[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-311437-105":59,"doc-detail-311437-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-calculus-ab-2025-free-response-questions-part-a","AP® Calculus AB 2025 - Free-Response Questions - Part A","","AP® Calculus AB 2025 Free-Response Questions, Section II, Part A, includes two problems to be completed in 30 minutes. Students must use a graphing calculator in radian mode and show complete setups and mathematical work for average rates of change, instantaneous rates, and limits describing long-term behavior. 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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).  \nCALCULUS AB  \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. 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 , 5 i.  \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_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 CALCULUS AB 2025 n FREE-RESPONSE QUESTIONS  \n1. An invasive species of plant appears in a fruit grove at time t = 0 and begins to spread. The function C defined by C_t i = 7.6arctan_0.2ti models the number of acres in the fruit grove affected by the species t weeks after the species appears. It can be shown that Cl_t i = 253~~ ~~t~~2 ~~ .(Note: Your calculator should be in radian mode.)  \nA. Find the average number of acres affected by the invasive species from time t = 0 to time t = 4 weeks. Show the setup for your calculations.  \nB. Find the time t when the instantaneous rate of change of C equals the average rate of change of C over the time interval 0 \\# t \\# 4. Show the setup for your calculations.  \nC. Assume that the invasive species continues to spread accord","cbCairmk5ep7nkhp","https://ap.wps.com/l/cbCairmk5ep7nkhp","pdf",300428,"English","# AP® Calculus AB 2025 Free-Response Questions\n## Section II Part A\n## Question 1: Invasive species model\n## Question 2: Shaded region bounded by f and g","[{\"question\":\"What are the time and question requirements for Section II Part A?\",\"answer\":\"Section II, Part A has 2 free-response questions and lasts 30 minutes.\"},{\"question\":\"What calculator mode is required for these questions?\",\"answer\":\"A graphing calculator is required, and it must be set to radian mode.\"},{\"question\":\"What type of work is expected for the free-response answers?\",\"answer\":\"Students must show setups and all mathematical steps, provide mathematical justifications with required conditions, and present work using standard mathematical notation.\"}]","AP® Calculus AB 2025 - Free-Response Questions - Part A | PDF",1789894284,23]