Ap calc bc exam mcq

AP Calculus BC Paper. 11. days. 9. hours. 38. minutes. 8. seconds. Friday 24th May 2024, 7:00:00 AM. AP Calculus BC Paper Late Test Date. 22. days. 9. hours. 38. minutes. 8.

Ap calc bc exam mcq. 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 …

Write your solution to each part in the space provided for that part. 6. Consider the curve given by the equation 6xy y. = 2 + . dy y. (a) Show that 2 . dx = y2 − 2x. (b) Find the coordinates of a point on the curve at which the line tangent to the curve is horizontal, or explain why no such point exists.

AP Calculus BC Paper. 11. days. 9. hours. 38. minutes. 8. seconds. Friday 24th May 2024, 7:00:00 AM. AP Calculus BC Paper Late Test Date. 22. days. 9. hours. 38. minutes. 8.AP classes prepare learners to take tests on college-level knowledge in 38 subjects. Students can take AP classes in 38 areas, including English. Updated March 21, 2023 • 5 min rea... See the AP Calculus AB and BC Course and Exam Description for details. However, students may bring any calculator on the list to the exam; any model within each series is acceptable. Only approved graphing calculators from the list are permitted for AP Calculus Exams. This list will be updated as necessary to include new approved calculators. Selected values of f(x) are given in. 1. the table above. Use a Left Riemann sum using the subintervals indicated by the table to approximate g(3). Find g’(x) and evaluate g’(3). Using the data in the table, estimate f’(3). Explain why there must be a …Having life insurance is a big deal. These are the top life insurance companies that don't require a medical exam to get covered. Home Insurance Having a life insurance policy is ...If you're preparing for the civil service exam, this page can help you gain insight into how the test works and how you can succeed. Written by Evan Thompson Contributing Writer Le...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....AP Calculus BC Practice Exam F rom the 2 014 Administration This Practic e Exa m is provided by the Colleg e Boar d fo r AP Exam preparation . Teacher s ar e permitted to download the material s an d mak e copies to use wit h thei r student s in a classroo m settin g onl y. T o maintai n th e securit y of this exam , teacher s shoul d collec t al l …

In this video we do 22 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document. I've always c...It is Thursday morning, May 19, and you will be taking either the AP Calculus AB Exam or the AP Calculus BC Exam. In a moment, you will open the packet that contains your exam materials. By opening this packet, you agree to all of the AP Program’s policies and procedures outlined in the 2015 - 16 Bulletin for AP Students and Parents.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.If you've been hard at work in school and haven't had the time to study for an exam, then perhaps you should set aside time the night before to cram for the exam. Depending on what...14 Mar 2016 ... ... Multiple Choice) and first part (Part A - No Calculator) of the AP Calculus BC 2012 Multiple Choice International Practice Exam. Full ...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. 36. 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org. AP Exam Instructions. the calculator to remove exam questions and/or answers from the room may result in the cancellation of AP Exam scores. The AP Calculus AB Exam and the AP Calculus BC Exam should be administered simultaneously. When you set up your wireless connection, the router or device that enables the connection is called an access point. The AP name is the name by which other devices list your wirel...

All AP Calculus BC Multiple Choice Practice Questions. ... » Download AP Calculus BC Practice Tests » Best AP Calculus BC Books; More AP Tests. AP Calculus BC Test 1; AP Calculus BC Test 2; AP Calculus BC Test 3; AP Calculus BC Test 4; AP Calculus BC Test 5; ... AP Calculus AB; AP Calculus BC; AP Physics 1; AP Physics 2; AP Physics C ...We reviewed six schools based on course features, pricing, and reviews to find the best California real estate exam prep for you. Real Estate | Buyer's Guide Download our exam prep...Are humans separate from chimps and other apes? Learn what separates us from chimps. Advertisement Human beings see themselves in everything. We establish emotional connections to ...2008 AP Calculus Multiple Choice Solutions: Home AB Non-Calculator Section: AB ... BC #86 AB/BC #87 BC #88 AB/BC #89 BC #90 BC #91 BC #92 Powered by Create your own unique website with customizable templates. Get Started ...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. AP Calculus AB Practice Exams Free Response Notes Videos Study Guides. We have links to the best online AP Calculus practice exams. These free resources provide thousands of challenging practice questions to work through. Choose from the listing below to get started with your AP Calc AB test prep!

