[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573238-105":53,"doc-detail-573238-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","ap-calculus-ab-2025-cheat-sheet","AP Calculus AB - 2025 Cheat Sheet","","Concise AP Calculus AB 2025 cheat sheet that compiles core tools for limits, continuity, and differentiation across units 1–8. Covers key ideas such as AROC and one-sided limits, continuity/removable and jump discontinuities, product/quotient/chain rules, implicit differentiation, and inverse trig derivatives. Includes guidance for MVT/EVT/Rolle and IVT-style problem setups, plus integration via accumulation and Riemann sums, L’Hôpital’s rule, optimization, related rates, and differential equations concepts like slope fields and separation of variables.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/ap-calculus-ab-2025-cheat-sheet/573238/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/ap-calculus-ab-2025-cheat-sheet/573238.png","ImageObject",442,249,{"name":88,"@type":89},"Jacob","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-18","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":76},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What does AROC mean and when should it be used in limits?","Question",{"text":108,"@type":109},"AROC refers to the value f(x) approaches as x approaches c from both sides. Use it when estimating limits from tables or graphs that require checking behavior on both sides of c.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Which differentiation rules are summarized for AP Calculus AB problems?",{"text":113,"@type":109},"The sheet summarizes the power rule and the product, quotient, and chain rules. It also includes guidance for implicit differentiation and notes on higher-order derivatives and inverse trig derivative patterns.",{"name":115,"@type":106,"acceptedAnswer":116},"How does the sheet guide integration and accumulation problems?",{"text":117,"@type":109},"It frames accumulation as the integral/area between a rate-of-change graph and the x-axis, including how to handle negative area. It also provides pointers for Riemann sums and using definite integrals (including cases with jump or removable discontinuities).","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},573238,1792022767,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":76,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":9},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","♾AP Calculus AB – 2025 Cheat Sheet | @thinkfiveable | See complete study guides →  \n| 􀀿Unit 1 Limits & Continuity |  | 􀁄Unit 2 Fundamentals of Differentiation |  |  |  |  | 􀀂Unit 3 Composite, Implicit, & Inverse Functions |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| ●\u003Cbr>●\u003Cbr>●\u003Cbr>●\u003Cbr>● |  is the value f(x) approaches when x- > c from BOTH sides\u003Cbr> is the value that f(x) approaches when x- > c from ONLY the right (if +) or left (if-) side\u003Cbr>| ●\u003Cbr>●●\u003Cbr>●\u003Cbr>●\u003Cbr>● | AROC = | |  |  | ●\u003Cbr>●\u003Cbr>●●\u003Cbr>● | Chain Rule: | |\n|  |  |  | When estimating f’(c) from a table, straddle both sides and use AROC, from a graph, slope of tangent line\u003Cbr>All differentiable functions are continuous, but not all continuous functions are differentiable |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | The chain rule is like unpeeling an onion, where you keep going from the outside in, you differentiate the outside function, plug in the inside function, and multiply by the derivative of the inside function.