Ap calc bc mc

The AP® Calculus BC exam is a 3-hour 15-minute, end-of-course test comprised of 45 multiple-choice questions (50% of the exam) and 6 free-response questions (50% of the exam). This guide offers an overview of the main tested subjects, along with sample AP multiple-choice questions that look like the questions you’ll see on test day.

The AP® Calculus BC exam is a 3-hour 15-minute, end-of-course test comprised of 45 multiple-choice questions (50% of the exam) and 6 free-response questions (50% of the exam). This guide offers an overview of the main tested subjects, along with sample AP multiple-choice questions that look like the questions you'll see on test day.The AP Calculus BC Exam will have both paper and digital formats in 2021. The paper administration is held on May 4, 2021 and May 24, 2021: 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.What is the sum of the series 1. (E) The series diverges. 21. A particle moves along a straight line. The graph of the particle’s position x ( t ) at time t is shown above for 0 < t < 6. The graph has horizontal tangents at t = 1 and t = 5 and a point of inflection at t = 2.Created Date: 5/1/2015 3:06:21 PMAP Calculus AB 2008 Multiple Choice Answers 1. B 2. D 3. D 4. B 5. A 6. A 7. B 8. E 9. D 10. C 11. B 12. D 13. A 14. E 15. C 16. D 17. C 18. A 19. E* 20. D 21. A 22. B 23. E 24. B 25. B 26. A 27. C 28. A 76.B ... *Although 45 multiple-choice items were admmistered in Section I #19 was not used in scormg for statistical purposes. Many students ...

The following provides scoring worksheet s and conversion table s used for calculating a composite score of the exam . 2017 AP Calculus BC Scoring Worksheet. Section I: Multiple Choice. × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response.30. (Calc) The graphs of i) y = x 2 , ii) y and iii) y = 21 —1 all pass through the points (0,0) and (l , l). Find the difference in arc length from the largest arc length to the shortest arc length of these functions on the interval [0, l]. c. 0.284 D. 0.361 E. 0.419 A. 0.058 B. 0081 29. (Calc) The yellow bird in the popular game2012 Practice Test AP Multiple Choice AB answers and solutions (BC below) ... Problems 76-84 Problems 85-92 2012 Practice Test AP Multiple Choice BC answers and solutions Part A no calculator allowed Problems 1-8 Problems 9-14 Problems 15-22 Problems 23-28 Part B calculator allowed Problems 76-85. Problems 86-92. Return to Mr Calculus ...AP Calculus BC includes topics from AP Calculus AB, such as integrals and the fundamental theorem of calculus, plus other concepts such as parametric equations, polar and vector functions and series. ... The multiple-choice questions on the AP Calculus exam count for 50% of your total score. The multiple-choice section consists of two parts ...The AP® Calculus AB exam is 3 hours and 15 minutes long. There are a total of 51 questions. Section 1 has 45 multiple choice questions and Section 2 has 6 free response questions. The content contains three big ideas: change, limits, and analysis of functions.All AP Calculus BC Multiple Choice Practice Questions. Home / AP Tests / AP Calculus BC Practice Tests. Real AP Past Papers with Multiple-Choice Questions.2012 Multiple Choice calculator section: https://youtu.be/GFPp8Cd_M0MIn this video I do a speed run through the 2012 AP Calculus BC Practice Exam. I go throu... AP® Calculus AB/BC 2021 Scoring Guidelines . Part A (AB or BC): Graphing calculator required Question 1 9 points . General Scoring Notes . Answers (numeric or algebraic) need not be simplified. Answers given as a decimal approximation should be correct to three places after the decimal point. Within each individual free-response question, at ...

