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It describes graphical representations of functions, including domain, range, intercepts, stationary points, asymptotic behaviour, symmetry, and inverse functions. It also specifies algebra of polynomial functions, transformations, parameterized families, and methods for solving polynomial and simultaneous equations. Additional coverage includes constant and instantaneous rate of change, interpreting empirical data graphs, and foundational probability with sample spaces, events, random variables, simulation, and counting principles.",{"@graph":69,"@context":123},[70,84,106],{"@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/vce-mathematical-methods-study-design-units-1-and-2-2023-2027/315895/",{"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/vce-mathematical-methods-study-design-units-1-and-2-2023-2027/315895.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are included in Unit 1 Area of Study 1?","Question",{"text":113,"@type":114},"Students study graphical representations of simple algebraic functions of a single real variable and the key features of those graphs, including intercepts, domain/codomain/range, stationary points, asymptotic behaviour, and symmetry.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does Unit 1 Area of Study 2 focus on?",{"text":118,"@type":114},"It focuses on algebra of low-degree polynomial functions and transformations of the plane, including symbolic notation, simplifying expressions, interpreting graph features, graphing power and polynomial functions, and solving polynomial equations and systems.",{"name":120,"@type":111,"acceptedAnswer":121},"What probability and statistics concepts are covered in Unit 1 Area of Study 4?",{"text":122,"@type":114},"Students cover experiments, outcomes, events, frequencies, probability, sample spaces, representations such as Venn diagrams and tables, counting principles, combinations (nCr), and probability techniques including simulation with random generators.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},315895,1790008823,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":105,"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},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","VCE Mathematical Methods Study Design  \nUnits 1 and 2  \n2023-2027  \nUnit 1  \nUnit 1-Area of Study 1  \nFunctions, relations and graphs  \nIn this area of study students cover the graphical representation of simple algebraic functions (polynomial and power functions) of a single real variable and the key features of functions and their graphs such as axis intercepts, domain (includingthe concept of maximal, natural or implied domain), co-domain and range, stationary points, asymptotic behaviour and symmetry. The behaviour of functions and their graphs is to be explored in a variety of modelling contexts and theoretical investigations.  \nThis area of study includes:  \n• functions and function notation, domain, codomain and range, representation of a function by rule, graph and table, inverse functions and their graphs  \nUnit 1-Area of Study 2  \nAlgebra, number and structure  \nThis area of study supports students’work in the‘Functions, relations and graphs’, ‘Calculus’ and‘Data analysis, probability and statistics’ areas of study, and content is to be distributed between Units 1 and 2.  \nIn Unit 1 the focus is on the algebra of polynomial functions of low degree and transformations of the plane.  \nThis area of study includes:  \n• use of symbolic notation to develop algebraic expressions and represent functions, relations, equations, and systems of simultaneous equations  \n• substitution into, and manipulation of, these expressions  \n• recognition of equivalent expressions and simplification of algebraic expressions involving different forms of polynomial and power functions, the use of distributive and exponent laws applied to these functions, and manipulation from one form of expression to an equivalent form  \n• qualitative interpretation of features of graphs of functions, including those of real data not explicitly represented by a rule, with approximate location of any intercepts, stationary points and points of inflection  \n• graphs of power functions f (x) = xn for n􀂏 􀁞−2,−1, ~~1~~3 , ~~1~~2 ,1, 2, 3, 4􀁠 , and transformations of these graphs  \nto the form 􀝕 = 􀜽 (􀝔 + 􀜾)􀯡 + 􀜿 where a, b, c􀂏 R and a 􀁺 0  \n• graphs of polynomial functions of low degree, and interpretation of key features of these graph  \n• use of parameters to represent families of functions and determination of rules of simple functions and relations from given information  \n• transformations of the plane and application to basic functions and relations by simple combinations of dilations (students should be familiar with both ‘parallel to an axis’ and ‘from an axis’ descriptions), reflections in an axis and translations (matrix representation may be used but is not required)  \n• the connection between the roots of a polynomial function, its factors and the horizontal axis intercepts of its graph, includingthe remainder, factor and rational root theorems  \n• solution of polynomial equations of low degree, numerically, graphically and algebraically, including numerical approximation of roots of simple polynomial functions using the bisection method algorithm  \n• solution of a set of simultaneous linear equations (geometric interpretation only required for two variables) and equations of the form f (x) = g (x) numerically, graphically and algebraically.  \nUnit 1-Area of Study 3  \nCalculus  \nIn this area of study students cover constant and average rates of change and an introduction to instantaneous rate of change of a function in familiar contexts, including graphical and numerical approaches to estimating and approximating these rates of change.  \nThis area of study includes:  \n• average and instantaneous rates of change in a variety of practical contexts and informal treatment of instantaneous rate of change as a limiting case of the average rate of change  \n• interpretation of graphs of empirical data with respect to rate of change such as temperature or  \npollution levels over time, motion graphs and the height of water in containers of different shapes that ","cbCaiiA7uWTyW32L","https://ap.wps.com/l/cbCaiiA7uWTyW32L","pdf",192375,"English","# Unit 1\n## Area of Study 1: Functions, relations and graphs\n## Area of Study 2: Algebra, number and structure\n## Area of Study 3: Calculus\n## Area of Study 4: Data analysis, probability and statistics\n## Unit 1 - Outcome 1: Key knowledge","[{\"question\":\"What topics are included in Unit 1 Area of Study 1?\",\"answer\":\"Students study graphical representations of simple algebraic functions of a single real variable and the key features of those graphs, including intercepts, domain/codomain/range, stationary points, asymptotic behaviour, and symmetry.\"},{\"question\":\"What does Unit 1 Area of Study 2 focus on?\",\"answer\":\"It focuses on algebra of low-degree polynomial functions and transformations of the plane, including symbolic notation, simplifying expressions, interpreting graph features, graphing power and polynomial functions, and solving polynomial equations and systems.\"},{\"question\":\"What probability and statistics concepts are covered in Unit 1 Area of Study 4?\",\"answer\":\"Students cover experiments, outcomes, events, frequencies, probability, sample spaces, representations such as Venn diagrams and tables, counting principles, combinations (nCr), and probability techniques including simulation with random generators.\"}]","VCE Mathematical Methods Study Design - Units 1 and 2 - 2023-2027 | PDF",1789907804,28]