This is a collection of different resources that you can utilize to get more Calculus practice. Several resources are listed as they all have their own strengths and weaknesses.
10 questions per unit. One answer should be "1", another one should be "2", etc. all the way up to 10. So, if you don't have answers 0-9 in the end then you know you have mistake(s) to find and correct.
Pros:
Quick unit practice with some guidance on what the answers should be.
Cons:
Not a lot of practice per unit.
Pros:
Lots of practice and videos that are organized by skill. When you miss a question, you can click the "get help" link and compare your work to the correct work to quickly learn from your mistake.
If you work on the site while logged in, it will keep a % of how much of the Calculus course you have gone through. It helps most people to stay motivated when they see that they are making progress, like KA tracks.
Cons:
Since the assignments focus on one skill at a time, it doesn't necessarily let you practice the connections between topics.
Pros:
Created by College Board (the people who make and grade your AP exams).
Cons:
You will have to let me know if you want any of the progress checks unlocked for practice.
Some of the questions are harder than you are ready for at the beginning of the year. I would not recommend this as a primary resource except when reviewing for this AP exam.
Pros:
Lots of practice and the solutions are provided for you to check your work.
Very detailed notes that are helpful to read through to make sure you fully understand the topic.
Cons:
This is really designed for College Calculus so some of the AP Calculus AB topics will be on their Calculus 1 and Calculus 2 pages. AP Calculus BC should cover the rest of the Calculus 2 topics.
Pros:
Videos!
Extra practice with explanations and some entertainment to make it more enjoyable.
Cons:
Most of this would be better at the end of the year when you are reviewing for the AP exam. These videos skim some important topics and instead try to help you see common errors and learn from those.
While textbooks are not as popular with students, our textbook still provides examples, explanations, tons of practice and solutions to check with.
You can access the pdf version of the textbook at this link. You will need to be logged into your FAYAR account for access.
This site has a ton of "practice test". Each practice test seems to have around 8 to 10 questions. Since most of these "practice tests" are not unit or content specific, these would be best utilized once you are reviewing for the AP exam.
Free Response Questions account for exactly half of the earnable points on the AP exam.
Many FRQs seem very challenging but with practice you can get better at the justifications, and you can learn what types and questions are most common on FRQs.
I have collected, organized, and tried to make it as user-friendly as possible by creating and providing the FRQ database that you can access on this link. Pay attention to the tabs at the bottom to get the most out of the database.
This is an uncommon question type for the AP exam, but I am providing this as practice for students want to learn this on their own.
Circuit - Derivatives of Inverse Functions - Download a new copy
Volumes of Rotations - Download a new copy -
AP Calculus AB circuit - Download a new copy -
Notes / Practice
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Solutions are on the bottom of the back page.
Matching Activity
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Solutions
Circuit
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Khan Academy Videos and Practice
Link
This tool allows you to practice making accurate graphs of a f(x) given its second derivative graph.
This tool allows you to visualize the graphs of tangent lines and derivative functions of basic derivative functions.
For example, it can help you visualize why the derivative of sin(x) is cos(x), or why the derivative of e^x is e^x, ect.
This tool allows you to practice checking the continuity of a function at specific x-values. Try all 10 examples!
This tool allows you to practice making accurate graphs of a f(x) given its derivative graph.
This USUB practice only focuses on picking the correct U and knowing what form it will be in after the substitution.
Link to the practice and the solutions are on the second page.
Khan Academy videos and practice quizzes.
Link
24 USUB practice questions in 3 different difficulties:
1) solve for du given u.
2) usub when you are told u.
3) usub when you have to pick u.
Link to the practice and the solutions are on the second page.
Practice these questions from when they appeared on released FRQs:
Access these FRQs and more on the class FRQ database.
1998 FRQ #6, 2000 FRQ #5, 2001 FRQ #6, 2004 FRQ #4, 2005B FRQ #5, 2007B FRQ #5, 2008B FRQ #6, 2011 FRQ #5, 2015 FRQ #4, 2015 FRQ #6, 2019 FRQ #4, 2021 FRQ #5, 2023 FRQ #6, and 2025 FRQ #6.
