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Unit 9: AP Calculus AB solved free response questions from past exams
About this unit.
Watch as Sal solves free response questions from past AP Calculus exams. This is a good preparation for your upcoming exam!
AP Calculus AB 2017 free response
- 2017 AP Calculus AB/BC 4a (Opens a modal)
- 2017 AP Calculus AB/BC 4b (Opens a modal)
- 2017 AP Calculus AB/BC 4c (Opens a modal)
AP Calculus AB 2015 free response
- 2015 AP Calculus AB/BC 1ab (Opens a modal)
- 2015 AP Calculus AB/BC 1c (Opens a modal)
- 2015 AP Calculus AB/BC 1d (Opens a modal)
- 2015 AP Calculus AB 2a (Opens a modal)
- 2015 AP Calculus AB 2b (Opens a modal)
- 2015 AP Calculus 2c (Opens a modal)
- 2015 AP Calculus AB/BC 3a (Opens a modal)
- 2015 AP Calculus AB/BC 3b (Opens a modal)
- 2015 AP Calculus AB/BC 3cd (Opens a modal)
- 2015 AP Calculus AB/BC 4ab (Opens a modal)
- 2015 AP Calculus AB/BC 4cd (Opens a modal)
- 2015 AP Calculus AB 5a (Opens a modal)
- 2015 AP Calculus AB 5b (Opens a modal)
- 2015 AP Calculus AB 5c (Opens a modal)
- 2015 AP Calculus AB 5d (Opens a modal)
- 2015 AP Calculus AB 6a (Opens a modal)
- 2015 AP Calculus AB 6b (Opens a modal)
- 2015 AP Calculus AB 6c (Opens a modal)
AP Calculus AB 2011 free response
- 2011 Calculus AB free response #1a (Opens a modal)
- 2011 Calculus AB Free Response #1 (b, c, & d) (Opens a modal)
- 2011 Calculus AB free response #2 (a & b) (Opens a modal)
- 2011 Calculus AB free response #2 (c & d) (Opens a modal)
- 2011 Calculus AB free response #3 (a & b) (Opens a modal)
- 2011 Calculus AB free response #3 (c) (Opens a modal)
- 2011 Calculus AB free response #4a (Opens a modal)
- 2011 Calculus AB free response #4b (Opens a modal)
- 2011 Calculus AB free response #4c (Opens a modal)
- 2011 Calculus AB free response #4d (Opens a modal)
- 2011 Calculus AB free response #5a (Opens a modal)
- 2011 Calculus AB free response #5b (Opens a modal)
- 2011 Calculus AB free response #5c (Opens a modal)
- 2011 Calculus AB free response #6a (Opens a modal)
- 2011 Calculus AB free response #6b (Opens a modal)
- 2011 Calculus AB free response #6c (Opens a modal)
AP Calculus AB Class Schedule and Homework Assignments
* Lesson recordings are from 2020-21, so they may not completely match the lessons from this year.
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Welcome to AP Calculus !
Welcome to AP Calculus! This site contains a lot of information I used with students when I taught AP Calculus. The syllabus I used for AP Calculus can be accessed by clicking on the following link:
AP Calculus Syllabus
Feel free to use whatever you think may help you, or teach your students. If you have any questions, or just want to drop me a line, you can contact me at [email protected] . Good luck and I hope that you have a successful experience learning and teaching this course!
Calculus AB
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Implicit Differentiation and Other Derivatives
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Fundamental Theorem of Calculus and Integration Methods
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Sat / act prep online guides and tips, the expert's guide to the ap calculus ab exam.
Advanced Placement (AP)
Are you taking the AP Calculus AB exam this spring and want to be well prepared on test day? The AP Calculus AB exam in 2022 will be held on Monday, May 9, at 8 am .
Before you sit down to take the exam, though, it's critical that you know how the Calculus AB test is formatted, what topics it covers, and how you'll be scored on it. This guide will go over all of that information while also showing you official sample problems and giving you tips on the best way to prepare for AP Calculus AB.
The AP Calculus AB exam can sometimes seem overwhelming, but we're here to break it down into clear and manageable information for you. You can also check out the College Board's new AP Classroom tool for AP Calculus AB , which has additional resources and information. Let's get started!
What's the Format of the AP Calculus AB Exam?
The AP Calculus AB exam is three hours and 15 minutes long and has two sections. Both of these sections are divided into two parts (based on whether or not a calculator is allowed).
Multiple-Choice Section
Here is an overview of the format of the AP Calculus AB multiple-choice section:
- 45 questions total
- One hour 45 minutes total
- Worth 50% of your total score
- 30 questions
- No calculator allowed
- 15 questions
- Calculator required
Note that the AP Calculus AB exam has had small changes made to its format. Previously, Part A of the multiple-choice section had 28 questions, and Part B had 17 questions.
