VCE Methods Question Thread!

[lzxnl]

Hey!
i remember doing this question in 2018 Australian Maths comp.
if i am not wrong the the fraction of the shaded area (triangle) is compared to the hexagon should be 1/3.
The way i did is, just found the area of 6 tiny triangles in hexagon with height of h/2
so, area of hexagon = 3sh/2
and area of shaded area triangle = sh/2
fraction of comparison = area of triangle(shade)/area of hexagon = 1/3

I just realised that edge of the hexagon doesn't lie on a circle so my plan wasn't going to work. Do it that way.

[aspiringantelope]

Hey!
i remember doing this question in 2018 Australian Maths comp.
if i am not wrong the the fraction of the shaded area (triangle) is compared to the hexagon should be 1/3.
The way i did is, just found the area of 6 tiny triangles in hexagon with height of h/2
so, area of hexagon = 3sh/2
and area of shaded area triangle = sh/2
fraction of comparison = area of triangle(shade)/area of hexagon = 1/3

Thanks a lot!!
Also have another question which I asked at an earlier point and got an answer but I still don't understand.

A shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells them all for $2.50 a dozen and makes $15 profit. How many dozens were there in each of the crates?

Can someone also give me an answer and step-by-step formula for it when they work it out?
Thanks a lot in advance.

[RuiAce]

Thanks a lot!!
Also have another question which I asked at an earlier point and got an answer but I still don't understand.

A shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells them all for $2.50 a dozen and makes $15 profit. How many dozens were there in each of the crates?

Can someone also give me an answer and step-by-step formula for it when they work it out?
Thanks a lot in advance.

Note that this variable \(x\) had to be introduced, or else we don't we don't have some kind of 'reference', i.e. something to base the entire problem off.




So the first crate had 9 dozens. Consequently, the second crate had 12 dozens.

[aspiringantelope]

Note that this variable \(x\) had to be introduced, or else we don't we don't have some kind of 'reference', i.e. something to base the entire problem off.




So the first crate had 9 dozens. Consequently, the second crate had 12 dozens.

Wow!
Thanks SOOO MUCH @RuiAce !! I've been stuck on this question for 20 minutes before -__________________-

[captainbobted]

Hello!

For the question, "Solve each of the following pairs of simultaneous equations, giving your answer in terms of a parameter lambda (let's call it ^). x-y+z=4 and -x+y+z=6". It eventually leads to me finding that z=5, which is correct, but for the use of the lambda to find the parameter which the equations exists in the answers say to let y = ^. So my question is what's the reasoning behind letting y=^ rather than x and then solving for y?

Thank youuuu ^_^

[RuiAce]

Hello!

For the question, "Solve each of the following pairs of simultaneous equations, giving your answer in terms of a parameter lambda (let's call it ^). x-y+z=4 and -x+y+z=6". It eventually leads to me finding that z=5, which is correct, but for the use of the lambda to find the parameter which the equations exists in the answers say to let y = ^. So my question is what's the reasoning behind letting y=^ rather than x and then solving for y?

Thank youuuu ^_^

You actually can let \(x\) be the parameter \(\lambda\) instead (and then solve for \(y\)).

There seems to be a convention that the variables that appear 'later on' instead of 'earlier' ones get used for \(\lambda\) (which, for those problems you can see that \(y\) appears just 'slightly after' \(x\) does). But in reality it doesn't matter and both of them will lead to correct answers, even though they look different.

[Evolio]

Hi.
I was wondering how to go about solving question 1.b?

[AngelWings]

Hi.
I was wondering how to go about solving question 1.b?

Hey Evolio. Why don’t you have a shot at this question first and tell us what you think the answer should be? It’s a lot better for everyone if you give it a try first or tell us which concepts you believe are involved in this question, if you’re stuck at the start.

As per Aaron’s post on the previous page:

PSA:

* If you are going to post a question, try to show current understanding so you can get meaningful help, not just answers/working out so you can rote learn that particular question. As we know, maths requires application of knowledge to a broad range of questions. If you just post a question with zero effort (meaning no working out and just a copy/pasted question expecting a full blown answer), it not only shows a lack of respect to the people who volunteer their time to help you but it also doesn't address the main issue that you have with your understanding.

Examples of showing understanding

* A brief written explanation as to what you know about this topic
* The particular point where you are stuck / the point where you are doubtful (e.g. is it -1 or +1?)
* Your current working out that you have.

* If you respond to questions, please encourage them to show to you what they currently know or even start off with a prompting question (Sine has done this perfectly as above) before giving them the answer/full solution. If they "do not know" or "don't know where to start", do they have prior content knowledge or is there a topic that they can think back to, to assist with their problem? Prompt them to think for themselves.

Examples of prompting

* What is the first step to solving this problem?
* Think about concept x or concept y... how does this relate to this problem?
* Giving short hints that will prompt the user to go back and have a think before posting again.

Thank you for reading and I hope that you'll consider this to ensure that student learning benefits in a meaningful way. Obviously I have posted this a few times now so I won't be posting it anymore, I really hope people will think about this (on both ends - those asking questions and those answering questions).

[redpanda83]

Idk if this is the right place for this, as this problem isnt mathods level.
If you know how to do solve the question below. Pls help! 
I dont know what to do with it. It would be more helpful if you could provide a technique/ procedure to solve this  as i am unaware what to do.
Thanks! 

[Lear]

Where’d you even get this question from?!

[redpanda83]

I was doing some past maths competition exams. I was bored...........
This one is 2018 melbourne uni senior mathematics competition but similar type of questions appear in AMC as well.
Idk what to do with these type of questions

[Evolio]

Hey Evolio. Why don’t you have a shot at this question first and tell us what you think the answer should be? It’s a lot better for everyone if you give it a try first or tell us which concepts you believe are involved in this question, if you’re stuck at the start.

As per Aaron’s post on the previous page:

I tried attaching an image of my graph but the file is too large apparently. So basically the period is 2pi. Amplitude is 3. Range is -3 to 3 inclusive. I got this stuff right. However, the answer's graph drew it up until the 5pi/2 instead of 2pi which is one period. The question is saying to show one complete cycle which is one period and so I am confused why they went over? They seem to have taken into account the translation in the question as it moves to the right. This is what I am confused about like do we draw it as they did or just draw it up until the period for one cycle.

[Aaron]

I tried attaching an image of my graph but the file is too large apparently.

You can upload it to http://imgur.com/ or another image uploading service and then edit your post by clicking 'Modify' in the top right hand corner, with the link to it.

Thank you for cooperating with the reasonable request of providing working out / explanation etc. to assist in rectifying your main problem for true understanding.

[Sine]

I tried attaching an image of my graph but the file is too large apparently. So basically the period is 2pi. Amplitude is 3. Range is -3 to 3 inclusive. I got this stuff right. However, the answer's graph drew it up until the 5pi/2 instead of 2pi which is one period. The question is saying to show one complete cycle which is one period and so I am confused why they went over? They seem to have taken into account the translation in the question as it moves to the right. This is what I am confused about like do we draw it as they did or just draw it up until the period for one cycle.

did they start at 0 or pi/2?

[Evolio]

You can upload it to http://imgur.com/ or another image uploading service and then edit your post by clicking 'Modify' in the top right hand corner, with the link to it.

I will try that next time!

Thank you for cooperating with the reasonable request of providing working out / explanation etc. to assist in rectifying your main problem for true understanding.

All good.

did they start at 0 or pi/2?

Pi/2