HSC Mathematics General 2 - Buying a houseand Trigonometry
Outcomes Assessed
MG2H-4analyses two-dimensional and three-dimensional models to solve practical problems, includingthose involving spheres and non-right-angled triangles
MG2H-5 interprets the results of measurements and calculations and makes judgements aboutreasonableness, including the degree of accuracy of measurements and calculations and theconversion to appropriate units
MG2H-6 makes informed decisions about financial situations, including annuities and loan repayments
MG-2H-10uses mathematical argument and reasoning to evaluate conclusions drawn from other sources,communicating a position clearly to others, and justifies a response
MG2H-VAappreciates the importance of mathematics in everyday life and its usefulness in contributing tosociety
Task
The following task is split into Part A and Part B. Part A will focus onpurchasing a house, Part B focuses on Trigonometry. You are also required to keep a journal of your progress and show this to you teacher in each lesson.
Part A - What Are The Costs? (14 Marks)
Answer this task in your own booklet.
Either from the internet (from sites like the real estate insert in your local newspaper or by visiting a Real Estate office (like LJ Hooker or McGrath) and picking up one of their brochures, you are to choose a house/apartment you wish to purchase.
Choose a property in Sydney that advertises a price (between $800 000 and $1 000 000), not one that is being sold by auction.
Cut out the advertisement for sale and paste it at the beginning of your assignment.
Assume that you have 15% of the purchase price for the deposit.
The rest of the money you will have to borrow.
Show working for your answers.
1. How much is the house you want to purchase? (0 mark)
2. Calculate the amount of the deposit. (1 mark)
3. How much money will you have to borrow? (1 mark)
4. You borrow the money from Safpac Bank at 7% p.a. over 20 years.
(Note: the table is based on compound interest monthly)
(i) Using the given table, calculate your monthly repayment. (2 marks)
(ii) What is the total amount you will repay in 20 years? (1 mark)
(iii) How much interest would you pay? (1 mark)
(iv) Calculate the equivalent annual flat rate of interest on your loan, (2 marks)
toone decimal place.
5. Comment on the difficulties that may be encountered in taking (2 marks)
out this loan and meeting the monthly repayments.
Take into consideration that you are a single person (earning $7000/month).
What are the options if you find it easy/difficult to meet your
monthly repayments?
6. How could you reduce the total amount of interest you pay? (1 marks)
7. Twelve years after taking out the loan, you need a new car but you (3 marks)
don’t have the cash to buy it. The cost of the car is $35 000.
The car company offers you a 5% pa simple interest loan for 8 years to repay the money.
Your alternative is to borrow the $35 000 from Safpac at the same rate as your home loan and pay it off monthly over the remaining 8 years of your loan. Determine the monthly repayment.
Which is the better option for you and why? Justify with working.
Part B - I can’t see the S Block door from the flagpole (14 Marks)
(Note this task is specific to the layout of this particular school, however, it can be adapted to any school layout)
From outside the N block (near the Flag Pole), your view of the S Block door (D) is obscured by C block and the wooden S block.
You need to calculate the bearing of the door (D) from your given position outside N block.
You will need to know how to read a compass (your teacher will show you), to calculate true bearings and meet with your teacher on Mon 1st June, Period 5 and possibly after school to make your angle measurements in the playground.
Measuring stations will be set up and you will be given individual locations along N block and W block to measure from.
A sheet with a diagram is attached for you to write your measurements on.
- Write the two distances you have been given, NW and WD, (0 marks)
on your diagram.
- Using your compass, measure the bearing from your point on (1 mark)
the N to your given point on the W block wall ...... write it on the diagram.
- Using your compass, measure the bearing from your given point (1 mark)
on the W block wall to the S block door...... write it on the diagram.
- Calculate the size of NWD using your bearing measurements. (2 marks)
Show working, including a sketch.
- Calculate the area enclosed in NWD, to 2 decimal places. (2 marks)
- Calculate the length ND using trigonometry, to nearest metre. (3 marks)
- Calculate WDN using trigonometry, to the nearest degree. (3 marks)
- State the bearing of the S block door (D), from N block. (2 marks)
Notes
- It is important to show your working to gain full marks.
- When using a compass, all bearings are measured from north.
- Apply practical measuring techniques for accuracy.
Assessment Criteria
Part A What are the costs?Possible marks / Criteria / Marks
Q1 / 0 / Purchase cost of chosen property / 0
Q2 / 1 / Correct calculation of deposit / 1
Q3 / 1 / Correct calculation of money borrowed / 1
Q4(i) / 2 / Correct Interest factor (monthly amount per $1000)
Correct monthly amount for total borrowed / 1
1
(ii) / 1 / Correct total repayment for loan / 1
(iii) / 1 / Correct interest calculation / 1
(iv) / 2 / Correct SI formula and substitution
Correct percentage rate per annum / 1
1
Q5 / 2 / Exceptional discussion of difficulties encountered and
option/s to overcome the difficulty eg backed by a calculation (justified) or clear estimation of living costs.
Basic discussion of difficulties encountered and option/s
to overcome the difficulty. / 2
1
Q6 / 1 / Valid method for reducing interest eg pay fortnightly,
pay more / 1
Q7 / 3 / Monthly repayment calculation for car company@5%
Monthly repayment calculation for Safpac@ 7%
Clearly stating which was the better option, backed by justification / 1
1
1
Total / /14
Part B - I can’t see the S Block door from the flagpole
Possible marks / Criteria / Marks
Q1 / Write FW and WS on diagram
(if measurements not on sheet or sheet not handed in penalty - 1 ) / 0
Q2 / 1 / Bearing of W block from N block ±20 / 1
Q3 / 1 / Bearing of D from W block ±20 / 1
Q4 / 2 / Calculates size of NWD must have appropriate diagram drawn
or
Calculates size of NWD without diagram drawn oror
Incorrect calculation with appropriate diagram drawn / 2
1
Q5 / 2 / Correct area working using NWD rounded 2dp, units indicated
or
Incorrect area working using NWD answer or
Correct area working to achieve answer using any angle, rounded oror
Correct area working using NWD answer unrounded / 2
1
Q6 / 3 / Calculates length ND (nearest m) using given data & NWD or
Calculates length ND (m) not using one of given data or NWD
Calculates length ND (m) not using two of given data or NWD
Calculates length ND (nearest m) not using given data or NWD / 3
2
1
Q7 / 3 / Calculates WDN nearest degree using given data Q6 &Q4
or
Applies correct formula not using one of ( given or Q6 or Q4)
or
Applies correct formula not using two of ( given or Q6 or Q4)or / 3
2
1
Q8 / 2 / Clearly explained method /diagram drawn, bearing stated.
or
Clear explained method /diagram with 1 error or bearing not statedoror
Correct answer not explained method or diagram drawn / 2
1
Total / /14
Journal
Teacher records at least three sightings and progress of journal
3 marks - substantial progress shown equally over 3 weeks
2 marks - substantial progress shown equally over 2 weeks
1 mark - substantial progress shown over 1 week / /3
Final Mark