn to find average value, net change, and displacement, then master area between curves and shaded regions. Step‑by‑step guides to cross‑sections, disc‑and‑washer volumes, and arc length equip you to solve any solid‑of‑revolution or area problem the exam throws your way.

8.1 Finding the Average Value of a Function on an Interval Review topic 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals Review topic 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts Review topic 8.4 Finding the Area Between Curves Expressed as Functions of x Review topic 8.5 Finding the Area Between Curves Expressed as Functions of y Review topic 8.6 Finding the Area Between Curves That Intersect at More Than Two Points Review topic 8.7 Volumes with Cross Sections: Squares and Rectangles Review topic 8.8 Volumes with Cross Sections: Triangles and Semicircles Review topic 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis Review topic 8.10 Volume with Disc Method: Revolving Around Other Axes Review topic 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis Review topic 8.12 Volume with Washer Method: Revolving Around Other Axes Review topic 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC) Review topic

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

How to find second derivative of parametric equations? How to find arc length? What is a vector valued function?

Sharpen skills with parametric, vector‑valued, and polar functions as you compute first and second derivatives, arc length, and areas between polar curves. From integrating vectors to spotting when a particle rests, these concise guides equip you for every advanced curve question on test day.

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

Unit 10: Infinite Sequences and Series (BC)

How to find the sum of an infinite series? What is the alternating series test? What is the taylor polynomial?

Lock in series mastery: learn every convergence test—geometric, p‑series, comparison, ratio, integral, alternating, and more—while distinguishing absolute vs conditional cases and bounding errors. Then harness power, Taylor, and Maclaurin series to represent functions and nail interval of convergence questions on exam day.

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

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The Best AP® Calculus AB-BC Review Guides | Albert Resources (2025)