math assessment 2015

  

20141222012212fv3102_assignment_brief_2014_15_1_.docxThe 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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