math assessment 2015

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The solution must be step by step and own work (no plagiarism ) with Harvard reference only .

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Assignment Brief 2014/15 Assignment Details This assignment is a series of five mathematical/computational questions, some requiring more than one computation and not all of equal value. The 100 marks for this assignment have been divided up amongst the series of problems. The marks for each problem are shown in square brackets at the end of the question. Attempt all five problems • • You must demonstrate that you have met the learning outcomes below As you construct and present your work, consider the assessment criteria Learning outcomes From the module descriptor the “indicative” assessment criteria were used to produce this test for you. It was also considered to focus on materials to be learned in the first block of teaching. The practice you gain with this assignment should help you to prepare for the way problems are written and marked in the final exam. The learning outcomes being tested here are: 1,2,3 o Apply Transforms to solve differential equations for engineering problems o Apply Linear programming and Markov modelling techniques to the solution of complex engineering problems o Critically evaluate probabilistic analysis techniques. These outcomes may be further assessed in the final exam, along with the remaining outcomes not tested here. Be assured you will be tested on everything. The deadline for submission is 4.00pm on the 3rd Feb 2015 Every attempt will be made to ensure that the work will be marked and available for collection by 24th Feb 2015. The assignment is worth 40% of the total module assessment. 1 Assessment Criteria For more information please see the marking guide at Appendix 1 • • Submission Your work must be submitted with: a front cover sheet (detailing the module code and title, coursework title, module name and student name, word count, date submitted). a firmly attached and fully completed School Assessment Cover Sheet. These are available from JBF203. It should not be submitted in folders, plastic wallets or paper clipped The assignment should be submitted: electronically to turn-it-in before the deadline using the link on the module area on blackboard Presentation Instructions The word limit is 2500 words (+/-10%). This excludes footnotes but includes quotations and appendices. Remember: You must keep to the word limit of 2500 words It is your responsibility to ensure that your work is neatly and accurately presented. • • • • • • • • • • The work must be: Word-processed Single sided 1.5 or double line spaced Times New Roman or Ariel 12 point font Justified Page numbered On A4 paper Margins left and right 3cm Stapled together at the top left-hand corner Attached to a cover sheet. Marks may be deducted for failure to follow these instructions. Please look at the Student Guide to Assessment for more information. Referencing All academic writing must be referenced. If you use other people’s ideas without referencing them you are plagiarising their work. Use either the Numeric or Havard system of referencing within your text. 2 1 Solve the following initial value problems (IVP) using the Laplace transform method. (i) d2y dy −9 +3=0, 2 dt dt y(0) = 1 , dy (0) = 1 dt (equation 1) [12 marks for this part] (ii) −2 T (0) = 2 dT = 10 − 4T , dt (equation 2) [8 marks for this part] [Total 20 marks for this question] 2 Your exam could be marked with a range of possible grades, simplified as on the following state diagram: Fail 0.5 0.6 Acceptible Acceptable 0.1 Standard 0.5 0.1 Genius 0.8 0.1 To begin with the chances are that you will pass with a standard result. Each 45 minutes (the time allocated for each answer) your grade could go up or down to a neighbouring grade or stay put. There is a chance that your Genius is so great that the examiner cannot appreciate what you are saying and incorrectly marks it as nonsense. What is your grade most likely to be after the 3 hour exam? What (if any) are the steady state results for a group of 14 students? [10 marks] [10 marks] [Total 20 marks for this question] 3 3 The Cannon Hill furniture Company produces tables and chairs. Each table takes five hours of labor from the carpentry department and three hours of labor from the finishing department. Each chair requires three hours of carpentry and two hours of finishing. During the current week, 230 hours of carpentry time are available and 90 hours of finishing time. Each table produced gives a profit of £85 and each chair a profit of £55. How many chairs and tables should be made? [Total 20 marks for this question] 4 A very new European “Rapid Reaction Force for Fire” has been created today and begins operation between three Countries “A”, “B” and “C”. It’s main resource is a super aircraft “Funderbird2” with a massive water cannon that even carries a small mini-submarine for fighting fires at sea. Unfortunately, it can only be in one Country at a time. A 0.1 0.1 0.4 B 0.3 C What is the matrix representation of this problem? [5 marks] The probabilities of going to a fire in another Country, given that the force are in a given Country to begin with, are shown on the sketch above (any resemblance to any particular Country or Nation is purely coincidence and not intended). The probabilities were obtained as a weekly average using statistics for fires over many recorded weeks. When will the plane take up permanent residence in one Country? [15 marks] [Total 20 marks for this question] 4 5 0.1 A 0.5 0.1 0.3 B C 0.05 Figure 3. State diagram for Question 3. For the state diagram shown on Figure 3 the initial state is ‘C’ and the time steps are days. Find the following: i) Find the stochastic transitional probability matrix [5 marks for this part] ii) Find the probability of being in state ‘C’ after two time steps [5 marks for this part] iii) What is the steady state probability of being in state ‘A’? [8 marks for this part] iv) What is the steady state probability of being in either state ‘B’ OR state ‘C’? [2 marks for this part] [Total 20 marks for this question] 5 Plagiarism The use of work produced for another purpose by you, working alone or with others, must be acknowledged. Copying from the works of another person (including Internet sources) constitutes plagiarism, which is an offence within the University’s regulations. Brief quotations from the published or unpublished works of another person, suitably attributed, are acceptable. You must always use your own words except when using properly referenced quotations. You are advised when taking notes from books or other sources to make notes in your own words, in a selective and critical way. General Criteria In grading your work we will be assessing the extent to which it matches the criteria attached. The criteria are not of equal importance, but it is not possible to ascribe an exact weighting to each. What follows is intended as a general guide to the standards. 