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Topics include deMoivre’s law, illustrative life tables, survival and probability calculations between ages, use of UDD assumptions, force of mortality and integrated lifetime measures, substandard mortality adjustments, and select-and-ultimate mortality table interpolation. The exam instructs candidates to write legibly and avoid answering after the time expires.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/math-3630-actuarial-mathematics-i-sample-test-1-time-allowed-1-hour/398957/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/math-3630-actuarial-mathematics-i-sample-test-1-time-allowed-1-hour/398957.png","ImageObject",300,407,{"name":42,"@type":43},"Kyle","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-27",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the duration and total marks of the Sample Test 1?","Question",{"text":63,"@type":64},"The time allowed is 1 hour and the total marks are 100 points.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How many written-answer questions are included, and must all be answered?",{"text":68,"@type":64},"There are ten written-answer questions and you are to answer all ten.",{"name":70,"@type":61,"acceptedAnswer":71},"What happens if a candidate writes after the time has expired?",{"text":72,"@type":64},"Anyone caught writing after time has expired will be given a mark of zero.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},398957,1790578698,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":55,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":113,"preview_page_count":4},3985741905716,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","MATH 3630  \nActuarial Mathematics I  \nSample Test 1  \nTime Allowed: 1 hour  \nTotal Marks: 100 points  \nPlease write your name and student number at the spaces provided:  \nName:   Student ID:    \n􀀏 There are ten (10) written-answer questions here and you are to answer all ten. Each question is worth 10 points.  \n􀀏 Please provide details of your workings in the appropriate spaces provided; partial points will be granted.  \n􀀏 Please write legibly.  \n􀀏 Anyone caught writing after time has expired will be given a mark of zero.  \nQuestion No. 1:  \nLet X be the age-at-death random variable.  \nAssume X follows deMoivre's law with ! = 100. Calculate 10m20.  \nQuestion No. 2:  \nAssume that mortality follows the Illustrative Life Table.  \nCalculate the probability that a life (65) will die between ages 80 and 90 .  \nQuestion No. 3:  \nYou are given:  \nkj q 0 = 0.1 (k + 1), for k = 0, 1, 2 and 3 .  \nSuppose UDD holds between integral ages.  \nCompute the value of 2.75p 0 and interpret this probability.  \nQuestion No. 4:  \nYou are given:  \n4 5p 40 = 5  \n3 10p 45 = 5  \n2 10p 55 = 5  \nFind the probability that a life (40) will die between ages 55 and 65 .  \nQuestion No. 5:  \nSuppose you are given the survival function:  \nSX(x ) =􀀐1 􀀀 x!􀀑 􀀋 , for 0 􀀔 x 􀀔 !.  \nProve the following: 􀀖x 􀀁 x =  􀀋   \n􀀋 + 1 .  \nQuestion No. 6:  \nSuppose that for an 80-year-old fellow, his force of mortality is given by  \n 1   \n􀀖80+t = 10 􀀀 t , for 0 􀀔 t \u003C 10.  \nCalculate the probability that this fellow will die between ages 85 and 90 .  \nQuestion No. 7:  \nThe following is an extract from a standard mortality table:  \nx qx  \n40 .00278  \n41 .00298 42 .00320  \nA substandard table is obtained from this standard table by adding a constant c = 0.10 to the force of mortality. This results in mortality rates denoted by qsx, with the superscript s denoting substandard.  \nCalculate the probability that a substandard life (40) will die between ages 41 and 42 .  \nQuestion No. 8:  \nSuppose you are given the following select-and-ultimate mortality table:  \n\n| x | ` [x] | ` [x]+1 | `x+2 |\n| --- | --- | --- | --- |\n| 95 | 300 | 60 | 15 |\n| 96 | 175 | 10 | 0 |\n| 97 | 15 | 0 | 0 |\n| 98 | 1 | 0 | 0 |\n\nAssuming UDD between integral ages, calculate 2j0.5q [95] .  \nQuestion No. 9:  \nSuppose you are given that:  \n`x = 1000 􀀒 27 􀀀 3~~10~~x 􀀓 1=3 , for 0 􀀔 x 􀀔 90.  \nCalculate the average future lifetime of a newborn.","cbCail8L9k2Bqmhu","https://ap.wps.com/l/cbCail8L9k2Bqmhu","pdf",87626,"English","# Sample Test 1\n## Instructions and scoring\n## Questions 1-10","[{\"question\":\"What is the duration and total marks of the Sample Test 1?\",\"answer\":\"The time allowed is 1 hour and the total marks are 100 points.\"},{\"question\":\"How many written-answer questions are included, and must all be answered?\",\"answer\":\"There are ten written-answer questions and you are to answer all ten.\"},{\"question\":\"What happens if a candidate writes after the time has expired?\",\"answer\":\"Anyone caught writing after time has expired will be given a mark of zero.\"}]","MATH 3630 - Actuarial Mathematics I - Sample Test 1 - Time Allowed - 1 hour | PDF",1790490431]