[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-451863-105":59,"doc-detail-451863-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-chapter-1-test-review","AP Calculus Chapter 1 Test Review","","AP Calculus Chapter 1 Test Review provides a set of practice problems targeting core calculus concepts used in an introductory unit. It covers identifying and classifying discontinuities, evaluating one-sided and two-sided limits using appropriate methods, and computing limits analytically through algebraic simplification. The review also includes tasks on graph sketching from limit and continuity information, checking the applicability of the Intermediate Value Theorem to guarantee zeros, and determining vertical asymptotes. A key supplies worked answers and brief reasoning for verification.",{"@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-chapter-1-test-review/451863/",{"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-chapter-1-test-review/451863.png","ImageObject",300,407,{"name":92,"@type":93},"Himbo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you classify discontinuities in AP Calculus Chapter 1 problems?","Question",{"text":113,"@type":114},"You find x-values where the function is discontinuous, then classify whether the discontinuity is removable (a hole) or non-removable (such as a vertical asymptote or jump).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What methods can be used to evaluate limits in this review?",{"text":118,"@type":114},"The review states you may choose any method as long as you show all work. Typical approaches include algebraic simplification and analytical evaluation of one-sided limits.",{"name":120,"@type":111,"acceptedAnswer":121},"Does the Intermediate Value Theorem guarantee a zero on an interval like [1, 3]?",{"text":122,"@type":114},"It guarantees a zero only if the function is continuous on the interval and takes values of opposite signs at the endpoints. The key discussion checks these conditions for f(x)=x^2-4 on [1,3].","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},451863,1790794987,{"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":8,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":81},687197100911,"https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697","AP Calculus Chapter 1 Test Review  \n1. Find all x-values where discontinuities exist. Classify as removable or non-removable.  \na) f (x ) = ~~ ~~2~~ ~~1~~ ~~ b) f (x ) = 􀀂􀀁 x2 − 4, x ≠ 1 c) f (x ) = cos x  \nx +16 􀀃2, x = 1  \n2. Evaluate each limit. Choose any method, but show all work.  \na) 0+ ~~ ~~x1 b) 6+ ~~ ~~xx~~ ~~−~~ ~~66~~ ~~ c) 8[[x]]  \n3. Find the following using the given information. 2 f (x ) = 3 and 2 g (x ) = 4  \na) 2 32 + g (x )  b) 2 (x4 f (x ))  \n1 1  \n4. Find each limit analytically a) lim  x2 − 6x + 8  b) lim   x + 8 −  8  \nx→4 x − 4 x→0 x  \n5. Sketch the graph of a function with the following conditions.  \nlim− fx→0  \nlim f  \nx→4 −  \n(x ) = −4  \n(x ) = 1  \nlim  \nx→0+  \nlim  \nx→4+  \nf (x ) = 4  \nf (x ) = −3  \nf ( 2 ) = 2 f (−2) is undefined  \n6. Does the Intermediate Value Theorem guarantee the existence of a zero for f (x ) = x2 − 4 on [1, 3]? Why or why not?  \n7. Find the limit. Make sure to show all work and/or explain your answer. lim  8 − x x→−10+ 10 + x  \n8. Find all vertical asymptotes if they exist. a) f (x ) = ~~ ~~x2~~ ~~−x1−2x2+~~ ~~20~~ ~~ b) f (x ) = ~~ ~~xx2525  \n9. Determine whether each statement is true/false. If false, explain why or give a counterexample.  \n􀀁 x − 6, x ≤ 7  \na) If f (x ) = M , then f ( d ) = M b) 7 f (x ) = 1 if f (x ) = 􀀂􀀃−x2 + 2x +10, x > 7  \nChapter 1 Test Review Key  \n1. a) none b) x = 1, hole (removable) c) none 2. a) ∞ b) 1 c) DNE 3. a) 6 b) 48  \n4. a) 2 b) -1/64 5. On the board  \n6. f ( 1) = −3, f ( 3) = 5 , so yes, b/c-3 \u003C 0 \u003C 5  \n7. Since x = -10 makes the bottom zero, it is a vertical asymptote. The limit must be ∞ or −∞ . If you substitute-9.999 for x (b/c-9.999 is right of-10), the fraction is 17.999/0.01, which is positive. So, the limit must be ∞ .  \n8. a) x = 10 is an asymptote, x = 2 is a hole b) x = 5 is an asymptote, x = -5 is a hole 9. a) False, limit is a behavior NEAR a point, it doesn’t have to pass thru (d, M) .  \nb) False, 7 – 6 = 1, -72 + 2(7) + 10 = -25, that is a jump.","cbCaiiLmAgniEEg9","https://ap.wps.com/l/cbCaiiLmAgniEEg9","pdf",16906,"English","# Test Review\n## Discontinuities\n## Limits\n## Graph Sketching\n## Intermediate Value Theorem\n## Vertical Asymptotes\n## True/False Statements","[{\"question\":\"How do you classify discontinuities in AP Calculus Chapter 1 problems?\",\"answer\":\"You find x-values where the function is discontinuous, then classify whether the discontinuity is removable (a hole) or non-removable (such as a vertical asymptote or jump).\"},{\"question\":\"What methods can be used to evaluate limits in this review?\",\"answer\":\"The review states you may choose any method as long as you show all work. Typical approaches include algebraic simplification and analytical evaluation of one-sided limits.\"},{\"question\":\"Does the Intermediate Value Theorem guarantee a zero on an interval like [1, 3]?\",\"answer\":\"It guarantees a zero only if the function is continuous on the interval and takes values of opposite signs at the endpoints. The key discussion checks these conditions for f(x)=x^2-4 on [1,3].\"}]","AP Calculus Chapter 1 Test Review | PDF",1790736071]