[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-434869-105":59,"doc-detail-434869-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-pre-ap-practice-test-day-1-derivatives","AP Calculus Pre-AP Practice Test - Day 1 Derivatives","","Practice set for AP Calculus Pre-AP focusing on derivatives, slope, and related analytic concepts. Includes multiple-choice problems covering derivative rules (product, chain, quotient), implicit differentiation, and applications such as derivative graphs, curve sketching tests for concavity, linear approximation, and particle motion (position–velocity–acceleration). Also provides formula sheet guidance for evaluating limits, continuity, L’Hopital’s rule, and key derivative and theorem frameworks like EVT, MVT, and Rolle’s theorem, plus selected trigonometric and natural log derivatives.",{"@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-pre-ap-practice-test-day-1-derivatives/434869/",{"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-pre-ap-practice-test-day-1-derivatives/434869.png","ImageObject",300,407,{"name":92,"@type":93},"MrHarris58","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are covered in the Day 1 derivatives practice test?","Question",{"text":113,"@type":114},"The problems cover derivative and slope concepts, including product/chain/quotient rule, implicit differentiation, related rates, derivative graphs, curve sketching (first derivative test and concavity), linear approximation, and particle motion.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the linear approximation section used in the practice problems?",{"text":118,"@type":114},"It estimates function values using the tangent line at a chosen point, replacing the multiplication by the given decimal input to get an approximation.",{"name":120,"@type":111,"acceptedAnswer":121},"Which calculus theorems and derivative rules are referenced in the accompanying formula sheet?",{"text":122,"@type":114},"The sheet summarizes continuity conditions and theorems such as EVT, MVT, and Rolle’s theorem, along with common derivative rules (power, product, quotient, and chain) and L’Hopital’s rule for limits.","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},434869,1790742664,{"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":29,"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":105},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","# AP Calculus Pre-AP Practice Test(Day 1 Derivatives)\n\n   \n*The below practice problems are not comprehensive,and are a sample of the topics you may see on the Pre-APPractice test.Be sure to review through the other MC worksheets covering the Fall Topics listed below:  \nFall Topics:1)Limits &Continuity &L'Hopital's Rule 2)Derivative &Slope concepts/Product/Chain/Quotient Rule 3)Implicit differentiation 4)Related Rates 5)Derivative Graph 6)Curve Sketching:First Derivative Test/Test forConcavity /Calculator Problems 7)Linear Approximation 8)Particle Motion(Position-Velocity-Acceleration)  \n   \n9)Theorems:EVT,MVT,Rolle's 10)Trig/Natural Log Derivatives 11)Derivative of Inverse at a point  \n1)If c≠0,thenis  \nA.0  \nB.  \nC.2c  \nD.2c²  \nE.nonexistent  \n2)  \nIf 3x²-4xy=1,then when x=1,  \nA  \nB.1  \nC.  \nD.0  \nE.  \n3)The function f whose derivative isgiven by f(x)=5x³-15x+7 has alocal maximum at x=(A)-1.930(B)-1.000(C)0.511(D)1.000(E)1.419  \n(A)  \n4)  \n(B)  \nLet,where his thegraph shown above.Which of the fol-lowing could be the graph of f?  \n(C)  \n(D)  \n(E)  \n5)  \nThe function fis given by f(x)=2x⁴-3x²+1.On which of the fol-lowing intervals is f decreasing?  \nA.  \nB.  \nC.  \nD.  \nE.  \n6)  \nLetfbe the function given by f(x)=(x-4)²and let gbe the func-tion given by g(x)=e³.At what value of x do the graphs have tan-gent lines that are perpendicular?  \nA.x=1.143  \nB.x≈-1.143  \nC.x=0.512  \nD.x≈-0.512  \nE.x≈-0.750  \n(A)-√3π  \n(B)√3π  \n(C)0  \n(D)  \n(E)-π  \n(D)6  \n(E)81  \n(B)  \n(C)  \n(A)  \n9)The graph ofa function,fis shown above.Leth(x)be defined ash(x)=(x+1)·f(x).Find h'(4).