MATHEMATICS A

SEMESTER 4

YEAR 12   2011

    ASSESSMENT #11
(Semester 4 Assignment)

NAME: ________________________________________

STUDENT NUMBER:  ____________________________     DUE DATE: _____________

TEACHER: ________________________	                  LATE: yes / no
                                                                                                   Circumstance: ___________

TOPICS ASSESSED:
•	Land measurement / Applied Geometry
•	Managing Money II (Borrowing)

Instructions:
Attempt all questions on your own paper.
Communicate your solutions clearly and concisely. Ensure student name is included in the footer of all excel and word processed documents.
Calculators and drawing instruments must be provided by the student. Some time will be provided in class time to access computers but students will need to complete in own time.

STATEMENT OF ORIGINAL AUTHORSHIP
I state that this evidence of assessment contains no material which has been produced by any other person except where due reference is made.   I make this statement in full knowledge of and understanding that, should it be found to be false, I will be subject to disciplinary action under Metropolitan South  Institute of TAFE student rules.
PRIVACY STATEMENT
Metropolitan South Institute of TAFE is collecting the information on this form to enable students to provide information to assessors in relation to the assessment item and to give the assessor access to providing feedback to students.   Only authorised departmental officers have access to this information.    Your personal information will not be disclosed to any other third party without your consent, unless authorised or required by law.
Student’s Signature:				Phone No.:			Date:


SUMMARY RESULTS:

KNOWLEDGE AND PROCEDURES	MODELLING AND PROBLEM SOLVING	COMMUNICATION AND JUSTIFICATION











COMMENTS:



Student Signature:                                                         Assessor Signature::		Date:
Assessor		Date:

Standards associated with exit criteria
Criterion	Standard A	Standard B	Standard C	Standard D	Standard E
Knowledge and procedures	The student’s work has the following characteristics:
•	accurate use of rules and formulas in simple through to complex situations	The student’s work has the following characteristics:
•	accurate use of rules and formulas in simple situations or use of rules and formulas in complex situations	The student’s work has the following characteristics:
•	use of rules and formulas in simple routine situations	The student’s work has the following characteristics:
•	use of given rules and formulas in simple rehearsed situations	The student’s work has the following characteristics:
•	attempted use of given rules and formulas in simple rehearsed situations
	•	application of simple through to complex sequences of mathematical procedures in routine and non-routine situations	•	application of simple sequences of mathematical procedures in non-routine situations or complex sequences in routine situations	•	application of simple sequences of mathematical procedures in routine situations	•	application of simple mathematical procedures in simple rehearsed situations	•	attempted use of simple mathematical procedures in simple rehearsed situations
	•	appropriate selection and accurate use of technology	•	appropriate selection and accurate use of technology	•	selection and use of technology	•	use of technology	•	attempted use of technology
Modelling and problem solving	The student’s work has the following characteristics:
•	use of strategies to model and solve problems in complex routine through to simple non-routine situations	The student’s work has the following characteristics:
•	use of strategies to model and solve problems in routine through to simple non-routine situations	The student’s work has the following characteristics:
•	use of familiar strategies for problem solving in simple routine situations	The student’s work has the following characteristics:
•	use of given strategies for problem solving in simple rehearsed situations	The student’s work has the following characteristics:
•	attempted use of given strategies for problem solving in well-rehearsed situations
	•	investigation of alternative solutions and/or procedures to complex routine through to simple non-routine problems	•	investigation of alternative solutions and/or procedures to routine problems
	•	informed decisions based on mathematical reasoning in complex routine through to simple non-routine situations 	•	informed decisions based on mathematical reasoning in routine situations 	•	informed decisions based on mathematical reasoning in simple routine situations
	•	reflection on the effectiveness of mathematical models including recognition of the strengths and limitations of the model	•	recognition of the strengths and limitations of the model in simple situations
Communication and justification	The student’s work has the following characteristics:
•	accurate and appropriate use of mathematical terminology and conventions in simple non-routine through to complex routine situations	The student’s work has the following characteristics:
•	accurate and appropriate use of mathematical terminology and conventions in simple non-routine and/or complex routine situations	The student’s work has the following characteristics:
•	appropriate use of mathematical terminology and conventions in simple routine situations	The student’s work has the following characteristics:
•	use of mathematical terminology and conventions in simple rehearsed situations	The student’s work has the following characteristics:
•	use of mathematical terminology or conventions in simple rehearsed situations
	•	organisation and presentation of information in a variety of representations in simple non-routine through to complex routine situations	•	organisation and presentation of information in a variety of representations in simple non-routine and/or complex routine situations	•	organisation and presentation of information in a variety of representations in simple routine situations	•	presentation of information in simple rehearsed situations
	•	analysis and translation of information displayed from one representation to another in complex routine situations	•	analysis and translation of information displayed from one representation to another in simple routine situations	•	translation of information displayed from one representation to another in simple routine situations
	•	use of mathematical reasoning to develop logical sequences in simple non-routine through to complex routine situations using everyday and/or mathematical language	•	use of mathematical reasoning to develop logical sequences in simple non-routine and/or complex routine situations using everyday and/or mathematical language	•	development of logical sequences in simple routine situations using everyday and/or mathematical language
	•	justification of the reasonableness of results obtained through technology or other means

