[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-314503-105":59,"doc-detail-314503-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-scoring-guidelines-2025","AP® Calculus AB Scoring Guidelines - 2025","","AP Calculus AB Scoring Guidelines (2025) specify how to award points on graphing calculator-required multiple free-response tasks. The document defines evaluation expectations for setup work, correct integral computation, average versus instantaneous rate of change, and end-behavior limits for a given calculus model C(t)=7.6arctan(0.2t). It details rounding rules, point allocation for partial credit, and how correct answers must link to correct work to count toward scoring.",{"@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-calculus-ab-scoring-guidelines-2025/314503/",{"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-ab-scoring-guidelines-2025/314503.png","ImageObject",300,407,{"name":92,"@type":93},"Rizky","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",22,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the general scoring expectations in these guidelines?","Question",{"text":113,"@type":114},"The guidelines emphasize correct mathematical notation, allow numeric or algebraic answers without mandatory simplification, and specify accuracy and rounding requirements (including decimal accuracy to three places). They also describe how partial credit points are awarded for setup and results.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is Part A (graphing calculator required) scored?",{"text":118,"@type":114},"Part A awards points for the correct integral setup and for the correct average value answer. Correct linkage between the integral and the final numeric result is treated as part of scoring rather than scratch work, and inappropriate rounding can prevent earning points.",{"name":120,"@type":111,"acceptedAnswer":121},"How do Parts B and C differ in the calculus concepts being evaluated?",{"text":122,"@type":114},"Part B focuses on finding the time when instantaneous rate of change equals the average rate of change over 0 ≤ t ≤ 4, requiring an appropriate setup and correct solution. Part C asks for a limit expression describing end behavior of the rate of change (or the correct limit-related quantity), emphasizing evaluation of that limit for t → ∞.","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},314503,1790000442,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","2025   \nAP® Calculus AB Scoring Guidelines  \n© 2025 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](collegeboard.org).  \n[AP Central is the official online home for the AP Program: apcentral.collegeboard.org](AP Central is the official online home for the AP Program: apcentral.collegeboard.org).  \nAP® Calculus AB/BC 2025 Scoring Guidelines  \n\n| Part A (AB or BC): Graphing calculator required\u003Cbr>Question 1 9 points |  |  |  |\n| --- | --- | --- | --- |\n|  |  |  |  |\n| General Scoring Notes |  |  |  |\n| • The model solution is presented using standard mathematical notation.\u003Cbr>• Answers (numeric or algebraic) need not be simplified. Answers given as a decimal approximation should be accurate to three places after the decimal point. Within each individual free-response question, at most one point is not earned for inappropriate rounding. |  |  |  |\n| 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 ) = 7.6arctan ( 0.2t) models the number of acres in the fruit grove affected by the species t weeks after the species appears. It can be shown that C ′( t ) = 253~~ ~~t~~ ~~2~~ ~~ .\u003Cbr>(Note: Your calculator should be in radian mode.) |  |  |  |\n|  |  |  |  |\n| \u003Cbr>Model Solution Scoring |  |  |  |\n| A | 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.\u003Cbr>|  |  |\n| 4~~ ~~~~ ~~0~~ ~~ ∫40C ( t ) dt\u003Cbr>= 14~~ ~~ ( 11.112896 ) = 2.778224\u003Cbr>From time t = 0 to t = 4 weeks, the average number of acres affected by the invasive species was 2.778 acres. |  | Average value formula | Point 1 (P1) |\n|  |  | Answer Point 2 (P2) |  |\n\n© 2025 College Board  \nAP® Calculus AB/BC 2025 Scoring Guidelines  \n\n| \u003Cbr>Scoring Notes for Part A |  |\n| --- | --- |\n| •\u003Cbr>•\u003Cbr>•\u003Cbr>• | P1 is earned for the correct integral, with or without the differential, along with evidence of division by 4. In the presence of the correct integral, the correct answer will suffice as evidence of division by 4. These may appear all in one step, as in the model solution, or in multiple steps.\u003Cbr>P2 is earned for the correct answer, with or without supporting work. A reported answer should be accurate to three places after the decimal point, rounded or truncated. An inappropriately rounded answer does not earn the point.\u003Cbr>Incorrect or unclear communication between the correct integral and the correct answer is treated as scratch work and is not considered in scoring. For example:\u003Cbr>o ∫40C ( t ) dt = 11.112896 so the average velocity is 2.778224.\u003Cbr>Note: This response earns P1 for the correct integral with the correct answer as evidence of division by 4. It also earns P2 for the correct answer.\u003Cbr>o ∫40C ( t ) dt = 11.1124896 = 2.778224\u003Cbr>Note: This response earns P1 for the correct integral with the correct answer as evidence of division by 4. It also earns P2 for the correct answer. (In this instance, incorrect linkage is not considered in scoring.)\u003Cbr>o ∫40C ( t ) dt = 2.778224\u003Cbr>Note: This response earns P1 for the correct integral with the correct answer as evidence of division by 4. It also earns P2 for the correct answer. (In this instance, incorrect linkage is not considered in scoring.)\u003Cbr>Note that the values 14~~ ~~ ( 11.112 ) and 14~~ ~~ ( 11.113) are accurate to three digits after the decimal and therefore earn P2 . |\n\n© 2025 College Board  \nAP® Calculus AB/BC 2025 Scoring Guidelines  \n\n| \u003Cbr>B 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. |  |  |\n| --- | --- | --- |\n| C ( 4 ) − C( 0 )\u003Cbr> 4 − 0  = 1.282008\u003Cbr>C ′( t ) = 253~~ ~~t~~ ~~2~~ ~~ = 1.282008 ⇒ t = 2.154298 | Uses average rate of change | Point 3 (P3) |\n|  | Answer with supporting work | Po","cbCaisHpb51Rd4OP","https://ap.wps.com/l/cbCaisHpb51Rd4OP","pdf",475389,27,"English","# General Scoring Notes\n# Model Solution Scoring\n## Part A (AB or BC)\n## Scoring Notes for Part A\n## Part B\n## Scoring Notes for Part B\n## Part C\n## Scoring Notes for Part C\n## Part D","[{\"question\":\"What are the general scoring expectations in these guidelines?\",\"answer\":\"The guidelines emphasize correct mathematical notation, allow numeric or algebraic answers without mandatory simplification, and specify accuracy and rounding requirements (including decimal accuracy to three places). They also describe how partial credit points are awarded for setup and results.\"},{\"question\":\"How is Part A (graphing calculator required) scored?\",\"answer\":\"Part A awards points for the correct integral setup and for the correct average value answer. Correct linkage between the integral and the final numeric result is treated as part of scoring rather than scratch work, and inappropriate rounding can prevent earning points.\"},{\"question\":\"How do Parts B and C differ in the calculus concepts being evaluated?\",\"answer\":\"Part B focuses on finding the time when instantaneous rate of change equals the average rate of change over 0 ≤ t ≤ 4, requiring an appropriate setup and correct solution. Part C asks for a limit expression describing end behavior of the rate of change (or the correct limit-related quantity), emphasizing evaluation of that limit for t → ∞.\"}]","AP® Calculus AB Scoring Guidelines - 2025 | PDF",1789900983,68]