**Year 12**

**Mathematics A**

**Assessment # 3.1**

**Extended Modelling & Problem Solving Task**

**Due: Wednesday 7th March 2012 Time Allowed: 2 weeks**

Name:

Teacher:

Result

Knowledge and Procedures

Modelling and Problem Solving

Communication and Justification

STUDENT DECLARATION

1. I declare that the work shown in the following solutions is solely my own and that I have not copied any other student’s work nor have I given any solution or part solution to any other student.

2. I am familiar with the Assignment Policy in the Student record Book/Diary.

Signature Date_______

Criteria for Knowledge & Procedures (Questions 1 & 2):

Rating

Description

The students work has the following characteristics:

A

· accurate use of rules and formulas in simple and complex situations.

· Application of simple and complex sequences of mathematical procedures in routine and non-routine situations.

· Appropriate selection and accurate use of technology, eg, accurate Excel spreadsheet and evidence of formulas.

B

· accurate use of rules and formulas in simple and complex situations.

· Application of simple sequences of mathematical procedures in non-routine or complex sequences in routine situations.

· Appropriate selection and accurate use of technology, eg, accurate Excel spreadsheet and evidence of formulas with minor errors.

C

· use of rules and formulas in routine situations.

· Application of simple sequences of mathematical procedures in routine situations.

· Selection and use of technology, eg, Excel spreadsheet and evidence of formula use with errors.

D

· use of given rules and formulas in rehearsed situations.

· Application of simple mathematical procedures in simple rehearsed situations.

· Some use of technology, eg, Excel spreadsheet and evidence of formulas use.

E

· No meaningful attempted use of given rules and formulas in rehearsed situations.

· No meaningful attempted use of simple mathematical procedures in simple rehearsed situations.

· No meaningful attempted use of technology eg, Excel spreadsheet and evidence of formulas use.

Criteria for Modelling and Problem Solving

Rating

Description

The students work has the following characteristics:

A

· Investigated alternative solutions to the complex routine problem of comparing property purchasing with renting and investing.

· Accurate informed decisions based on mathematical reasoning in complex routine situations, such as selecting a term deposit, debenture, or Bond to suit the situation.

· Reflection on the effectiveness of mathematical models including recognition of the strengths and limitations of the model, such as comparing purchasing property to renting/investing.

B

· Investigated alternative solutions (with some omissions/minor errors) to the complex routine problem of comparing property purchasing with renting and investing.

· Mostly accurate informed decisions based on mathematical reasoning in complex routine situations, such as selecting a term deposit, debenture, or Bond to suit the situation.

· Reflection with minor errors or omissions on the effectiveness of mathematical models including recognition of the strengths and limitations of the model, such as comparing purchasing property to renting/investing.

C

· Some investigated alternative solutions (with omissions/errors) to the complex routine problem of comparing property purchasing with renting and investing.

· some informed decisions based on mathematical reasoning in complex routine situations, such as selecting a term deposit, debenture, or Bond to suit the situation.

· Reflection with errors and omissions on the effectiveness of mathematical models including recognition of the strengths and limitations of the model, such as comparing purchasing property to renting/investing.

D

· Some attempt at investigated alternative solutions (with omissions/errors) to the complex routine problem of comparing property purchasing with renting and investing.

· Some parts of informed decisions based on mathematical reasoning in complex routine situations, such as selecting a term deposit, debenture, or Bond to suit the situation.

· Some reflection on the effectiveness of mathematical models including recognition of the strengths and limitations of the model, such as comparing purchasing property to renting/investing.

E

· No meaningful attempt at investigated alternative solutions to the complex routine problem of comparing property purchasing with renting and investing.

· No meaningful attempt at informed decisions based on mathematical reasoning in complex routine situations, such as selecting a term deposit, debenture, or Bond to suit the situation.

· No meaningful attempt on reflection on the effectiveness of mathematical models including recognition of the strengths and limitations of the model, such as comparing purchasing property to renting/investing.

