2017 ap calculus ab free response

2017: Free-Response Questions; Questions. Scoring. Samples and Commentary. Free-Response Questions. Scoring Guidelines. Chief Reader Report. Scoring Statistics. Scoring Distributions. Sample Responses Q1. Sample Responses Q2. Sample Responses Q3. Sample Responses Q4. Sample Responses Q5. Sample Responses Q6

2017 ap calculus ab free response. multiple choice and free response questions are grouped by section in order to help students master discrete concepts for the AP Calculus Test. There are 2 AB practice tests and 2 BC practice tests, each with 45 multiple choice questions and 6 free response questions. Many prep books use some of the same questions in their AB and BC tests,

Problem 1 1.1 Part a AP Calculus AB 2017 Free-Response Solutions Louis A. Talman, Ph.D. Emeritus Professor of Mathematics Metropolitan State University of Denver May 18, 2017 The approximation with a left-hand sum using the intervals given is 1.2 Part b 50:3 2 + 14:4 3 + 6:5 5 = 176:3:

2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS. 6. Let f be the function defined by sin x. f x = cos 2 x + e. ( ) ( ) . Let g be a differentiable function. The ...2017 AP Calculus AB Free Response #6 Allen Tsao The STEM Coach 3.33K subscribers Subscribe 189 views 4 years ago AP Calculus AB FRQ: All Walkthrough of the 2017 AP Calculus AB FRQ #6....Problem 2 from the 2017 AP Calculus AB Exam. The problem deals with competing rates of change (the rates at which bananas are removed from and then placed on...AP Calculus 2005 AB (Form B) FRQ Solutions Louis A. Talman, Ph. D. Emeritus Professor of Mathematics Metropolitan State University of Denver July 17, 2017 1 Problem 1 1.1 Part a We must first locate the right-hand corner of the region R—that is, the smallest positive value x= afor which 1+sin2x= ex=2. Numerical solution gives a= 1:13569. The ... AP ® CALCULUS AB 2019 SCORING COMMENTARY . Question 6 (continued) Sample: 6C Score: 3 . The response earned 3 points: 1 point in part (a), 2 points in part (b), no points inpart (c), and no point in part (d). In part (a) the response earned the point for the value of . h 2 2 3 . In part (b) the response earned the first andAP® CALCULUS AB/CALCULUS BC 2018 SCORING COMMENTARY Question 1 Overview The context of this problem is a line of people waiting to get on an escalator. The function r models the rate at which people enter the line, where t t3 7 rt 44 1 100 300 for 0 t 300, rt 0 and for t 300; rtProblem 1 from the 2017 AP Calculus AB and BC Exams. The problem deals with using cross sectional areas to model the volume of a tank. Part c involves the Fu...

AP Calculus AB 2016 Free-Response Questions Author: ETS Subject: Free-Response Questions from the 2016 AP Calculus AB Exam Keywords: Calculus AB; Free-Response Questions; 2016; exam resources; exam information; teaching resources; exam practice Created Date: 2/7/2017 8:58:10 PM ...2013 answers to released free response AP questions 2012 answers to free response AP questions ... Click here to see the solutions to the 2017 AP Released Free Response questions. As ... Mr. Calculus is a College Board endorsed AP* Calculus AB and AP* Calculus BC consultant and teaches at Diamond Bar High School in Diamond Bar ...Cracking the AP Calculus AB Exam 2017, Premium Edition (College Test Preparation) by Princeton Review; Kahn, David - ISBN 10: 1101919841 - ISBN 13: ...If you have any questions or ideas for improvement, feel more than free to comment them below!If this video has helped you, I would greatly appreciate it if ...2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS 6. Let f be the function defined by fx ( ) cos 2 x e sin x. Let g be a differentiable function. The table above gives values of g and its derivative g at selected values of x. Let h be the function whose graph, consisting of five line segments, is shown in the figure above. (a) Find the slope of the line tangent to …AP Calculus AB Scoring Guidelines, 2016 Author: The College Board Subject: AP Calculus AB Keywords: AP Calculus AB, Scoring Guidelines, 2016 exam, exam resources; teacher resources; exam preparation; scoring information Created Date: 7/15/2016 10:38:53 AMMay 5, 2022 · Overview of the AP Calculus AB Exam The AP Calculus AB Exam tests your ability to understand and apply calculus concepts. The exam format is as follows: Section I: Multiple Choice, 50% of exam score. No calculator: 30 questions (60 minutes) Calculator: 15 questions (45 minutes) Section II: Free Response, 50% of exam score multiple choice and free response questions are grouped by section in order to help students master discrete concepts for the AP Calculus Test. There are 2 AB practice tests and 2 BC practice tests, each with 45 multiple choice questions and 6 free response questions. Many prep books use some of the same questions in their AB and BC tests,