2003 Calculus BC Multiple Choice Exam Part A. is. 4) For 0 £ t £ 13 an object travels along an elliptical path given by the parametric equations x = 3cos t and y = 4sin t . At the point where t = 13 , the object leaves the path and travels along the line tangent to the path at that point. What is the slope of the line on which the object travels?AP Calculus BC Multiple Choice 2012 Question 1. If y = sin 3 x, then dy/dx =. (A) cos 3 x (B) 3cos 2 x (C) 3sin 2 x (D) -3sin 2 xcos x (E) 3sin 2 x cos x. Show Video Lesson. AP Calculus BC Multiple Choice 2012 Question 2. 2. The position of a particle moving in the xy-plane is given by the parametric equations x (t) = t 3 2 and y (t) = 12t - 3t 2.You would need verification to get 2018. Some teachers will allow students to get the exams but it puts the teacher at a lot of risk and the students are very unlikely to share them for this reason. A lot of teachers also like to use these for finals. 2. Reply.About this unit. Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point matches the function's value at that point. These simple yet powerful ideas play a major role in all of calculus.

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Removable discontinuity is basically like a empty circle in a smooth curve. For BC students, the answer was 3 only. Reply. 1. Sith_Lord_Yoda Calc BC (5), Biology (4), Physics C (5), APUSH (5), Calc AB (5), • 6 yr. ago. It asked for a removable discontinuity ( hole) so I think the answer is 2. Reply. 2.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.The following provides scoring worksheet s and conversion table s used for calculating a composite score of the exam . 2017 AP Calculus BC Scoring Worksheet. Section I: Multiple Choice. × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response.CALCULUS AB/BC: AP EXAM 2018 DETAILS AP Exam Date: Tuesday, May 15th 2018 (8am) The exam is approximately three hours and 15 minutes long and has two parts — multiple choice and free response. Each section is worth 50% of the final exam grade. Section I: Multiple Choice — 45 questions; 1 hour and 45 minutesAP Calculus BC Multiple Choice 2012 Question 1. If y = sin 3 x, then dy/dx =. (A) cos 3 x (B) 3cos 2 x (C) 3sin 2 x (D) -3sin 2 xcos x (E) 3sin 2 x cos x. Show Video Lesson. AP Calculus BC Multiple Choice 2012 Question 2. 2. The position of a particle moving in the xy-plane is given by the parametric equations x (t) = t 3 2 and y (t) = 12t - 3t 2. Varsity Tutors' AP Calculus AB and AP Calculus BC diagnostic tests. For free skill practice, try: Fiveable's streams and study guides. Khan Academy's AP Calculus AB and AP Calculus BC courses. If you want more AP-style multiple choice practice, consider buying a prep book. They usually sell for under $20 and have upwards of 3 full-length ...

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.Start Unit test. Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point matches the function's value at that point. These simple yet powerful ideas play a major role in all of calculus.AP Calculus BC - Parametric Equations AP Test Practice FRQ.1 (calculator) FRQ.2 (calculator) FRQ.3 (calculator) MC.1 MC.2 MC.3 MC.4. MC.5 MC.6 MC.7 MC.9 (calculator) MC.10 (calculator) At time t O, a particle moving along a curve in the xy-plane has position (x(t), y(t)) with velocity vector 0.51 v(t) — COS t l, the particle is at the point ...Limits and continuity. About the course: Limits and continuity Defining limits and using limit …Mar 7, 2016 ... Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship.Enrolling in AP Calculus comes with the understanding that you will take the AP exam in May. ... 5.4: 2016 MC Questions from BC Exam Day 1 2018 AB 5; MC Questions from 2016 BC Exam; AP Calculus AB Review 3; AP EXAM ON 5/5/2020. Powered by Create your own unique website with customizable templates.View Unit 3 Progress Check Key MC.pdf from MAT 132 at Middlesex County College. AP Calculus BC Scoring Guide Unit 3 Progress Check: MCQ 1. If derivative of and is a differentiable function of , whichAP Calculus BC 2016 released MCQ Test. ap calculus bc practice exam from the 2016 administration this exam may not be posted on school or personal websites, nor. Skip to document. ... Section I: Multiple-Choice Questions This is the multiple-choice section of the 2016 AP exam. It includes cover material and other administrative instructions to ...I don't know how it's done at your school, but at mine, I was able to go straight from precalc to Calc BC as the natural continuation of the sequence. My district treats BC as an accelerated track in comparison to AB, and I learned both AB and BC content in the same year class. If that's how your school's BC class is structured then it ...Unit 2 Videos. Lesson 1 Part 1. Lesson 2 - Derivative shortcuts. Lesson 1 Part II. VIDEO OF PAGE 4 (BOLDEN'S GUIDED NOTES) Lesson 3 - pva. Lesson 4 - Product & Quotient Rules. lesson 5 - chain rule. Lesson 6 - Implicit Part 1.AP Classroom. AP Classroom is a free and flexible online platform that provides instructional 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.

