Let's address the theory component of Further Maths

[Yacoubb]

Okay so the Further Maths exams are now showing some aspects where application or theoretical knowledge is required; e.g. 2012 VCAA exam 1 for Further Maths asked:

Which of the following cannot be a negative?
a) median
b) residual
c) standardised score
d) the IQR
e) correlation coefficient

the answer is in fact d. However, I can imagine many students not knowing how to appropriately approach such questions. Further Maths students lets address these theory components and have forum discussions regarding them Hope that contributions are made so we can maximise our study scores by potentially doing so !

[Quantum.Mechanic]

(a) Median can be negative for the fact in univariate data, each piece of data can be negative, hence the median can potentially be negative.
(b) Common sense dictates that for a residual graph there are points plotted above and below the zero line, which indicates a positive or negative residual.
c) Standardized score. This is a difficult one actually, only those people that have done methods would definately know that a standardized score can be negative. We realise that for a standardized score, it is the conversion of scores into a form where we have 0 as the mean, and 1 as the standard deviation, hence as standard deviation is added and subtracted from the mean a negative standardized score can exist
(d) Interquartile range is the easiest to prove that there cannot be negative.
i.e We know that IQR = Quartile 3 - Quartile 1, and that Quartile 3> Quartile 1. We can let Quartile 1 be either postive or negative
Therefore Quartile 3- Quartile 1 is positive ( if quartile 1 is positive, it makes logical sense, from 2 positive numbers a higher - a lower one is positive). However even if Quartile 1 is negative, it is Quartile 3 -- Quartile 1, which is Quartile 3 + Quartile 1 from simple addition. Hence d is always positive.
(e) Correlation co-efficient as stated in the book tells us the strength of a relationship, whether it is positive or negative. Hence a negative correlation co-efficient tells use that there is negative relationship between 2 variables

[Yacoubb]

(a) Median can be negative for the fact in univariate data, each piece of data can be negative, hence the median can potentially be negative.
(b) Common sense dictates that for a residual graph there are points plotted above and below the zero line, which indicates a positive or negative residual.
c) Standardized score. This is a difficult one actually, only those people that have done methods would definately know that a standardized score can be negative. We realise that for a standardized score, it is the conversion of scores into a form where we have 0 as the mean, and 1 as the standard deviation, hence as standard deviation is added and subtracted from the mean a negative standardized score can exist
(d) Interquartile range is the easiest to prove that there cannot be negative.
i.e We know that IQR = Quartile 3 - Quartile 1, and that Quartile 3> Quartile 1. We can let Quartile 1 be either postive or negative
Therefore Quartile 3- Quartile 1 is positive ( if quartile 1 is positive, it makes logical sense, from 2 positive numbers a higher - a lower one is positive). However even if Quartile 1 is negative, it is Quartile 3 -- Quartile 1, which is Quartile 3 + Quartile 1 from simple addition. Hence d is always positive.
(e) Correlation co-efficient as stated in the book tells us the strength of a relationship, whether it is positive or negative. Hence a negative correlation co-efficient tells use that there is negative relationship between 2 variables

LOL I do know the answer; that was merely an example to demonstrate that it is imperative we don't disregard the theory component of Further Maths because obviously you're being examined on it ^. I apologise for the energy you invested into that. Though it may be beneficial to other students!

[Yacoubb]

c) Standardized score. This is a difficult one actually, only those people that have done methods would definately know that a standardized score can be negative. We realise that for a standardized score, it is the conversion of scores into a form where we have 0 as the mean, and 1 as the standard deviation, hence as standard deviation is added and subtracted from the mean a negative standardized score can exist

I have to disagree because I think this one would be one of the easiest ones to distinctly realise it can be a negative. Any value + or negative (e.g. -0.2) indicates its position [no. of standard deviations] from the actual approximate mean. Therefore, knowing the 68-95-99.7% rule + knowing, again, the theory behind it would be beneficial for answering such questions!

[pi]

I don't think you need Further knowledge to know the IQR can't be negative... Isn't that covered in year 10 maths? (which is how I answered the question upon first seeing it)

[Yacoubb]

I don't think you need Further knowledge to know the IQR can't be negative... Isn't that covered in year 10 maths? (which is how I answered the question upon first seeing it)

MY TOPIC POST IS NOT ABOUT THE BLOODY QUESTION LOL. I mean actually coming to terms with the fact that there are OTHER components of Further Maths where some disregard the theory of it, and for 2013, we should regard the theory to potentially maximise our study scores. There's been an increasing trend in the number of theory questions over the last few years And I think its a pretty smart way of seperating the really good students who know the topics really well (theory+arithmetic) from the ones who only know how to do the arithmetic work (not sufficient!)

[Quantum.Mechanic]

Ah. That was poorly worded.
It should have been easily recognisable rather than the most difficult. Its done in probability in methods, that was how I recognised that standardized score could always be negative.

But you also clarify the point that they are all easy. It is simple, the theory is important in Further. You cannot disregard that component because its not the multiple choice questions that are hard at all, but rather the explanation/interpretations of what questions mean in Exam 2.

Pi is right. It's also done in statistic for GMA, and GMB. Its known that you will never get a negative Interquartile range

[Stick]

Exam 1 Business-related Mathematics Question 9. I cannot wait to see how much of the state got it wrong.

[Yacoubb]

Exam 1 Business-related Mathematics Question 9. I cannot wait to see how much of the state got it wrong.

Stick what modules did you do?
I'm doing Number Patterns, Graphs + Relations and Matrices.

[Stick]

I did Geometry and Trigonometry, Graphs and Relations and Business-related Mathematics.

[Yacoubb]

I did Geometry and Trigonometry, Graphs and Relations and Business-related Mathematics.

What was the answer? lol logically it looks like A, but obviouslty I don't do business-related maths + I cannot be 100% sure.

[Stick]

The answer is A. Most people chose C, I believe.

[Yacoubb]

The answer is A. Most people chose C, I believe.

Yeah I mean it logically looks correct, but again, due to disregarding the theoretical aspect of it, some people may have completely neglected the doubling in month 5 due to failing to pay month 4.