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