LJMU Algebra Worksheet

INTERNATIONAL FOUNDATION YEAR ENGINEERING AND COMPUTINGAssessment Brief
PURE MATHS 1 – 3510IFESG
Cohort: January, 2022
Due Date: 1st April 2022
Submission Requirement: Document containing evidence of planning
(submitted through Turnitin on Canvas) and timed VLE test (Möbius).
Assessment Details and Instructions:
• You will be required to attempt a timed Möbius test, which will be worth 90% of the
grade for this assessment.
• The duration of the Möbius test is 2 hours.
• There will be only 1 attempt at the Möbius test. You will have the “How did I do?”
feature enabled during the test, allowing you to see whether your response to a
particular question is correct before submitting the assignment.
• The other 10% is weighted towards a plan and research-type task.
• Five brief summaries of different scenarios are given in this assessment brief. You
will be expected to apply some of the mathematical techniques and operations you
have learnt in Pure Maths 1 to these scenarios.
• In order to prepare for this test, you need to research into potential ways to model the
problems. This research will then be collated within a word-processed document and
will be submitted on the same day as the Möbius test, using the Turnitin assignment
handler on Canvas.
• To take the Möbius test you must attend a Zoom meeting, where the invigilator will
grant you access to the test. You must remain in the Zoom meeting until you have
completed your attempt.
• An announcement will be made in the Pure Maths 1 module on Canvas detailing the
Zoom meeting and the specific time of the test. A register will be taken to ensure that
you have attended the Zoom meeting.
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• Once registered, an invigilator will remotely authorise you to access the assignment.
• Mobile phones are not permitted in the test.
• Any communication, via any means, between yourself and other students, is not
permitted.
• The test is open-book, meaning that you can take whatever notes and paper-based
resources into the test that you may find useful.
• Internet access will also be available.
• It should be noted that this is a timed assessment and constantly browsing the
internet and looking through notes will take up valuable time.
• If you have not done so already, please familiarise yourself with the Möbius enviroment.
A number of homeworks have been released over the duration of this semester that
will enable you to do this.
Scenario 1: Golf Ball Trajectory
The trajectory of a golf ball is described by a quadratic polynomial function. The
function will describe the height of the golf ball with respect to time.
– Determine the function which describes the average velocity of the golf ball.
– Using the average gradient function, approximate the instantaneous velocity of
the golf ball for a given time.
– Find the best approximation for the velocity at a given time.
Scenario 2: Modelling a Person Running
A person is running up and down a straight hallway. The person’s position, s, is
described in terms of t time. The function that describes the position is a fifth
order polynomial. Find a function that determines the instantaneous velocity and
acceleration. Determine the points at which the person is stationary.
Scenario 3: Vehicle Dynamics
Two cars are in a race and you are to model the dynamics of these vehicles. Firstly,
you will be given two quartic polynomial descriptions allowing you to model the
distance at any point (as a function of time). Using these equations you will need
to determine:
– an equation which describes the velocity of each car;
– an equation which describes the acceleration of each car;
– at what times the cars are stationary;
– the maximum velocity of each car within the allotted time;
– find the total distance covered by each vehicle within the allotted time.
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After this analysis has been performed, you find that a third car has actually entered
the race and you are to analyse the performance of this vehicle also. For the third
car, you are not given any function but instead presented with a velocity versus time
graph. Based on this plotted function, you are to find the quadratic equation that
describes the velocity of the third car (the intercept(s) with each axis will be clearly
presented). For the same time period that was used to analyse cars 1 and 2, you
shall also determine the total distance travelled by the third car.
Scenario 4: Maximising Component Volume
The diagram below shows a solid engineering component which consists of a solid
cylinder of length L and radius r, together with a right circular cone with semi-vertical
angle θ.
The component is to be manufactured so as to have maximum volume (for a given
surface area and angle).
Scenario 5: The Corridor Problem
The diagram below shows a right-angled corridor. The width of the top corridor is G
units wide and the side corridor is A units wide. It is required to determine the longest
ladder, represented by the line LM, that can be carried around the corner, as shown.
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Specification for the Planning document
• The planning document should be no more than 5 pages long.
• Carefully read the scenario descriptions. Certain keywords and phrases should give
away certain aspects of the mathematics that will be asked about.
• The plan should be split up into sections, one for each of the scenarios.
• Each section should contain an example of the mathematics that you predict will
appear in the test.
• A clear and brief description of the maths shown should be presented (in your own
words).
• Do not quote sections of text from other sources. You will recieve a lower mark for
this component if examples of this is contained within your planning document.
• Diagrams are welcomed, but not compulsory.
• It is advised to convert your word-processed document into pdf format, before submitting
to Turnitin, in order to overcome any issues with conversion.
Assessment Criteria and Marking Scheme:
• The planning document is worth 10% of the overall mark for this assignment.
• The timed Möbius test will be marked out of 100 and is worth 90% of the overall mark
for this assignment.
• Grades and feedback for the Möbius test will be provided once the testing period has
finished. 15 working days should be allowed for grading on planning document.
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Detailed Marking Criteria:
The table below will be used to assign a mark to the planning document.
Criteria
Research
into Maths
Needed
Rating
No evidence of
mathematics.
(0 marks)
Very little evidence of
research into possible
mathematics for each
scenario. (1 marks)
Marks
Good evidence of
research into possible
mathematics for each
scenario. (3 marks)
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No explanation presented. Any
Fair demonstration of
Explanation
evidence of text quoted in blocks
understanding the maths
of Maths
from another source. (0 marks)
presented. (1 mark)
Presented
English
Poor English grammar.
Adequate English grammar. A
Grammar
Poorly presented with little
section clearly presented for each
&
structure. (0 marks)
scenario. (1 marks)
Presentation
Each scenario details a
thorough analysis of the
maths required to model
each scenario. (5 marks)
5
Excellent explanations contained
throughout text with technical
keywords being used. (3 marks)
3
Excellent English grammar.
Well-thought out structure for each
scenario. (2 marks)
2
TOTAL OUT OF 10 MARKS