2017 AP Calculus AB Exam Free Response Question #5Particle motion problem. Given position of particle P and velocity of particle Q. Determine direction of ...AP Calculus 2017 AB FRQ Solutions Louis A. AP Calculus AB 2016 Exam (videos, questions, solutions). The AP Calculus AB Exam will test your understanding of ...AP® CALCULUS AB/CALCULUS BC 2018 SCORING COMMENTARY Question 1 Overview The context of this problem is a line of people waiting to get on an escalator. The function r models the rate at which people enter the line, where t t3 7 rt 44 1 100 300 for 0 t 300, rt 0 and for t 300; rt2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB . SECTION II, Part B . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function . f . is differentiable on the closed interval [−6, 5 ] and satisfies . f (− ) 2 = 7. The graph of . f ¢, the . derivative of . f, consists of a semicircle and three line segments, as shown in the ...AP® Calculus AB/BC Exam Regularly Scheduled Exam Date: Tuesday morning, May 9, 2017 Late-Testing Exam Date: Thursday morning, May 18, 2017 Section I Total Time: 1 hour 45 minutes Number of Questions: 45* Percent of Total Score: 50% Writing Instrument: Pencil required *The number of questions may vary slightly depending on the form of the exam.

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2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB . SECTION II, Part B . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function . f . is differentiable on the closed interval [−6, 5 ] and satisfies . f (− ) 2 = 7. The graph of . f ¢, the . derivative of . f, consists of a semicircle and three line segments, as shown in the ...AP® Calculus AB/BC 2022 Scoring Guidelines Part A (AB): Graphing calculator required Question 2 9 points . ... Within each individual free-response question, at most one point is not earned for inappropriate rounding. Let f and g be the functions defined by f (x) =ln ( 4 x + 3 ) and gx( ) =x + 2 x 3.2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS 6. Let f be the function defined by sin x f x = cos 2 x + e ( ) Let g be a differentiable function. The table above gives values of g and its derivative g ¢ at selected values of x Let h be the function whose graph, consisting of five line segments, is shown in the figure above.2017 AP ® CALCULUS BC FREE-RESPONSE QUESTIONS CALCULUS BC SECTION II, Part B NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function f is differentiable on the closed interval [−6, 5 ] and satisfies f (− ) 2 = 7. The graph of f ¢, the derivative of f, consists of a semicircle and three line segments, as shown in the figure …{ : approximation : overestimate with reason : { 1 : integral : answer dt 3 : 2 : dV 1 : answer 2 2 (a) ∫ f ( t ) dt = 0

Every single AP Calculus AB and BC past paper including full papers, multiple choice, free response questions and practice papers from 1968 onwards. NEW. Hiring - A Level Maths students (predicted an A*) or Further Maths students (predicted an A or A* ) to write solutions for worksheets & other resources. Please get in touch via the contact ...2018 answers to released free response AP questions 2017 ... Mr. Calculus is a College Board endorsed AP* Calculus AB ...2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS 6. Let f be the function defined by fx ( ) cos 2 x e sin x. Let g be a differentiable function. The table above gives values of g and its derivative g at selected values of x. Let h be the function whose graph, consisting of five line segments, is shown in the figure above. (a) Find the slope of the line tangent to …2017 AB AP Calculus Free-Response Solutions and Notes Question AB-1 (a) The left Riemann sum approximation is 50.3 2 14.4 3 6.55 cubic feet. 1 (b) This is an overestimate of the volume of the tank since A()h is decreasing. (c) The volume is 10 0 f hdh 101.325 cubic feet. 2 Apr 4, 2021 · Except from the 1988 and 1998 past exam questions, there are no other complete past exam questions. However, you still can start from page 5 of AP Calculus AB Official Past Exams. This section has 16 multiple-choice questions, answers, the description of the range, and 2 free-response questions. AP Calculus AB Free-Response Questions 10 сент. 2018 г. ... Walkthrough of the 2017 AP Calculus AB FRQ #1. Thanks for watching the video. I have a lot more free problem solving videos on my website ...AP® Calculus AB/BC Exam Regularly Scheduled Exam Date: Tuesday morning, May 9, 2017 Late-Testing Exam Date: Thursday morning, May 18, 2017 Section I Total Time: 1 hour 45 minutes Number of Questions: 45* Percent of Total Score: 50% Writing Instrument: Pencil required *The number of questions may vary slightly depending on the form of the exam. AP® Calculus AB 2012 Free-Response Questions . About the College Board . The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association isThe AP Calculus AB Exam and the AP Calculus BC Exam should be administered simultaneously. ... ® AP Calculus BC Exam 2017 SECTION II: Free Response DO NOT ...Fall Semester Summary Sheet Spring Semester Summary Sheet AP Calc Formula Practice WS Derivative/Integral Rules College Board Released FRQs from 2000-2018 (Solution Keys under "Scoring Guidelines") AB Calculus Free Response Notebook (Collection of 1990-2010 AB FRQs & Solutions Organized by Topics/Category) 2019 AP FRQ Questions …Problem 6 from the 2017 AP Calculus AB Exam. The problem deals with derivatives (product rule, chain rule) and utilizing tables and graphs to determine deriv...