1. Severe weakness in understanding the issues/arguments/theory is likely to result in a mark of less than 40%. 2. Thorough coverage of the relevant material, with statements supported by data, evidence, literature or examples, is necessary to gain 52% or above. 3. Work which is disorganised with points randomly ordered is unlikely to gain more than 48%. 4. A logical, well-explained argument, combined with other good characteristics is usually necessary to obtain 75%. 5. Fluent grammatical expression is important for expressing ideas clearly. Errors in this area are likely to lead to a reduction in marks. 6 Grade 70 – 100% Relevance 20% Directly relevant to title. Able to address the implications, assumptions and nuances of the title. Relevance thoroughly addressed. 60-69% to practice is and explicitly Directly relevant to title. Is able to demonstrate effective practice relevance. 50-59% Generally addresses the title, sometimes addresses irrelevant issues. Knowledge 20% Makes effective use of a comprehensive range of theory and practice knowledge. Demonstrates ability in the manipulation and transfer of subject material to demonstrate a solid understanding of the issues in both theory and practice. Makes effective use of good theory and practice knowledge. Manipulates and transfers some material to demonstrate a clear grasp of the themes, questions and issues in theory and practice. Adequate knowledge of a fair range of relevant theoretical and practice related material with evidence of an appreciation of its significance. Relevance to practice effectively addressed, may be implicit in places. 41-49% Some degree of irrelevance to the title. Superficial consideration of the issues. 40% Relevance to practice tends towards superficiality and is largely implicit. Some degree of irrelevance to the title is common. Adequate knowledge of a limited range of relevant theoretical and practice related material with intermittent evidence of an appreciation of its significance. Basic understanding of a limited range of relevant theoretical and practice related material. Only the most obvious issues are addressed at a superficial level and in unchallenging terms. 0-39% Relevance to practice is superficially addressed and rarely made explicit Relevance to the title is intermittent or missing. The topic is reduced to its vaguest and least challenging terms. Relevance to practice is barely considered or not at all. Analysis 15% A comprehensive analysis of the material resulting in clear and illuminating conclusions. Argument & Structure 20% Coherent and logically structured, making creative use of an appropriate mode of argument and/or theoretical model. Originality 15% Distinctive work showing independent thought and critical engagement with alternative views. Generally coherent logically constructed. Contains some distinctive independent thinking. or Well written with standard spelling and syntax. Uses an appropriate mode of argument or theoretical model. Beginning to formulate independent position an Style is lucid utilising an appropriate format and bibliographical apparatus. Adequate analytical treatment, with occasional descriptive or narrative passages which lack clear analytical purpose. Adequate attempt to construct a coherent argument, but may suffer loss of focus and consistency. Sound work which expresses a personal position, often in broad terms and tends towards uncritical conformity to one or more standard views of the topic. Competently written with only minor lapses from standard spelling and syntax. Conclusions are clear. Issues at stake may lack clarity or theoretical models couched in simplistic terms. Some attempt to construct an argument is evident but it lacks sufficient clarity and coherence. Largely derivative. Attempts to present a personal view, but only in broad terms. Generally competent writing although intermittent lapses from standard syntax and spelling and pose occasional obstacles for the reader. Issues at stake vaguely stated. Is largely uncritical and conforms to one or more standard views. Format and bibliography is generally error free and acceptable. A basic argument is evident but tends to be supported by assertion and lacks proper development. Largely derivative. Style of presentation makes reading difficult. Coherence and clarity are evident only intermittently Wholly uncritical and conforming to one or more standard views. Little evidence of coherent argument. Almost wholly derivative. Good analysis of the material resulting in clear and logical conclusions. Evidence of analytical ability. Intermittent passages of descriptive or narrative material which lack clear analytical purpose. Conclusions are not always clear and logical. Largely descriptive or narrative in style with limited evidence of analytical capability. Conclusions are not always clear or logical A limited understanding of a narrow range of relevant theoretical and practice related material or a lack of basic knowledge in either or both theory and practice necessary for an understanding of the topic Heavy dependence description and/or narrative. on Paraphrase is common. Evidence of analysis is lacking. are and only There is a lack of development and the work may be repetitive and/or thin. Style is lucid and resourceful with an appropriate bibliographical apparatus. No personal view is adequately formulated The writer’s contribution rarely goes beyond simplifying paraphrase. No evidence of personal thought. Clear and logical conclusions are sparse 1 Presentation 10% A very well written answer with standard spelling and syntax. Style is readable with acceptable format and bibliographical status. Deficiencies in spelling, syntax, format or bibliographical apparatus impact significantly upon clarity. Poorly written with numerous deficiencies in syntax, spelling, expression and presentation. The writer may achieve clarity (if at all) only by using simplistic or repetitious style. ...
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Robert__F (42786)
Boston College

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