2007 VCAA Geo and Trig. Question 5

[angryusb]

I dont understand why you would do "4000m^2/10cm^2" (what the assessors report did)
shouldnt you convert the units so they are the same??

[abcdefghi]

k factor? I think we're looking at the same question..

Are you sure it wasn't ^.5?

[angryusb]

yeah thats the one, k factor.. but should you convert those numbers into the same units before anything?

[abcdefghi]

Only 18 per cent of students correctly answered Question 5. In this question, students were given the actual area of a block of land. They were also given its area on a map. From this information a scale factor for area (k2 = 400) can be determined. The majority of students (58 per cent) apparently obtained this area scale factor but then incorrectly applied it directly to scaling the given length rather than first converting it into the corresponding linear scale factor.

I assume so, I did atleast.

I did (40000000^.5)/(10^.5) = 2000

Since it's area and 1m^2 = 10000cm^2

Which equalled 2000cm = 20m

[angryusb]

sorry but what do you mean by "^.5"?

[abcdefghi]

sorry but what do you mean by "^.5"?

Square root.

[paulsterio]

The scale factor doesn't even have any units, it's a factor, it's a constant.

And yes, because it is an area, you will need to ^0.5 in order to get the ratio of the length.

[astone788]

shouldnt you convert the units so they are the same??

Yes:
Because we are given a linear measurement of "1cm"  and the area of the map (10cm^2) It makes this the Original.

Therefore K factor = Image / original
                              = 4000metresSquare/10centremetres      NOTE: These units must be the same
                              = 4000metresSquare/.001metresSquare

NOTE: This K-factor uses measurements of Area. Because we want to find the distance of a straight line, we need to convert this Area k-factor to a straight-line K-factor. To do this we Square-root it.
                              = √ 4000/.001
                              = 2000 metres
                             
Once we have the K-factor we multiply it by the corresponding value that we are looking for. But because K-factor has been converted to metres, we need to also convert the corresponding value is in metres (1cm = .01metres)
Answer                  = 2000x.01
                              = 20
 

I wish VCAA had spent more time in their assessment reports. They just brush over things. The hell do they think we are, nerds? I signed up for further maths, the least they could do is make the solutions clear.