TASK 1:  Topographic Maps

This task refers to the attached Wilderness map in Appendix 3. This wilderness area is to be opened up as a national park.

(a)  What is the scale ratio of the Wilderness map?			                                                    (KP*)

(b)  On the same axes construct two profiles of the wilderness area as you look north from the road. One which runs east-west through the falls, the other which runs east-west through the highest peak.

Determine the vertical exaggeration of the profiles.       						      (KP***)

 NOTE: Vertical Exaggeration =

(c)  Briefly describe the landscape from the road as represented by the profiles you have drawn as you look from west to east.                                                                                                                                                   (KP**)


(d)                                                                                                                                                                         (KPS****)

A walking track is planned.
•	The grade of the track must not exceed 1:6.
•	The track must be between 4 and 7 kilometres.
•	The track will start from the bridge (X), visit the falls, the swamp, the higest peak (if possible) and return to bridge.

Mark your track on the map clearly in red.

You must show calculations for determining:
(i)	how to ensure the track is not too steep?
(ii)	How long the track is?









Reducing Balance Loans

You decide to borrow a considerable sum towards the purchase of a house.
Negotiations with a bank will determine the amount they will lend you, the interest rate and the monthly repayments. The formula they use to determine the periodic monthly repayment is:

            where   PV = Amount of the loan
                           p = Monthly repayment
                           i  =  Rate of interest as a decimal per month
            and         n = Length of the loan in months

TASK 2

(a) Using the loan conditions you have been assigned (see Appendix 1), calculate the monthly repayment on your loan by substituting into the formula above.                                                                                                (KP*)

TASK 3

(a)  In Excel create a spreadsheet to enable you to track the progress of your loan until it is paid out completely.  (see notes below)   								    (MPS**)

You will use the data as assigned to you in Appendix 1 and the re-payment as calculated in Task 2 a.

(b)  In Excel draw an appropriate well-labelled graph showing the balance of the loan over the period of the loan.    												    (MPS**)

(c) From the spread sheet calculate:
  	       (i)  The total cost of the loan
                     (ii)  The total interest paid                                                         				       (MPS*)

Note the following:
•	Your spread sheet must be constructed using formulas so that differing loan amounts, interest rates, payments per year, and regular repayment can be entered and the spreadsheet will automatically adjust to the new values.
•	You are encouraged to “pretty up” your spreadsheet as appropriate to the Bank etc
•	Copy the first 10-12 lines and the last 3-4 lines of your spreadsheet into a word document.
LOAN   SCHEDULE
Interest Rate =
Payments per Year =
Original Principal =
Regular Re-payment =
Interest Rate per rest =
Payment Number	Principal	Interest	Repayment	Balance of Loan
0
1
2
•	Provide a copy of the same spreadsheet with formulas revealed (use Ctrl~). Just the first 10-12 lines will be sufficient.











