VCE Methods Question Thread!

[james.358]

Although your solution is technically correct, I do not believe you will be awarded the mark if it was a VCAA exam. Either way, now that you know the correct method, you shouldn't have to worry about it

[schoolstudent115]

Hello,

Prove that if (a/n) is irreducible then (a/n)^2 will also be irreduicble for a =/= 1, 0, n and n =/= 1, 0, a.

Thanks.

I have a direct proof of this.

Suppose a/n is irreducible. Therefore a and n share no common factor.

Factors of a:
Factors of b:

Now note that the quotient of any two factors of b and a will not be an integer.
*sub-proof:
*Suppose there does exist an i and j such that , then this would imply that . If some x is a factor of y, and y is a factor of z, then x is a factor of z. (Y=kx, z=ly = (lk)x). Therefore it follows that since b_j is a factor of a_i, then b_j is a factor of a, which is a contradiction since A and B share no factors.
— back to the proof
If there is no integer quotient , then the square of this will also not be an integer, is not an integer. And more generally, no product of quotients is an integer. But every factor of a^2 is either a factor of a or a product of 2 factors. So if there is no integer result to , then there is no integer result to , therefore is irreducible**.

** That last statement is not true generally but is true in relation to factors. I could prove that but it is a bit complex.

[keltingmeith]

Although your solution is technically correct, I do not believe you will be awarded the mark if it was a VCAA exam. Either way, now that you know the correct method, you shouldn't have to worry about it

Entirely untrue - there can very easily be multiple methods to solve a maths equation, with all of them being just as correct as each other. Hell, there's often multiple ways that any given mathematical fact can be proven - did you know that there are over 100 ways to prove Pythagoras' theorem?

Now, the study design does not specifically list general solutions to circular functions at all - and while I doubt this means they're NOT assessable (there are still points that can be interpreted to mean, you should know the general solution to circular functions), this DEFINITELY means VCAA does not have a prescribed method for answering these questions. If your answer is still correct, you'll still get the marks - and if you answered it a mathematically correct way, you'll still get the answers for that method. But also, to claim that there is a "correct" or an "incorrect" method in this case is kind of insulting to maths as a profession, so sorry if I got a little snarky

-snip-

I just want to add that I really like this proof, and discrete maths in general is just <3, but this further proves my point about this not being a methods question lol

[a weaponized ikea chair]

Entirely untrue - there can very easily be multiple methods to solve a maths equation, with all of them being just as correct as each other. Hell, there's often multiple ways that any given mathematical fact can be proven - did you know that there are over 100 ways to prove Pythagoras' theorem?

Now, the study design does not specifically list general solutions to circular functions at all - and while I doubt this means they're NOT assessable (there are still points that can be interpreted to mean, you should know the general solution to circular functions), this DEFINITELY means VCAA does not have a prescribed method for answering these questions. If your answer is still correct, you'll still get the marks - and if you answered it a mathematically correct way, you'll still get the answers for that method. But also, to claim that there is a "correct" or an "incorrect" method in this case is kind of insulting to maths as a profession, so sorry if I got a little snarky

I just want to add that I really like this proof, and discrete maths in general is just <3, but this further proves my point about this not being a methods question lol

Okay, I admit it.

This is not a methods question. But it is also not a specialist question. Here's what happened:

I was doing methods homework when I reached 3/5 and I had to square it, getting 9/25.  Well, one thought led to another and I noticed that if (a/b) was irreducible so was (a/b)^2 (got completely sidetracked form the homework). I tried to prove it using my elementary understanding of proof by contradiction but could not. But because I was so interested in it, and I thought that there could be an exception to the rule, I had to find out. A google search came up with nothing, so, lo and behold, I came to my good old friend, AtarNotes.

[schoolstudent115]

But this further proves my point about this not being a methods question lol

Lol true. Even in spec they wouldn't ask this most likely. If they did you would have to have first gone through the unit on number theory (euclidean algorithm etc.) to have a good base.

[keltingmeith]

Okay, I admit it.

This is not a methods question. But it is also not a specialist question. Here's what happened:

I was doing methods homework when I reached 3/5 and I had to square it, getting 9/25.  Well, one thought led to another and I noticed that if (a/b) was irreducible so was (a/b)^2 (got completely sidetracked form the homework). I tried to prove it using my elementary understanding of proof by contradiction but could not. But because I was so interested in it, and I thought that there could be an exception to the rule, I had to find out. A google search came up with nothing, so, lo and behold, I came to my good old friend, AtarNotes.

Loooool

I'm not against asking random level questions on AN, but maybe discuss with the mods on a better place to post it so as to not frighten other students 😅

Lol true. Even in spec they wouldn't ask this most likely. If they did you would have to have first gone through the unit on number theory (euclidean algorithm etc.) to have a good base.

