[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-311486-105":59,"doc-detail-311486-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-2025-section-ii-part-a-free-response-questions","AP Precalculus 2025 - Section II Part A - Free-Response Questions","","AP Precalculus 2025 Section II Part A includes two timed free-response questions requiring graphing calculator use in radian mode. The questions assess function composition and inverse function evaluation, solving for zeros of a cubic polynomial, analyzing end behavior using limits, and selecting the best model type from a value table with supporting justification. The second question models a song’s cumulative streaming plays with a quadratic function, requiring equation setup for parameters, average rate of change, and predictions based on the model.",{"@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-2025-section-ii-part-a-free-response-questions/311486/",{"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-2025-section-ii-part-a-free-response-questions/311486.png","ImageObject",300,407,{"name":92,"@type":93},"Mabel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How many free-response questions are in AP Precalculus Section II Part A, and how long is the section?","Question",{"text":113,"@type":114},"Section II, Part A has 2 free-response questions and lasts 30 minutes.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What calculator settings and tools are required for this part?",{"text":118,"@type":114},"A graphing calculator is required, and it must be in radian mode. A handheld graphing calculator or the calculator available in the application may be used.",{"name":120,"@type":111,"acceptedAnswer":121},"What mathematical topics are assessed in Question 1 and Question 2?",{"text":122,"@type":114},"Question 1 focuses on function composition, inverse evaluation, solving for zeros, and end behavior via limits, plus modeling function type from a table. 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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](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, but you must write your answers in the freeresponse booklet. In the free-response 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 _xi 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.  \n© 2025 College Board.  \n[Visit College Board on the web:](Visit College Board on the web: collegeboard.org 2)[ collegeboard.org](Visit College Board on the web: collegeboard.org 2)[ 2](Visit College Board on the web: collegeboard.org 2)  \nAP PRECALCULUS 2025 n FREE-RESPONSE QUESTIONS  \n1. The functionf is decreasing and is defined for all real numbers. The table gives values for f _xi at selected values of x.  \n\n| x | -2 | -1 | 0 | 1 | 2 |\n| --- | --- | --- | --- | --- | --- |\n| f _xi | 14 | 7 | 3.5 | 1.75 | 0.875 |\n\nThe function g is given by g_xi = -0. 167x3 +x2-1.834.  \nA.  \ni. The function h is defined by h_xi = _g ° f i_xi = g `f _xij. Find the value of h_ 1 i as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer.  \nii. Find the value of f-1_3.5 i, or indicate that it is not defined.  \nB.  \ni. Find all values of x, as decimal approximations, for which g_xi = 0 , or indicate that there are no such values.  \nii. Determine the end behavior of g as x increases without bound. Express your answer using the mathematical notation of a limit.  \nC.  \ni. Based on the table, which of the following function types best models function f: linear, quadratic, exponential, or logarithmic?  \nii. Give a reason for your answer in part C (i) based on the relationship between the change in the output values off and the change in the input values off. Refer to the values in the table in your reasonin","cbCaibwJ5HZamU3L","https://ap.wps.com/l/cbCaibwJ5HZamU3L","pdf",284438,"English","# Section II Part A\n## Question 1\n## Question 2","[{\"question\":\"How many free-response questions are in AP Precalculus Section II Part A, and how long is the section?\",\"answer\":\"Section II, Part A has 2 free-response questions and lasts 30 minutes.\"},{\"question\":\"What calculator settings and tools are required for this part?\",\"answer\":\"A graphing calculator is required, and it must be in radian mode. A handheld graphing calculator or the calculator available in the application may be used.\"},{\"question\":\"What mathematical topics are assessed in Question 1 and Question 2?\",\"answer\":\"Question 1 focuses on function composition, inverse evaluation, solving for zeros, and end behavior via limits, plus modeling function type from a table. Question 2 focuses on building and interpreting a quadratic model for cumulative streaming plays, including parameter finding and rate of change.\"}]","AP Precalculus 2025 - Section II Part A - Free-Response Questions | PDF",1789894362,18]