This computational engine can solve any limit, derivative or integral. This tool is a great way to check your technical skills.
A compilation of instructional videos spanning over all topics covered in the AP Calculus AB Curriculum.
Organized notes and animations to help students visualize concepts covered in Calculus.
One of the most condensed yet concise notes for Calculus. Some students may find his notes to be information overload, but this is a website that is easy to navigate and provides a lot of guided practice.
All released Free Response Questions as well as grading rubrics for all past AP Calculus AB tests.
Free Response Questions sorted by mathematical topic.
An AP Calculus Review book includes practice tests and a comprehensive practice for topics covered on the AP Exam.
For those of you who want to practice multiple choice type questions, this resource has MCQ's for all topics.
Another AP Calculus Review book.
An AP Calculus Exam grader's advice on how not to lose tedious points on the AP Exam's Free Response Section.
In order to succeed in AP Calculus, proficiency of the following topics are absolutely necessary. Although the AP test will not directly assess you on these skills, they are important tools you will need to use to apply to problem solving.
What to Know Before Taking Calculus (An Article from Kahn Academy)
Factoring Polynomials
Factor Theorem (Factoring polynomials with degrees greater than 2)
Evaluating Trigonometric Functions With a Unit Circle
How to Memorize the Unit Circle
AP Exam Weighting: 10% - 12%
How does knowing the value of a limit, or that a limit does not exist, help you to make sense of interesting features of functions and their graphs? How do we close loopholes so that a conclusion about a function is always true? Can change occur at an instant?
AP Exam Weighting: 10% - 12%
Why do mathematical properties and rules for simplifying and evaluating limits apply to differentiation? Derivatives allow us to determine instantaneous rates of change. To develop understanding of how the definition of the derivative applies limits to average rates of change, we will explore average rates of change over increasingly small intervals.
Stewart Chapter 3: Differentiation Rules
Stewart Chapter 3: Select Answers
Differentiation Rules
Power Rule Part 2 [Negative Exponents]
Power Rule Part 3 [Fractional Exponents]
Velocity and Other Rates of Change
Differentiating Trigonometric Functions
AP Exam Weighting: 9% - 13%
In this unit, students learn how to differentiate composite functions using the chain rule and apply that understanding to determine derivatives of implicit and inverse functions. Students need to understand that for composite functions, y is a function of u while u is a function of x. Leibniz notation for the chain rule, dy/dx = dy/du * du/dx , accounts for these relationships.
AP Exam Weighting: 15% - 18%
In this unit, we will focus on abstract structures and formal conclusions. Reasoning with definitions and theorems establishes that answers and conclusions are more than conjectures; they have been analytically determined. Students will learn to present justifications for their conclusions about the behavior of functions over certain intervals or the locations of extreme values or points of inflection. The unit concludes this study of differentiation by applying abstract reasoning skills to justify solutions for realistic optimization problems
Unit 4 Notes Packet
Stewart Chapter 4: Applications of Differentiation
Stewart Chapter 4: Select Answers
Extreme Values
Mean Value Theorem
First Derivative Test
Second Derivative Test
Connecting Functions and Their First and Second Derivatives
Derivative Plotter Tool This tool helps you visually see graphs of derivatives.
2nd Derivative Animation This tool shows you how f(x) relates to f'(x) and f''(x)
AP Exam Weighting: 10-15%
In this unit we will begin applying concepts from previous units to scenarios encountered in the world. To solve these problems, students will need to be able to identify key information, determining which procedure applies to the scenario presented (i.e., that “rates of change” indicate differentiation), stating what is changing and how, using correct units, and explaining what their answer means in the context of the scenario. Differentiation is a common underlying structure on which to build understanding of change in a variety of contexts. Students’ understanding of units of measure often reinforces their understanding of contextual applications of differentiation in problems involving related rates, identifying the independent variable common to related functions.
Stewart Chapter 3: Differentiation Rules
Stewart Chapter 3: Select Answers
Stewart Chapter 4: Applications of Differentiation
Stewart Chapter 4: Select Answers
Above Kahn Academy module includes guided examples and practice problems.
Paul's Notes: More guided practice
Optional Problems: Includes answer key
Related Rates
Introduction and Guided Examples: How to relate equations to each other.
Solving Related Rates Problems: Guided practice and examples
Paul's Notes: More guided practice
Optional Problems: Includes answer key
AP Exam Weighting: 17-20%
This unit establishes the relationship between differentiation and integration using the Fundamental Theorem of Calculus. Students begin by exploring the contextual meaning of areas of certain regions bounded by rate functions. Integration determines accumulation of change over an interval, just as differentiation determines instantaneous rate of change at a point. Students should understand that integration is a limiting case of a sum of products (areas) in the same way that differentiation is a limiting case of a quotient of differences (slopes).
Stewart Chapter 5: Integrals
Stewart Chapter 5: Select Answers
Stewart Chapter 6: Applications of Integrals
Stewart Chapter 6: Select Answers
Stewart Chapter 7: Techniques of Integration
Stewart Chapter 7: Select Answers
Estimating with Finite Sums
The Definite Integral
Summation Notation [Sigma Notation]
The Fundamental Theorem of Calculus
Average Value Theorem [Various Worked Out Examples]
Reverse Power Rule, Rationals, Radicals, Trig, Log, Absolute Value, Piecewise Functions
AP Exam Weighting: 6-12%
In this unit, students will learn to set up and solve separable differential equations. Slope fields can be used to represent solution curves to a differential equation and build understanding that there are infinitely many general solutions to a differential equation, varying only by a constant of integration. Students can locate a unique solution relevant to a particular situation, provided they can locate a point on the solution curve. By writing and solving differential equations leading to models for exponential growth and decay, students build understanding of topics introduced in Algebra II and other courses.
Stewart Chapter 3: Differentiation Rules
Stewart Chapter 3: Select Answers
Stewart Chapter 5: Integrals
Stewart Chapter 5: Select Answers
Stewart Chapter 7: Techniques of Integration
Stewart Chapter 7: Select Answers
Stewart Chapter 9: Differential Equations
Stewart Chapter 9: Select Answers
Differential Equations
Integrating using long division/completing the square
Integration by Parts
AP Exam Weighting: 10-15%
This unit involves the interpretation of the integral as an accumulator and applications of finding areas and volumes. The definite integral is used to find the areas of regions between curves using all types of functions. These are areas on an interval, areas between curves including curves with more than two intersections, also incorporating change of axis. The next application is volume beginning with three dimensional shapes of uniform cross sections. Next included are volumes of rotation using the disk, and washer method, also incorporating the change of axis.
Stewart Chapter 5: Integrals
Stewart Chapter 5: Select Answers
Stewart Chapter 6: Applications of Integrals
Stewart Chapter 6: Select Answers
Stewart Chapter 8: Further Applications of Integrals
Stewart Chapter 8: Select Answers
Integrals as Net Change
As Functions of y [Integrating y sideways]
Volume by Method of Slicing
Volume of Rotational Solids