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Practice. Free Response. Assessments. Overview. Looking for an AP® Calculus score calculator? Click here for this and more tips for your test! Standards. Tags. Review Albert's AP® Calculus math concepts, from limits to infinity, with exam prep practice questions on the applications of rates of change and the accumulation of small quantities.Hi all, here's a score chart for the Calc BC exam (using the 2023 data). The overall exam score is based 71% on AB topics and 29% on BC-only topics, but the subscore is based only on the AB questions. According to this graph, the absolute minimum you need to get correct on the BC exam in order to get a 5 on both is ~64% on AB-level questions ...AP Calculus Multiple-Choice Question Collection 109 Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.Be prepared for the types of AP calculus questions you will encounter on the test. What is the Format of the Test? Both the Calculus AB and Calculus BC exams have the same basic format.. There are two main section, multiple choice (MC) and free response (FR). Within each section there is a part that requires a calculator and a part in which calculators are not permitted.2003 BC Multiple Choice Answers and Solutions. Return to Mr. Calculus. Return to Mr. Calculus. 2024 AP Calculus AB/BC exam study guides, practice quizzes, live reviews, community support | Fiveable ... AP Calculus AB/BC Multiple Choice Help (MCQ) 2008 AP Calculus Multiple Choice Solutions: ... BC Calculator Section: BC #76 BC #77 BC #78 BC #79 AB/ BC #80 BC #81 BC #82 AB/BC #83 ...

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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.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 totalThe AP Calculus BC exam takes 3 hours and 15 minutes, but the time is broken up so that you have a break in the middle. There are two main sections, multiple choice and free response, and each section has one part requiring a graphing calculator and one that does not allow a calculator at all. The Calculus AB and Calculus BC exams both have the ...AP Calculus BC 2021 Free Response Question 1. The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of the dish is given by an increasing, differentiable function f, where f (r)is measured in milligrams per square centimeter. Values of f (r) for selected values of r are given in the table above.Removable discontinuity is basically like a empty circle in a smooth curve. For BC students, the answer was 3 only. Reply. 1. Sith_Lord_Yoda Calc BC (5), Biology (4), Physics C (5), APUSH (5), Calc AB (5), • 6 yr. ago. It asked for a removable discontinuity ( hole) so I think the answer is 2. Reply. 2.1985 AP Calculus BC Exam, Section 1 47 1988 AP Calculus AB Exam, Section 1 57 1988 AP Calculus BC Exam, Section 1 67 1993 AP Calculus AB Exam, Section 1 78 1993 AP Calculus BC Exam, Section 1 89 1997 AP Calculus AB Exam, Section 1 100 Part A 100 Part B 108 1997 AP Calculus BC Exam, Section 1 113 Part A 113 Part B 120AP® CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES. feet per hour, t is measured in hours, and 0 ≤ t ≤ 8. The pipe is partially blocked, allowing water to drain out the other end of the pipe at a rate modeled by D ( t ) = − 0.04 t 3 + 0.4 t 2 + 0.96 t cubic feet per hour, for 0 ≤ t ≤ 8. There are 30 cubic feet of water in the pipe ...Dr. Debra Rose Wilson is a professor, researcher, and holistic healthcare practitioner. She teaches graduate-level psychology and nursing courses. Dr. Wilson has over 200 publicati...AP Calculus BC - Polar Coordinates AP Test Practice FRQ.1 (calculator) ... MC.1 MC.2 (calculator) MC.3. MC.4 MC.5. The graphs of the polar curves r — 2 and r 3 + 2cos are shown in the figure above. The curves intersect 2 It 4 It when and (a) Let R be the region that is inside the graph of r 2 and also inside the graph of r 3+2cose, as shadGood morning, Quartz readers! Good morning, Quartz readers! A$AP Rocky awaits his verdict. The American rapper, whose real name is Rakim Meyers, was detained and charged with assau... ….