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Visit the College Board on the Web: www.collegeboard.org. AP Central is the oficial online home for the AP Program: apcentral.collegeboard.org. 1. 300 (a) ∫ r ( t ) dt = 270. 0. According to the model, 270 people enter the line for the escalator during the time interval 0 ≤ t ≤ 300. (b) 20 + ∫ ( 300 ( 300.Excerpted from the AP Calculus AB and BC Course and Exam Description, the Course at a Glance document outlines the topics and skills covered in the AP Calculus courses, along with suggestions for sequencing. ... Exam Weighting (Multiple-Choice Section) Exam Weighting (Free-Response Section) 1. Implementing Mathematical Processes. …Write your solution to each part in the space provided for that part. 6. Consider the curve given by the equation 6xy y. = 2 + . dy y. (a) Show that 2 . dx = y2 − 2x. (b) Find the coordinates of a point on the curve at which the line tangent to the curve is horizontal, or explain why no such point exists.All the best online AP Calculus BC practice exams. Hundreds of challenging practice problems to work through. Choose from the listing below to get started with your test prep right now!In this video we do 22 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document. I've always c...Note: You may not take both AP Calculus AB and Calculus BC Exams within the same year. Exam Date Mon, May 13, 2024. 8 AM Local. AP Calculus AB Exam ... Exam Components. Expand All Collapse All. Section I: Multiple Choice. 45 questions 50% of Score Part A: Graphing calculator not permitted (33.3% of score) Part B: Graphing …

AP Calculus AB Exam and AP Calculus BC Exam, and they serve as examples of the types of questions that appear on the exam. Each question is accompanied by a table …There are 45 problems in the AP Calculus BC Exam multiple choice section. Let’s take a look at the kinds of questions you might see on the test. Below, you can find some information about the format of the …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 help familiarize students with the mechanics of the exam. (Note that future exams may differ in look from the following content.) AP ® Calculus AB Exam. SECTION I: Multiple Choice 20162023 AP Daily: Practice Sessions AP Calculus BC Session 1 – MCQ 1. Which of the following is a logistic differential equation whose solution has carrying capacity of 50? A. 𝑑 =50 𝑑𝑡 B. 𝑑 = (1− ) 𝑑𝑡 50 C. 𝑑 =50 (1− ) 𝑑𝑡 D. 𝑑 = (1− ) 𝑑𝑡 50 2.In this video, we’ll unpack sample multiple-choice questions.Download questions here: https://tinyurl.com/53xrdbacStay motivated and keep preparing for AP Ex... 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. Section I: Multiple Choice. 45 questions (1 hour 45 minutes), 50% of exam score. Section II: Free Response. 6 questions (1 hour 30 minutes), 50% of exam score. …With our score calculator, you can learn what you’ll need to score a 3, 4, or 5. AP® score calculators are a great way to motivate yourself when you’re studying. You can quickly realize how close you may be to getting the score you want. We recommend you run our calculator regularly in your AP® exam prep, so you can understand where you ...