Criteria for Communication and Justification:

Rating

Description

The students work has the following characteristics:

A

· accurate and appropriate use of mathematical terminology and conventions in simple non-routine through to complex routine situations.

· Organisation and presentation of information in a variety of representations in simple non-routine through to complex routine situations.

· Analysis and translation of information displayed from one representation to another in complex 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.

· Justification of the reasonableness of results obtained through technology or other means.

B

· accurate and appropriate use of mathematical terminology and conventions in simple non-routine and/or complex routine situations.

· Organisation and presentation of information in a variety of representations in simple non-routine and/or complex routine situations.

·

· Analysis and 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 and/or complex routine situations using everyday and/or mathematical language.

C

· appropriate use of mathematical terminology and conventions in simple routine situations.

· Organisation and presentation of information in a variety of representations in simple routine situations.

· translation of information displayed from one representation to another in simple routine situations.

· development of logical sequences in simple routine using everyday and/or mathematical language.

D

· use of mathematical terminology and conventions in simple rehearsed situations.

· presentation of information in simple rehearsed situations.

E

· use of mathematical terminology or conventions in simple rehearsed situations.

Background

The James family have just moved to the Gold Coast from interstate. They plan to stay for three years before they are transferred to an overseas posting. They wish to know whether they should purchase a property, knowing they will have to sell in three years time, or should they rent.

After selling their previous home the James family have $160 000 in their savings account which will be used for purchase expenses/deposit on a property purchase, or, if they rent, will be placed in a term deposit, debenture or Bond account for the three years.

Question 1: (Knowledge & Procedures)

a) You are to find and submit an advertisement for a property, which could be a house, townhouse or unit on the Gold Coast between $500 000 and $600 000, which the James’s will purchase.

b) You are to show and fully justify with appropriate mathematical calculations, the steps and the costs incurred to:

i) complete the purchase of the property;

ii) hold the property for the three years;

iii) sell the property at the end of the three years.

To help you complete b), you are to take into account the following dot points;

· Assume property prices are predicted to rise by 2% each year, for the next 3 years.

· Costs and rates of purchase and selling are to be sourced from the current text.

· An allowance of $1 500 per transaction (purchase or sale) for fees such as bank and solicitors fees;

· The balance is to be borrowed after taking into account the available money held by the James’s;

· Costs associated with owning or renting can be collected from the list here: electricity per quarter $550,excess water per half $340, rates per half $990, house insurance per annum $760, contents insurance $300 per annum, maintenance on the house per annum $1600.

· Consider a 20-year loan for the amount borrowed in (b) at the current variable interest rate (to be supported by data from a financial institution);

· Consider preparing an Excel spreadsheet which shows the month by month breakdown of the closing balance (as in the first table Pg 127 of your text) for the 3 years. Demonstrate extensive use of Excel formulas which are to be submitted with the figures.

Question 2: (Knowledge & Procedures)

a) You are to find and submit a rental advertisement for a property in the same suburb as used in Question 1. The rent range will be from $500 to $600 per week. This is the home the James family will rent as the alternative to purchasing.

b) You are to fully justify with appropriate mathematical calculations, the costs and income to:

i) Rent a property for the family, and;

ii) Invest any spare money the James family has for the three years;

To help you complete b), you are to take into account the following dot points:

· Check the dot points in Question 1 for information on costs or expenses appropriate to renting.

· rent rises of 2.6% are expected at the end of each year for the 3 years,

· research the available deposit investment rates of term deposits, debentures and Bonds and choose an investment for the James family that offers good rates balanced by acceptable risk, and the money has to be available in 3 years. Submit all the details of the investment.

Question 3: (Modelling & Problem Solving)

You are to write to the James family summarising the data obtained in Questions 1 and 2 – preferably in an Excel spreadsheet- and use this information to make a fully informed recommendation whether they should buy or rent.

Outline the strengths and limitations of any relevant factors which may affect the advisability of purchasing or renting.

NOTE: Evidence

· A screen shot of a website stating a current interest rate is appropriate evidence, and other evidence as indicated above as well.

· All websites used should also be added to your list of references. See the Library page for “How to reference” page.

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