[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-311530-105":59,"doc-detail-311530-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","ap-calculus-bc-free-response-questions","AP® Calculus BC - Free-Response Questions","","AP® Calculus BC Section II includes two free-response parts with timed instructions, calculator policies, notation requirements, and grading guidance. Part A (30 minutes) contains four subparts focused on modeling arrival rates, approximating rates via average rate of change and midpoint Riemann sums, interpreting definite integrals, solving a trigonometric-defined function for a time interval, and analyzing when the rate difference equals zero. Part B (1 hour) contains four questions on polar curves, including area, tangency slope relationships, critical-point analysis using derivative tests, and average distance computations from the origin.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ap-calculus-bc-free-response-questions/311530/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ap-calculus-bc-free-response-questions/311530.png","ImageObject",300,407,{"name":92,"@type":93},"Himbo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":46},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the time limits and calculator rules for AP Calculus BC Section II Part A?","Question",{"text":112,"@type":113},"Section II Part A lasts 30 minutes and includes 2 free-response questions. A graphing calculator is required, and it should be set to radian mode.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should solutions be written to receive credit?",{"text":117,"@type":113},"Work must be in standard mathematical notation rather than calculator syntax, with units indicated where appropriate. Supporting work is required; answers without the necessary method usually do not receive credit.",{"name":119,"@type":110,"acceptedAnswer":120},"What topics are covered in the Section II Part A questions?",{"text":121,"@type":113},"The questions cover approximating change using average rate of change, using midpoint Riemann sums to approximate definite integrals and interpret them, evaluating an interval for a given function model, and analyzing when the difference between two rates equals zero.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},311530,1789894420,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":46,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143,"preview_page_count":4},687197100911,"https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697","2026  \nAP® Calculus BC Free-Response Questions  \n© 2026 College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered [trademarks of College Board. Visit College Board on the web: collegeboard.org](trademarks of College Board. Visit College Board on the web: collegeboard.org).  \nAP Central is the official online home for [the AP Program: apcentral.collegeboard.org](the AP Program: apcentral.collegeboard.org).  \nCALCULUS BC  \nSECTION II PART A  \nTIME – 30 MINUTES  \nDirections:  \nSection II, Part A has 2 free-response questions and lasts 30 minutes.  \nA graphing calculator is required for the questions on this part ofthe exam. You may use a handheld graphing calculator or the calculator available in this application. Make sure your calculator is in radian mode.  \nYou may use the available paper for scratch work and planning, but only work written in the freeresponse booklet will be scored. Any work done on scratch paper will not be scored. In the freeresponse booklet, write your solution to each part of each question in the space provided for that part. For questions that have sub-parts, be sure to label those clearly in your solution. Use a pencil or a pen with black or dark blue ink.  \nYou are permitted to use your calculator to solve an equation, find the derivative of a function ata point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Show all of your work, even though a question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.  \nYour work must be expressed in standard mathematical notation rather than calculator syntax. For example, y15 x2 dx may not be written as fnInt^ X2, X,1, 5h.  \nUnless otherwise specified, answers (numeric or algebraic) need not be simplified. If you use decimal approximations in calculations, your work will be scored on accuracy. Unless otherwise specified, your final answers should be accurate to three places after the decimal point.  \nUnless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f^x h is a real number.  \nYou can go back and forth between questions in this part until time expires. The clock will turn red when 5 minutes remain—the proctor will not give you any time updates or warnings.  \nNote: This exam was originally administered digitally. It is presented here in a format optimized for teacher and student use in the classroom.  \n1. Male birds of a certain species arrive at a nesting area over a thirty-day period. The rate at which the male birds arrive at the nesting area at time t days is modeled by a differentiable function M, where M^t h is measured in number of birds per day. Selected values of M^t h are shown in the table.  \n\n| t (days) | 0 | 5 | 10 | 15 | 20 | 25 | 30 |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| M^t h (birds per day) | 2 | 7 | 16 | 6 | 5 | 2 | 0 |\n\n(Note: Your calculator should be in radian mode.)  \nPart A  \nApproximate M l ^7 .5h using the average rate of change of M over the interval 5 \\# t \\# 10. Show the work that leads to your answer, and indicate units of measure.  \nPart B  \ni. Use a midpoint Riemann sum with the three subintervals 60, 10@, 610, 20@, and 620, 30@ to approximate y030 M^t hdt . Show the work that leads to your answer.  \nii. Interpret the meaning of y030 M^t hdt in the context of the problem.  \nPart C ","cbCaihpXWnymovf0","https://ap.wps.com/l/cbCaihpXWnymovf0","pdf",300601,"English","# Section II Part A\n## Directions\n## Question 1\n## Question 2\n# Section II Part B\n## Directions","[{\"question\":\"What are the time limits and calculator rules for AP Calculus BC Section II Part A?\",\"answer\":\"Section II Part A lasts 30 minutes and includes 2 free-response questions. A graphing calculator is required, and it should be set to radian mode.\"},{\"question\":\"How should solutions be written to receive credit?\",\"answer\":\"Work must be in standard mathematical notation rather than calculator syntax, with units indicated where appropriate. Supporting work is required; answers without the necessary method usually do not receive credit.\"},{\"question\":\"What topics are covered in the Section II Part A questions?\",\"answer\":\"The questions cover approximating change using average rate of change, using midpoint Riemann sums to approximate definite integrals and interpret them, evaluating an interval for a given function model, and analyzing when the difference between two rates equals zero.\"}]","AP® Calculus BC - Free-Response Questions | PDF",23]