2017 ap ® calculus ab free-response questions 2 d h 4. At time t 0 , a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 91 degrees Celsius 0 t q C ( ) at time , and the internal temperature of the potato is greater than q 27 C ! 0 t for all times .

Start Course challenge Math AP®︎/College Calculus AB Unit 9: AP Calculus AB solved free response questions from past exams About this unit Watch as Sal solves free …Walkthrough of the 2017 AP Calculus AB FRQ #5. Thanks for watching the video. I have a lot more free problem solving videos on my website for AP Calculus as ...AP® Calculus AB 2012 Free-Response Questions . About the College Board . The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association isThe response earned 6 points: 2 points in part (a), 2 points in part (b), 2 points in part (c), and no points in part (d). In part (a) the student earned both points by presenting a correct expression for fx ′ ( ) and evaluating it correctly2017 AB AP Calculus Free-Response Solutions and Notes Question AB-1 (a) The left Riemann sum approximation is 50.3 2 14.4 3 6.55 cubic feet. 1 (b) This is an overestimate of the volume of the tank since A()h is decreasing. (c) The volume is 10 0 f hdh 101.325 cubic feet. 2 AP® Calculus AB 2013 Free-Response Questions . About the College Board . The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association isTitle: AP® Calculus AB Scoring Statistics 2017 Free-Response Questions Author: College Board Subject: AP; Advanced Placement Keywords: 2017 AP Exam Administration; Scoring Statistics; score information; exam materials; exam information; scoring information; teacher resources; exam resources; ADA In this video I go over Problem 2 from the Free-Response Calculator-Allowed Section of the 2017 AP Calculus AB Practice Exam.

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AP Calculus AB Scoring Guidelines Author: College Board Subject: 2018 AP Exam Administration Keywords: AP Scoring Guidelines; 2018 AP Exam Administration; Advanced Placement; scoring information; scoring resources; exam resources; exam information; teacher resources; student resources; ADA Created Date: 6/22/2018 4:54:13 PMPart a 2017 AP Calculus AB Free Response #5 Tom Cochran Life is a PiWay 1K subscribers Subscribe Like Share 20K views 6 years ago Problem 5 from the 2017 AP Calculus AB Exam. The problem...AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes . Number of questions—2 . A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. 1. People enter a line for an escalator at a rate modeled by the function r given by ⎧ ⎪ t t. 3 7 ⎪⎪ 44 1 for 0 ££ t ⎪ ()(rt ()=⎨ 100 300− ) 300 ...... free response questions. 2017 AP CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes Number of questions—2 A GRAPHING ...Walkthrough of the 2017 AP Calculus AB FRQ #1. Thanks for watching the video. I have a lot more free problem solving videos on my website for AP Calculus as ...In this video, I go through the AP Calculus AB/BC Free Response question 3. This question covers ideas such as the Fundamental Theorem of Calculus, Definite ...2017 AP Calculus AB & AP Calculus BC Exam Free Response Question #1Table problem. Volume with known cross sections. Left Riemann sum. Over or underestimat...2017 AP ® CALCULUS BC FREE-RESPONSE QUESTIONS CALCULUS BC SECTION II, Part B NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function f is differentiable on the closed interval [−6, 5 ] and satisfies f (− ) 2 = 7. The graph of f ¢, the derivative of f, consists of a semicircle and three line segments, as shown in the figure above. 2014 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS © 2014 The College Board. Visit the College Board on the Web: www.collegeboard.org. GO ON TO THE NEXT PAGE. ….

