Clayfield College MATHEMATICS A 代写

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MATHEMATICS A
Year 12, 2016
Assessment Instrument 3.1
Teacher:SON    STO    Student:
Due:25 Feb 2016(beginning of Lesson 2)
Subject Matter:  Exploring and understanding data
You received this assignment task sheet on 1/2/16
You may seek feedback on your planning for this assignment by making one appointment with your teacher up until the Monday before the submission of the assignment is due, i.e. up until 18/02/16.
On 18/02/16 lesson 4, you are required to hand in to your teacher a copy of some evidence of your work to date on this assignment which will be retained by your teacher. If your completed assignment is not submitted by the stipulated due date, this work will constitute your assignment for assessment purposes.
When submitting your completed assignment, this cover and task sheet, including the associated criteria sheet, is to be stapled to the front of your assignment; do not use paper clips of any sort nor plastic sleeves, covers or binding.
The use of a graphics calculator and/or other technology is expected.
Collectively, assessment in this subject addresses the general objectives as listed below.
All items on this assessment instrument contribute to the KP, MPS and CJcriteria.
Grades in each criterion for this assessment instrument are awarded based on the specific requirements detailed in the table over the page.
Knowledge and Procedures    Modelling and Problem Solving    Communication and Justification
manipulate simple rules and formulas
access, select and apply rules and formulas
recall, select and apply mathematical procedures to situations that are similar to situations already encountered
apply a sequence of mathematical procedures in situations that are similar to situations already encountered
use mathematical technology and geometrical instruments    interpret, clarify and analyse problems
use strategies to model and solve problems
investigate alternative solutions and/or procedures to problems
make decisions informed by mathematical reasoning
reflect on the effectiveness of mathematical models, including the recognition of strengths and limitations    interpret and use appropriate mathematical terminology, symbols and conventions
organise and present information for different purposes and audiences, in a variety of representations (such as written, symbolic, pictorial and graphical)
analyse information displayed in a variety of representations (such as written, symbolic, pictorial and graphical) and translate information from one representation to another
develop logical sequences within a response expressed in everyday language, mathematical language, or a combination of both, as required, to justify conclusions, solutions or propositions
justify the reasonableness of results obtained through technology or other means using everyday language, mathematical language or a combination of both, when appropriate
    
I have had the opportunity to view my grading on this assessment instrument and discuss it with my teacher.
Signature:    
    Date:   
 
    Objective reference    
    AAcross the full range:    BAcross a range:    CIn routine situations:    DIn rehearsed simple situations:    EEvidence of some:    
Knowledge and Procedures    rules and formulas    Perfect Response    accurate use of rules and formulas
·         to find statistical features     accurate use of rules and formulas
·         to find statistical features     use of rules and formulas
·         to find statistical features     use of rules and formulas    attempted use of given rules and formulas    No Meaningful response
mathematical procedures    accurate application of sequences of mathematical procedures
·         to investigate data sets    accurate application of mathematical procedures
·         to investigate data sets    application of mathematical procedures
·         to investigate data sets    application of simple mathematical procedures    attempted use of simple mathematical procedures
mathematical technology and instruments    appropriate selection and accurate use of technology
·         to present findings from given data sets
·         to manipulate self-generated data sets    selection and accurate use of technology
·         to present findings from given data sets
·         to manipulate self-generated data sets    selection and use of technology
·         to present findings from given data sets

