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The assessment covers core mathematics tasks including calculus differentiation and integration, inverse or antiderivative rules, solving parameter-dependent systems, probability for repeated independent draws, logarithmic domains, trigonometric graph transformations, and equation solving in given intervals.",{"@graph":14,"@context":72},[15,34,55],{"@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/victorian-certificate-of-education-2022-mathematical-methods-written-examination-1/315285/",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/victorian-certificate-of-education-2022-mathematical-methods-written-examination-1/315285.png","ImageObject",300,407,{"name":42,"@type":43},"Ben Jamin","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-07","2026-09-20",true,{"@type":52,"interactionType":53,"userInteractionCount":30},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What equipment is allowed and what is not allowed in the exam room?","Question",{"text":62,"@type":63},"Allowed items include pens, pencils, highlighters, erasers, sharpeners and rulers. Not permitted are any technology such as calculators or software, notes of any kind, blank sheets of paper, and correction fluid/tape.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How long are the reading and writing periods for this examination?",{"text":67,"@type":63},"The reading time is 15 minutes from 9:00 am to 9:15 am. The writing time is 1 hour from 9:15 am to 10:15 am.",{"name":69,"@type":60,"acceptedAnswer":70},"What rules apply to answering questions requiring numerical answers?",{"text":71,"@type":63},"For numerical answers, an exact value must be given unless otherwise specified. Where more than one mark is available, appropriate working must be shown.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},315285,1790745545,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":30,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"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":107,"preview_page_count":4},2336478466772,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Victorian Certificate of Education 2022  \nSUPERVISOR TO ATTACH PROCESSING LABEL HERE  \nSTUDENT NUMBER  \n\n|  |  |\n| --- | --- |\n\n\n|  |  |  |\n| --- | --- | --- |\n\n\n|  |  |  |\n| --- | --- | --- |\n\nMATHEMATICAL METHODS  \nWritten examination 1  \nWednesday 2 November 2022  \nReading time: 9.00 am to 9.15 am (15 minutes)  \nWriting time: 9.15 am to 10.15 am (1 hour)  \nQUESTION AND ANSWER BOOK  \nStructure of book  \n\n| Number of | Number of questions | Number of |\n| --- | --- | --- |\n| questions | to be answered | marks |\n| 8 | 8 | 40 |\n\n• Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners and rulers.  \n• Students are NOT permitted to bring into the examination room: any technology (calculators or software), notes of any kind, blank sheets of paper and/or correction fluid/tape.  \nMaterials supplied  \n• Question and answer book of 13 pages  \n• Formula sheet  \n• Working space is provided throughout the book.  \nInstructions  \n• Write your student number in the space provided above on this page.  \n• Unless otherwise indicated, the diagrams in this book are not drawn to scale.  \n• All written responses must be in English.  \nAt the end of the examination  \n• You may keep the formula sheet.  \nStudents are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.  \n© VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2022  \n\n| 2022 MATHMETH EXAM 1 2 | d o n o t w r i t e i n t h i s area |\n| --- | --- |\n| THIS PAGE IS BLANK |  |\n\n3 2022 MATHMETH EXAM 1  \ndo n o t w r i t e i n t h i s area  \nInstructions  \nAnswer all questions in the spaces provided.  \nIn all questions where a numerical answer is required, an exact value must be given, unless otherwise specified. In questions where more than one mark is available, appropriate working must be shown.  \nUnless otherwise indicated, the diagrams in this book are not drawn to scale.  \nQuestion 1 (3 marks)  \na. Let y = 3xe2x.  \ndy  \nFind . 1 mark  \ndx  \nb. Find and simplify the rule off ′(x), where f : R R, f (x) 􀀞 cox(x) . 2 marks  \n\n|  |\n| --- |\n|  |\n|  |\n\nTURN OVER  \n\n| 2022 MATHMETH EXAM 1 4 | d o n o t w r i t e i n t h i s area |\n| --- | --- |\n| Question 2 (4 marks)\u003Cbr>􀀞3 􀀛 3\u003Cbr>a. Let g : 􀀝􀀜 2 , 􀀚􀀙 􀀘 R, g (x) 􀀗 2x 􀀖3 .\u003Cbr>Find the rule for an antiderivative of g(x) . 1 mark\u003Cbr>\u003Cbr>b. Evaluate 􀀜10􀀞 f (x) 􀀞 2 f (x) 3􀀝􀀝 dx , where 􀀜10 f (x)􀀞 2 dx 􀀝 15 and 10f (x) dx 􀀞 13 . 3 marks\u003Cbr>|  |\n\n5 2022 MATHMETH EXAM 1  \ndo n o t w r i t e i n t h i s area  \nQuestion 3 (3 marks)  \nConsider the system of equations  \nkx – 5y = 4 + k  \n3x + (k + 8)y = −1  \nDetermine the value ofk for which the system of equations above has an infinite number of solutions.  \nTURN OVER  \n\n| 2022 MATHMETH EXAM 1 6 | d o n o t w r i t e i n t h i s area |\n| --- | --- |\n| Question 4 (5 marks)\u003Cbr>A card is drawn from a deck of red and blue cards. After verifying the colour, the card is replaced in the deck. This is performed four times.\u003Cbr>1   1\u003Cbr>Each card has a probability of of being red and a probability of of being blue.\u003Cbr>2 2\u003Cbr>The colour of any drawn card is independent of the colour of any other drawn card.\u003Cbr>Let Xbe a random variable describing the number of blue cards drawn from the deck, in any order.\u003Cbr>a. Complete the table below by giving the probability of each outcome. 2 marks\u003Cbr>x 0 1 2 3 4 Pr(X = x)  1 \u003Cbr>16  6 \u003Cbr>16\u003Cbr>b. Given that the first card drawn is blue, find the probability that exactly two of the next three cards\u003Cbr>drawn will be red. 1 mark\u003Cbr>c. The deck is changed so that the probability of a card being red is 23 and the probability of a card being 1\u003Cbr>blue is .\u003Cbr>3\u003Cbr>Given that the first card drawn is blue, find the probability that exactly two of the next three cards\u003Cbr>drawn will be red. 2 marks\u003Cbr> |  |\n\n7 2022 MATHMETH EXAM 1  \ndo n o t w r i t e i n t h i s area  \nQuestion 5 (5 marks)  \na. Solve 103x – 13 = 100 for x. 2 marks  \n\n|  |\n| --- |\n|  |\n|  |\n\nb. Find the maximal domain ","cbCaitNhlZLw7rwg","https://ap.wps.com/l/cbCaitNhlZLw7rwg","pdf",705033,16,"English","# Structure of book\n## Materials and permitted equipment\n## Instructions\n## At the end of the examination\n# Questions\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n## Question 6\n## Question 7","[{\"question\":\"What equipment is allowed and what is not allowed in the exam room?\",\"answer\":\"Allowed items include pens, pencils, highlighters, erasers, sharpeners and rulers. Not permitted are any technology such as calculators or software, notes of any kind, blank sheets of paper, and correction fluid/tape.\"},{\"question\":\"How long are the reading and writing periods for this examination?\",\"answer\":\"The reading time is 15 minutes from 9:00 am to 9:15 am. The writing time is 1 hour from 9:15 am to 10:15 am.\"},{\"question\":\"What rules apply to answering questions requiring numerical answers?\",\"answer\":\"For numerical answers, an exact value must be given unless otherwise specified. Where more than one mark is available, appropriate working must be shown.\"}]","Victorian Certificate of Education 2022 - Mathematical Methods - Written Examination 1 | PDF",1789904287]