Funnily enough, there's an argument that it could fit specialist 1/2, but definitely not 3/4 because you're right - the relevant mathematics isn't taught there

[schoolstudent115]

Okay, I admit it.

This is not a methods question. But it is also not a specialist question. Here's what happened:

I was doing methods homework when I reached 3/5 and I had to square it, getting 9/25.  Well, one thought led to another and I noticed that if (a/b) was irreducible so was (a/b)^2 (got completely sidetracked form the homework). I tried to prove it using my elementary understanding of proof by contradiction but could not. But because I was so interested in it, and I thought that there could be an exception to the rule, I had to find out. A google search came up with nothing, so, lo and behold, I came to my good old friend, AtarNotes.

Here is my complete proof (I left out one small part in the post I made before, but here is the full version).

[a weaponized ikea chair]

Here is my complete proof (I left out one small part in the post I made before, but here is the full version).

Thanks

[Bri MT]

I'm not against asking random level questions on AN, but maybe discuss with the mods on a better place to post it so as to not frighten other students 😅

Agreed that asking questions is good but would be best not to potentially scare other students unnecessarily.

Imo - in general if there's no clear place to post it best practice would be to guess for closest fit (or ask if you're really unsure & would like guidance) and let people know in the post that it's outside the scope of the study design

[Corey King]

Hey guys,
I am beginning the year 11 textbook for Methods. In it, there are revision questions for previous years at the beginning.
I am stuck on this question: https://www.symbolab.com/solver/solve-for-equation-calculator/solve%20for%20x%2C%20%5Cfrac%7Ba%7D%7Bx%2Ba%7D%2B%5Cfrac%7Bb%7D%7Bx-b%7D%3D%5Cfrac%7Ba%2Bb%7D%7Bx%2Bc%7D.
There must be a simpler way to solve for x in this equation than the method Symbolab is suggesting.
Anybody know how to solve this?
Would be much appreciated,
Corey

[james.358]

Hey Corey！

There is indeed a much simpler way. One problem with Symbol Lab is that it "brute forces" its way to the answer. It is much easier if you do a bit of algebraic manipulation. If you have any questions with my solution don't hesitate to ask!

James

[thatdumbstudent]

Can someone please explain this Bernoulli trial question to me?
During the wet season, the probability that it rains on any given day in Cairns in northern Queensland is 0.89. I am going to Cairns tomorrow and it is the wet season. Let X be the chance that it rains on any given day during the wet season.

- Find Pr(μ−2σ≤X≤μ+2σ)

so I had no problem figuring this out and got Pr(0.2642 ≤ X ≤ 1.5158)

however... I don't get why the final answer is this? (photo attached)

I just don't get why it equals to the Pr(X = 1) thingy. this is probably a dumb question but if someone could explain why I'd appreciate it lol

[ArtyDreams]

Can someone please explain this Bernoulli trial question to me?
During the wet season, the probability that it rains on any given day in Cairns in northern Queensland is 0.89. I am going to Cairns tomorrow and it is the wet season. Let X be the chance that it rains on any given day during the wet season.

- Find Pr(μ−2σ≤X≤μ+2σ)

so I had no problem figuring this out and got Pr(0.2642 ≤ X ≤ 1.5158)

however... I don't get why the final answer is this? (photo attached)

I just don't get why it equals to the Pr(X = 1) thingy. this is probably a dumb question but if someone could explain why I'd appreciate it lol

Someone correct me if I'm wrong (I've already seriously forgotten my probability from last year lol)

So: we know that Pr(0.2642 ≤ X ≤ 1.5158).
This is a range - since we are talking about days you can't actually have 1.5158 of a day, etc.
So we need to fix that domain that its given. Since X must be less that 1.5158, that gets rounded to 1. You also cannot have less than 0.2642, making that become 1 as well.

Therefore, Pr(X=1).

In simple terms, you just need to fix that domain so you have whole numbers.

Hope this helps somewhat! (I feel like I've forgotten so much so I'm sure theres a better explanation for this, but I hope it helps in the meantime!)

[Azila2004]

Hello! I hope you all are doing well

I have a question on sinusoidal graphs, it's a small part of a larger question.
Find h if d=0 when h=0 for the equation d= 2 +/- 3sin(2pi/15(t-h))

I wrote the 3 as either negative or positive as we only know that the amplitude is 3. I'm unsure whether this is enough information to find h, and I am confused since wouldn't there be an unlimited values of h? The answer states that h = 1.74202.

I would really appreciate some help!  (•◡•) /

[zhouzhennan]

Can someone pls confirm this: Dom of f(g(x)) = dom of g(x)
And how would i find the range of f(g(x)) with tech free? Would it just be the intersection of the ranges of both functions?