The nice thing about implicit in the FRQ section, is that they often tell you what the derivative is equal to, and you just have to show why that is true.
Notes and practice for implicit differentiation:
Explanation, notes and examples:
Link
Khan Academy videos and practice
FTC
Circuit
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Practice these questions from when they appeared on released FRQs:
Access these FRQs and more on the class FRQ database.
1999 FRQ #5, 2002 FRQ #4, 2002 FRQ #6, 2006B FRQ #2, 2007 FRQ #3, 2008B FRQ #4, 2009 FRQ #5, 2011 FRQ #2, 2011 FRQ #4, 2011B FRQ #4, 2011B FRQ #6, 2012 FRQ #1, 2016 FRQ #3, 2016 FRQ #6, 2019 FRQ #3, 2021 FRQ #4, 2023 FRQ #5, 2024 FRQ #1, 2024 FRQ #4, 2025 FRQ #3, and 2025 FRQ #4.
Explanation, notes and examples
Link
Khan Academy videos and practice - INTRO TO RELATED RATES
Related Rates INTRO
Khan Academy videos and practice
Related Rates - Solving
Circuit
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Explanation, notes and examples:
Link
Circuit:
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Khan Academy (the derivative & tangent line equations) Quiz:
Link
Practice these questions from when they appeared on released FRQs:
Access these FRQs and more on the class FRQ database.
1998 FRQ #4, 1998 FRQ #6, 1999 FRQ #4, 1999 FRQ #6, 2000 FRQ #5, 2001 FRQ #4, 2002 FRQ #6, 2003 FRQ #4, 2003B FRQ #1, 2004 FRQ #4, 2004B FRQ #4, 2005 FRQ #6, 2005B FRQ #5, 2006 FRQ #3, 2006B FRQ #2, 2007 FRQ #5, 2008 FRQ #6, 2008B FRQ #4, 2008B FRQ #6, 2009 FRQ #5, 2009B FRQ #5, 2010 FRQ #6, 2010B FRQ #2, 2011 FRQ #3, 2011 FRQ #5, 2012 FRQ #4, 2013 FRQ #6, 2014 FRQ #1, 2014 FRQ #4, 2014 FRQ #6, 2015 FRQ #6, 2016 FRQ #6, 2017 FRQ #4, 2018 FRQ #6, 2019 FRQ #6, 2021 FRQ #5, 2023 FRQ #3, 2024 FRQ #5, and 2025 FRQ #6.
Defining the Derivative of a Function and Using Derivative Notation from FLIPPEDMATH:
However, the tangent line questions are mixed in with the other content from this section.
Notes and practice for linear approximations:
Coming soon...
AP Calculus BC Topics ONLY below this point:
Which series convergence test do I use? (TFD, P-Series, Telescoping, DCT, LCT, AST, Ratio, & more). 19 minutes and 55 seconds long.
16 Practice questions / Try each question before he goes over it!
Warning: At least one of the questions is a telescoping series, which is good to know for the AP exam but not required.
Warning: It also describes the root test that you are not responsible for.
Calculus 2 - Geometric Series, P-Series, Ratio Test, Root Test, Alternating Series, Integral Test. 43 minutes and 51 seconds long.
Review Geometric Series, P-Series, Ratio Test, Root Test (not required for Calculus BC), Alternating Series, Integral Test and has practice questions.
Improper Integrals - Download a new copy -
Parametrics and Vectors - Download a new copy -
Series - Download a new copy -
Taylor Polynomials and Taylor Series - Download a new copy -
Pros:
Videos!
Extra practice with explanations and some entertainment to make it more enjoyable.
Cons:
Most of this would be better at the end of the year when you are reviewing for the AP exam. These videos skim some important topics and instead try to help you see common errors and learn from those.