[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-466340-105":59,"doc-detail-466340-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","math-1a-final-exam-practice","MATH 1A FINAL EXAM - (PRACTICE)","","Practice final exam for a Math 1A course covering 10 graded questions. Topics include differentiation of logarithmic and trigonometric expressions, limits, integral computations, and sketching a curve with asymptotes, extrema, and concavity. Additional problems address applied temperature change in a refrigerator, geometry of the largest inscribed rectangle in a circle, and train motion with time-dependent acceleration, displacement, and total distance within a fixed time window.",{"@graph":69,"@context":122},[70,84,105],{"@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/math-1a-final-exam-practice/466340/",{"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/math-1a-final-exam-practice/466340.png","ImageObject",300,407,{"name":92,"@type":93},"McGucket","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-19","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What rules apply during the Math 1A Final Exam practice?","Question",{"text":112,"@type":113},"Calculators are not permitted, and you may use your own blank paper for rough work. Students must stay until the exam is finished, and solutions should be written neatly and coherently to receive full credit.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How many questions are on this practice final exam?",{"text":117,"@type":113},"The exam consists of 10 questions.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of topics are included in the practice questions?",{"text":121,"@type":113},"The practice covers derivatives, limits, integrals, an applied temperature-change word problem, curve sketching with key features, tangent line determination, an optimization area problem in a circle, and train motion with acceleration and reversal.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},466340,1791432161,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":41},1236954412713,"https://us-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","MATH 1A FINAL EXAM (PRACTICE) PROFESSOR PAULIN  \nDO NOT TURN OVER UNTIL INSTRUCTED TO DO SO .  \nCALCULATORS ARE NOT PERMITTED  \nYOU MAY USE YOUR OWN BLANK PAPER FOR ROUGH WORK  \nSO AS NOT TO DISTURB OTHER STUDENTS, EVERYONE MUST STAY UNTIL THE EXAM IS FINISHED  \nREMEMBER THIS EXAM IS GRADED BY A HUMAN BEING . WRITE YOUR SOLUTIONS NEATLY AND COHERENTLY, OR THEY RISK NOT RECEIVING FULL CREDIT  \nName and section:    \nGSI's name:    \nMath 1A Final Exm (Practice)  \nThis exam consists of 10 questions. Answer the questions in the  \nspaces provided.  \n1. Calculate the following (you do not need to use the limit de􀀌nition):  \n(a) (10 points)  \nddx ln(3x)e2x  \nSolution:  \n(b) (15 points)  \nddx tan(e(xx ))  \nSolution:  \nPLEASE TURN OVER  \n2. Calculate the following (you do not need to use the (􀀏; 􀀎)-de􀀌nition):  \n(a) (10 points)  \nsin(x2 )  \nlim ~~ ~~  \nx!0 tan x  \nSolution:  \n(b) (15 points)    \np 1 + 4x6  \nlim ~~ ~~  \nx!􀀀1 2 + x3  \nSolution:  \nPLEASE TURN OVER  \n3. Calculate the following (you do not need to use Riemann sum de􀀌ntion):  \n(a) (10 points)  \nZ 2xx2~~ ~~~~ ~~41dx  \nSolution:  \n(b) (15 points)  \nZee2 x~~ ~~l1n(x)dx  \nSolution:  \nPLEASE TURN OVER  \n4. (25 points) A cup of water is placed in a refrigerator. The refrigerator has temperature 5C. After 10 minutes the water is 15C. After 20 minutes the water is 10C. Determine the temperature of the water when it was placed in the refrigerator.  \nSolution:  \nPLEASE TURN OVER  \n5. (25 points) Sketch the following curve. Be sure to indicate asymptotes, local maxima and minima and concavity. Show your working on this page and draw the graph on the  \nnext page.  \ny =  \nSolution:  \nx2 ex  \nx  \nPLEASE TURN OVER  \nSolution (continued) :  \nPLEASE TURN OVER  \n6. (25 points) Determine the equation of the tangent line at x = 1 of the following curve:  \ny = Zx 3x cos(􀀙t)dt + 2x  \nSolution:  \nPLEASE TURN OVER  \n7. (25 points) Determine the area of the largest rectangle inscribed in the circle of radius r.  \nSolution:  \nPLEASE TURN OVER  \n8. A train is travelling along a straight track at a constant speed of 75 metres per second. It then begins to slow down, with acceleration a (t) = 􀀀6t, at time t seconds after the breaks have been applied. Once the train stops it immediately begins reversing with constant velocity 10 metres per second.  \n(a) (15 points) What is the displacement of the train in the 10 seconds after applying the brakes.  \nSolution:  \n(b) (10 points) What is the total distance travelled by the train in the 10 seconds after the brakes are applied.  \nSolution:  \nPLEASE TURN OVER","cbCaiuUtIUZ7M17E","https://ap.wps.com/l/cbCaiuUtIUZ7M17E","pdf",113594,12,"English","# Instructions\n## Rules and submission guidance\n# Questions\n## Problem 1: Derivatives\n## Problem 2: Limits\n## Problem 3: Integrals\n## Problem 4: Temperature in a refrigerator\n## Problem 5: Curve sketching","[{\"question\":\"What rules apply during the Math 1A Final Exam practice?\",\"answer\":\"Calculators are not permitted, and you may use your own blank paper for rough work. Students must stay until the exam is finished, and solutions should be written neatly and coherently to receive full credit.\"},{\"question\":\"How many questions are on this practice final exam?\",\"answer\":\"The exam consists of 10 questions.\"},{\"question\":\"What kinds of topics are included in the practice questions?\",\"answer\":\"The practice covers derivatives, limits, integrals, an applied temperature-change word problem, curve sketching with key features, tangent line determination, an optimization area problem in a circle, and train motion with acceleration and reversal.\"}]","MATH 1A FINAL EXAM - (PRACTICE) | PDF",1790771089]