2019 ap calculus ab practice exam

find the time interval Q AP® CALCULUS AB 2019 SCORING COMMENTARY Question 2 Note: Student samples are quoted verbatim and may contain spelling and grammatical errors. Overview In this problem a particle P moves along the x-axis with velocity given by a differentiable function vP, where vP t is measured in meters per hour and t is measured …

The AP Calculus BC exam has 2 sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes. Below is a summary of the different parts of ... Give students approximately 3 minutes to answer the survey questions. 2018-19 AP Exam Instructions. 46 AP Calculus AB/BC Exams Then say: Close your booklet and put your answer sheet on your desk, faceup. Make sure you have your AP number label and an AP Exam label on page 1 of your answer sheet. 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 …AB Calculus AP - Differentiation and Integration rules. 10 terms. Justin_Nguyen5387. Preview. MA 16010 exam 3. 15 terms. Jake_M46. Preview. CALC II Exam 2 Integrals. 42 terms. daniell-g4. Preview. calc - comparison, ratio, root. 7 terms. annangole. Preview. Terms in this set (37) Find all points of relative minima and maxima: y = x^2 + 6x + 5.Apr 3, 2020 ... AP Calculus AB AP Calculus AB 2019 Exam Free Response Problem #6.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.228 Sample AP Calculus AB and BC Exam Questions SCORING GUIDELINES 241 Part A (AB or BC): Graphing Calculator Required 243 Part B (AB or BC): Calculator not Permitted 245 Part A (BC ONLY): Graphing Calculator Required 247 Part B (BC ONLY): Calculator not Permitted. THIS PAGE IS INTENTIONALLY LEFT BLANK.Exam Instructions The following contains instructions taken from the 2016−17 AP Exam Instructions book. 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 ...

The AP Calculus BC Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted). Part B: 15 questions; 45 minutes …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 …The AP Calculus AB exam has two sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes. AP Calculus AB Exam. This course is organized around the foundational concepts of calculus. This includes limits, derivatives, integrals, and the Fundamental Theorem of Calculus. The AP Calculus AB exam format is: Sections I and II each account for 50% of the total exam score. In the free-response section students are required to show their work. 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?Score Distributions. Sample Responses Q5. Sample Responses Q6. Exam paper questions organised by topic and difficulty. Our worksheets cover all topics from GCSE, IGCSE and A Level courses. Give them a try and see how you do! mr. calculus 2019 released free response solutions ab/bc 1 ab 2 ab/bc 3 ab/bc 4 ab 5 ab 6 bc 2 bc 5 ...

The model for exponential growth and decay that arises from the statement “The rate of change of a quantity is proportional to the size of the quantity” is. MPAC 3. Implementing algebraic/computational processes. MPAC 4. Connecting multiple representations Te Collee oar. 10 Sample uestions A Calculus AB/BC Exam. Practice for the AP Exams. The best way to prepare for an AP Exam is to participate in your AP class. It also helps to set aside consistent study time, complete all assignments from your teacher, and become familiar with the exam by practicing with exam questions created by AP. On AP Central, we release the free-response questions for exams ...AP Calculus AB 2017 International Practice Exam Scoring Worksheet Section I: Multiple Choice × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response Question 1 × 1.0000 = (out of 9) (Do not round) Question 2 × 1.0000 = (out of 9) (Do not round) Question 3 × 1.0000 = (out of 9) (Do not round ... 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. 1000+ Exam-Like Questions. Realistic problems mimic the style and difficulty of the AP Calculus AB exam. Organized in the same way as the AP Calculus AB course, so you learn as you go, all year long. Prepares you to excel on quizzes, unit tests, and the AP exam.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.

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1000+ Exam-Like Questions. Realistic problems mimic the style and difficulty of the AP Calculus AB exam. Organized in the same way as the AP Calculus AB course, so you learn as you go, all year long. Prepares you to excel … 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 ... In this video I go over Problem 6 from the Free Response Non-Calculator Section of the 2019 AP Calculus AB Practice Exam. 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 ... Cracking the AP Calculus AB Exam, 2020 Edition: Practice Tests and Proven Techniques to Help You Score A 5 College Test Preparation Series: Author: The Princeton Review: Publisher: Random House Children's Books, 2019: ISBN: 0525568158, 9780525568155: Length: 656 pages: SubjectsAdd to Cart. Free AP English Literature Practice Test Online. $0 USD. Add to Cart. Show More. View All Courses. The Princeton Review offers several free AP test prep options. Sign up for a free AP practice test online to discover your strengths and weaknesses.

