Senior Mathematics B

NAME:ITEM: 1.1

TEACHER:Mr Tsakisiris /Mr WhitakerTIME: 2 weeks

SYLLABUS TOPICS: Introduction to Functions I

(IN THE CRITERIA OF KAPS, MAPS AND C&J)

RESULTS

KAPS / MAPS / C&J

TASK1: Simple Routine

Shazza has decided to take a day trip to see the sights of Maryborough. As she is planning on arriving by aeroplane, she will need to rent a car. Rent-a-Total-Wreck has car hire options with costs that are based upon the distance driven. Shazza has decided that the maximum that she will drive is 200km.

Option 1

$20 for the day plus $0.25 per kilometre

  1. What is the independent variable?
  2. Using Microsoft Excel, construct a table showing the cost based on how far Shazza drives.
  3. What is the domain?
  4. What is the range?
  5. Draw a graph from this table, using Microsoft Excel.
  6. What is the value of the y-intercept?
  7. What does the y-intercept represent in this application?
  8. Calculate the gradient.
  9. What does the gradient represent in this application? (Clearly explain)

Option 2

  1. Rent-a-Total-Wreck has a second option that has no flat daily fee, but a cost of $0.40 per kilometre. How far would Shazza have to drive before the second option is more expensive?

TASK 2: Simple Non Routine to Complex Routine

  1. Aussie! Aussie! Aussie!

1896 saw the birth of the modern Olympic Games. The Olympics have been held every four years since (except for the interruption caused by the World Wars).

Your task is to research the winning times or distances for two Olympic events from 1896 to 2008. You must include one swimming event and one field event.

  • Present this data in a table.

You are Australia’s representative on the Olympic Drug Testing Committee. Your task is to create linear models of the above data and analyse the relationship between the year and performance to determine or predict reasonable estimates of gold medal performances in 2012 in an attempt to expose drug cheats.

  • You are to present your findings to the Olympic Drug Testing Committee advising them of gold medal performance predictions, how you established the predictions including limitations of your models and any anomalies in the data which need to be discussed.

Using your linear models, predict the Olympic performances for the 2012games.

Use your model to comment on your predictions in relation to actual Gold medal performances from the 2012 games and comment on your findings.

Criteria Item

Criterion / Standard A / Standard B / Standard C / Standard D / Standard E
Knowledge and procedures / The student work has the following characteristics:
  • recall, access, selection of mathematical definitions, rules and procedures in routine and non-routine simple tasks through to routine complex tasks, in life-related and abstract linear function situations
/ The student work has the following characteristics:
  • recall, access, selection of mathematical definitions, rules and procedures in routine and non-routine simple tasks through to routine complex tasks, in life-related and abstract linear function situations
/ The student work has the following characteristics:
  • recall, access, selection of mathematical definitions, rules and procedures in routine, simple life-related or abstract linear function situations
/ The student work has the following characteristics:
  • use of stated rules and procedures in simple linear function situations
/ The student work has the following characteristics:
  • statements of relevant mathematical facts

  • appropriate selection and accurate use of technology
/
  • appropriate selection and accurate use of technology
/
  • selection and use of technology
/
  • use of technology
/
  • use of technology

Criterion / Standard A / Standard B / Standard C / Standard D / Standard E
Modelling and problem solving / The student work has the following characteristics: / The student work has the following characteristics: / The student work has the following characteristics: / The student work has the following characteristics: / The student work has the following characteristic:
  • identification of assumptions and their associated effects, parameters and/or variables
/
  • identification of assumptions, parameters and/or variables

  • use of data to synthesise mathematical models and generation of data from mathematical models in simple through to complex linear function situations
/
  • use of data to synthesise mathematical models in simple linear function situations and generation of data from mathematical models in simple through to complex linear function situations
/
  • use of mathematical models to represent routine, simple linear function situations and generate data
/
  • use of given simple mathematical models to generate data

Criterion / Standard A / Standard B / Standard C / Standard D / Standard E
Communication and justification / The student’s work has the following characteristics: / The student’s work has the following characteristics: / The student’s work has the following characteristics: / The student’s work has the following characteristics: / The student’s work has the following characteristics:
  • organisation and presentation of information in a variety of representations
/
  • organisation and presentation of information in a variety of representations
/
  • organisation and presentation of information
/
  • presentation of information
/
  • presentation of information

  • analysis and translation of information from one representation to another in life-related and abstract linear function situations from simple through to complex and from routine through to non-routine
/
  • analysis and translation of information from one representation to another in life-related or abstract linear function situations, simple or complex, and from routine through to non-routine
/
  • translation of information from one representation to another in simple routine linear function situations

  • coherent, concise and logical justification of procedures, decisions and results
/
  • coherent and logical justification of procedures, decisions and results
/
  • justification of procedures, decisions or results

  • justification of the reasonableness of results