[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-314756-105":59,"doc-detail-314756-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-bc-chapter-6-test-no-calculator-part-i-multiple-choice-questions","AP Calculus (BC) Chapter 6 Test - No Calculator - Part I - Multiple-Choice Questions","","AP Calculus (BC) Chapter 6 Test No Calculator contains multiple-choice and free-response problems on differential equations, slope fields, and initial-value problems. Sections include evaluating definite/indefinite integrals involving trigonometric and polynomial factors, applying limits to long-term behavior of logistic and exponential-type models, and analyzing concavity, asymptotes, and tangency conditions. It also covers constructing tangent line approximations and solving for constants using given infection/spread dynamics.",{"@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-bc-chapter-6-test-no-calculator-part-i-multiple-choice-questions/314756/",{"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-bc-chapter-6-test-no-calculator-part-i-multiple-choice-questions/314756.png","ImageObject",300,407,{"name":92,"@type":93},"Riley","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are assessed in the multiple-choice section of the test?","Question",{"text":113,"@type":114},"The multiple-choice questions focus on solving or analyzing differential equations, including logistic-type limits, exponential/decay behavior, and properties inferred from slope fields.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What skills are required for the free-response questions?",{"text":118,"@type":114},"The free-response problems require evaluating integrals, solving initial-value differential equations, computing constants from model conditions, and performing tangent-line/approximation tasks.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the test connect to real-world modeling?",{"text":122,"@type":114},"One free-response question models measles spread using a logistic differential equation, asking for parameters, half-infection timing, and related outcomes.","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},314756,1789901762,{"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":52,"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":130,"read_time":144,"preview_page_count":4},1374391975076,"https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051","AP Calculus (BC) Chapter 6 Test No Calculator Section  \nName:  Date:   Period:    \nPart I. Multiple-Choice Questions (5 points each; please circle the correct answer.)  \n1. Z0p􀀙=2 x cos x2 dx =  \n(A) 1  \n(B) 􀀀1  \n1  \n(C)  \n2  \n1  \n(D) 􀀀  \n2  \n(E) 0  \n2. The slope field indicated below most likely depicts solutions of the differential equa-  \n3. Z0 􀀙=2 x sin 2x dx =(A) 0  \n􀀙  \n(B)  \n4  \n􀀙  \n(C) 􀀀  \n4  \n􀀙  \n(D)  \n2  \n􀀙  \n(E) 􀀀  \n2  \n4. Given the logistic differential equation ddAt = A 􀀒 20 􀀀 A4􀀓 , where A(0) = 15, what is lim A(t)?  \nt!1  \n(A) 20  \n(B) 40  \n(C) 60  \n(D) 80  \n(E) 100  \n5. Given the differential equation dTdt = 􀀀 14 (T 􀀀 20); T (0) = 100 ; then T (20) =  \n(A) 80e􀀀5  \n(B) 100e􀀀5  \n(C) 80e􀀀5 + 20  \n(D) 80e􀀀5 􀀀 20  \n(E) 20  \nPart II. Free-Response Questions  \n6. (A) (5 points) Evaluate the indefinite integral Z x2 cos 2x dx.  \n(B) (4 points) Using your result in (A), compute Z0 􀀙=4 x2 cos 2x dx.  \n7. Consider the differential equation dydx = 3~~ ~~~~ ~~x :  \n(A) (8 points) Let y = f (x) be the particular solution to the given differential equation for 1 􀀔 x 􀀔 5 such that the line y = 􀀀2 is tangent to the graph of f. Find the x-coordinate of the point of tangency, and determine whether f has a local maximum, local minimum, or neither at this point. Justify your answer.  \n(B) (8 points) Compute y = f(x) explicitly, given the above information.  \nAP Calculus (BC) Chapter 6 Test Calculators Allowed  \nName:   Date:   Period:    \nPart III. Multiple-Choice Questions (5 points each; please circle the correct answer.)  \n8. You are given the differential equation dydx = 􀀀 15py, where y(0) = 25 . For which value(s) of x is y = 0?  \n(A) 􀀆5  \n(B) 10  \n(C) 50  \n(D) 10 and 􀀀10  \n(E) 5  \n9. Z􀀀􀀙􀀙 pc4x~~ ~~dx3~~ ~~sin~~ ~~x =  \n4  \n(A) ~~ ~~  \n3  \n4  \n(B) 􀀀  \n3  \n(C) 0  \n(D) 43p7  \n(E) 􀀀 43p7  \n10. Z01 sin􀀀1 x dx =  \n(A) 0  \n􀀙 + 2  \n(B)  \n2  \n􀀙 􀀀 2  \n(C)  \n2  \n􀀙  \n(D)  \n2  \n􀀙  \n(E) 􀀀  \n11. The initial-value problem dydx = f (x; y); y(0) = y0 > 0 has its slope field represented below. Which of the following are true?  \nI. The graph of the solution is concave up for all x.  \nII. lim y = 􀀀1 . x!􀀀1  \nIII. The graph of the solution has a slant asymptote.  \n(A) I only  \n(B) II only  \n(C) III only  \n(D) I and II  \n(E) I and III  \n12. If s is the displacement of a particle, then v = dsdt is its velocity. Assume that we are given that the particle has positive mass m and that m dvdt = 􀀀kv; v(0) > 0 ; where kis a positive constant. Which of the following are true?  \nI. lim s = 1 .  \nt!1  \nII. lim v = 0 .  \nt!1  \nIII. The graph of v as a function of t is concave up.  \n(A) I only  \n(B) II only  \n(C) I and II  \n(D) II and III  \n(E) I and III  \nPart IV. Free-Response Questions  \n13. Suppose that the spread of measles in our high school is predicted by the logistic differential equation  \ndP   k   \n= (650 􀀀 P )P; P (0) = 1 ;  \ndt 650  \nwhere t is the number of days after a student comes into contact with an infected student. We have seen that this has solution given by  \n 650  P (t) = 1 + Ce􀀀kt ; t 􀀕 0 ;  \nand where C; k are positive constants.  \n(A) (2 points) Compute C.  \n(B) (5 points) Assuming that the maximum rate of infections is 10 students/day,find k.  \n(C) (3 points) After how many days will half of the students have become infected?  \n14. Consider the differential equation  \ndy   2x = 􀀀 :  \ndx y  \n(A) (4 points) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.  \n(B) (6 points) Let y = f (x) be the particular solution to the differential equation with the initial condition f (1) =􀀀1 . Write an equation for the line tangent to the graph of f at (1 ; 􀀀1) and use it to approximate f (1:1) .  \ny  \n\n|  | 6 |  |  |\n| --- | --- | --- | --- |\n| 􀀏 | 2 􀀏 |  | 􀀏 |\n| 􀀏\u003Cbr>􀀛 | 1 􀀏 |  | 􀀏\u003Cbr>- |\n| 􀀀 1 |  |  | 1 |\n| 􀀏 | 􀀀1􀀏 |  | 􀀏 |\n| 􀀏 | 􀀀2􀀏? |  | 􀀏 |\n\nx  \n(c) (5 points) Find the particular solution y = f(x) to the given differential equation with the initial condition f (1) = 􀀀1 .","cbCairSuaN5jeQsU","https://ap.wps.com/l/cbCairSuaN5jeQsU","pdf",131369,"English","# Part I. Multiple-Choice Questions\n# Part II. Free-Response Questions\n# Part III. Multiple-Choice Questions\n# Part IV. Free-Response Questions","[{\"question\":\"What topics are assessed in the multiple-choice section of the test?\",\"answer\":\"The multiple-choice questions focus on solving or analyzing differential equations, including logistic-type limits, exponential/decay behavior, and properties inferred from slope fields.\"},{\"question\":\"What skills are required for the free-response questions?\",\"answer\":\"The free-response problems require evaluating integrals, solving initial-value differential equations, computing constants from model conditions, and performing tangent-line/approximation tasks.\"},{\"question\":\"How does the test connect to real-world modeling?\",\"answer\":\"One free-response question models measles spread using a logistic differential equation, asking for parameters, half-infection timing, and related outcomes.\"}]","AP Calculus (BC) Chapter 6 Test - No Calculator - Part I - Multiple-Choice Questions | PDF",25]