In this video, I go through the AP Calculus BC 2008 Multiple Choice (no calculator) section, questions 1-28. I cover topics from each unit of AP Calculus BC....2008 AP Calculus BC Multiple Choice Answer.pdf. Utah State University. MATH 1100. 2008 AB MC.pdf. Solutions Available. Rutgers University. CALC 136. quiz2-versionA.pdf. York University. MATH 1310. Unit 6 Learning Journal Math1211 Calculus Unit 6.docx. University of the People. MATH 1211. View More.Jan 29, 2024 · We can analyze the average AP® Calculus BC score more efficiently by considering a multi-year trend. We can refer to the AP® Student Score Distributions, released by the College Board annually. These reports show us that the mean score was 3.81 in 2014, 3.72 in 2015, 3.80 in 2016, 3.78 in 2017, 3.74 in 2018, 3.80 in 2019 and 3.84 in 2020. This is a PDF package of the official AP Calculus BC 2019 full Exam, complete with all sections including: 1. SECTION I: Multiple Choice (Part A & B) 2. SECTION II: Free Response. 3. Answer Key. You can obtain full PDF package of the official AP Calculus BC 2019 full exam here. Below is a preview of each sections.• The exact value of ( ) 150 0 1 150 ∫ g t dt is 12 25sin . 125 16 • A response may present the average value formula in single or multiple steps. For example, the following response earns both points: ( )Results 1 - 24 of 300+ ... Browse ap calculus multiple choice resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original ...2008 AP Multiple Choice BC answers and solutions Part A no calculator allowed Problems 1-8 Problems 9-14 Problems 15-22 Problems 23-27 Problem 28 Part B calculator allowed Problems 76-85 Problems 86-92. Return to Mr CalculusAP Calculus BC 2014 Free Response Question 4. 4. Train A runs back and forth on an east-west section of railroad track. Train A's velocity, measured in meters per minute, is given by a differentiable function V A (t), where time t is measured in minutes. Selected values for V A (t) are given in the table above. (a) Find the average acceleration of train A over the interval 2 ≤ t ≤ 8.AP Calculus 2018 BC FRQ Solutions Louis A. Talman, Ph.D. Emeritus Professor of Mathematics Metropolitan State University of Denver May 22, 2018 1 Problem 1 1.1 Part a During the time interval 0 t 300, Z 300 0 r(t)dt= 44 Z 300 0 t 100 3 1 t 300 7 dt= 270 (1) people enter the line for the escalator. (Fortunately, the problem is calculator active ... Ap calc bc mc, Home / AP Tests / AP Calculus BC Practice Tests. Real AP Past Papers with Multiple-Choice Questions., AP Calculus AB Scoring Guidelines from the 2019 Exam Administration Keywords: scoring guidelines; 2019 AP exam administration; teacher resources; exam resources; exam practice; exam scoring information; exam preparation; course preparation; AP Scoring Guidelines from the 2019 Exam Administration; £½?, In this video I go over MCQ #1-11 from the Multiple Choice Non Calculator Section of the 2015 AP Calculus AB Exam., Study with Quizlet and memorize flashcards containing terms like Let f be a continuous function such that 2~3 f(2x)dx = 8. What is the value of 4~6 f(x)dx?, If f(x)=2x^3 then the average rate of change of f on the interval [0,2] is, The graph of a polynomial function f(x) is shown above. In the interval shown, how many times will the graph of f1(x), the derivative of f(x), cross the x-axis ..., After AP projects. For the origami project, get at least 80 sheets of origami paper. Origami Project. File Size: 32 kb. File Type: pdf. Download File. Origami Project due 5/22 beginning of class., As in the case with most AP Exams, AP Calculus BC also comprises two sections: multiple-choice (MCQs) and free-response (FRQs). This is a lengthy exam, lasting three hours and 15 minutes. Each section accounts for 50% of the total exam weight, with 45 MCQs in Section I and six FRQs in Section II., Using the chain rule you get (d/dt) ln|N| = (1/N)* (dN/dt). Sal used similar logic to find what the second term came from. So Sal found two functions such that, when you took their derivatives with respect to t, you found the terms that were on the left side of the differential equation. Since the left side of the differential equation came ..., BuzzFeed revealing the identities of these NFT tycoons wasn't doxxing—it was journalism On Feb. 4, BuzzFeed published an article that revealed the identities of two of the most inf..., Level up on all the skills in this unit and collect up to 2,000 Mastery points! Start Unit test. Series are sums of multiple terms. Infinite series are sums of an infinite number of terms. Don't all infinite series grow to infinity? It turns out the answer is no. Some infinite series converge to a finite value., AP Calculus AB/BC Exam AP Calculus AB/BC Exam 47 2017-18 AP Exam Instructions If any students used extra paper for a question in the free-response section, have those students staple the extra sheet(s) to the 昀椀rst page corresponding to that question in their exam booklets. ... Section I: Multiple-Choice Questions This is the multiple ..., In this video I go over MCQ #76-81 from the Multiple Choice Calculator Allowed Section of the 2015 AP Calculus AB Exam., Start Free Trial. Format of AP Calculus BC Multiple-Choice Section. The MCQs on the AP Calculus BC exam, collectively called Section I, are split into two parts, A and B. Part A consists of 30 questions on which you …, AP Calculus BC Multiple Choice Midterm Review The problems in this packet are not meant to be an all-inclusive representation of what will appear on your midterm exam. However, they can serve as an excellent place to start preparation. ... important for multivariable calculus, vectors in BC calculus are little more than parametric equations In —, Section I of this exam contains 45 multiple-choice questions and 4 survey questions. For Part A, fill in only the circles for numbers 1 through 28 on page 2 of the answer sheet. For Part B, fill in only the circles for numbers 76 through 92 on page 3 of the answer sheet. The survey questions are numbers 93 through 96., Smart 2. Calculators are not allowed for any other AP Exams, including Computer Science A and Computer Science Principles, unless a student has an approved accommodation for use of a four-function calculator. *Graphing calculators with the expected built-in capabilities for AP Calculus are indicated with an asterisk., An interactive course framework combines with the exciting on-line course delivery to make calculus an adventure. The course includes a study of limits, continuity, differentiation, integration, differential equations, and the applications of derivatives and integrals, parametric and polar equations, and infinite sequences and series., Click through our free AP Calculus BC study guides and Calc BC flashcards below: AP Calculus BC Multiple Choice Practice Problems. AP Calculus BC AP Free Response Practice Problems. Ultimate AP Calculus BC Study Guide. The only resource you need to get a 5 on the AP Calculus BC exam. Note., Answers and solutions to 2012 Practice Test Multiple Choice BC 1-8. Returnto Mr Calculus., AP® Calculus BC Exam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions Section I of this examination contains 45 multiple-choice questions. Fill in only the ovals for numbers 1 through 45 on your answer sheet. CALCULATORS MAY NOT BE USED IN THIS PART OF THE EXAMINATION., I'd suggest taking some shortcuts if you're running out of time, for example if they ask you to take an integral of a polynomial, only integrate the first term or so and check if your answer matches any of the choices. this tip applies to all types of questions with multiple terms, such as asking for the first x terms of a taylor series or ..., AP Calculus BC Scores. AP scores are reported from 1 to 5. Colleges