(a)-6(b)-2(c)4(d)14  \nA spherical balloon is being inflated at a rateof 3 cubic inches per second.Determine therate of change of the radius of the balloonwhen the balloon's radius is 5 inches,accurateto three decimal places.The volume of asphere of radius ris(A)3.000 inches per second(B)1.667 inches per second(C)0.010 inches per second(D)-2.000 inches per second(E)0.120 inches per second  \n11),then there exist a numberc i the intervalthat satisfies the conclusion ofthe Mean Value Theorem.Which of the following could be c?  \n(4)(B)(C)E)(D)π  \n12.The derivative of a function fis given by f'(x)=esin×-cosx-1 for 0\u003Cx\u003C9.On whatintervals isfdecreasing?  \n(A)0\u003Cx\u003C0.633 and 4.115\u003Cx\u003C6.916(B)0\u003Cx\u003C1.947 and 5.744\u003Cx\u003C8.230(C)0.633\u003Cx\u003C4.115 and 6.916\u003Cx\u003C9(D)1.947\u003Cx\u003C5.744 and 8.230\u003Cx\u003C9  \n13)Use the linear approximation of f(x)=√1+x at a=0 to estimate √0.95.(B)0.9750(A)0.9502(C)0.9747 (D)0.9942(E)None of them.  \n# AP Pre-Test MC Formula Sheet\n\n   \n## I.Evaluate Limits Algebraically:\n\n   \nAlgebraic Steps(for x approaching Real Number):1)Plug in x-value first (IGNORE one-sided limit notation (example:  \n2)If resultis a real number value,the value is the limit.3)If the result i(indeterminate form)then reduce by i)factoring ii)conjugatemethod iii)simplify complex fraction 4)Re-evaluate the reduced Expression 4)If result is undefined (example:),and it'sa one-sided limit problem,then test using decimals.(choose between±∞).  \nEvaluate Limits forxapproaching ±):1)Compare Degrees:i)if Numerator\u003CDenominator,Limit=0 ii)If Numerator=Denominator,Limit =ratio of coefficients ii)If Numerator>Denominator,Limit=DNE(+co or-∞)  \n   \nL'Hopital's Rule Option:If Evaluating Limits produces  \nthen  \n(Evaluate limit after taking numerator  \n   \nand denominator's derivative separately)  \n\n| Ⅱ.Continuity Conditions:  \u003Cbr>i.f(c)is defined *point exists  \u003Cbr>ii.  \u003Cbr>*the limit exists  \u003Cbr>the limit exists at same location as the point  \u003Cbr>ii.   | IⅢI.Intermediate Value Theorem(IVT):If a function is   |\n| --- | --- |\n|  | continuous on closed interval [a,b],we can guarantee a  \u003Cbr>specific y-value on the graph if one endpoint is below the  \u003Cbr>y-value and the other endpoint is above the y-value.  \u003Cbr>(Example:Since f(4)=2\u003C5\u003C7=f(-1),there exists a c-  \u003Cbr>value where f(c)=4 on interval-1≤x≤4)   |\n\n## IV.Common Derivative Rules:\n\n\n| 1)Power Rule   |  | 3)   |  |\n| --- | --- | --- | --- |\n| 5)   |  |  |  |\n\n## V.General Der","cbCaivK7OdEhcZX0","https://ap.wps.com/l/cbCaivK7OdEhcZX0","pdf",821986,"English","# AP Calculus Pre-AP Practice Test (Day 1 Derivatives)\n## Derivatives and slope concepts\n## Common derivative and theorem references\n## Selected multiple-choice problems","[{\"question\":\"What topics are covered in the Day 1 derivatives practice test?\",\"answer\":\"The problems cover derivative and slope concepts, including product/chain/quotient rule, implicit differentiation, related rates, derivative graphs, curve sketching (first derivative test and concavity), linear approximation, and particle motion.\"},{\"question\":\"How is the linear approximation section used in the practice problems?\",\"answer\":\"It estimates function values using the tangent line at a chosen point, replacing the multiplication by the given decimal input to get an approximation.\"},{\"question\":\"Which calculus theorems and derivative rules are referenced in the accompanying formula sheet?\",\"answer\":\"The sheet summarizes continuity conditions and theorems such as EVT, MVT, and Rolle’s theorem, along with common derivative rules (power, product, quotient, and chain) and L’Hopital’s rule for limits.\"}]","AP Calculus Pre-AP Practice Test - Day 1 Derivatives | PDF",1790670910]