Free-Response Section
Here is a rundown of the format of the AP Calculus AB free-response section:
- Six questions total
- One hour 30 minutes total
- Two questions
- Four questions
This can all look a little complicated, but basically, the AP Calculus AB exam consists of four parts. The first two are multiple choice, and the last two are free response.
You are required to use a calculator for the middle two parts (one each for multiple choice and free response), but you may not use a calculator for the first and last parts of the exam.
What Topics Does the AP Calculus AB Exam Cover?
Content on the Calculus AB exam can be divided into three main topic areas, referred to by the College Board as Big Ideas . Within these three Big Ideas are more specific topics called Enduring Understandings (often abbreviated as "EU"). Each Enduring Understanding contains both Learning Objectives and Essential Knowledge that the student should have learned by the time of the exam.
As I mentioned, there have been some updates to the AP Calculus AB exam. Namely, the Big Ideas are now integrated within each of the eight units covered in the AP Calculus AB course.
The good news is that there haven't been any changes to the structure of the AP Calculus AB exam!
I've listed each of the Big Ideas and their Learning Objectives below, since these are the most relevant for students looking for what the exam covers.
For the sake of length and clarity, I left out the Enduring Understandings and Essential Knowledge. If you'd like to see these, as well as more detailed information on the content covered by the exam, check out the official AP Calculus AB Course Description. Still, know that the information below will give you a solid look at what you're expected to know for the exam.
Learning Objectives are listed below Big Ideas. These Learning Objectives are skills that students are expected to know how to do for the exam.
Big Idea 1: Change
- Understand how and when change occurs
- Determine the rate of change
- Interpret how different equations are structurally similar
- Determine change over an interval of time
- Analyze functions for intervals of continuity or points of discontinuity
- Determine the applicability of important calculus theorems using continuity
- Find the rate of change based on the area of a region between a curve and the x-axis
- Model motion not constrained to a linear path
Big Idea 2: Limits
- Understand limits, and making sense of features of functions and their graphs
- Mathematical properties and rules for simplifying and evaluating limits applies to differentiation
- Prove a limit exists
- Recognize the connection between differentiability and continuity
- Interpret the meaning of a derivative within a problem
- Solve problems involving the slope of a tangent line
- Solve problems involving related rates, optimization, and rectilinear motion
- Solve problems involving rates of change in applied contexts
- Solve how the sum if infinitely discrete terms can be a finite value represented in a continuous function.
Big Idea 3: Analysis of Function
- Close loopholes so a conclusion about a function is always true
- Understand how the change of two units of measurement relate to one another, and the rate at which they change.
- Interpret what numbers might tell you about other rates of change
- Apply the Mean Value Theorem to to justify a conclusion
- Include additional information in a sound mathematical argument that optimizes a simple equation
- Integrate to find areas related to differentiating to find slopes
- Calculate derivatives and antiderivatives
- Evaluate definite integrals
- Analyze graphs defined using parametric equations or polar functions using chain rules.
- Apply definite integrals to problems involving the average value of a function, motion, and area and volume.
- Analyze differential equations to obtain general and specific solutions
- Interpret, create, and solve differential equations from problems in context
AP Calculus AB Units
Since the Big Ideas of AP Calc AB are covered throughout the course, it's also useful to know what each unit covers.
In the table below, you'll find each of the course's units, along with a brief description of the topics covered in that unit. We've also included the weighted breakdown of questions on the AP Calc AB exam that come from each unit. So for example, 10-12% of your exam grade will come from questions about Limits and Continuity, while 17-20% of your exam grade will come from questions about Integration and Accumulation of Change.
Knowing the topics covered in AP Calc AB, along with how they factor into your AP exam score, will help guide your studying and make it more productive!
Also, keep in mind there's a lot more to know about these units and unit topics . For more information, be sure to check out the official AP Calculus AB Course Guide provided by the College Board.
AP Calculus AB Sample Questions
Looking at sample questions is one of the best ways to get a feel for what the AP Calculus AB exam will be like. Here are four sample questions, one from each part of the AP exam. Each of these questions was taken from the official AP Calculus AB Course Description , which you can look at for more complete answer explanations and additional sample problems.
Multiple Choice (No Calculator)
This question tests your ability to calculate derivatives. You'll need to use the chain rule to differentiate composite functions. The correct answer to this problem is B.
Multiple Choice (Calculator Allowed)
This question tests your ability to solve problems with rapid rates of change. You'll have to find the derivative in order to find the rate of change of the temperature of the water. The correct answer is B.
Free Response (Calculator Allowed)
This question tests your knowledge of integrals. Parts A, B, and C are each worth 3 points.
