[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-315145-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-315145-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","2023-vce-specialist-mathematics-1-external-assessment-report","2023 VCE Specialist Mathematics 1 - External Assessment Report","","2023 VCE Specialist Mathematics Examination 1 external assessment report evaluates student performance across 10 questions totalling 40 marks. General comments highlight new tested topics including integration by parts, area of a surface of revolution, proof by induction, and planes, noting uneven difficulty with proof by induction. Strengths include sketching rational functions, correct use of integration by parts, mean and standard deviation for sums of independent random variables, substitution to evaluate integrals, and plane cross products. Weaknesses focus on acceleration alternatives, limits, implicit differentiation rules, and induction proofs.",{"@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/2023-vce-specialist-mathematics-1-external-assessment-report/315145/",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/2023-vce-specialist-mathematics-1-external-assessment-report/315145.png","ImageObject",300,407,{"name":42,"@type":43},"Franzy","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-20",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What were the total number of questions and marks in the 2023 VCE Specialist Mathematics Examination 1?","Question",{"text":63,"@type":64},"The examination comprised 10 questions worth a total of 40 marks.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which new topics were tested in 2023?",{"text":68,"@type":64},"New topics tested included integration by parts, area of a surface of revolution, proof by induction, and planes.",{"name":70,"@type":61,"acceptedAnswer":71},"What skills and question types were commonly strong for students?",{"text":72,"@type":64},"Students showed strength in sketching rational functions, integration by parts, substitution techniques for integrals, working with planes and cross products, and using trigonometric identities.","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},315145,1789903502,{"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":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":113,"preview_page_count":4},2336478945519,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","2023 VCE Specialist Mathematics 1 external assessment report  \nGeneral comments  \nThe 2023 VCE Specialist Mathematics Examination 1 comprised 10 questions worth a total of 40 marks.  \nNew topics tested in 2023 included integration by parts (Question 5), area of a surface of revolution (Question 7), proof by induction (Question 8) and planes (Question 9) . While some students had difficulty with proof by induction, a majority of students were able to demonstrate that they understood what was required in the questions on the new topics.  \nMany of the questions in this paper required students to show appropriate working , which may include algebraic manipulation, solving equations or using calculus. To attract full marks, it was important that students didn’t omit steps or otherwise abbreviate their working.  \nAreas of strength included:  \n• sketching rational functions (Question 1b. )  \n• integration by parts (Question 5)  \n• calculating the mean and standard deviation of the sum of independent random variables (Question 6a. )  \n• using substitution techniques to evaluate integrals (Question 7)  \n• working with planes and evaluating cross products (Question 9)  \n• using trigonometric identities (Question 10) .  \nAreas of weakness included:  \n• remembering to use an alternative form for acceleration, for example v ~~ ~~dvdx (Question 3a. )  \n• evaluating simple limits (Question 3b. )  \n• using the product and/or chain rule when performing implicit differentiation (Question 4)  \n• proof by induction (Question 8) .  \n2023 VCE Specialist Mathematics 1 external assessment report  \nSpecific information  \nNote: This report provides sample answers, or an indication of what answers may have been included. Unless otherwise stated, these are not intended to be exemplary or complete responses.  \nThe statistics in this report may be subject to rounding resulting in a total more or less than 100 per cent.  \nQuestion 1a.  \n\n| Mark | 0 | 1 | Average |\n| --- | --- | --- | --- |\n| % | 13 | 87 | 0.9 |\n\nx2 + x-6   x(x-1) + 2(x-1) -4  \n=  \nx-1 x-1  \n= x + 2-x~~ ~~4-1  \nThis question was answered well. Various approaches were seen, including long and synthetic division. Some students made algebraic or arithmetic errors in their calculations.  \nQuestion 1b.  \n\n| Mark | 0 | 1 | 2 | 3 | Average |\n| --- | --- | --- | --- | --- | --- |\n| % | 18 | 20 | 23 | 39 | 1.9 |\n\nThe graph needed to have both asymptotes, x = 1 and  \ny = x + 2 , correct and labelled. While the axial  \nintercepts did not need to be labelled, the graph line needed to pass through the correct points.  \nSome graphs did not display asymptotic behaviour, retreating from the asymptotes. The oblique asymptote y = x + 2 was sometimes missing, even when a graph with reasonable asymptotic behaviour was drawn.  \n© VCAA Page 2  \n2023 VCE Specialist Mathematics 1 external assessment report  \nQuestion 2  \n\n| Mark | 0 | 1 | 2 | 3 | Average |\n| --- | --- | --- | --- | --- | --- |\n| % | 38 | 14 | 11 | 37 | 1.5 |\n\narg ((b-i )3 ) = - ~~ ~~p2 Þ arg( b-i ) = - ~~ ~~p6 æ p ö 1  \nÞ tan çè -  6  ø÷ = -band so b = 3 .  \nSome students used graphical approaches or expanded; for example,( b-i )3 = b3-3b + ( 1-3b2 ) i  \nIf arg(z) = - ~~ ~~p2 then b3-3b = 0 Þ b = 3 since b > 0 .  \nQuestion 3a.  \n\n| Mark | 0 | 1 | 2 | Average |\n| --- | --- | --- | --- | --- |\n| % | 44 | 21 | 35 | 0.9 |\n\nStudents needed to use an appropriate alternative form for acceleration:  \ndva = v ~~ ~~  \ndx  \n3x + 2 -7  \n=  2x-1 ´ ( 2x-1)2 When x = 2 , a = - ~~ ~~5627 .  \nA smaller number of students evaluated  \nd æ 1 dx çè  2  \n2 ö v ø÷  \nA large number of students evaluated dvdx at  \nx = 2  \nwhen x = 2 to obtain the same result.  \nand proceeded no further.  \n© VCAA Page 3  \n2023 VCE Specialist Mathematics 1 external assessment report  \nQuestion 3b.  \n\n| Mark | 0 | 1 | Average |\n| --- | --- | --- | --- |\n| % | 50 | 50 | 0.5 |\n\n3 2  \nSome students separated the fraction to find the limit:  \n3x + 2 3 7  \n~~ ~~ =  + ~~  ~~2x-1 2 2(2x-1)  \nOther s","cbCain7ScrI0vgrS","https://ap.wps.com/l/cbCain7ScrI0vgrS","pdf",1970616,12,"English","# General comments\n## Specific information by question\n## Question 1\n## Question 2\n## Question 3a\n## Question 3b\n## Question 4\n## Question 5\n## Question 6a","[{\"question\":\"What were the total number of questions and marks in the 2023 VCE Specialist Mathematics Examination 1?\",\"answer\":\"The examination comprised 10 questions worth a total of 40 marks.\"},{\"question\":\"Which new topics were tested in 2023?\",\"answer\":\"New topics tested included integration by parts, area of a surface of revolution, proof by induction, and planes.\"},{\"question\":\"What skills and question types were commonly strong for students?\",\"answer\":\"Students showed strength in sketching rational functions, integration by parts, substitution techniques for integrals, working with planes and cross products, and using trigonometric identities.\"}]","2023 VCE Specialist Mathematics 1 - External Assessment Report | PDF"]