VCE General & Further Maths Question Thread!

[RazzMeTazz]

When would you say there is random variation in a time-series data?

Would it be whenever the trend is none of: cyclical or seasonal?

[MightyBeh]

Marcia is 1.5 m tall and casts a shadow 4 m long. Her shadow and the shadow cast by a tree
nearby are parallel on the ground. The end of Marcia’s shadow on the ground lines up with
the end of a shadow cast by the tree h m high. If the distance between the tree and Marcia
is 20 m, find h, the height of the tree.

Not sure it's right, but I just had a quick look and got this:

Spoiler

My diagram, if you're interested
Don't judge me, I'm not an artist 

So what we have here is two triangles - Marcia and her shadow (triangle ABC); and the tree and its shadow (triangle ADE, don't fall for DCE. That'd be silly ).

Firstly, we have to find the scalar (let's call that x). We do that by taking the lengths of the same edge of the triangles.



Next, we apply that to the length that corresponds to h.




If you have time, you can also check that h is a reasonable number:
Value 'h' must be:
(true)
(true)
(true)
And finally, checking through the ratio between lines BC and AC, which should be the same and DE and AE.



So now we check that:

(true)

Therefore, the tree must be 9 metres tall.
You could also just do this problem by find the ratio I used before and doing some algebra by hand or on your CAS, like so:

My textbook says: "Bivariate or (x,y,) data is data where both x and y could vary independently."

I thought in bivariate data there was always one independent and dependent variable?

Edit: Totally misread that. If both variables are independent, there's no relation between x and y. By extension, that means that Pearson's Correlation Coefficient and the Coefficient of Determination are either really low, or 0. I'm very close to 100% sure that you'll never get a question where both variables are dependent or independent as there's not much you can do with those in the way of SAC/exam questions. It's probably mentioned as a bit of background, so you're not totally blindsided if the VCAA or whoever brings it up in the future.

So you're pretty much guaranteed your normal dependent/independent combo, but there can be data that is fully independent or dependent.

When would you say there is random variation in a time-series data?

Would it be whenever the trend is none of: cyclical or seasonal?

Unless your time series is a perfect line, there's always at least a little bit of random variation

[Escobar]

kinda worried about mark allocations in further

i have a question where part a) (worth 2 marks) asks to find an interior angle of a (regular) pentagon
i just applied the rule that interior angle=180-360/n, where n= number of sides
=108 degrees

but in the solutions, the method used is dividing 360 by 5 (pentagon is made up of 5 triangles) to find the angles of each little triangle (=72 degrees) then doing 180-this (=108 degrees)
they allocated 1 mark for finding the angle after dividing (72) & 1 mark for the final answer (108)
however if i apply the formula, i skip the dividing step (well i still divide, but it is just part of the formula. the solutions name the inside angle etc, very specific)
would i not be awarded the mark? would a question this simple even be worth 2 marks?

[MightyBeh]

would i not be awarded the mark? would a question this simple even be worth 2 marks?

I'd give you full marks for that; one mark for applying the formula and one mark for the correct answer. Well, as long as you wrote down your working out.

A question like this is probably only worth one mark on the exam though, so it's best to ask your teacher if you'd get the full marks on a SAC.

[Escobar]

Thanks!
I have another question:
if a question asks you to find an answer and round to 1 decimal place (part a.), then asks you to do something else for part b that uses the answer to part a, should we uses the rounded number or the actual number?
eg
a) find radius to 1 d.p
b) calculate the perimeter of the circle

do you use the rounded radius or the actual value when calculating the perimeter?
I think that in methods you are supposed to use the actual number (unless specifically instructed not to), but in further questions & worked solutions, i noticed that they have always used the rounded number

[biy]

Thanks!
I have another question:
if a question asks you to find an answer and round to 1 decimal place (part a.), then asks you to do something else for part b that uses the answer to part a, should we uses the rounded number or the actual number?
eg
a) find radius to 1 d.p
b) calculate the perimeter of the circle

do you use the rounded radius or the actual value when calculating the perimeter?
I think that in methods you are supposed to use the actual number (unless specifically instructed not to), but in further questions & worked solutions, i noticed that they have always used the rounded number

If it says to use the answer in Part a). then you must use the rounded answer, as that was the answer from part a). that you were instructed to use for part b).

[Escobar]

thanks biy
so if it does not tell you to use your rounded answer, you use the actual number?
or does it just always tell you to use the rounded answer

[e]
ive been doing a few years of further exams & noticed that the working in the assessor's reports always use the rounded numbers, whether or not it states to use them in the question

[e]
interestingly, i found one instance where both the rounded and unrounded answers were accepted
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/further2_assessrep_07.pdf
module 2, q 1c

[e]found a statement about it in the 2005 assessment report
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/furthermaths2nov05.pdf
"Exact numbers should be retained in the calculator and used in the second step unless the first step was the answer to a specific question. "
so it seems that if it is an answer to a previous question, it is assumed to be applied to other parts

[RazzMeTazz]

 Can someone please explain how to do parts d.) and e.) ? [in the image attached below]
I've also attached a photo with the answers

I keep getting the wrong answer :/ so I would appreciate any explanations! 

