[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-314761-105":59,"doc-detail-314761-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-unit-6-mcq-b-progress-check-mcq-part-b","AP Calculus Unit 6-MCQ B - Progress Check - MCQ Part B","","AP Calculus Unit 6 progress check provides multiple-choice problems focused on single-variable calculus techniques. The questions cover evaluating function values using the Fundamental Theorem of Calculus, finding antiderivatives such as for cos(z^2-5), and performing definite integrals through substitution of variables, including explicit steps for transforming u and du. Additional items require algebraic preparation like completing the square and long division to apply power rules and simplify integrands before integration.",{"@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-unit-6-mcq-b-progress-check-mcq-part-b/314761/",{"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-unit-6-mcq-b-progress-check-mcq-part-b/314761.png","ImageObject",300,407,{"name":92,"@type":93},"Levi","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How is f(3) evaluated in the unit test?","Question",{"text":113,"@type":114},"It uses the second formulation of the Fundamental Theorem of Calculus together with the chain rule to relate f(3) to g(9), then reads g(9) from the given graph.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which technique is used for the numerical integration in Question 2?",{"text":118,"@type":114},"The solution uses substitution of variables with u=2g(z)+1, converting the integral into du form and evaluating the transformed bounds.",{"name":120,"@type":111,"acceptedAnswer":121},"What preparation steps are used before applying integration rules in later questions?",{"text":122,"@type":114},"The answers use completing the square and long division to rearrange the integrand so that standard rules like the power rule can be applied directly.","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},314761,1789962610,{"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":41,"preview_page_count":4},7971461740909,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","AP Calculus Practice test solution  \n# AP Calculus Unit 6-MCQ B\n\nUnit 6 Progress Check:MCQ Part B  \n## Question 1\n\nLetfbe a differentiable function such that).What is the value of f(3)?  \n2.899  \n3.321  \nAnswer C  \nto do the numerical integration.  \nAP Calculus Practice test solution  \nUnit 6Progress Check:MCQ Part B  \n⑦  \n④  \n⑪  \n⑩  \n## Question 2\n\n\n| z   | 0   | 1   | 2   | 3   |\n| --- | --- | --- | --- | --- |\n| g(z)   | 5   | 4   | 1   | -2   |\n\nSelected values of the twice-differentiable function gare given in the table above.What is the value o  \n⑧  \n◎  \nAnswer B  \nCorrectUse the technique of substitution of variables with u=2g(z)+1.B=2g(z)+1→du=2g(z)dz→g(z)dz=duWhen z=0,u=2g(0)+1=2(5)+1=11.When z=3,u=2g(3)+1=2(-2)+1=-3The calculator is used to do the numerical integration of the definite integral.  \nAP Calculus Practice test solution  \n## Question 3\n\nWhich of the following is an antiderivative of f(z)=cos(z²-5)?  \nA  \nsin(z⁵-5)  \n⑥  \nC  \n①  \nAnswer D  \nAP Calculus Practice test solution  \nGraph of g  \nThe graph of the function gon the closed interval [0,10]consists of four line segments,as shown above.Let fbe thefunction defined  \n⑧  \nAnswer D  \nCorrect.The second formulation of the Fundamental Theorem of Calculus along with the chain rule results in the following.f(3)=g(9)·6=4-6=24The graph of gis used to find the value of g(9).  \nAP Calculus Practice test solution  \n## Question 5\n\nUsing the substitutionis equivalent to which of the following?  \nA  \n⑧  \n①  \nAnswer D  \nCorrect.The substitution u=4x-3 is used.  \nSubstituting for 4x-3,for z,and for dz gives the following.  \nAP Calculus Practice test solution  \n## Question 6\n\n-e²cos(6eᵗ+3)+C  \n-6 cos(6eᵗ+3)+C  \nAnswer C  \nCorrect.The substitution u=6e®+3 is used.  \nAP Calculus Practice test solution  \n## Question 7\n\nln|-z²+6x-10|+C  \n-tan-¹(x-3)+C  \nC  \n-tan-¹(x+3)+C  \n①  \ntan-¹(x-3)+C  \n## Answer B\n\nCorrect.Before doing the integral,the integrand can be rearranged by completing the square.Let u=z-3.Then du=dr.Substituting these into the integral gives the following.  \n## Question 8\n\nA 20√8x-4z²+C  \n⑧  \n5sin-¹(x-1)+C  \n5sin-¹(x+1)+C  \n## Answer C\n\nCorrect.Before doing the integral,the integrand can be rearranged by completing the square.  \nLet u=z-1.Then du=dr.Substituting these in the integral gives the following.  \nAP Calculus Practice test solution  \nQuestion 9  \n3ln 2  \nC  \n①  \nAnswer B  \nCorrect.Before doing the integration,the integrand can be rearranged by using long division.  \nThis leads to the following.  \nAP Calculus Practice test solution  \n## Question 10\n\nWhich of the following is equivalent to  \n⑧  \nC  \n①  \n## Answer A\n\nCorrect.Expanding the integrand will give a rearrangement for which the power rule can be applied directly.","cbCaial3ghGv6bSK","https://ap.wps.com/l/cbCaial3ghGv6bSK","pdf",437931,12,"English","# AP Calculus Unit 6-MCQ B\n## Unit 6 Progress Check: MCQ Part B\n## Question 1\n## Question 2\n## Question 3\n## Question 5\n## Question 6\n## Question 7\n## Question 8\n## Question 9\n## Question 10","[{\"question\":\"How is f(3) evaluated in the unit test?\",\"answer\":\"It uses the second formulation of the Fundamental Theorem of Calculus together with the chain rule to relate f(3) to g(9), then reads g(9) from the given graph.\"},{\"question\":\"Which technique is used for the numerical integration in Question 2?\",\"answer\":\"The solution uses substitution of variables with u=2g(z)+1, converting the integral into du form and evaluating the transformed bounds.\"},{\"question\":\"What preparation steps are used before applying integration rules in later questions?\",\"answer\":\"The answers use completing the square and long division to rearrange the integrand so that standard rules like the power rule can be applied directly.\"}]","AP Calculus Unit 6-MCQ B - Progress Check - MCQ Part B | PDF",1789901771]