Free Response (No Calculator)
This question tests your knowledge of multiple topics, including derivatives and integrals. You can receive up to 1 point for part A, 2 points for part B, and 3 points each for parts C and D.
How Is the AP Calculus AB Exam Scored?
As mentioned, the multiple-choice section and the free-response section are each worth 50% of your total exam score.
For the multiple-choice section, you earn 1 point for each question you answer correctly. No points are deducted for incorrect answers, so you should answer every question! You can earn up to 45 points for this section.
For the free-response section, each of the six questions is worth 9 points, so you can earn up to 54 points. Different parts of each question can be worth a different amount of points (for example, on one question you may be able to earn up to 1 point for part A, 3 points for part B, 3 points for part C, and 2 points for part D).
After your points are added up for each of your sections, your AP Calculus AB score is converted to the standard AP scoring scale of 1-5 . The exact formula for doing this can change slightly from year to year.
However, in 2008, the process for converting raw AP scores to scaled scores involved multiplying the number of multiple-choice questions you answered correctly by 1.2272, and then adding that number to the points you received on the free-response section. This value is rounded to the nearest whole number and becomes your composite score.
Each AP score (from 1-5) corresponds to a range of composite scores. Below, you can see the conversion chart and score distributions for test takers from the 2020 Calculus AB exam :
Source: The College Board
3 Tips for Preparing for the AP Calculus AB Exam
Studying for the AP Calculus AB exam can be tough. Use these three tips to make your studying more effective and increase your chances of getting a great score.
Tip 1: Memorize Important Formulas
There are certain formulas for AP Calculus AB that you should have down pat. There's no formula sheet given on the AP exam, so you'll have to memorize the formulas you'll need. Many teachers give out formula sheets for students to memorize.
There are also various formula cheat sheets you can use to review before the exam. To find these, simply Google "AP Calculus AB formula sheet" and look at your options.
In general, any formula you use regularly in class is a good one to memorize. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems.
Tip 2: Know How to Use Your Calculator
You're allowed to use your calculator for two of the four exam parts, and most of the questions in these two sections will be difficult, if not impossible, to solve without a graphing calculator.
While it might seem obvious that you should know how to work your calculator, knowing exactly how and when to use its different functions can save you a lot of time on the exam and increase your chances of getting the correct answer.
According to the College Board, the four calculator capabilities you'll use the most during the AP Calculus AB exam and should easily be able to do with your calculator are as follows:
- Plot the graph of a function within an arbitrary viewing window
- Find the zeros of functions (solve equations numerically)
- Numerically calculate the derivative of a function
- Numerically calculate the value of a definite integral
When you're preparing for the exam, be sure that you know how to do each of these (completing practice problems can help!).
Tip 3: Get Used to Showing All Your Work
For most free-response questions on the AP Calculus AB test, the final answer to a problem is only worth 1-2 points out of a possible 9. This means that the majority of points are earned through intermediate steps of the problem —and if you don't show how you reached those intermediate steps, you won't get a high score on this section.
Even if you get a correct answer by using your calculator, you have to write the setup (such as the equation being solved or the derivative being evaluated) as well as the answer in order to get credit for your work.
You might be used to not writing down certain work that seems particularly obvious on homework and class tests. However, even if your teacher doesn't mind, AP graders will.
Remember that AP graders are more interested in how you reached your final answer than they are in what that final answer is, so get yourself in the habit of showing each step of your work well before exam time.
Conclusion: What to Know About the AP Calculus AB Exam
The AP Calculus AB exam can be intimidating if you don't know what to expect. Knowing how the exam will be formatted and what types of questions it will ask can go a long way toward helping you feel more prepared and confident on test day.
The exam has two sections, multiple-choice and free-response, which are each divided into two parts, based on whether or not you may use a calculator. Each of these sections is worth 50% of your total AP score.
The exam itself covers three main topics:
- Derivatives
- Integrals and the Fundamental Theorem of Calculus
In order to prepare for the AP Calculus AB exam in the best way, keep these three tips in mind during your review:
- Memorize important formulas
- Know how to use your calculator
- Get used to showing all your work
What's Next?
Now that you know what the AP Calculus AB exam covers, the next step is to practice! Read our guide to get links to every Calculus AB practice test available online .
Wondering how challenging other AP classes are? Learn what the easiest AP classes are and what the hardest AP classes are so that you know exactly what to expect!
Not sure which other math classes you should take? Math is often the trickiest school subject to choose classes for, but our guide will help you figure out exactly which math classes to take for each year of high school .
Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.
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Day #12 Homework —x Find lim for each of the functions below. Then, find the equation of the tangent line to of x atthe envalueofx. h-Þ0 2. Find the equation of the line tangent to the graph 4. ... Daily Lessons and Assessments for AP* Calculus AB, A Complete Course Mark Sparks 2012 . Created Date: 9/24/2018 7:42:22 AM ...
Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected]. The ...
Meet an AP®︎ teacher who uses AP®︎ Calculus in his classroom. 3:26. Bill Scott uses Khan Academy to teach AP®︎ Calculus at Phillips Academy in Andover, Massachusetts, and he's part of the teaching team that helped develop Khan Academy's AP®︎ lessons. Phillips Academy was one of the first schools to teach AP®︎ nearly 60 years ago.
Complete Practice Tests. The College Board has released two complete exams from prior administrations of the AP Calculus AB exam. The tests are from 1988 and 1998. The 1988 test has an answer key included; however, for some reason, the 1998 exam does not. The College Board provided answers for the free-response questions in a separate document ...
Watch as Sal solves free response questions from past AP Calculus exams. This is a good preparation for your upcoming exam!
AP Classroom is a free and flexible online platform that provides i nstructional resources for each AP course to support student learning of all course content and skills. AP Classroom r esources, including AP Daily videos, help your students learn and practice all year.. Learn about all instructional resources in AP Classroom. Learn more about AP Daily videos and their features.
Scoring notes: The first point can be earned by presenting y 2 = 2 x or y. The second point can be earned for the substitution of y =. substituting x = 2 + y 3 into y 2 − 2 x = 0. 6 y. A response earns all three points by setting y 2 − 2 x = 0, declaring the point. = 2 x . 2 x into 6 xy = 2 + y 3 , or for. (.
Unit 5: Analytical Applications of Differentiation. After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems. Topics may include: Mean Value Theorem and Extreme Value Theorem. Derivatives and properties of functions.
For more advanced practice with these concepts, try Units 4 and 8 to apply the derivative and integral to context. Here are some tips for passing an AP Calculus AB class: Practice at least 30 minutes a day, every day. Try hard on your homework, even if you don't fully get it yet; that's where you build your skills.
AP Calculus AB Class Schedule and Homework Assignments ... Date. Class Activities. Lesson Recordings* Homework Assignment. 8/23. Introductions. Policy Sheet. First Day Survey . 8/24. Sections 1.1, 1.2, and 1.5. Video. p. ... 4/12. AP Review, Part 3 Riemann Sum Worksheet . AP Review, Part 4. Video . 4/16. Derivative Quiz.
Welcome to AP Calculus! Welcome to AP Calculus! This site contains a lot of information I used with students when I taught AP Calculus. The syllabus I used for AP Calculus can be accessed by clicking on the following link: AP Calculus Syllabus. Feel free to use whatever you think may help you, or teach your students. If you have any questions ...
AP Calculus AB. Course Information; Chapter 6. The Definite Integral. A Day: B Day: Section: Lesson Name: Homework: 12/9: 12/12: 6.1/6.5: Estimating Area: 12/13: 12/14: Definite Integrals in Context: 12/15: 12/16: Optional Quarter 2 Exam: ... Riemann Sums and Definite Integrals DeltaMath Homework: 1/6: 1/9: 6.4: Indefinite Integrals and ...
Don't stress. AP Calculus AB homework help is available 24/7. Log On 24/7 . With 24/7 tutoring access you can receive the help you've been looking for. In home or on the go, no matter where you are or what time it is, we're here to help you get the AP Calculus AB homework help you need when you need it.
AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of ...
AP Calculus AB Name _____ The following are the daily homework assignments for Chapter 4 - Applications of Differentiation Section Pages Topics Assignment 4.1 Day 1 p.268-271 Related Rates Practice Problems WS # 1-2, 4-5, 8-12, 16, 18, 20 4.1 Day 2
Two questions. 30 minutes. Calculator required. Part B. Four questions. 60 minutes. No calculator allowed. This can all look a little complicated, but basically, the AP Calculus AB exam consists of four parts. The first two are multiple choice, and the last two are free response.
AP Calculus AB Name _____ The following are the daily homework assignments for Chapter 5 - Integrals Section Pages Topics Assignment 4.9 Day 1 p.332-338 Anti-derivatives; initial value problems p.338: # 1-11, 13, 21 4.9 Day 2 p.332-338 Slope fields p.338: # 12, 16, 19-20, complete
Summer Packet. This packet is intended to prepare you for AP Calculus AB by. reviewing prerequisite algebra and pre-calculus skills and covering the first chapter calculus textbook. (With the amount of curriculum to be covered before the AP Exam in May, we need to cover this review chapter over the summer.) It is due on the first day of school ...
The Course at a Glance provides. useful visual organization of the AP Calculus AB and AP Calculus BC curricular components, including: Sequence of units, along with approximate weighting and suggested pacing. Please note, pacing is based on 45-minute class periods, meeting five days each week for a full academic year.