Find the best online AP Calculus practice exams for your test prep. Choose from multiple choice, full-length, flashcards, quizzes and more. Get detailed explanations, course description and study guides for the AP Calculus AB exam.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 Practice Exam downloaded from open.773.im. noncommercial distribution permitted under our eula. commercial use may lead to legal actions. 严禁商业用途 advanced ... 2019/2020. Listed books C++ ... Recommended for you. 86. 2018 Collegeboard AP Calculus AB Practice Exam. AP Calculus AB. Practice materials. 90% (10) 9. …AP Calculus BC Practice Tests. AP Physics 1 Practice Tests. AP Physics 2 Practice Tests. AP Physics C: Mechanics Practice Tests. AP Physics C: Electricity and Magnetism Practice Tests. AP Human Geography Practice Tests. AP Environmental Science Practice Tests. AP Computer Science Principles Practice Tests.Apr 3, 2020 ... AP Calculus AB AP Calculus AB 2019 Exam Free Response Problem #6.AP Calculus AB Practice Tests. Use our free AP Calculus AB tests to prepare for your test prep. We have 10 tests which cover the major topics of this course, followed by a full-length AP Calculus AB practice exam. Answers and detailed explanations are included with all of our practice questions. Choose a test from the listing below to start ...The following provides a scoring worksheet and conversion table used for calculating a composite score of the exam . 2014 AP Calculus AB Scoring Worksheet. Section I: Multiple Choice. × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response.May 5, 2015 · Instructions. 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. In this video I go over Problem 6 from the Free Response Non-Calculator Section of the 2019 AP Calculus AB Practice Exam.Instructions. 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.This is the weekend from hell for secondary school students in China as they take the national university entrance exam, known as the gaokao. This is the weekend from hell for seco...

About the Exam. The AP Calculus AB Exam will test your understanding of the mathematical concepts covered in the course units, as well as your ability to determine the proper formulas and procedures to use to solve problems and communicate your work with the correct notations. A graphing calculator is permitted for parts of the exam.

About the Exam. The AP Calculus AB Exam will test your understanding of the mathematical concepts covered in the course units, as well as your ability to determine the proper formulas and procedures to use to solve problems and communicate your work with the correct notations. A graphing calculator is permitted for parts of the exam.The tips below will help you fill out Ap Calculus Ab Practice Exam 2019 Pdf easily and quickly: Open the document in our full-fledged online editor by clicking Get form. Complete the requested fields that are yellow-colored. Press the green arrow with the inscription Next to jump from box to box. Use the e-signature tool to add an electronic ...The AP Calculus BC Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted). Part B: 15 questions; 45 minutes …May 17, 2019 ... 2019 AP Calculus BC Exam Free Response Question #2 Polar question! polar area; average value of a function; dividing a region into two parts ...AP Calculus AB Practice Questions. Teacher 47 terms. mamackay. Preview. Unit 2- AP Computer Science Principles. 15 terms. gibsonthoeletess. Preview. ... Financial Derivatives Exam 1. 23 terms. Katie_Egan50. Preview. MATH 220 Midterm 3. 6 terms. arodehav. Preview. MA 113 Important Derivatives and Trig Identities. 21 terms. nabaloking3.Ap calculus ab 2017 practice exam. Assignments 95% (164) 86. 2018 Collegeboard AP Calculus AB Practice Exam. Practice materials 77% (22) 3. Day 4 - end of the year ap exam prep day 4. Assignments None. 114. 1000+ Exam-Like Questions. Realistic problems mimic the style and difficulty of the AP Calculus AB exam. Organized in the same way as the AP Calculus AB course, so you learn as you go, all year long. Prepares you to excel on quizzes, unit tests, and the AP exam. AP Calculus AB Practice Questions. Teacher 47 terms. mamackay. Preview. Unit 2- AP Computer Science Principles. 15 terms. gibsonthoeletess. Preview. ... Financial Derivatives Exam 1. 23 terms. Katie_Egan50. Preview. MATH 220 Midterm 3. 6 terms. arodehav. Preview. MA 113 Important Derivatives and Trig Identities. 21 terms. nabaloking3.