Thank you!

 

[MightyBeh]

Can someone please explain how to do parts d.) and e.) ?

Ew, time series are annoying (imo).

2d

Use the least squares regression line and seasonal indices to estimate the sales for the business in the third quarter of 2004. Compare this with the actual figure for the third quarter of 2004 and find the percentage difference.

First off, there's two things the question is asking us for - a prediction of the cash made in the third quarter of 2004 and a calculation to show how accurate this is. I'm going to put these into two different spoilers because damn, I love spoilers. 

First part

Right, so I've highlighted above the important parts of this question. First we need to use the regression line you worked out in part c - according to the answers, it was:

But first we need to put in the third quarter of 2004, which can be calculated like this:

Where 1 is the number of years that have passed, 4 is the number of seasons (well, quarters) in that year and the +3 is to represent the third quarter of the next year. So our quarter 7. This could also be found by counting it out on the table or graph, but... I like formulas, so nyuh.

So now we can substitute that into our regression equation to make a prediction like everything else in the core module:

(rounded to 2 decimal places)

But wait a second here, that prediction is wayyyy off. The actual value is 128. We're not finished yet, we need to multiply this by the appropriate seasonal index in order to get a deseasonalised value. I'm going to work out the seasonal index because a), I couldn't see it in the answers, and b) people often make a mistake here and that might be your issue .
(I am, however, skipping through the seasonal averages here because I'm too lazy to type that out. Unless you want it, in which case just let me know)


Ignore how that's messy, on a question like this I'd usually just throw that straight into my calculator. There's two values on top because we're working out a kind of average between the two appropriate seasonal indices so we can make a (slightly?) more accurate prediction. So our seasonal index is:


So like I said before, we just multiply this by our predicted value to deseasonalise it:

This is still not quite our answer, because the question states that all values are in thousands of dollars. All we need to do is multiply by 1000, so the sales in dollars for the third quarter of 2004 is (was? It's been ten years. ) $128,174. My answer is 4 dollars off of the one you showed, because my rounding was a teensy bit inconsistent (hey, I blame the question for not stating how many decimal places!), but the method is the same.

second part

2e

Use the equation of the least squares regression line and the seasonal indices to forecast the sales for the business in the third quarter of 2005

Same stuff as before, but it's really important to note that's it's asking you for a totally unique value. So we first need to work out the value of the third quarter of 2005.

And then, like before, we put that in our regression equation:


This is not our final value! I seriously can't stress this enough - I tutor around my school casually (which means I work slave rates or for food  ) and this is seriously one of the most common mistakes people make (second only to not answering the question in context). We have to deseasonalise it first, by multiplying by the appropriate seasonal index. Luckily this is the third quarter like before so we can just grab that value instead of making me work out another one.


So that's our deseasonalised value. But we still haven't answered the question; remember that pesky context thing I mentioned like two sentences ago? That applies. Thankfully, you've highlighted the line in thousands of dollars so I'm pretty confident you already know

Like the last one, I'm off by a teensy bit - that's a rounding issue. I think it's from the regression line, but it's not too much of a big deal here. Like I said before, my rounding was inconsistent. If the question doesn't sate how many decimal places to use, don't do what I did - pick a number and stick to it. Working with data, I'd recommend 4 decimal places (as that's easy to convert to percentage, and is more accurate than one or two).

I've also attached a photo with the answers

Legend. Saved me some time <3

[StupidProdigy]

I can't figure out how to do part b (see attachment). I've tried using the sine rule and made a mistake somewhere I think...any help would be awesome

[BakedDwarf]

I can't figure out how to do part b (see attachment). I've tried using the sine rule and made a mistake somewhere I think...any help would be awesome

i got 67.7m for part b. Is that correct? (if it is, i'll post the working out)

[StupidProdigy]

i got 67.7m for part b. Is that correct? (if it is, i'll post the working out)

Yeah that's it. That would be sooo good if you could, TIA!!!

[MorgnD]

How do i complete this question from the core module? The answer booklet says the answer is e.

http://imgur.com/yvCKNrw

Thanks.

[StupidProdigy]

The total sum of all indices must be 12. we are missing one of the twelve values. To find it use 12 minus the sum of the given values

[MorgnD]

The total sum of all indices must be 12. we are missing one of the twelve values. To find it use 12 minus the sum of the given values

Thanks