[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-315371-105":59,"doc-detail-315371-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","mathematical-methods-unit-1-study-of-simple-elementary-functions","Mathematical Methods - Unit 1 - Study of simple elementary functions","","Mathematical Methods Unit 1 provides an introductory study of simple elementary functions of a single real variable, combining algebraic functions, calculus ideas, and the foundations for probability and statistics. It develops balanced and progressive skills across functions and graphs, algebra, calculus, and probability and statistics, with connections carried consistently from Units 1 and 2. Students apply rational and real arithmetic, equations and graphs, differentiation with and without technology, and interpret graph features in modelling and theoretical investigations.",{"@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/mathematical-methods-unit-1-study-of-simple-elementary-functions/315371/",{"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/mathematical-methods-unit-1-study-of-simple-elementary-functions/315371.png","ImageObject",300,407,{"name":92,"@type":93},"Skyler","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What skills are students expected to apply in Unit 1?","Question",{"text":112,"@type":113},"Students apply techniques involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, and differentiation with and without technology.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What topics are covered under Functions and graphs in Unit 1?",{"text":117,"@type":113},"Students study graphical representation of simple algebraic functions, key graph features (intercepts, domain, range, stationary points, asymptotic behaviour, symmetry), and uses such as the vertical line test and modelling interpretations.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the Algebra area of study relate to other parts of the course?",{"text":121,"@type":113},"Algebra supports work in Functions and graphs, Calculus, and Probability and statistics, with content distributed between Units 1 and 2, focusing in Unit 1 on low-degree polynomial functions and transformations.","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},315371,1789904611,{"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":52,"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":129,"read_time":144,"preview_page_count":4},2336464648746,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Mathematical Methods Unit 1  \nMathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions of a single real variable, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts. They are designed as preparation for Mathematical Methods Units 3 and 4 and contain assumed knowledge and skills for these units. The focus of Unit 1 is the study of simple algebraic functions, and the areas of study are ‘Functions and graphs’, ‘Algebra’, ‘Calculus’ and ‘Probability and statistics’. At the end of Unit 1, students are expected to have covered the content outlined in each area of study, with the exception of ‘Algebra’which extends across Units 1 and 2. This content should be presented so that there is a balanced and progressive development of skills and knowledge from each of the four areas of study with connections between and across the areas of study being developed consistently throughout both Units 1 and 2.  \nIn undertaking this unit, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs and differentiation with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout the unit as applicable.  \nArea of Study 1  \nFunctions 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 (including the 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 explored in a variety of modelling contextsand theoretical investigations.  \nThis area of study includes: s review of coordinate geometry  \ns functions and function notation, domain, co-domain and range, representation of a function by rule, graph and table  \ns use of the vertical line test to determine whether a relation is a function or not, including examples of relations that are not functions and their graphs such as x = k, x = ay2 and circles in the form (x – h)2 + (y – k)2 = r2  \ns qualitative interpretation of features of graphs of functions, including those of real data not explicitly represented by a rule, with approximate location of stationary points  \ns graphs of power functions f(x) = xn for n ∈ N and n ∈ {–2 ,–1 , 13 , 12 }, and transformations of these graphs to the formy = a(x + b)n + c where a, b, c ∈ R and a ≠ 0  \ns graphs of polynomial functions to degree 4 and other polynomials of higher degree such as g(x) = (x + 2)2(x – 1)3 + 10  \ns graphs of inverse functions.  \nUpdated June 2015  \nArea of Study 2  \nAlgebra  \nThis area of study supports students’ work in the ‘Functions and graphs’,‘Calculus’ and ‘Probability and statistics’areas of study, and content is to be distributed between Units 1 and 2. In Unit 1 the focus is on the algebra of polynomial functions of low degree and transformations of the plane.  \nThis area of study includes:  \ns use of symbolic notation to develop algebraic expressions and represent functions, relations, equations and systems of simultaneous equations  \ns substitution into and manipulation of these expressions  \ns 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 for","cbCaisknx1pVUnSe","https://ap.wps.com/l/cbCaisknx1pVUnSe","pdf",150710,11,"English","# Unit Overview\n## Functions and graphs\n## Algebra\n## Calculus","[{\"question\":\"What skills are students expected to apply in Unit 1?\",\"answer\":\"Students apply techniques involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, and differentiation with and without technology.\"},{\"question\":\"What topics are covered under Functions and graphs in Unit 1?\",\"answer\":\"Students study graphical representation of simple algebraic functions, key graph features (intercepts, domain, range, stationary points, asymptotic behaviour, symmetry), and uses such as the vertical line test and modelling interpretations.\"},{\"question\":\"How does the Algebra area of study relate to other parts of the course?\",\"answer\":\"Algebra supports work in Functions and graphs, Calculus, and Probability and statistics, with content distributed between Units 1 and 2, focusing in Unit 1 on low-degree polynomial functions and transformations.\"}]","Mathematical Methods - Unit 1 - Study of simple elementary functions | PDF",28]