TASK 4

It is often recommended that people with a home loan could be helped by paying half the regular re-payment every fortnight.  Assuming that the interest then will also be charged fortnightly, determine if there is any advantage in doing that with your loan and if so what money and/or time is saved. Remember to justify your conclusion with spreadsheets and graphs. 				                                 (MPS**)


TASK 5

After negotiating the loan as in Task 3, you decide you actually could afford to set aside an extra $100 per month.

Which would be the better option?

A: Increasing the monthly re-payment on your home loan by $100 a month   OR
B: Investing the $100 each month into an interest bearing account of 5.9% pa interest calculated monthly.

(Remember to provide justification for your answer using appropriate spreadsheet and or calculations)										                                              (MPS***)


TASK 6

Search the sites such as Wizard Home Loans, Aussie Home Loans, Westpac bank or similar.  These sites will have automatic calculators to determine the repayment s on any loan at a given rate of interest. They will also inform you of the maximum amount they are prepared to lend to people in different circumstances.


(a)	 Enter your original loan, interest rate and length of loan into the automatic calculator and determine the monthly repayment required. Comment on how this answer compares with the result in Task 2.

Provide a printout of this page as evidence of your calculation.
                                 									          (KP*)

(b)	Determine the maximum amount that could be borrowed for the client(s) highlighted in the table in Appendix 2.

Provide a printout of this page as evidence of your calculation.				        (KP**)







TASK 7												(MPS****)

Many people will say that one can be financially better off by renting in contrast to buying ones own home.

Research the rental versus buying argument and determine the advantages and disadvantages of each. In your discussion make reference to current average rents and average home prices in the area in which you live.

Support your argument with estimates of costs and benefits in each situation.

In conclusion make recommendations as to:
(a) when rental would be better
(b) when buying is the best option

You must indicate all sources you have used and where appropriate attach copies of materials used in your argument.




APPENDIX 1


Option	Bank	Amount Borrowed	Interest Rate per annum	Length of Loan
A	ANZ	$100 000	5.91% pa	15 years
B	Bank of Queensland	$150 000	5.89% pa	15 years
C	Westpac	$200 000	6.03% pa	15 years
D	NAB	$250 000	6.19% pa	20 years
E	Aussie Home Loans	$300 000	5.96% pa	20 years




APPENDIX 2

John and Sam 	John has a gross salary of $65 000 and is the prime borrower
Sam is studying but earns $30 000 per year. They are looking for a joint loan to build their first house.
They are paying off a car loan at $400 per month and pay rent of $350 per week. General living (food etc) cost them about $300 per week
They have no dependents and are wishing to buy their first home.
Neither use a bankcard.
Michelle	Michelle is looking at what she could borrow for an Investment property.
She has an annual salary of $70 000 per annum. She pays rent of $300 per week but owns her car outright. Her bankcard limit is $2500.  Her weekly food bill is around $100 a week. (Eats at her parents several nights a week!!)
Thomas	A single parent with one dependent child. He pays rent of $420 per week. He is on a salary of $61000 per year. Due to a divorce settlement he no longer owns his own home but is not classified as a first home owner. He has cash investments which return him about $12000 per year. His bankcard limit is $3000. Weekly food and school expenses amounts to about $400 per week.
Maree and Jayne	Combined income $6300 per month. Bank card limit of $5000. Existing car loan of $450 per month. Rent payments of $480 per week. They are first home buyers.
They spend about $300 a week on food and entertainment.











 SCORING GRID
Assessment Item # 11 Year 12 2010

Name:__________________________________________   Student Number: _______________________

Knowledge and Procedures

Task
*
**
***
****	Communication and Justification
1a					N E D C
1b					N E D C B
1c					N E D C
1d					N E D C B A
6a					N E D C
6b					N E D C

Modelling and Problem solving

Task
*
**
***
****	Communication and Justification
3(a)					N E D C
3(b)					N E D C
3(c)					N E D C
4					N E D C
5					N E D C B
7					N E D C B A

Note: N grade will be awarded for a non-attempted question
           In C & J an N indicates that a correct answer was provided without any C&J

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