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Doing a skin self-exam involves checking your skin for any unusual growths or skin changes. A skin self-exam helps find many skin problems early. Finding skin cancer early may give...AP Calculus AB 2017 International Practice Exam Scoring Worksheet Section I: Multiple Choice × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response Question 1 × 1.0000 = (out of 9) (Do not round) Question 2 × 1.0000 = (out of 9) (Do not round) Question 3 × 1.0000 = (out of 9) (Do not round ...Based on an AP fact-check of last night's democratic debate, here are the big money flashes that were made by the presidential candidates. By clicking "TRY IT", I agree to receive ...Ap calculus ab 2017 practice exam. Assignments 95% (164) 86. 2018 Collegeboard AP Calculus AB Practice Exam. Practice materials 77% (22) 3. Day 4 - end of the year ap exam prep day 4. Assignments None. 114.AP Calculus BC - Unit 6-BC (Reflecting the New CED) - Guided Practice/Class NotesAdvanced Integration TechniquesThis .PDF file contains detailed solutions for the complete notes for the small portion of Unit 6 (Topics 6.11-6.13) under the CED for AP Calculus BC as set forth by the College Board in 2019.Topics within the document also contain ...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...The following provides a scoring worksheet and conversion table used for calculating a composite score of the exam . 2014 AP Calculus AB Scoring Worksheet. Section I: Multiple Choice. × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response.May 17, 2019 ... 2019 AP Calculus BC Exam Free Response Question #5 It's a let's do calculus problem! Finding a value of k to make the derivative equal a ... ….

