[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-313850-105":3,"doc-detail-313850-en":81,"detail-sidebar-cat-0-en-105":98},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","ap-calculus-ab-study-guide","AP Calculus AB: Study Guide","","AP Calculus AB: Study Guide outlines the structure and content emphasis of the AP Calculus AB exam, including 45 multiple-choice questions and 6 free-response questions over a 3-hour 15-minute test. It breaks down major topic categories and their approximate question ranges, then develops core limit concepts through definitions, tables/graphs/algebra methods, algebraic limit properties, one-sided and infinite limits, asymptotic behavior, and the Squeeze Theorem. It also introduces continuity criteria and how continuity can fail.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/ap-calculus-ab-study-guide/313850/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/ap-calculus-ab-study-guide/313850.png","ImageObject",300,407,{"name":42,"@type":43},"Stanford","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-09-20",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How long is the AP Calculus AB exam, and how many questions are there?","Question",{"text":63,"@type":64},"The exam is 3 hours and 15 minutes and contains 45 multiple-choice questions and 6 free-response questions, with both sections accounting for 50% each.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What topics make up the Limits and Continuity portion of the exam?",{"text":68,"@type":64},"Limits and Continuity questions cover limits defined via approaching x-values, methods such as tables/graphs/algebra, one-sided limits, infinite limits and asymptotes, and the Squeeze Theorem.",{"name":70,"@type":61,"acceptedAnswer":71},"When is a function continuous at a point x = c?",{"text":72,"@type":64},"A function is continuous at x = c if f(c) exists, the limit as x approaches c exists, and the limit equals the function value f(c).","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},313850,1790459098,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":91,"language":92,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":93,"faqs":94,"seo_title":95,"seo_description":12,"update_tm":96,"read_time":97,"preview_page_count":4},2336477552062,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","| |\n| --- |\n| \u003Cbr>AP Calculus AB: Study Guide |\n| \u003Cbr>AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. |\n\nKey Exam Details  \nThe AP® Calculus AB exam is a 3-hour and 15-minute, end-of-course test comprised of 45 multiple-choice questions (50% of the exam) and 6 free-response questions (50% of the exam) .  \nThe exam covers the following course content categories:  \n• Limits and Continuity: 10–12% of test questions  \n• Differentiation: Definition and Basic Derivative Rules: 10–12% of test questions  \n• Differentiation: Composite, Implicit, and Inverse Functions: 9–13% of test questions  \n• Contextual Applications of Differentiation: 10–15% of test questions  \n• Applying Derivatives to Analyze Functions: 15–18% of test questions  \n• Integration and Accumulation of Change: 17–20% of test questions  \n• Differential Equations: 6–12% of test questions  \n• Applications of Integration: 10–15% of test questions  \nThis guide offers an overview of the core tested subjects, along with sample AP multiple-choice questions that are like the questions you ’ll see on test day.  \nLimits and Continuity  \nAround 10‒12% of the questions on your AP Calculus AB exam will feature Limits and Continuity questions.  \nLimits  \nThe limit of a function f as x approaches c is L ifthe value off can be made arbitrarily close to L by taking x sufficiently close to c (but not equal to c) . If such a value exists, this is denoted limf (x) = L . If no such value exists, we say that the limit does not exist, abbreviated DNE.  \nx→c  \nLimits can be found using tables, graphs, and algebra.  \nExample  \nSome values ofa function are given in the table below.  \n| x | 0.9 | 0.99 | 0.999 | 1.001 | 1.01 | 1.1 |\n| --- | --- | --- | --- | --- | --- | --- |\n| f(x) | 2.488 | 2.490 | 2.499 | 2.501 | 2.504 | 2.513 |\n\ngrowing close to 2.5 as c approaches 1.  \nImportant algebraic techniques for finding limits include factoring and rationalizing radical expressions. Other helpful tools are given by the following properties.  \nSuppose limf (x) = L , limg(x) = M , lim h(x) = N , and a is any real number. Then,  \nx→c x→c x→L  \n• c 􀀾 f (x) + g(x)􀁀 = L + M  \n• c 􀀾 f (x) − g(x)􀁀 = L − M  \n• c 􀀾af (x) 􀁀 = aL  \n• lim  f (x) =  L  , as long as M 􀁺 0 x→c g (x) M  \n• c h ( f (x) ) = N  \nFor many common functions, evaluating limits requires nothing more than evaluating the function at the point c (assuming the function is defined at the point) . These include polynomial, rational, exponential, logarithmic, and trigonometric functions.  \nTwo special limits that are important in calculus are 0 sinxx = 1 and 0 1~~ ~~−~~ ~~coxsx = 0 .  \nOne-Sided Limits  \nSometimes we are interested in the value that a function f approaches as x approaches c from only a single direction. If the values off get arbitrarily close to L as x approaches c while taking on values greater than c, we say lim f (x) = L . Similarly, if x is taking on values less than c, we  \nx→c+  \nwrite lim f (x) = L .  \nx→c −  \nWe can now characterize limits by saying that c f (x) exists if and only if both lxc+ f (x) and lim f (x) exist and have the same value. A limit, then, can fail to exist in a few ways:  \nx→c −  \n• lim f (x) does not exist x→c+  \n• lim f (x) does not exist x→c −  \n• Both of these one-sided limits exist, but have different values  \nThe function shown has the following limits:  \n• lim f (x) =− 1 x→−2 −  \n• lim f (x) = 1 x→−2+  \n• lim f (x) DNEx→−2  \n• lim f (x) = 4 x→1−  \n• lim f (x) = 4 x→1+  \n• limf (x) = 4 x→1  \nNote that f (1) = 3 , but this is irrelevant to the value of the limit.  \nInfinite Limits, Limits at Infinity, and Asymptotes  \nWhen a function has a vertical asymptote at x = c, the behavior of the function can be described using infinite limits. If the function values increase as they approach the asymptote, we say the limit is ¥ , whereas if the values decrease as they approach the asymptote, the limit is -¥ . It is important ","cbCaio8TfTDA1eHx","https://ap.wps.com/l/cbCaio8TfTDA1eHx","pdf",2763343,63,"English","# Key Exam Details\n## Course Content Categories\n# Limits and Continuity\n## Limits\n## One-Sided Limits\n## Infinite Limits, Limits at Infinity, and Asymptotes\n## The Squeeze Theorem\n## Continuity","[{\"question\":\"How long is the AP Calculus AB exam, and how many questions are there?\",\"answer\":\"The exam is 3 hours and 15 minutes and contains 45 multiple-choice questions and 6 free-response questions, with both sections accounting for 50% each.\"},{\"question\":\"What topics make up the Limits and Continuity portion of the exam?\",\"answer\":\"Limits and Continuity questions cover limits defined via approaching x-values, methods such as tables/graphs/algebra, one-sided limits, infinite limits and asymptotes, and the Squeeze Theorem.\"},{\"question\":\"When is a function continuous at a point x = c?\",\"answer\":\"A function is continuous at x = c if f(c) exists, the limit as x approaches c exists, and the limit equals the function value f(c).\"}]","AP Calculus AB: Study Guide | PDF",1789899479,159,{"code":4,"msg":82,"data":99},[100,104,108,111,116,121,126,131,135,138,142],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":109,"slug":110},70,"exam",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":113,"show_sort_weight":114,"slug":115},5,"Comic",60,"comic",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":118,"show_sort_weight":119,"slug":120},6,"Technology",50,"technology",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":124,"slug":125},7,"Healthcare",40,"healthcare",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":129,"slug":130},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":133,"slug":134},"Religion & Spirituality",20,"religion-spirituality",{"id":133,"doc_module":4,"doc_module_name":25,"category_name":136,"show_sort_weight":133,"slug":137},"World Cup","world-cup",{"id":139,"doc_module":4,"doc_module_name":25,"category_name":140,"show_sort_weight":139,"slug":141},10,"Lifestyle","lifestyle",{"id":143,"doc_module":4,"doc_module_name":25,"category_name":144,"show_sort_weight":112,"slug":145},19,"General","general"]