\u003Cbr>Implicit Differentiation: Differentiate each term with respect to the |  |\n|  |  |  | Power Rule:\u003Cbr>|  | |  |  |  |  |\n| ●\u003Cbr>● \u003Cbr>● Methods to algebraically simplify limits if you can’t directly plug in: Completing the square, Rationalization, Factoring\u003Cbr>● Order of growth rates from fastest to slowest:\u003Cbr>|  | ●\u003Cbr>●\u003Cbr>● | \u003Cbr>|  |  |  | ● | individual variables, and whenever you differentiate a y, multiply by \u003Cbr>Ex. \u003Cbr>Inverses: |  |\n| ● For f(x)/g(x), if highest power of f > highest power of g: infinite limit DNE, if \u003C, HA at y=0, if =, HA at y = ratio of first terms\u003Cbr>● Continuity if \u003Cbr>● Removable: hole, Asymptote, and Jump: Piecewise where y-values different\u003Cbr>● IVT PROBLEMS: Write “Since f(x) is continuous on [a, b] and f(c) is between f(a) and f(b), by the IVT there is a c in (a, b) such that f(c) = f(c)” |  | ●\u003Cbr>●\u003Cbr>●\u003Cbr>●\u003Cbr>●\u003Cbr>●\u003Cbr>●\u003Cbr>●\u003Cbr>● | \u003Cbr>Product Rule: |  |  | | ●\u003Cbr>●\u003Cbr>●●\u003Cbr>●\u003Cbr>● | \u003Cbr>Derivatives of inverse trig cofunctions are the negative of the derivative of the other 3 inverse trig functions\u003Cbr>Higher order derivatives: Just repeat!\u003Cbr>Second derivatives of implicit functions are functions of  |  |\n|  |  |  | Quotient Rule: \u003Cbr>\u003Cbr>|  |  |  |  |  |  |\n\n♾AP Calculus AB – 2025 Cheat Sheet | @thinkfiveable | See complete study guides →  \n| 􀀮Unit 4 Contextual Applications of Differentiation |  | ✨ Unit 5\u003Cbr>Analytical Applications of Differentiation | 􀀓Unit 6 Integration of Accumulation of Change |  |  |\n| --- | --- | --- | --- | --- | --- |\n| ● The derivative of a function is the rate of change of that function\u003Cbr>● If you are being asked about the rate of change of a rate of change, that’s basically the derivative of f’(x), orf”(x)\u003Cbr>|  | ● MVT PROBLEMS: Write “Since f(x) is continuous on [a, b] and differentiable on\u003Cbr>(a. b), there exists a c in (a, b) where  by the MVT”\u003Cbr>● Rolle’s Theorem is MVT where f(b) = f(a)\u003Cbr>● EVT PROBLEMS: Write “Since f(x) is continuous on (a, b), by the EVT, there exists at least one local maximum and one local minimum on (a, b) . | ● Accumulation/Integral = area between a rate of change graph and the x-axis ● If below x-axis, then accumulating negative area\u003Cbr>● Can use geometry to find integral from a graph (look for circles, triangles, squares, and places where positive and negative area cancel out)\u003Cbr>● When a function is split into multiple subdivisions,  is the left boundary,  is the right boundary,  is in the middle of an interval, and  is the interval width between the values that give  and  |  |  |\n| ● Particle motion:\u003Cbr>● Steps for Related Rates:\u003Cbr>1. Draw picture\u003Cbr>2. List knowns and unknowns\u003Cbr>3. Write an equation to model the situation (DO NOT PLUG IN STUFF THAT CHANGES) |  | ● Critical Points: Where f’(x) = 0 or undefined\u003Cbr>● Local Extrema: Point that is greater/less than surrounding points, always at critical points or endpoints\u003Cbr>● Global Extrema: Greatest or Least value of function\u003Cbr>● f’(x) > 0: inc, f’(x) \u003C 0: dec\u003Cbr>● If asking","cbCainKpR7p8ioyR","https://ap.wps.com/l/cbCainKpR7p8ioyR","pdf",1071124,"English","# Unit 1 Limits & Continuity\n## Unit 2 Fundamentals of Differentiation\n## Unit 3 Composite, Implicit, & Inverse Functions\n# Unit 4 Contextual Applications of Differentiation\n## Unit 5 Analytical Applications of Differentiation\n## Unit 6 Integration of Accumulation of Change\n# Unit 7 Differential Equations\n## Unit 8 Applications of Integration","[{\"question\":\"What does AROC mean and when should it be used in limits?\",\"answer\":\"AROC refers to the value f(x) approaches as x approaches c from both sides. Use it when estimating limits from tables or graphs that require checking behavior on both sides of c.\"},{\"question\":\"Which differentiation rules are summarized for AP Calculus AB problems?\",\"answer\":\"The sheet summarizes the power rule and the product, quotient, and chain rules. It also includes guidance for implicit differentiation and notes on higher-order derivatives and inverse trig derivative patterns.\"},{\"question\":\"How does the sheet guide integration and accumulation problems?\",\"answer\":\"It frames accumulation as the integral/area between a rate-of-change graph and the x-axis, including how to handle negative area. It also provides pointers for Riemann sums and using definite integrals (including cases with jump or removable discontinuities).\"}]","AP Calculus AB - 2025 Cheat Sheet | PDF",1791935445]