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The report reviews student performance across eight short-answer questions, highlighting strengths in clear methodology and common issues such as bracket errors, incorrect algebraic transposition, and not checking domain validity. 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This reduction was reflected directly in the examination content.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What common errors affected students’ results in the short-answer questions?",{"text":117,"@type":113},"Students often confused themselves or made arithmetic errors when doing several manipulations in one line. Particular issues included incorrect use of logarithmic laws, missing brackets in chain rule or algebraic work, and not checking solutions for validity within the allowed domain.",{"name":119,"@type":110,"acceptedAnswer":120},"What key study advice does the report give students for improving performance?",{"text":121,"@type":113},"The report urges regular review and practice of exponent and logarithmic laws, careful algebraic manipulation (including transposition of algebraic fractions), correct bracket placement, and familiarity with exact values for circular functions. It also recommends reviewing past papers and considering alternative geometric methods where appropriate.","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},315955,1790734719,{"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":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},2336478945635,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","2020 VCE Mathematical Methods 1 examination report  \nGeneral comments  \nIn 2020 the Victorian Curriculum and Assessment Authority produced an examination based on the VCE Mathematics Adjusted Study Design for 2020 only. Most of the content from the ‘Probability and statistics’area of study was removed, and this was reflected in the examination content.  \nThe examination consisted of eight short-answer questions. A range of well thought-out and presented responses were given.  \nAdvice to students:  \n• Students who produced responses that were detailed with clear and legible methodology generally scored well. It was observed that students who attempted to do several manipulations in one line of working often confused themselves or made arithmetic errors. This was particularly evident in Question 4 (solving a logarithmic equation) and in Questions 6c. and 8c. (both involving the evaluation of definite integrals) .  \n• Students are urged to regularly review and practise exponent and logarithmic laws and their application.(This is relevant to Questions 4, 5, 6c. , 8a. and 8c. )  \n• Students need to practise algebraic manipulation, especially transposition of algebraic fractions (Questions 2 and 3) and take care with placement of brackets (Questions 1, 5 and 6c. ) and notation when dealing with integrals or domains.  \n• Students need to be familiar with the required exact values for circular functions (see Question 3) .  \n• Working through past papers (available on the VCAA website), consider alternative solutions that maybe obtained using geometric methods. (See Questions 6c. , 7c. and 8d. )  \n• ‘Show that  ’ questions require a reasoned argument. Remember the answer is given and students are required to provide detailed progression to the answer given.  \nSpecific information  \nThis report provides sample answers or an indication of what answers may have included. Unless otherwise stated, these are not intended to be exemplary or complete responses.  \nThe statistics in this report may be subject to rounding resulting in a total more or less than 100 per cent.  \nQuestion 1a.  \n\n| Marks | 0 | 1 | Average |\n| --- | --- | --- | --- |\n| % | 14 | 86 | 0.9 |\n\ndydx = 2x sin ( x ) + x2 cos ( x )  \nThis question was well answered. Most students competently and confidently applied the product rule.  \nQuestion 1b.  \n\n| Marks | 0 | 1 | 2 | Average |\n| --- | --- | --- | --- | --- |\n| % | 20 | 21 | 60 | 1.4 |\n\nff ′′((x1))==e(32x −1) ex −x+3  \n2  \nStudents applied the chain rule; however, too often the lack of brackets resulted in an incorrect answer: for example, ( 2x −1) e ≠ 2x −1e  \nx2 −x+3 x2 −x+3  \nQuestion 2a.  \n\n| Marks | 0 | 1 | Average |\n| --- | --- | --- | --- |\n| % | 47 | 53 | 0.5 |\n\n2 1  \n~~ ~~ =  = 0.1 20 10  \nStudents who scored the mark for this question generally used a Venn diagram or a table. The most common incorrect answer was 4900 , obtained by incorrectly assuming that the events F (air filter change) and 􀜱 ′ (without an oil change) were independent, thus using Pr (􀜨 ∩ 􀜱 ′) = Pr (􀜨) × Pr (􀜱 ′) .  \nQuestion 2b.  \n\n| Marks | 0 | 1 | 2 | Average |\n| --- | --- | --- | --- | --- |\n| % | 31 | 39 | 30 | 1.0 |\n\nStudents who obtained both marks typically used a Venn diagram or a table such as:  \n\n|  | F | F ′ |  |\n| --- | --- | --- | --- |\n| O | 1\u003Cbr>m + n |  | m\u003Cbr>m + n |\n| O′ | 0.05 |  |  |\n|  | n\u003Cbr>m + n |  | 1 |\n\nPr ( F )− Pr( F ∩ O ) = Pr ( F ∩ O ′)  \nn 1 1  \n~~ ~~ − ~~ ~~ = ~~ ~~  \nm + n m + n 20  \n20 + ( m + n ) = 20n  \nm = 19n − 20  \nWhile many students saw the connection to part a. of the question, many did not set up the correct equation or did not correctly transpose their equation to make ‘m’ the subject. Students generally recognised the conditional probability. Many did not go further than stating a rule.  \nQuestion 3  \n\n| Marks | 0 | 1 | 2 | 3 | Average |\n| --- | --- | --- | --- | --- | --- |\n| % | 27 | 22 | 28 | 23 | 1.5 |\n\nUsing (1, 1) gives: −1 = tan ( −􀜽 + 􀜾) or − 􀰗4 = −􀜽 + 􀜾 and using 􀵫1, √3􀵯 gives √3 = 􀜽 + 􀜾 or ","cbCaiddKVYInHq8g","https://ap.wps.com/l/cbCaiddKVYInHq8g","pdf",425515,"English","# General comments\n## Advice to students\n# Specific information\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5","[{\"question\":\"What changes were made to the 2020 Mathematics Adjusted Study Design for this examination?\",\"answer\":\"The exam was produced for 2020 only, and most probability and statistics content from the study area was removed. This reduction was reflected directly in the examination content.\"},{\"question\":\"What common errors affected students’ results in the short-answer questions?\",\"answer\":\"Students often confused themselves or made arithmetic errors when doing several manipulations in one line. Particular issues included incorrect use of logarithmic laws, missing brackets in chain rule or algebraic work, and not checking solutions for validity within the allowed domain.\"},{\"question\":\"What key study advice does the report give students for improving performance?\",\"answer\":\"The report urges regular review and practice of exponent and logarithmic laws, careful algebraic manipulation (including transposition of algebraic fractions), correct bracket placement, and familiarity with exact values for circular functions. It also recommends reviewing past papers and considering alternative geometric methods where appropriate.\"}]","2020 VCE Mathematical Methods 1 Examination Report - General Comments and Student Advice | PDF",1789908422,23]