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They may not be otherwise reproduced or distributed. The copyright of Neap Trial Exams remains with Neap. No Neap Trial Exam or any part thereof is to be issued or passed on by any person to any party inclusive of other schools, non-practising teachers, coaching colleges, tutors, parents, students, publishing agencies or websites without the express written consent of Neap.  \nCopyright © 2019 Neap ABN 49910906643 58 Pelham St Carlton VIC 3053 Tel: (03) 9639 4318 Fax: (03) 8610 0090 MMU34EX1 _QA_2019.FM  \nInstructions  \nAnswer all questions in the spaces provided.  \nIn all questions where a numerical answer is required, an exact value must be given, unless otherwise specified.  \nIn questions where more than one mark is available, appropriate working must be shown. Unless otherwise indicated, the diagrams in this booklet are not drawn to scale.  \nQuestion 1 (4 marks)  \na. Let y = 􀀋3loge􀀋x􀀌􀀌 2 . dy  \nFind -----dx.  \n1 mark  \n\n|  |\n| --- |\n|  |\n|  |\n\nb. Let f􀀋x􀀌 = ---􀀋--2- .  \nx Find f 􀁣 2----  .  \n3 marks  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n\nQuestion 2 (4 marks)  \nLet f 􀁣􀀋x􀀌 = 1 + -2-- .  \ne  \na. Given f􀀋0􀀌 = 4, find the rule for f􀀋x􀀌 .  \n2 marks  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n\nb. Find the equation of the tangent to y = f􀀋x􀀌 at the y-intercept. 2 marks  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n\nQuestion 3 (2 marks)  \nSolve tan2 􀀋2x􀀌 – 1 = 0 for x, where x 􀂏 􀀾0􀀏 􀁓 􀁀 .  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n\nQuestion 4 (5 marks)  \na. Solve the equation 5 – 2loge􀀋x􀀌 = loge􀀋 x 􀀌 for x. 2 marks  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n\nb. Find the value(s) of k for which the equation 5x = 125k – x2 has no solutions for x. 3 marks  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n\nQuestion 5 (6 marks)  \nLet f : 􀀋–2􀀏 4 􀁀 􀁯 R􀀏 f􀀋x􀀌 = 4 – x – 1.  \na. Sketch the graph of on the axes below. Label the axis intercepts and endpoints with their coordinates.  \ny = f􀀋x􀀌  \n\n|  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  | O |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |\n\n\n|  | 21.51 0.5\u003Cbr>|  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| –2 | –1 | –0.5\u003Cbr>–1\u003Cbr>–1.5 |  | 1 | 2 | 3 | 4 |\n\nx  \ny  \nb. Find the area bounded by the graph of y = f􀀋x􀀌 , the x-axis and the y-axis.  \n3 m","cbCaik2yHk4xFmMl","https://ap.wps.com/l/cbCaik2yHk4xFmMl","pdf",198073,"English","# Structure of booklet\n# Instructions\n## Answering rules and allowed items\n# Questions 1-8","[{\"question\":\"What are the allowed and prohibited items for the trial examination?\",\"answer\":\"Allowed items include pens, pencils, highlighters, erasers, sharpeners and rulers. Prohibited items include any technology such as calculators or software, notes of any kind, blank sheets of paper, correction fluid/tape, and mobile phones or other unauthorised electronic devices.\"},{\"question\":\"What rules apply to answering the questions?\",\"answer\":\"Write your name and teacher’s name in the spaces provided. Answer all questions in the provided spaces, give exact values for numerical answers when required, and show appropriate working when more than one mark is available. Responses must be in English.\"},{\"question\":\"What topics are covered across the 8 questions?\",\"answer\":\"The exam covers logarithmic differentiation, function rules and tangents, solving trigonometric and logarithmic equations, sketching a function and finding a bounded area, probability density functions (including finding parameters, mean, and derived density mean), probability with complements and independence, and analysis of a hyperbola graph.\"}]","VCE Mathematical Methods Units 3-4 - Written Examination 1 - Trial Examination 2019 | PDF",1789903772,23]