AP Calculus BC Multiple Choice 2016 Questions - Practice Exam (pdf) Part A, Q1 - 14. Part A, Q15 - 28. Part B, Q76 - 92. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.The following contains instructions taken from. the 2011−12 AP Exam Instructions book. AP® Calculus BC Exam. Regularly Scheduled Exam Date: Wednesday morning, May 9, 2012. Late-Testing Exam Date: Thursday morning, May 24, 2012. Section I: At a Glance. Section I: Multiple Choice Booklet Instructions.A breast self-exam is a check-up a woman does at home to look for changes or problems in the breast tissue. Many women feel that doing this is important to their health. A breast s...A diabetic foot exam checks for common foot problems found in people with diabetes. If not treated early, these problems can lead to amputation. Learn more. People with diabetes ha...Do you want to become a real estate broker? Here are the eight steps that will help you prepare to pass the real estate broker exam. Real Estate | How To Download our exam prep e-b...AP Calculus BC Multiple Choice 2016 Questions - Practice Exam (pdf) Part A, Q1 - 14. Part A, Q15 - 28. Show Video for Q15 - 28. Part B, Q76 - 92. Show Video for Q76 - 92. Limits. For time > 0, the position of a particle moving in the xy-plane is given by the vector. Consider the series.AP Calculus AB Scoring Guide Unit 3 Progress Check: MCQ Copyright © 2017. The College Board. These materials are part of a College Board program.Special Score Structure: Calculus BC. If you take the AP Calculus BC Exam, you’ll get a Calculus AB subscore (1–5) in addition to your regular score. The Calculus AB subscore shows how you did on the part of the exam devoted to Calculus AB topics, which is approximately 60% of the exam. The subscore gives colleges and universities more ...Section I: Multiple Choice. 45 questions (1 hour 45 minutes), 50% of exam score. Section II: Free Response. 6 questions (1 hour 30 minutes), 50% of exam score. …AP Calculus Practice Exams. This site is sponsored by the Department of Mathematics at the University of Houston. Please report any errors to Jennifer Marsala at [email protected]. Check out the current practice materials, and register to access the online practice exams and practice quizzes by topic that are automatically graded.

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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? Attempts by students to use the calculator to remove exam questions and/or answers from the room may result in the cancellation of AP Exam scores. The AP Calculus AB Exam and the AP Calculus BC Exam should be administered simultaneously. They may be administered in separate rooms, or in the same room if it is more convenient. 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. MAKE SURE YOU HAVE USED THE SAME SET OF AP NUMBER LABELS ON ALL AP EXAMS YOU HAVE TAKEN THIS YEAR. -22- Multiple-Choice Answer Key The following contains the answers to the multiple-choice questions in this exam. Answer Key for AP Calculus BC Practice Exam, Section I Question 1: E Question 24: D Question 2: B Question 25: B Question 3: E ... Show Video with Solutions Q15 - 22. Show Video with Solutions Q23 - 24. Show Video with Solutions Q25 - 28. AP Calculus AB Multiple Choice 2014 Practice Exam Questions and Solutions Part B. Integrate. What is the slope of the line tangent to the graph of y = ln (2x) at the point where x = 4 ? If f (x) = 4x -2 + 1/4 x 2 + 4, then f' (2) =.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. 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. Bigfoot or an Ancient Ape? - Sasquatch researchers have no conclusive evidence that sasquatches exist. Learn about scientific explanations for the sasquatch, like the gigantopithec...2. 2. - x with a constant speed of. when the particle is at the point. (E) 6 10. 2008 AP Calculus BC Multiple Choice Exam. ….

