VCE General & Further Maths Question Thread!

[theBRENDAN97]

How do you confirm the skew of something, is it something to do with the proportion of mean to median?
Thanks

[StupidProdigy]

When asked to list what types of transformations would be suitable for a table of data values, should I only base my answer on the 'circle of transformations' suggestion, or compare r-values for more accuracy? One of the transformations in the 'circle of transformations' gives a pretty low r value compared to the other transformations.

[AngelWings]

How do you confirm the skew of something, is it something to do with the proportion of mean to median?
Thanks

You can, if you're just given these pieces of information.
A positively skewed graph will have the median on the left of the mean.
A symmetric one (similar to a bell curve/ normal distribution) will have the median and the mean at the same point/ value.
A negatively skewed graph will have the median on the right of the mean.

Alternatively, on a box plot, you will see this as:
positively skewed - the right 'whisker' will be longer than the left. (or the line from Q3 to the maximum)
symmetric - Q2 will be in the centre, both whiskers are equally long.
negatively skewed - the left 'whisker' will be long than the left.

Of course, you can work it out if you're given raw data as well.

(Source: some of this has been taken from my Further teacher's notes from last year.)

When asked to list what types of transformations would be suitable for a table of data values, should I only base my answer on the 'circle of transformations' suggestion, or compare r-values for more accuracy? One of the transformations in the 'circle of transformations' gives a pretty low r value compared to the other transformations.

I'm not really sure what you meant here (could you provide an example?), but how I interpreted this question, you're asking about questions which ask you what's the best transformation to apply for that set of data.

Well... the first thing is to see the overall look of the data. Is it curved? Which way is it curved?
How would an x² or a 1/y transformation affect the data?
Would it have the highest possible r² value? (Since the highest r² value will provide you with the closest fitting transformation and 'neatest' line - i.e. "more accuracy" in your terms.) (I know I'm explaining this horribly, I'm sorry. I hope I explained it well enough. It's sort of difficult to word it.)

[MightyBeh]

When asked to list what types of transformations would be suitable for a table of data values.

I think the keyword here is list; definitely base it off the circle of transformations. As long as you're taking it from the right quadrant, it will be suitable. I'm 90% sure that they'll ask for 'most' suitable or appropriate if they want an r². If it's a question written by a teacher you might want to double check though.

Generally, go by the marks. Not that it's always applicable, but if there's more marks for your question than transformations in your quadrant than I'd say it's also a good idea to list the r² values and state which is most accurate.

(I know I'm explaining this horribly, I'm sorry. I hope I explained it well enough. It's sort of difficult to word it.)

^^^
This 100%. I would come around with answers way sooner if I knew how to put them into legible English.

[Wackky]

Esssential Further Mathematics Question 21A 7b)

"Wendy and Frank buy and sell a block of land within the same financial year, making a profit of $62 000.
If Frank has other income of $32 000, and the profit is all his, how much capital gains tax must be paid on the land?"

The textbook answer says $21 480 but I keep getting $18 600 (Frank is in tax subdivision 3 so 62 000*0.30=18 600). Could I please have a second opinion from someone to clarify if I'm doing something wrong? Thanks.

[scarletmoon]

When sketching inequalities do you shade the wanted or unwanted region. Does it matter as long as you have a key (stating what the shaded region represents) next to the graph?

[Peanut Butter]

When sketching inequalities do you shade the wanted or unwanted region. Does it matter as long as you have a key (stating what the shaded region represents) next to the graph?

You can shade either area as long as your key matches what you have shaded

[random_person]

When sketching inequalities do you shade the wanted or unwanted region. Does it matter as long as you have a key (stating what the shaded region represents) next to the graph?

On exams they usually specify what region they want you to shade in. If you have a key you should be fine, but don't give the examiner a reason to deduct marks - easy thing is to just do what they have specified.

[dankfrank420]

If you had to label the axis of a residual plot, what would you label them as?

Also, I had a conceptual question on a SAC.

You're given 200 data points (univariate data). You randomly select 20. You find the mid/min/max of your data.

If another person randomly selected 20 from the same 200 data points, do you expect the mid/min/max to be the same?

[Vexna]

Can someone explain to me what a triangular matrix is?

Thanks.

[keltingmeith]

Can someone explain to me what a triangular matrix is?

Thanks.

It's when all the 0s of a matrix form a triangle on or just before the leading diagonal. They can be in the upper or lower corner, here's some examples:



Note that it doesn't matter what happens on the leading diagonal. The 0s in the last one could have a mixture of non-zeroes as well, I have just illustrated this way so that you can clearly see the "triangle".

[Vexna]

It's when all the 0s of a matrix form a triangle on or just before the leading diagonal. They can be in the upper or lower corner, here's some examples:



Note that it doesn't matter what happens on the leading diagonal. The 0s in the last one could have a mixture of non-zeroes as well, I have just illustrated this way so that you can clearly see the "triangle".

Thanks for such a clear explanation!

[StupidProdigy]

How many modes does there have to be before the data is considered to have "no modes"?

Example: 1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9

The modes for this data are 1, 3, 5, 7, 9

Is having 5 modes too many?

It wouldn't matter. It wouldn't just randomly switch to "no modes", there is no set point for such a thing to happen haha!

[random_person]

In a further core sac are we suppose to draw residuals/ scatterplots and all those other charts accurately? It just seems too time consuming tbh

Quite accurately in SACs depending on your teacher. My further teacher marked graphs quite harsh. Definitely label your axes and make your scale nice and even. On the exam, most questions will ask you to fill in a missing point, never seen an exam yet where you have to draw all the points.

[Losingmotivation]

Hi everyone,
Had a question regarding residuals..
Say if I had a residual plot and it had a pattern (like the parabola kind of shape in the image attached), what transformation would you apply to make it linear?



Thanks! and goodluck for all your sacs everyone