[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-207500-105":59,"doc-detail-207500-en":124},{"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":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","gcse-further-mathematics-unit-1-with-calculator-pure-mathematics-mv18-paper","GCSE Further Mathematics - Unit 1 (With calculator) Pure Mathematics - MV18 Paper","","GCSE Further Mathematics 2022 Unit 1 Pure Mathematics (with calculator) paper MV18, for the morning session on 1 June. Instructions cover recording centre and candidate numbers, answering all thirteen questions in the provided spaces using black ink, and showing all working. The paper includes a formula sheet covering quadratic equations, differentiation, integration, logarithms, and matrices, followed by problems on derivatives, integration, matrix operations, solving matrix equations, sketching and solving trigonometric equations.",{"@graph":69,"@context":116},[70,84,99],{"@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/gcse-further-mathematics-unit-1-with-calculator-pure-mathematics-mv18-paper/207500/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Emma Wilson","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What are the required instructions for completing this paper?","Question",{"text":106,"@type":107},"Write centre and candidate numbers in the spaces provided, answer all questions in the given spaces using black ink, and show all working clearly. Rounding is to 2 decimal places unless stated otherwise, and partial credit may be awarded for partially correct solutions.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"What formula topics are provided on the formula sheet?",{"text":111,"@type":107},"The formula sheet covers quadratic equations, differentiation for y=ax^n, integration of ax^n, logarithm rules, and matrix determinant and inverse relationships.",{"name":113,"@type":104,"acceptedAnswer":114},"What types of questions appear in the paper?",{"text":115,"@type":107},"The questions include finding derivatives and integrals, performing matrix operations such as B+C and AB, solving for a matrix X in equations like LX=M, sketching y=sin x over a specified interval, and solving trigonometric equations.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},207500,1788599787,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":133,"language":134,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":67,"update_tm":123,"read_time":138},3848291630094,"https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Centre Number  \n\n|  |  |  |  |  |\n| --- | --- | --- | --- | --- |\n\nGeneral Certificate of Secondary Education 2022  \nCandidate Number  \n\n|  |  |  |  |\n| --- | --- | --- | --- |\n\nFurther Mathematics  \nUnit 1 (With calculator) Pure Mathematics  \n[GFM11]  \nWEDNESDAY 1 JUNE, MORNING  \nMV18  \nTime  \n2 hours, plus your additional time allowance.  \nInstructions to Candidates  \nWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.  \nYou must answer the questions in the spaces provided.  \nComplete in black ink only.  \nAll working must be clearly shown in the spaces provided. Marks may be awarded for partially correct solutions.  \nWhere rounding is necessary give answers correct to 2 decimal places unless stated otherwise.  \nAnswer all thirteen questions.  \nInformation for Candidates  \nThe total mark for this paper is 100.  \nFigures in brackets printed at the end of each question indicate the marks awarded to each question or part question.  \nYou may use a calculator.  \nThe Formula Sheet is on page 2.  \nFormula Sheet  \nPure Mathematics  \nQuadratic equations: If ax2 + bx + c = 0 (a Þ 0)  \nthen x = –b~~ ~~rb22a–~~ ~~4ac~~ ~~  \nDifferentiation: If y = axn then ~~ d~~y~~d~~x~~ ~~ = nax n–1  \nIntegration: 􀂜 axn dx = ~~ ~~axnn􀀎1~~ ~~ + c (n Þ –1)  \nLogarithms: If ax = n then x = logan  \nlog (ab ) = log a + log b  \nlog e ~~ ~~ab~~ ~~ e = log a – log b  \nlog an = n log a  \nMatrices: If A = 3ac bd4  \nthen det A = ad – bc  \nand A–1 = ad–1~~ ~~bc 3–d –bc a4  \n(ad – bc Þ 0)  \n13063.02 MV18 2  \nBlank Page  \n(Questions start overleaf)  \n13063.02 MV18  \n3  \n[Turn over  \n1 Find ~~ d~~y~~d~~x~~ ~~ if y = 8x4 + ~~5~~4x2 + 3 [3 marks]  \nAnswer    \n13063.02 MV18 4  \n2 Find ∫ f 2x4– 1x3~~ ~~ +1p dx [4 marks]  \nAnswer    \n13063.02 MV18  \n5  \n[Turn over  \n3 (a) Matrices A, B and C are defined by  \nA = –11 34 , B = –21 12 14 and C = ––42 Calculate  \n(i) B + C [2 marks]  \n1  \n–2  \n–7R  \n0  \nAnswer    \n(ii) AB [2 marks]  \nAnswer    \n13063.02 MV18  \n7  \n[Turn over  \n(b) Matrices L and M are defined by  \nL = –51 ––34 and M = 25 –63  \nFind the matrix X such that LX = M. [4 marks]  \nAnswer    \n13063.02 MV18 8  \n4 (a) Sketch the graph of y = sin x for –360° \u003C x \u003C 0 ° on the axes below. [1 mark]  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | y |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n13063.02 MV18  \n9  \n[Turn over  \n(b) (i) Solve the equation  \n5 sin x – 4 = 0  \nfor –360° \u003C x \u003C 0 ° [3 marks]  \nAnswer","cbCaipkdHfst78Od","https://ap.wps.com/l/cbCaipkdHfst78Od","pdf",448098,44,"English","# Instructions to Candidates\n# Formula Sheet\n## Pure Mathematics\n# Questions\n## Differentiation and Integration\n## Matrices\n## Graphs and Trigonometry","[{\"question\":\"What are the required instructions for completing this paper?\",\"answer\":\"Write centre and candidate numbers in the spaces provided, answer all questions in the given spaces using black ink, and show all working clearly. Rounding is to 2 decimal places unless stated otherwise, and partial credit may be awarded for partially correct solutions.\"},{\"question\":\"What formula topics are provided on the formula sheet?\",\"answer\":\"The formula sheet covers quadratic equations, differentiation for y=ax^n, integration of ax^n, logarithm rules, and matrix determinant and inverse relationships.\"},{\"question\":\"What types of questions appear in the paper?\",\"answer\":\"The questions include finding derivatives and integrals, performing matrix operations such as B+C and AB, solving for a matrix X in equations like LX=M, sketching y=sin x over a specified interval, and solving trigonometric equations.\"}]","GCSE Further Mathematics - Unit 1 (With calculator) Pure Mathematics - MV18 Paper | PDF",111]