[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-311492-105":59,"doc-detail-311492-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","ap-precalculus-free-response-questions-section-ii-part-a-time-30-minutes","AP Precalculus Free-Response Questions - Section II Part A - Time 30 Minutes","","AP Precalculus Section II Part A provides two timed free-response questions (30 minutes total) requiring a graphing calculator in radian mode. The directions emphasize complete supporting work in the response booklet, precision without unnecessary rounding, and correct use of calculator features for graphs, tables, function evaluation, and equation solving. The questions include function composition, solving equations, limit-based behavior analysis, invertibility reasoning from a graph, and a car depreciation model using exponential parameters and average rate of change.",{"@graph":69,"@context":123},[70,84,106],{"@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-precalculus-free-response-questions-section-ii-part-a-time-30-minutes/311492/",{"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-precalculus-free-response-questions-section-ii-part-a-time-30-minutes/311492.png","ImageObject",300,407,{"name":92,"@type":93},"Graffin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How long is Section II Part A, and how many free-response questions does it include?","Question",{"text":113,"@type":114},"Section II, Part A lasts 30 minutes and includes 2 free-response questions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What calculator requirement and mode are specified for Section II Part A?",{"text":118,"@type":114},"A graphing calculator is required, and it must be set to radian mode.",{"name":120,"@type":111,"acceptedAnswer":121},"What modeling information is given in Question 2 about the car’s value?",{"text":122,"@type":114},"The car’s value is modeled by V(t)=ab^t (in thousands of dollars), with V(1)=27.2 and V(6)=14.8 based on the given year-to-time mapping.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},311492,1790158659,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":46,"preview_page_count":4},3573418547284,"https://eur-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","2026  \nAP® Precalculus 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).  \nPRECALCULUS  \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. Use a pencil or a pen with black or dark blue ink.  \nShow all of your work. Your work will be scored on the correctness and completeness of your responses, including your supporting work and answers. Answers without supporting work may not receive credit in cases where supporting work is requested.  \nYou are expected to use your graphing calculator for tasks such as producing graphs and tables, evaluating functions, solving equations, and performing computations.  \nAvoid rounding intermediate computations on the way to the final result. Unless otherwise specified, any decimal approximations reported in your work should be accurate to three places after the decimal point.  \nIt may be helpful to use your graphing calculator to store information such as computed values for constants, functions you are working with, solutions to equations, and any intermediate values. Computations with the graphing calculator that use the stored information help to maintain as much precision as possible and ensure the desired accuracy in final answers.  \nUnless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f^xh 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. The figure shows the graph of the increasing functionf on its domain of-3 \\# x \\# 3.  \nThe function g is given by g ^xh = -4.792 + ln ^6x-6h.  \nA.  \ni. The function h is defined by h ^xh = ^g ° f h^xh = g ^ f^xhh. Find the value of h^2 h as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer.  \nii. Find all values of x for which f^xh = 3, or indicate that there are no such values.  \nB.  \ni. Find all values of x, as decimal approximations, for which g^xh = -1.5, or indicate that there are no such values.  \nii. Determine the behavior of g as x-values decrease and get arbitrarily close to 1. Express your answer using the mathematical notation of a limit.  \nC.  \ni. Is the function f invertible?  \nii. Give a reason for your answer in part C (i) based on properties of the function f. Refer to points on the graph off in your reasoning.  \n2. A person purchased a car at the end of the year 2019 ( t = 0 ) . The car’s value decreases overtime. At the end of the year 2020 ( t = 1), the car was valued at 27.2 thousand dollars. At the end of the year 2025 ( t = 6 ), the car was valued at 14.8 thousand dollars.  \nThe value of the car can be modeled by the function V given by V^ t h = abt , where V^ t h is the value of the car, in thousands of dollars, at time t, and t is the number of years since the end of 2019.  \nA.","cbCaigEdG0MiTUls","https://ap.wps.com/l/cbCaigEdG0MiTUls","pdf",293558,"English","# Section II Part A (Time – 30 Minutes)\n## Directions\n## Question 1\n## Question 2\n# Section II Part B (Time – 30 Minutes)\n## Directions\n## Question Content (truncated in provided text)","[{\"question\":\"How long is Section II Part A, and how many free-response questions does it include?\",\"answer\":\"Section II, Part A lasts 30 minutes and includes 2 free-response questions.\"},{\"question\":\"What calculator requirement and mode are specified for Section II Part A?\",\"answer\":\"A graphing calculator is required, and it must be set to radian mode.\"},{\"question\":\"What modeling information is given in Question 2 about the car’s value?\",\"answer\":\"The car’s value is modeled by V(t)=ab^t (in thousands of dollars), with V(1)=27.2 and V(6)=14.8 based on the given year-to-time mapping.\"}]","AP Precalculus Free-Response Questions - Section II Part A - Time 30 Minutes | PDF",1789894371]