2017 ap ® calculus ab free-response questions 2 d h 4. At time t 0 , a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 91 degrees Celsius 0 t q C ( ) at time , and the internal temperature of the potato is greater than q 27 C ! 0 t for all times .2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS dH2 dt 2 4. At time t 0, a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 91 degrees Celsius ()qC at time t 0, and the internal temperature of the potato is greater than 27 Cq for all times t ! 0. ... scoring guidelines, sample responses from exam takers, and scoring distributions. AP® CALCULUS AB/CALCULUS BC 2017 SCORING GUIDELINES Question 1 (a) h ...AP Calculus AB & AP Calculus BC 2018 Exam Free Response Question #4Table problem! Reasoning from a table. Approximating a derivative at a point. Using MVT...2019 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part B . Time—1 hour . Number of questions—4 . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The continuous function f is defined on the closed interval . −6 £ x £ 5. The figure above shows a portion of . the graph of . f 2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS 2. When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by where ft()is measured in pounds per hour and t is the number of hours after the store opened. After theAbout 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 Learn 2017 AP Calculus AB/BC 4a 2017 AP Calculus AB/BC 4b 2017 AP Calculus AB/BC 4c AP Calculus AB 2015 free response Learn 2015 AP Calculus AB/BC 1ab 2015 AP Calculus AB/BC 1c{ : approximation : overestimate with reason : { 1 : integral : answer dt 3 : 2 : dV 1 : answer 2 2 (a) ∫ f ( t ) dt = 02017 AP Calculus AB Exam Free Response Question #2Rate in/rate out problem. Calculator. Definite integral. Integrating rate gives total. Finding value of... 2017 ap calculus ab free response, In this video I go over the first problems 25 through 28 of the Multiple-Choice Section of the 2017 AP Calculus AB Practice Exam., AP® Calculus AB Scoring Statistics 2017 Free-Response Questions Question Mean . Standard Deviation Number of Possible Points ; 1 3.32 ; 2.34 : 9 : 2 4.01 ; 2.75 ; 9 : 3 3.63 ; 2.63 ; 9 : 4 1.54 ; ... www.collegeboard.org . CollegeBoard . Title: AP® Calculus AB Scoring Statistics 2017 Free-Response Questions Author: College Board Subject: AP ..., 12 мая 2017 г. ... Problem 2 from the 2017 AP Calculus AB Exam. The problem deals with competing rates of change (the rates at which bananas are removed from ..., The following comments on the 2018 free-response questions for AP ® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response question and of how students performed on the question, including typical student errors. General comments, Problem 3 from the 2017 AP Calculus AB and BC Exams. The problem deals with a graph of a derivative and utilizing the graph to determine function and second ..., AP ® CALCULUS AB/CALCULUS BC 2019 SCORING COMMENTARY . Question 4 (continued) include a factor of . dh dt. Thus the second point was not earned, and the response is not eligible for the third point. In part (c) the response earned the first point with a correct separation of variables 1 1. dh dt h. 10 in line 2 on the left. The correct ..., AP Calculus AB 2017 free response: AP Calculus AB solved free response questions from past exams AP Calculus AB 2015 free response: AP Calculus AB solved free ..., 2015 Frq Ap Calc AbHere is what I have for FRQ#1 and 2. AP Calculus AB 2015 Free Response Question 2 Let f and g be the functions defined by f (x) = 1+ x + ..., Calculus BC Calculus AB Subscore Number of Students Scored 139,195 Score Distribution Exam Score N %At Global Mean 4.04 The following comments on the 2019 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response, AP Calculus AB 2015 Free-Response Questions Author: ETS Subject: Free-Response Questions from the 2015 AP Calculus AB Exam. Keywords: exam; 2015; Free-Response Questions; Calculus AB Created Date: 2/16/2015 7:51:58 AM, 2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS 2. When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by where ft()is measured in pounds per hour and t is the number of hours after the store opened. After the, 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 Learn 2017 AP Calculus AB/BC 4a 2017 AP Calculus AB/BC 4b 2017 AP Calculus AB/BC 4c AP Calculus AB 2015 free response Learn 2015 AP Calculus AB/BC 1ab 2015 AP Calculus AB/BC 1c, 38) Mon (5/8) - AP CALCULUS AB EXAM DAY Monday May 8th @8am Main Gym I. Multiple-choice questions (MCs) Part A: Graphing calculator not permitted 30 MCs 60 minutes Part B: Graphing calculator required 15 MCs 45 minutes II. Free-response questions (FRQ) Part A: Graphing calculator required 2 FRQs 30 minutes, AP Calculus AB 2017 free response. Learn. 