May 6, 2017 ... AP Calculus AB Practice Exam Multiple Choice Problem 76 The derivative of function f is given by f' = (2x - x^2) / e^(2x).Scoring notes: • To earn the point the interpretation must include “medication in the patient,” “approaches 12,” and units (milligrams), or their equivalents. Total for part (b) 1 point. (c) Use separation of variables to find y = A ( t ) , the particular solution to the differential equation dy = …AP Calculus AB and BC Course and Exam Description About AP College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses36. 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.Free-Response Questions. 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 ssd@info ...In this exam: (1) Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which. f (x) is a real number. (2) The inverse of a trigonometric function f may be indicated using the inverse function notation f − 1 or with the. prefix “arc” (e.g., sin−1 x = arcsin x ). -3-.The AP Calculus AB exam has two sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes.AP Calculus AB 2022 Free-Response Questions 2019 ap calculus ab practice exam, The Series 65, also known as the Uniform Investment Adviser Law Examination, is a test and license required of most financial professionals. Calculators Helpful Guides Compare Rate..., Sample: 1B. Score: 6. The 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). 5. In part (a) the first point was earned with the definite integral E t d t , and the second point was earned with. 0., 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 …, Calculus AB Calculus BC Calculus BC Calculus AB Subscore Chemistry no data N % At; N % At N % At N % At N % At N % At 5 2,905; 11.9: 18,800: 7.2 57,352: ... AP Exams - May 2019 (continued) Exam Score Italian Language (Standard Group) ** Japanese Language (Total Group) Japanese Language, AP Calculus AB Scores. AP scores are reported from 1 to 5. Colleges are generally looking for a 4 or 5 on the AP Calculus AB 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 AB students scored on the May 2022 test: Score., Introduction. These sample exam questions were originally included in the AP Calculus AB and AP Calculus BC Curriculum Framework, published in fall 2014. The AP Calculus AB and AP Calculus BC Course and Exam Description, which is out now, includes that curriculum framework, along with a new, unique set of exam questions., Apr 24, 2023 · Step by Step worked out solutions for the 2019 AP Calculus AB Exam Free Response Questions , Give students approximately 3 minutes to answer the survey questions. 2018-19 AP Exam Instructions. 46 AP Calculus AB/BC Exams Then say: Close your booklet and put your answer sheet on your desk, faceup. Make sure you have your AP number label and an AP Exam label on page 1 of your answer sheet. , About the Exam. The AP Calculus AB Exam will test your understanding of the mathematical concepts covered in the course units, as well as your ability to determine the proper formulas and procedures to use to solve problems and communicate your work with the correct notations. A graphing calculator is permitted for parts of the exam., Click on New Document and choose the file importing option: upload AP Calculus AB 2019 Practice Exam. AP Calculus AB 2019 Practice Exam from your device, the cloud, or a secure link. Make changes to the template. Use the upper and left-side panel tools to change AP Calculus AB 2019 Practice Exam. AP Calculus AB 2019 Practice Exam., Learn about the benefits of no exam life insurance; an accessible policy that lets you get life insurance with no medical exam. By clicking "TRY IT", I agree to receive newsletters..., Sample: 4B. Score: 6. The response earned 6 points: 2 points in part (a), no points in part (b), and 4 points in part (c). In part (a) the response earned the first point with the presentation of a correct expression for the derivative of V with respect to t, dV r2 dh , while handling r as a constant., 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. , 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 and BC Course and Exam Description About AP College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses , As you age, it is important to stay up-to-date on your driving skills and knowledge. Taking a practice test before your senior driver’s exam can help you prepare and ensure that yo..., The AP Calculus BC exam has 2 sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes. Below is a summary of the different parts of ..., AP Exams - May 2019 (continued) ** This table reflects 5,098,815 AP Exams taken by 2,825,710 students from 22,678 secondary schools. ** Standard students generally receive most of their foreign language training in U.S. schools. They did not indicate on their answer sheet that they regularly speak or hear the foreign language of the exam, or ... , The AP Calculus AB exam has two sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes., This is the weekend from hell for secondary school students in China as they take the national university entrance exam, known as the gaokao. This is the weekend from hell for seco..., Completing a medical exam is an important task involved in buying life insurance. Learn everything you need to know about life insurance medical exams here. By clicking "TRY IT", I..., Sample Questions. This packet from the College Board includes 8 AP Calculus BC multiple choice questions and 2 free response. They start on page 25, and are based on the latest curriculum., 2020 Exam Sample Question 1. General Notes: The questions you will see on the 2020 AP Calculus Exam are similar to questions you might have seen on items used on past AP Calculus Exams. The practice item below is constructed from items from the 2019 AP Calculus AB Exam, with minor modifications: Question 1, below, combines elements …, Look over any material and tests from class this year, and go through these AP Calculus AB; study guides.AP Practice : Acing the exam is all about being able to recall the information quickly on the exam. Make sure to do a few rounds of the AP Calculus AB Practice Exam Room daily to get really good at recalling the concepts., x 2 x 2. in lines 7 and 8. Although not required, the response correctly states use of the squeeze theorem. Sample: 6B Score: 6. The response earned 6 points: 1 point in part (a), 3 points in part (b), 2 points in part (c), and no point in part (d). In part (a) the response earned the point for the value of h 2 ., When an AP Exam is administered, psychometric analysis determines the score ranges corresponding with each AP Exam score (5, 4, 3, 2, and 1) based on a composite score scale that combines and weights the different exam parts. Earning 40-50% of the available points can result in a score of 3 or better on many AP Exams. , AP® Calculus AB 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 …, AP Calculus 2019 AB FRQ Solutions Louis A. Talman, Ph.D. Emeritus Professor of Mathematics Metropolitan State University of Denver May 18, 2019 1 Problem 1 1.1 Part …, AP Calculus AB 2017 International Practice Exam Scoring Worksheet Section I: Multiple Choice × 1.2000 = Number Correct Weighted Section I Score (out of 45) (Do not round) Section II: Free Response Question 1 × 1.0000 = (out of 9) (Do not round) Question 2 × 1.0000 = (out of 9) (Do not round) Question 3 × 1.0000 = (out of 9) (Do not round ..., 2006 AP Calculus Practice Exams (Keys Are Provided For The Multiple Choice Portions) 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 …, Exam Instructions The following contains instructions taken from the 2016−17 AP Exam Instructions book. 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% …, 1: limits of integration. 2 : . 1 : answer with integral. 2019 The College Board. Visit the College Board on the web: collegeboard.org. AP® CALCULUS AB/CALCULUS BC. 2019 SCORING GUIDELINES. Question 3., 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