We wish you every success in your test prep and college admission! What’s included (Updated as of 02 Jan 2023) AP Calculus BC 1969 Full Exam Paper with Multiple-Choice Question. AP Calculus BC 1973 Full Exam Paper with Multiple-Choice Question. AP Calculus BC 1985 Full Exam Paper with Multiple-Choice Question.The AP Calculus BC exam assesses high school students’ ability to apply the content and skills learned in the AP Calculus course. The content of the AP Calculus BC exam is pulled straight from the study units that students learn in the AP Calculus BC course: Unit 1: Limits and Continuity. Unit 6: Integration and Accumulation of Change.Jul 23, 2021 · The May 4 In-School Paper Exam. The largest exam date for AP Calculus BC was May 4, so the following information is specific to the exam version administered on that date. As usual, students scored significantly higher on the multiple-choice section than on the free-response questions. Multiple-Choice Section. Course Units: AP Calculus BC ... First, let's look at the format of the exam, which is the same for both AP Calculus AB and BC. The multiple-choice section makes up 50% of your score, and you have an hour and 45 minutes to answer 45 questions. This section has 2 parts: Part A: 60 minutes for 30 non-calculator questions. Part B: 45 minutes for 15 calculator-required … AP Calculus AB Practice Exams Free Response Notes Videos Study Guides. We have links to the best online AP Calculus practice exams. These free resources provide thousands of challenging practice questions to work through. Choose from the listing below to get started with your AP Calc AB test prep! How much is an eye exam at Target? We detail Target eye exam costs, including the cost with and without insurance and the cost of an exam for contacts. Target eye exam costs vary b...Do you want to become a real estate broker? Here are the eight steps that will help you prepare to pass the real estate broker exam. Real Estate | How To Download our exam prep e-b...Questions And Worked Solutions For AP Calculus BC Multiple Choice 2008, Practice Exam. AP Calculus BC Multiple Choice 2008 Questions - Practice Exam (pdf) Part A, Q1 - 28. Part B, Q76 - 92. Show Video for Q76 - 92. At time t ≥ 0, a particle moving in the xy-plane has velocity vector given by. Antiderivative. Ap calc bc exam mcq, The multiple choice sections of the exam combine to count as 50% of the exams score. (The other 50% comes from the free response questions). For each question there will be 4 choices. AP Scores your multiple choice questions by taking the number of questions you got write and multiplying by 1.2. This makes your total out of 54%., Note: You may not take both AP Calculus AB and Calculus BC Exams within the same year. Exam Date Mon, May 13, 2024. 8 AM Local. AP Calculus AB Exam ... Exam Components. Expand All Collapse All. Section I: Multiple Choice. 45 questions 50% of Score Part A: Graphing calculator not permitted (33.3% of score) Part B: Graphing …, 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 120 1998 AP Calculus AB Exam, Section 1 125 Part A 125 Part B 133 1998 AP Calculus BC Exam, Section 1 138, AP® Calculus Multiple-Choice Tips. In this section, we review some specific tips regarding the multiple-choice portions of the AP® Calculus exam. Although some of these may also be extended to the FRQ portion, these tips are more tailored to the multiple-choice questions on the test. 1. Use the Process of Elimination Technique (POE)., This is Part A of the multiple choice section of our free AP Calculus AB practice exam. There are a total of 30 test questions which must be answered within 60 minutes. A calculator may not be used on this part of the AP Calculus multiple choice test. A plane in horizontal (level) flight is travelling at a speed of 500 feet per second., You've studied hard, had a good night's sleep, eaten a good breakfast, and now you're ready for your big test. You might consider walking to the exam—20 minutes of activity, walkin..., The AP Calculus BC exam assesses high school students’ ability to apply the content and skills learned in the AP Calculus course. The content of the AP Calculus BC exam is pulled straight from the study units that students learn in the AP Calculus BC course: Unit 1: Limits and Continuity. Unit 6: Integration and Accumulation of Change., Like on the exam’s multiple-choice section, the AP Calculus BC exam’s free-response section begins by giving students thirty minutes to answer two questions while using a graphing calculator, and concludes by giving students an hour to answer four questions without using a calculator., AP Calc BC 2019 - MCQ FRQ. MCQ FRQ. Course. Calculus I (MATH 180) 285 Documents. University. University of Illinois at Chicago. Academic year: 2019/2020. Uploaded by: , Scoring notes: • The response must be a definite integral with correct lower and upper limits to earn this point. 