[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-620210-105":59,"doc-detail-620210-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","as-and-a-level-further-maths-content-version-11","AS and A-level Further Maths content - Version 1.1","","Sets out the complete AS and A-level Further Mathematics course of study for AQA, based on the Department for Education (DfE) framework plus the exam board’s additional choice where applicable. Specifies which content is assessed at AS under overarching themes, with AS requirements shown in bold and AS-only standard-type content assessed at A-level only. Details assessment-ready topic statements covering proof, complex numbers, matrices, determinants, eigenvalues, diagonalisation, further algebra, functions, and related series and graph work.",{"@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/as-and-a-level-further-maths-content-version-11/620210/",{"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/as-and-a-level-further-maths-content-version-11/620210.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-10-20",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is the AS Further Mathematics content for AQA organised?","Question",{"text":112,"@type":113},"The AS course includes DfE-set subject content and additional exam-board choice. Content shown in bold is AS required and represents 100% of AS content when assessed within AS overarching themes.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which topics are included under Complex numbers?",{"text":117,"@type":113},"The specification includes solving quadratic, cubic, and quartic equations with real coefficients, operations with complex numbers in x+iy form, complex conjugates, Argand diagrams, and links to De Moivre’s theorem and roots of unity.",{"name":119,"@type":110,"acceptedAnswer":120},"What matrix skills are required at A-level in this document?",{"text":121,"@type":113},"It requires adding, subtracting, and multiplying conformable matrices, using zero and identity matrices, representing linear transformations, working with determinants, inverse matrices, simultaneous equations via inverses, and eigenvalues/eigenvectors with diagonalisation.","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},620210,1793074193,{"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":24,"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":145,"preview_page_count":4},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","| AS and A-level Further Maths content\u003Cbr>Version 1.1 |\n| --- |\n| The subject content for 50% of AS and A-level Further Mathematics is set out by the Department for Education (DfE) and is common across all exam boards. The remaining 50% could be chosen by each exam board. The content set out in this document covers the complete AS and A-level course of study for AQA.\u003Cbr>Content required for AS Further Mathematics is shown in bold text. This, assessed in the context of the AS overarching themes, represents 100% of the AS content.\u003Cbr>The content in standard type is assessed at A-level only.\u003Cbr>A-level specifications in Further Mathematics must include the all of the following content in bold and standard type. This, assessed in the context of the overarching themes, represents 100% of the content. |\n| A: Proof\u003Cbr>A1\u003Cbr>Construct proofs using mathematical induction; contexts include sums of series, divisibility, and powers of matrices.\u003Cbr>B: Complex numbers\u003Cbr>B1\u003Cbr>Solve any quadratic equation with real coefficients; solve cubic or quartic equations with real coefficients (given sufficient information to deduce at least one root for cubics or at least one complex root or quadratic factor for quartics) .\u003Cbr>B2\u003Cbr>Add, subtract, multiply and divide complex numbers in the form x + iy with x andy real; understand and use the terms ‘real part’ and ‘imaginary part’.\u003Cbr>B3\u003Cbr>Understand and use the complex conjugate; know that non-real roots of polynomial equations with real coefficients occur in conjugate pairs.\u003Cbr>B4\u003Cbr>Use and interpret Argand diagrams. |\n\nAQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723) . Our registered address is AQA, Devas Street, Manchester M15 6EX.  \n1 of 22  \nB5  \nConvert between the Cartesian form and the modulus-argument form of a complex number (knowledge of radians is assumed) .  \nB6  \nMultiply and divide complex numbers in modulus-argument form (knowledge of radians and compound angle formulae is assumed) .  \nB7  \nConstruct and interpret simple loci in the Argand diagram such as z 􀀐 a  \u003C r and arg(z 􀀐 a) 􀀠 􀁔 (knowledge of radians is assumed) .  \nB8  \nUnderstand de Moivre’s theorem and use it to find multiple angle formulae and sums of series.  \nB9  \nKnow and use the definition ei􀁔 􀀠 cos 􀁔 􀀎 isin􀁔 and the form z= rei􀁔  \nB10  \nFind the n distinct nth roots of rei􀁔 for r 􀁺 0 and know that they form the vertices of a regular n-gon in the Argand diagram.  \nB11  \nUse complex roots of unity to solve geometric problems.  \nC: Matrices  \nC1  \nAdd, subtract and multiply conformable matrices; multiply a matrix by a scalar.  \nC2  \nUnderstand and use zero and identity matrices.  \nC3  \nUse matrices to represent linear transformations in 2D; successive transformations; single transformations in 3D (3D transformations confined to reflection in one of x = 0, y = 0, z = 0 or rotation about one of the coordinate axes) (knowledge of 3D vectors is assumed) .  \nC4  \nFind invariant points and lines for a linear transformation.  \nAQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723) . Our registered address is AQA, Devas Street, Manchester M15 6EX.  \n2 of 22  \nC5  \nCalculate determinants of 2×2 matrices and 3× 3 matrices and interpret as scale factors, including the effect on orientation.  \nC6  \nUnderstand and use singular and non-singular matrices; properties of inverse matrices. Calculate and use the inverse of non-singular 2×2 matrices and 3× 3 matrices.  \nC7  \nSolve three linear simultaneous equations in three variables by use of the inverse matrix.  \nC8  \nInterpret geometrically the solution and failure of solution of three simultaneous linear equations.  \nC9  \nFactorisation of determinants using row and column operations.  \nC10  \nFind eigenvalues and eigenvectors of 2× 2 and 3× 3 matrices.  \nFind and use the characteristic equation.  \nUnder","cbCaictqvahlxcZf","https://ap.wps.com/l/cbCaictqvahlxcZf","pdf",147155,22,"English","# Proof\n## Complex numbers\n# Matrices\n## Further algebra and functions","[{\"question\":\"How is the AS Further Mathematics content for AQA organised?\",\"answer\":\"The AS course includes DfE-set subject content and additional exam-board choice. Content shown in bold is AS required and represents 100% of AS content when assessed within AS overarching themes.\"},{\"question\":\"Which topics are included under Complex numbers?\",\"answer\":\"The specification includes solving quadratic, cubic, and quartic equations with real coefficients, operations with complex numbers in x+iy form, complex conjugates, Argand diagrams, and links to De Moivre’s theorem and roots of unity.\"},{\"question\":\"What matrix skills are required at A-level in this document?\",\"answer\":\"It requires adding, subtracting, and multiplying conformable matrices, using zero and identity matrices, representing linear transformations, working with determinants, inverse matrices, simultaneous equations via inverses, and eigenvalues/eigenvectors with diagonalisation.\"}]","AS and A-level Further Maths content - Version 1.1 | PDF",1792463824,55]