VCE Methods Question Thread!

[dylan.kumar21]

This isn't a result you have to prove - you can just use it directly. If you're still unsure, feel free to post an answer to that question, and we can let you know if you've shown enough working

ok, thankyou

[Corey King]

Hey guys,
Should the domain for b) not be [-1,1]. Why are they allowed to express it as an inequality when there are only two discrete values included in the set?
https://gyazo.com/eaff941de2318f3c5b06128b4f254efb
Many thanks,
Corey

[Corey King]

Additionally,
For question c), why can you not just state the domain as x >/= 0?
We seemed to happily assume for the other questions that the numbers all existed in the domain and range of the real numbers.

[keltingmeith]

Hey guys,
Should the domain for b) not be [-1,1]. Why are they allowed to express it as an inequality when there are only two discrete values included in the set?
https://gyazo.com/eaff941de2318f3c5b06128b4f254efb
Many thanks,
Corey

The set [-1,1] is identical to the set \(\{x:-1\leq x\leq 1\}\) - they're the exact same thing, just written in two different ways. Also, that set has infinitely many discrete values - it's a continuous set.  You can write either \(x\in [-1,1]\) or what they've given as a response, both are equally correct.

Additionally,
For question c), why can you not just state the domain as x >/= 0?
We seemed to happily assume for the other questions that the numbers all existed in the domain and range of the real numbers.

I mean - the technical answer is you can't just state that because it's not appropriate mathematical/computational language. It sounds stupid that you need to include the curly brackets and the x and all that to give \(\{x:x\geq 0\}\), but yeah, you kinda got to. The curly brackets let you know that it's a set of solutions, and not just a restricted pronumeral, hence why we do it. Tbh, it's all just semantics, and not worth worrying about or thinking too much about.

I'm also not sure what you mean by that last sentence, either? None of these questions have domains or ranges that we assume are all the real numbers - hell, the whole for these questions is that none of them have domains that are all the real numbers, and the ranges should be similar. Potentially you can clarify the question somewhat?

[Corey King]

Ah I see, got you

That restricted pronumeral statement provided some clarity . I was more asking though why you cant say \{x:-1\leq x\leq 1\} instead of what they wrote as the domain, being R+ u {0}.
I understand what they wrote, just not why they couldn't have written \{x:-1\leq x\leq 1\} instead. It seemed easier as it was already included in the question, just making sure it's not wrong to have said that (as I did).

I think being confused about why they wrote R in the domain answer led me to believe you may have to state R instead of just using an inequality, and also I thought they didnt use it earlier because I thought [1,3] were just two points and not an interval. I see now how the question doesn't make sense.

Thanks Kelting,
Corey

[keltingmeith]

Ah I see, got you

That restricted pronumeral statement provided some clarity . I was more asking though why you cant say \{x:-1\leq x\leq 1\} instead of what they wrote as the domain, being R+ u {0}.
I understand what they wrote, just not why they couldn't have written \{x:-1\leq x\leq 1\} instead. It seemed easier as it was already included in the question, just making sure it's not wrong to have said that (as I did).

I think being confused about why they wrote R in the domain answer led me to believe you may have to state R instead of just using an inequality, and also I thought they didnt use it earlier because I thought [1,3] were just two points and not an interval. I see now how the question doesn't make sense.

Thanks Kelting,
Corey

ooooo okay

Yeah, so there's two notations you need to be familiar with - and I'm going to explain them both just so that you're crystal clear on the difference, because it's not quite as clear as you might think you've interpreted.

The first notation is set notation - this one, I think you're fine with. Set notation is the only way to write x as a set of discrete numbers - e.g., {-1,5,2,7,6,-503}, which is a key point.

The second notation, the one you didn't realise was one, is interval notation. The way this notation works is that the two displayed numbers are the end-points, and all of the numbers on the continuous real interval are included. However - a key point is that the shape of the bracket tells you whether to include the end points or not. Essentially, [a,b] means all the numbers between a and b, including a and b, and (a,b) means all the numbers between a and b, but NOT including a and b. You can mix and match these, as well - so (-1,2] would mean all of the numbers between -1 and 2, including 2, but not including 1. In set notation:

\[[a,b]=\{x:a\leq x\leq b\}\]
\[(a,b)=\{x:a<x<b\}\]

Next - for the attachment you gave, none of the questions wrote the domain as \(\mathbb{R}^+\cup\{0\}\)? Is there one you forgot to attach?

[Corey King]

ooooo okay

Yeah, so there's two notations you need to be familiar with - and I'm going to explain them both just so that you're crystal clear on the difference, because it's not quite as clear as you might think you've interpreted.

The first notation is set notation - this one, I think you're fine with. Set notation is the only way to write x as a set of discrete numbers - e.g., {-1,5,2,7,6,-503}, which is a key point.

