[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-311440-105":59,"doc-detail-311440-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","study-guide-for-the-advanced-placement-calculus-ab-examination","Study Guide for the Advanced Placement Calculus AB Examination","","Study guide for the Advanced Placement Calculus AB Examination, authored by Elaine Cheong. It explains the AP program context, the exam structure across multiple-choice Parts A and B and the free-response section, and how scoring and the 1–5 grade scale are determined. The guide outlines key AB topics such as elementary functions, limits, continuity, and foundational differentiation and integration concepts, supplemented with useful formulas, calculator tips, and selected review materials and references.",{"@graph":69,"@context":122},[70,84,105],{"@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/study-guide-for-the-advanced-placement-calculus-ab-examination/311440/",{"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/study-guide-for-the-advanced-placement-calculus-ab-examination/311440.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is the AP Calculus AB exam divided, and which sections allow or require calculators?","Question",{"text":112,"@type":113},"The exam has three sections: Multiple Choice Part A (25 questions, 45 minutes, no calculators), Multiple Choice Part B (15 questions, 45 minutes, graphing calculators required for some questions), and Free Response (6 questions, 45 minutes, graphing calculators required for some questions).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are AP Calculus AB grades on the 1 to 5 scale determined?",{"text":117,"@type":113},"Both the multiple-choice and free-response sections carry equal weight. A grade of 3 or higher typically requires about 50% correct on multiple choice and acceptable performance on the free-response section, with a scoring adjustment in which 1/4 of incorrectly answered multiple-choice questions are subtracted from the number answered correctly.",{"name":119,"@type":110,"acceptedAnswer":120},"What does it mean for a function to be continuous at a point?",{"text":121,"@type":113},"A function f is continuous at c if f(c) is defined, the limit of f(x) as x approaches c exists, and that limit equals f(c). The guide also gives a graphical interpretation: the graph should be traceable through (c, f(c)) without lifting a pencil.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},311440,1790456410,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":31,"preview_page_count":4},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","Study Guide for the Advanced Placement Calculus AB Examination  \nBy Elaine Cheong  \nCopyright 1996,1997 Elaine Cheong  \nAll Rights Reserved  \nTable of Contents  \nINTRODUCTION 2  \nTOPICS TO STUDY 3  \n∙ Elementary Functions 3  \n∙ Limits 5  \n∙ Differential Calculus 7  \n∙ Integral Calculus 12  \nSOME USEFUL FORMULAS 16  \nCALCULATOR TIPS AND PROGRAMS 17  \nBOOK REVIEW OF AVAILABLE STUDY GUIDES 19  \nACKNOWLEDGEMENTS 19  \nIntroduction  \nAdvanced Placement 1 is a program of college-level courses and examinations that gives high school students the opportunity to receive advanced placement and/or credit in college. The Advanced Placement Calculus AB Exam tests students on introductory differential and integral calculus, covering a full-year college mathematics course.  \nThere are three sections on the AP Calculus AB Examination:  \n1. Multiple Choice: Part A (25 questions in 45 minutes) -calculators are not allowed  \n2. Multiple Choice: Part B (15 questions in 45 minutes) -graphing calculators are required for some questions  \n3. Free response (6 questions in 45 minutes) -graphing calculators are required for some questions  \nScoring  \nBoth sections (multiple choice and free response) are given equal weight.  \nGrades are reported on a 1 to 5 scale:  \nExamination Grade  \nExtremely well qualified 5  \nWell qualified 4  \nQualified 3  \nPossibly qualified 2  \nNo recommendation 1  \nTo obtain a grade of 3 or higher, you need to answer about 50 percent of the multiple-choice questions correctly and do acceptable work on the free-response section. In both Parts A and B of the multiple choice section, 1/4 of the number of questions answered incorrectly will be subtracted from the number of questions answered correctly.  \n1 Advanced Placement Program® and AP® are trademarks ofthe College Entrance Examination Board.  \nTopics to Study  \nElementary Functions  \nProperties of Functions  \nA function ƒ is defined as a set of all ordered pairs (x, y), such that for each element x, there corresponds exactly one element y.  \nThe domain of ƒ is the set x.  \nThe range of ƒ is the sety.  \nCombinations of Functions  \nIf ƒ(x) = 3x + 1 and g(x) = x2-1  \na) the sum ƒ(x) + g(x) = (3x + 1) + (x2-1) = x2 + 3x  \nb) the difference ƒ(x) -g(x) = (3x + 1) - (x2-1) = -x2 + 3x + 2 c) the product ƒ(x)g(x) = (3x + 1)(x2-1) = 3x3 + x2-3x-1 d) the quotient ƒ(x)/g(x) = (3x + 1)/(x2-1)  \ne) the composite (ƒ ° g)(x) = ƒ(g(x)) = 3(x2-1) + 1 = 3x2-2  \nInverse Functions  \nFunctions ƒ and g are inverses of each other if ƒ(g(x)) = x for each x in the domain ofg  \ng(ƒ(x)) = x for each x in the domain of ƒ The inverse of the function ƒ is denoted ƒ-1 .  \nTo find ƒ-1, switch x andy in the original equation and solve the equation for y in terms of x.  \nExercise: If ƒ(x) = 3x + 2, then ƒ-1(x) =  \n(A) 3x1~~+~~2  \n(B) x3 -2  \n(C) 3x-2  \n(D) 12~~ ~~ x + 3  \n(E) x~~ ~~2  \nThe answer is E. x = 3y + 2  \n3y = x-2  \ny = x~~ ~~2  \nEven and Odd Functions  \nThe function y = ƒ(x) is even if ƒ(-x) = ƒ(x) .  \nEven functions are symmetric about they-axis (e.g. y = x2)  \nThe function y = ƒ(x) is odd if ƒ(-x) = -ƒ(x) .  \nOdd functions are symmetric about the origin (e.g. y = x3)  \nExercise: If the graph ofy = 3x + 1 is reflected about they-axis,  \nthen an equation of the reflection is y =  \n(A) 3x-1  \n(B) log3 (x-1)  \n(C) log3 (x + 1)  \n(D) 3-x + 1  \n(E) 1-3x  \nThe answer is D. The reflection of y = ƒ(x) in the y-axis is y = ƒ(-x)  \nPeriodic Functions  \nYou should be familiar with the definitions and graphs of these trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant  \nExercise: If ƒ(x) = sin(tan-1 x), what is the range of ƒ?  \n(A) (-p /2, p /2)  \n(B) [-p /2, p /2]  \n(C) (0, 1]  \n(D) (-1, 1)  \n(E) [-1, 1]  \nThe answer is D. The range of sin x is (E), but the points at which sin x = ± 1 ( p /2 + kp ), tan-1 x is undefined. Therefore, the endpoints are not included.  \nNote: The range is expressed using interval notation:(a , b) ⇔ a \u003C x \u003C b  \n[a , b] ⇔ a ≤ x ≤ b  \nZeros of a Function  ","cbCaivJfjFcUfMPC","https://ap.wps.com/l/cbCaivJfjFcUfMPC","pdf",76574,"English","# Introduction\n# Topics to Study\n## Elementary Functions\n## Limits\n# Some Useful Formulas\n# Calculator Tips and Programs\n# Book Review of Available Study Guides\n# Acknowledgements","[{\"question\":\"How is the AP Calculus AB exam divided, and which sections allow or require calculators?\",\"answer\":\"The exam has three sections: Multiple Choice Part A (25 questions, 45 minutes, no calculators), Multiple Choice Part B (15 questions, 45 minutes, graphing calculators required for some questions), and Free Response (6 questions, 45 minutes, graphing calculators required for some questions).\"},{\"question\":\"How are AP Calculus AB grades on the 1 to 5 scale determined?\",\"answer\":\"Both the multiple-choice and free-response sections carry equal weight. A grade of 3 or higher typically requires about 50% correct on multiple choice and acceptable performance on the free-response section, with a scoring adjustment in which 1/4 of incorrectly answered multiple-choice questions are subtracted from the number answered correctly.\"},{\"question\":\"What does it mean for a function to be continuous at a point?\",\"answer\":\"A function f is continuous at c if f(c) is defined, the limit of f(x) as x approaches c exists, and that limit equals f(c). The guide also gives a graphical interpretation: the graph should be traceable through (c, f(c)) without lifting a pencil.\"}]","Study Guide for the Advanced Placement Calculus AB Examination | PDF",1789894288]