    use of technology    attempted use of technology
Modelling and Problem Solving    strategies    Perfect Response    accurate use of appropriate strategies to model and solve problems
·         to compare and contrast data sets in a range of formats    accurate use of appropriate strategies to model and solve problems
·         to compare and contrast data sets    use of familiar strategies for problem solving
·         to compare data sets    use of strategies for problem solving    attempted use of given strategies for problem solving    No Meaningful response
procedures and decisions    informed decisions based on mathematical reasoning
·         with written evidence of reasoning    informed decisions based on mathematical reasoning
·         with written evidence of reasoning    informed decisions based on mathematical reasoning
·         with written evidence of reasoning    decisions based on mathematical reasoning    decisions based on mathematical reasoning
reflecting, including strengths and limitations    comprehensive reflection on the effectiveness of mathematical models including recognition of the strengths and limitations of the model
·          to compare datasets to reach meaningful conclusions
·          to accurately predict run times 40 years from now    thoughtful recognition of the strengths and limitations of the model
·         to compare datasets to reach conclusions
·         to predict run times 40 years from now    recognition of a strength or a limitation of the model
·         to compare datasets to reach conclusions    cursory recognition of a strength or a limitation of the model    attempt at recognition of a strength or a limitation of a model
Communication and Justification    terminology, symbols and conventions    Perfect Response    accurate and appropriate use of mathematical terminology and conventions    accurate and appropriate use of mathematical terminology and conventions    appropriate use of mathematical terminology and conventions    use of mathematical terminology and conventions    use of mathematical terminology or conventions    No Meaningful response
representations    coherent and logical organisation and presentation of information in a variety of representations
accurate analysis and translation of information displayed from one representation to another    logical organisation and presentation of information in a variety of representations
analysis and translation of information displayed from one representation to another    logical organisation and presentation of information in a variety of representations
translation of information displayed from one representation to another    presentation of information    presentation of information
sequences    use of mathematical reasoning to develop logical sequences in using every day and/or mathematical language    use of mathematical reasoning to develop logical sequences using every day and/or mathematical language    development of logical sequences    development of simple logical sequences    development of sequences
justification    coherent and logical justification of procedures used, including of the reasonableness of results    logical justification of procedures used, including of the reasonableness of results    justification of procedures used    simple justification of procedures used    rudimentary justification of procedures used
 
Acknowledgement
This assignment is based on materials originally sourced from the QSA Assessment Bank.
Much of the material on p. 1-3 of this assignment is reproduced from Forty years from now - Student booklet.doc, accessed 19 Mar 2013, https://assessmentbank.qsa.qld.edu.au/assessmentbank/with kind permission of The State of Queensland (Queensland Studies Authority). Further information, including any updates, is available at <www.qsa.qld.edu.au>.
Setting the scene
In this assignment, you will access, interpret and use real-world data to make predictions based on that data using a variety of models. You will also analyseyour processes to identify strengths and limitations of the strategies you used in responding to the tasks.
 
Item 1. How fast can they run?
The following raw data was collected at a recent athletics meet in Brisbane (all times in format mm:ss.00):
100 M Event
Men    Women
00:10.22     00:10.58     00:11.04     00:12:33
00:15.32     00:10.99     00:11.55     00:11.01
00:10.55     00:10.67     00:11.37     00:12.55    00:10.98     00:11.04     00:11.33     DQ
00:11.57     00:13.13     00:12.02     00:12.44
00:11.87     00:12.02     00:11.88     00:12.59
200m Event
Men    Women
00:20.98     00:20.97     00:22.95     DQ
00:20.95     00:22.17     00:21.56     00:22.02
00:21.37     00:21.67     00:22.11     00:25.79    00:22.34     00:23.03     00:23.07     00:24.65
00:24.01     00:23.98     00:24.65     00:25.18
00:22.69     00:24.14     00:24.76     00:24.98
400m Event
Men    Women
00:44.12     00:43.98     00:45.67     00:46.87
00:45.56     00:48.88     01:01.33     DQ
00:44.77     00:44.22     00:47.54     00:46.06    00:49.56     00:50.13     00:47.90     00:48.98
00:49.67     00:51.33     00:49.99     00:50.25
00:50.33     01:00.32     00:51.86     00.49.86   
DQ = Disqualified
 
Using any means that you see fit, describe the relationship between time and distance, and the differences in terms of gender.
In your response, you will need to use mathematical arguments to support your decisions. These arguments will be show clearly how they support your decisions and conclusions.

Item 2. How fast will they run forty years from now?
World record times for the men’s 1500 metres run have been continually dropping over the past 100 years, as shown in the table below.
In this section, you need to comprehensively analyse data in the table to write a mathematical report as outlined over the page.
 
World record times: men’s 1500 metres run    
Date    Athlete    Time
(mm:ss.0)    Date    Athlete    Time
(mm:ss.0)    Source: International Association of Athletics Federations  (IAAF) 2009, 12th IAAF World Championships in Athletics: IAAF Statistics  Handbook, p. 549, www.iaaf.org/mm/document/competitions/competition/05/15/63/20090706014834_httppostedfile_p345-688_11303.pdf, Berlin.