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) , The AP Calculus Course and Exam Description (Fall 2019) (.pdf/2.29MB), which has everything you need to know about the course and exam. An AP Calculus AB Exam from 2012, previously available only through your AP Course Audit account. Since this exam is now publicly available, you can use the questions without restriction., Calculus BC Calculus AB Subscore Number of Students Scored 139,195 Score Distribution Exam Score N %At Global Mean 4.04 The following comments on the 2019 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response, 2017 AP Calculus AB & AP Calculus BC Exam Free Response Question #4Separable differential equation. Finding equation of a tangent line. Using a tangent lin..., calculus with Math 3 strengthening those topics, or Math 2 could focus on single variable calculus with Math 3 being exclusively multivariate calculus. When what is now the ollege oard redesigned AP alculus, it adopted a majority of the UPM model. ( ressoud, 2010) Originally, AP alculus covered a full year of single variable calculus., AP® CALCULUS AB 2019 SCORING COMMENTARY Question 2 (continued) quotient . 55 55 . 2.5 Numerical simplification is not required. The response simplifies the difference quotient to 0 in line 3 of the boxed work, and the first point was earned. In lines 1, 2, and 3 of the boxed work, the response earned the second point with “[s]ince . v. P (t , Problem 2 from the 2017 AP Calculus AB Exam. The problem deals with competing rates of change (the rates at which bananas are removed from and then placed on..., 2017 AP Calculus AB Exam Free Response Question #5Particle motion problem. Given position of particle P and velocity of particle Q. Determine direction of ..., BC FRQ Resources: AB Calculus Free Response Notebook 1999 - 2015 College Board (BC): Free Response Questions/Solutions 9. AP BC Quiz 3: FRQ Topics Review WS (Antiderivative Word Problem, Interpret Derivative Graphs) (Thurs 3/30) BC FRQ Quiz 3 10. BC Polar Curves/Polar Area Practice FRQs 11., In this video I go over FRQ #1 from the Free Response Calculator Allowed Section of the 2017 AP Calculus AB Practice Exam., The following comments on the 2017 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response question and of how students performed on the question, including typical student errors. General, AP® CALCULUS AB/CALCULUS BC 2018 SCORING COMMENTARY Question 1 Overview The context of this problem is a line of people waiting to get on an escalator. The function r models the rate at which people enter the line, where t t3 7 rt 44 1 100 300 for 0 t 300, rt 0 and for t 300; rt, View 2017-19 AP Calculus AB Free Response Questions.pdf from MATH 12 at Modern Public School & College, Abbottabad. 2017 AP Calculus AB Free Response Questions 2018 AP Calculus AB Free Response Upload to Study, AP Classroom is a platform that allows you to create customized quizzes and assignments for your AP Calculus AB students. You can choose from a variety of questions that cover the course content and skills, and get instant feedback on student performance. AP Classroom also helps you prepare your students for the AP exam with practice questions and exam simulations. , AP Calculus AB Practice Exams Free Response Notes Videos Study Guides. Here are the resources you will need for the AP Calculus AB free response questions. Be sure to try out the prior year questions and check out the video solutions. Working through these problems is an important part of your FRQ test prep. , Problem 4 from the 2017 AP Calculus AB and BC Exam Free Response section., 2017 AP Calculus AB Free Response #6 Allen Tsao The STEM Coach 3.33K subscribers Subscribe 189 views 4 years ago AP Calculus AB FRQ: All Walkthrough of the 2017 AP Calculus AB FRQ #6...., AP Calculus AB 2023 Free-Response Questions Author: ETS Subject: Free-Response Questions from the 2023 AP Calculus AB Exam Keywords: Calculus AB; Free-Response Questions; 2023; exam resources; exam information; teaching resources; exam practice Created Date: 4/14/2023 10:29:22 AM, Apr 27, 2023 · In this video I go over Problem 2 from the Free-Response Calculator-Allowed Section of the 2017 AP Calculus AB Practice Exam. , The following comments on the 2017 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response question and of how students performed on the question, including typical student errors. General