are generally looking for a 4 or 5 on the AP Calculus BC exam, but some may grant credit for a 3. Learn more about college AP credit policies. Each test is curved so scores vary from year to year. Here’s how AP Calculus BC students scored on the May 2020 test: Score., In this video, I go through the AP Calculus BC 2003 Multiple Choice (no calculator) section, questions 1-28. I cover topics from each unit of AP Calculus BC...., 2003 Calculus BC Multiple Choice Exam Part A. is. 4) For 0 £ t £ 13 an object travels along an elliptical path given by the parametric equations x = 3cos t and y = 4sin t . At the point where t = 13 , the object leaves the path and travels along the line tangent to the path at that point. What is the slope of the line on which the object travels?, 2024 AP Exam Dates. The 2024 AP Exams will be administered in schools over two weeks in May: May 6–10 and May 13–17. AP coordinators are responsible for notifying students when and where to report for the exams. Early testing or testing at times other than those published by College Board is not permitted under any circumstances., Smart 2. Calculators are not allowed for any other AP Exams, including Computer Science A and Computer Science Principles, unless a student has an approved accommodation for use of a four-function calculator. *Graphing calculators with the expected built-in capabilities for AP Calculus are indicated with an asterisk., Questions And Worked Solutions For AP Calculus BC Multiple Choice 2012 (Part B) The function f, whose graph is shown above, is defined on the interval -2 ≤ x ≤ 2. Which of the following statements about f is false? (A) f is continuous at x = 0. (B) f is differentiable at x = 0. (C) f has a critical point at x = 0., Hey there! Preparing for the AP Calculus BC exam and seeking additional resources is a great strategy to assess your knowledge and practice your skills. Here are a few places where you can find multiple-choice practice tests or questions for AP Calculus BC: 1. **College Board**: Start with the official provider of the AP exams. The College Board website offers a few sample questions and a ..., tangent line is vertical. derivative is undefined. tangent line is horizontal. derivative is 0. sin2x. 2sinxcosx. cos2x. cos²x - sin²x. Study with Quizlet and memorize flashcards containing terms like trig adding rules, dy/dx sinx, dy/dx cosx and more., AP®Calculus BC Exam. SECTION I: Multiple-Choice Questions. DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions. Section I of this examination contains 45 multiple-choice questions. Fill in only the ovals for numbers 1 through 45 on your answer sheet. CALCULATORS MAY NOT BE USED IN THIS PART OF THE …, A Walt Disney World annual pass is the cheapest way to visit Disney World theme parks multiple times a year plus discounts! Save money, experience more. Check out our destination h..., AP Calculus B/C – Power Series AP Test Practice FRQ.1 FRQ.2. MC.1 MC.2 MC.3 MC.4. MC.5 MC.6 (calc.) MC.7 (calc.) MC.8. MC.9 MC.10 MC.11 MC.12. The function f has a Taylor series about x — 1 that converges to f (x) for all x in the interval of convergence. and the nth derivative of f at x — I is given by f (n) (1) It is known that f (1), AP Calculus BC 2015 Free Response Question 1 The rate at which rainwater flows into a drainpipe is modeled by the function R, where cubic feet per hour, t is measured in hours, and 0 ≤ t ≤ 8. The pipe is partially blocked, allowing water to drain out the other end of the pipe at a rate modeled by D(t) = -0.04t 3 + 0.4t 2 + 0.96t cubic feet ..., Fundamental Theorem of Calculus to calculate the signed area of the semicircle, ∫4 f ′( x) dx = −2π , and subtracts. 0. this value from the initial condition, f ( 4 ) = 3, to obtain a value of 3 + 2π . To find f (5) a correct response would. 5. add the initial condition to the signed area ∫ f ′(x) dx = 1.