    
8/06/1912    Abel Kiviat    03:55.8    6/09/1955    Gunnar Nielsen    03:40.8    
5/08/1917    John Zander    03:54.7    3/08/1956    István Rózsavölgyi    03:40.6    
19/06/1924    Paavo Nurmi    03:52.6    11/07/1957    Olavi Salsola    03:40.2    
11/09/1926    Otto Peltzer    03:51.0    11/07/1957    Olavi Salonen    03:40.2    
5/10/1930    Jules Ladoumegue    03:49.2    12/07/1957    Stanislav Jungwirth    03:38.1    
9/09/1933    Luigi Beccali    03:49.2    28/08/1958    Herb Elliott    03:36.0    
17/10/1933    Luigi Beccali    03:49.0    6/09/1960    Herb Elliott    03:35.6    
30/06/1934    Bill Bonthron    03:48.8    8/07/1967    Jim Ryun    03:33.1    
6/08/1936    Jack Lovelock    03:47.8    2/02/1974    Filbert Bayi    03:32.2    
10/08/1941    Gunder Hägg    03:47.6    15/08/1979    Sebastian Coe    03:32.1    
17/07/1942    Gunder Hägg    03:45.8    15/07/1980    Steve Ovett    03:32.1    
17/08/1943    Arne Andersson    03:45.0    27/08/1980    Steve Ovett    03:31.4    
7/07/1944    Gunder Hägg    03:43.0    28/08/1983    Sydney Maree    03:31.2    
15/07/1947    Lennart Strand    03:43.0    4/09/1983    Steve Ovett    03:30.8    
29/06/1952    Werner Lueg    03:43.0    16/07/1985    Steve Cram    03:29.7    
4/06/1954    Wes Santee    03:42.8    23/08/1985    Saïd Aouita    03:29.5    
21/06/1954    John Landy    03:41.8    6/09/1992    Noureddine Morceli    03:28.9    
28/07/1955    Sándor Iharos    03:40.8    12/07/1995    Noureddine Morceli    03:27.4    
6/09/1955    László Tábori    03:40.8    14/07/1998*    Hicham El Guerrouj    03:26.0    

    *Current record as of December 2015    
   
Use the data in the table on the previous page to write a mathematical reportthat investigates the world record times of the 1500m race in the past, present and future. This report should include:
·          A brief introduction that describes the goals of the report and outlines what will be presented.
·          A description of the mathematical methods used, including any models developed and assumptions made.
·          A justified prediction on what you predict the world record time will be forty years from now?
·          Analysis of the data that investigates and makes informed decision regarding
i.      the year that the 4 minute mile was finally cracked?
ii.     Whether there will there be a time in the future when the record could never be broken?
iii.    How can different models be used to assist in solving this problem?
·          A discussion on the strengths and limitations identified within the devised models
·          A conclusion that comments on the plausibility, expectedness and significance of the findings.
 
Item 3  Bringing it all together…
In this third and final item on this assignment, you need to identify and accurately use appropriate data sampling methods to collect data about two related variables with which you can make your own comparisons, analyses and predictions, and to produce a mathematical report of your findings.
The data you collect must allow a valid investigation of the relationship between the two variables you have identified in your sampling processes. Your report must contain in-depth mathematical justification to support your processes and your analyses and predictions. This report format can be in any format that you see fit.
You will be given Lesson 2 on Tuesday, 24 February to collect data from your Year 12 Mathematics A peers that you can use (if you wish). If you intend to complete a survey or experiment for data, it would be expected that you have approved this with your teacher prior to this lesson (i.e. in the less on Monday, Feb 23).
 
 
A comprehensive data set is one that:
·          Shows consideration to the removal of outliers and anomalous data
·          Informs the reader on a topic using mathematical and everyday language
·          Details how errors have been minimised and eliminatedthrough the collection of data
·          Displays the information in an easy to interpret way such as a box and whisker plot, scatter plot with line of best fit or two way table.
·          Generates informed decisions and conclusions based on mathematical reasoning