5 5 • Because A ( t) = A ( t ) for 1 ≤ t ≤ 5, a response of ∫ 450 sin ( 0.62t ) dt or ∫ A ( t ) dt earns the. 1 1. point. A response missing dt …, In part (a) students were asked to find the acceleration vector of the particle at time t = 1. This requires using a. d x 2 2 calculator to find the values = − 1.444 and d y dt 2 dt 2 = − 1.683. t = 1 t = 1. In part (b) students were asked to find the first time t at which the speed of the particle is 1.5., CALCULUS AB SECTION I, Part A NO CALCULATOR IS ALLO WED FOR THIS PART OF THE EXAM. Directions: Solve each of the following problems, using the available space for scratch work. After examining the form of the choices, decide which is the best of the choices given and fill in the corresponding circle on the answer sheet., 2. 2. - x with a constant speed of. when the particle is at the point. (E) 6 10. 2008 AP Calculus BC Multiple Choice Exam., 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 ..., AP Calculus BC Exam - 2023 US Discussion. Is an exam mode setting mandatory on any of the approved graphing calculators for the calc bc exam? My child is using the CB approved Casio FX CG50 in his prep for the Calc BC exam for 2024, and is trying to figure out the valid exam mode setting., Approaches 0 and is decreasing so it is convergent. Comparison Test. Let 0 ≤ an ≤ bn, for all n. 1) If ∑bn converges, then ∑an converges. 2) If ∑an diverges, then ∑bn diverges. Limit Comparison Test. if the limit as n approaches infinity of (given series/chosen series) is >0, the two series will converge/diverge together. Integral ..., 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 …, 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?, A diabetic foot exam checks for common foot problems found in people with diabetes. If not treated early, these problems can lead to amputation. Learn more. People with diabetes ha..., MAKE SURE YOU HAVE USED THE SAME SET OF AP NUMBER LABELS ON ALL AP EXAMS YOU HAVE TAKEN THIS YEAR. -22- Multiple-Choice Answer Key The following contains the answers to the multiple-choice questions in this exam. Answer Key for AP Calculus BC Practice Exam, Section I Question 1: E Question 24: D Question 2: B Question 25: B Question 3: E ..., The AP Calculus AB exam is 3 hours and 15 minutes long and has two sections. Both of these sections are divided into two parts. For reference, here's the current format of the exam: Multiple-Choice Section. 45 questions total; 1 hour 45 minutes total; Worth 50% of your total exam score; Part A: 30 questions; 60 minutes long; No calculator ... , 1973 AP Calculus BC Exam, Section 1 29 1985 AP Calculus AB Exam, Section 1 38 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 , The position of a particle moving in the xy-plane is given by the vector (4t^3 , y(2t)). where y is a twice-differentiable function of t. At time t=1/2, what is the acceleration vector of the particle?, Here are the six best New York real estate exam prep providers that will prepare and help you pass your NY real estate license exam. Real Estate | Buyer's Guide Download our exam p..., AP ® Calculus BC Directions for Administration The AP Calculus BC Exam is 3 hours and 15 minutes in length and consists of a multiple-choice section and a free-response section. • The 105-minute two-part multiple-choice section contains 45 questions and accounts for 50 percent of the final grade., A breast self-exam is a check-up a woman does at home to look for changes or problems in the breast tissue. Many women feel that doing this is important to their health. A breast s..., AP ® Calculus BC Directions for Administration The AP Calculus BC Exam is 3 hours and 15 minutes in length and consists of a multiple-choice section and a free-response section. • The 105-minute two-part multiple-choice section contains 45 questions and accounts for 50 percent of the final grade., 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 120 1998 AP Calculus AB Exam, Section 1 125 Part A 125 Part B 133 1998 AP Calculus BC Exam, Section 1 138, AP Calculus BC 2014 Free Response Question 1. A graphing calculator is required for these problems. 1. Grass clippings are placed in a bin, where they decompose. For 0 ≤ t ≤ 30, the amount of glass clippings remaining in the bin is modeled by A (t) = 6.687 (0.931) t, where A (t) is measured on pounds and t is measured in days., AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics …, AP Calculus BC Multiple Choice 2003 Questions - Practice Exam (pdf) Part A, Q1 - 28. Part B, Q76 - 92. 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., Use the menu above to start your test prep with the best AP Calculus BC practice exams, free response questions, notes, videos, and study guides. A complete listing of the online resources that you need for your AP Calc review. AP Calculus BC Exam. This course is organized around the following big ideas: Big Idea 1: Limits; Big Idea 2: Derivatives , 5. State the component form and length of the vector ν with initial point A (2, -1) and terminal point B (-1, 3) . 6. Given compute the derivative vector. 7. The graphs of the polar curves r = 2 + cos θ and r = -3 cos θ are shown on the graph below. The curves intersect when and . Region R is in the second quadrant, bordered by each curve ...