The second notation, the one you didn't realise was one, is interval notation. The way this notation works is that the two displayed numbers are the end-points, and all of the numbers on the continuous real interval are included. However - a key point is that the shape of the bracket tells you whether to include the end points or not. Essentially, [a,b] means all the numbers between a and b, including a and b, and (a,b) means all the numbers between a and b, but NOT including a and b. You can mix and match these, as well - so (-1,2] would mean all of the numbers between -1 and 2, including 2, but not including 1. In set notation:

\[[a,b]=\{x:a\leq x\leq b\}\]
\[(a,b)=\{x:a<x<b\}\]

Next - for the attachment you gave, none of the questions wrote the domain as \(\mathbb{R}^+\cup\{0\}\)? Is there one you forgot to attach?

Hey Kelting,
Example 4 question c) had a domain of (\mathbb{R}^+\cup\{0\}\) if I remember correct.

[keltingmeith]

Hey Kelting,
Example 4 question c) had a domain of (\mathbb{R}^+\cup\{0\}\) if I remember correct.

Double check what you sent us - question c has it written as \(\{x:x\geq0\}\) - which is certainly the same thing, but written in set notation instead of interval notation, so sorry if I'm arguing semantics. Just wanted to make sure I haven't missed a question you meant to send. (btw, you missed the \ before the ( in your math code)

[Corey King]

Double check what you sent us - question c has it written as \(\{x:x\geq0\}\) - which is certainly the same thing, but written in set notation instead of interval notation, so sorry if I'm arguing semantics. Just wanted to make sure I haven't missed a question you meant to send. (btw, you missed the \ before the ( in your math code)

Oh I see, I didn't clip all of the stuff in.
https://gyazo.com/1e57a14d04b22f33708258a3e2c4dacf
Hopefully this clears up my question. You've already answered it though, saying those two notations are both valid. Just wanted to make sure the Interval notation was also acceptable as an answer since it seemed weird to me they would re-write it.

[55232Jeremy]

Hi guys,
This may be a really stupid question, but I've done a couple of methods exams now and for questions like 'Find the area of the shaded region', i am just confused on whether to include 'units^2' or not at the end of my answer. Some of the examiner reports I've looked at include 'units^2' at the end of the answer for one question to this type of question and then don't include it in another similar question. Will i get marked down for not including it or am i just being overly stressed for no reason?

[The Cat In The Hat]

Hi guys,
This may be a really stupid question, but I've done a couple of methods exams now and for questions like 'Find the area of the shaded region', i am just confused on whether to include 'units^2' or not at the end of my answer. Some of the examiner reports I've looked at include 'units^2' at the end of the answer for one question to this type of question and then don't include it in another similar question. Will i get marked down for not including it or am i just being overly stressed for no reason?

It's not a stupid question - it's one I'd never even noticed before - thank you! I think if you remember to do it, always do it, but I don't think you should be stressed over it. I could be wrong, though, since I'm only a year 12 student (and doing quite badly too).

[Corey King]

Hi guys,
This may be a really stupid question, but I've done a couple of methods exams now and for questions like 'Find the area of the shaded region', i am just confused on whether to include 'units^2' or not at the end of my answer. Some of the examiner reports I've looked at include 'units^2' at the end of the answer for one question to this type of question and then don't include it in another similar question. Will i get marked down for not including it or am i just being overly stressed for no reason?

I'd say it's always worth including it. There's no need to worry about whether you should or shouldn't include it that way, as since it is the most correct answer you won't be running the risk of losing a mark

[Corey King]

Hey guys,
I'm doing Functions at the moment (Units 1 -2).
I'm learning about writing relations in function notation, and there's something I don't quite understand.
So there is the Domain, and then there is the Maximal domain within which the domain can be defined.
Then there's the Codomain, within which the Range can be defined.
So why is it that when we write out a relation in function notation, we use the domain and then the codomain?
Why would we not want to show the Range along with the Domain?
An example:
(example 10, question b)
https://gyazo.com/5696f658cb7a6b99ddabc3dfd4e15538
Instead of R, wouldn't (-inf,5] be more logical/useful?

What am I missing
Many thanks,
Corey

[james.358]

Hey Corey,

The co-domain is simply any values that y can take, which at Methods its just R. There is no point defining a range in the function as we can simply work it out using the domain, so it would be redundant.

I think Keltingmeith will be more qualified to explain why we don't have it, but for now just be glad you don't have to do even more work when defining a function 

Hope this helps!
James

[Corey King]

Hey Corey,

The co-domain is simply any values that y can take, which at Methods its just R. There is no point defining a range in the function as we can simply work it out using the domain, so it would be redundant.

I think Keltingmeith will be more qualified to explain why we don't have it, but for now just be glad you don't have to do even more work when defining a function 

Hope this helps!
James

Hahah fair point!
It's good to know the codomain will stay at R. So I don't need to really worry about it rn.

Thanks James