Mathematics Extension 2 Predictions (1 Viewer)

[jklol]

I lowkey like inequalities guys

 

[MemeCognoscente]

I lowkey like inequalities guys View attachment 36605

anything else >>>>> inequalities

 

[yanujw]

anything else >>>>> inequalities

And yet the statement you have just written is phrased as an inequality. That's beautifully ironic.

 

[okkk]

You know I've found that half the inequalities I've ever seen are all Am-Gm and then you like get multiple equations and add/times them together
If you don't know what you're doing fr just Am-Gm it

 

[jklol]

idk even just "am-gm" ing something may be difficult if you cant find the appropriate subsitutions, and in the majoity of cases it can be quite difficult to find the subsitutions and sometimes you need to do it more dawg

 

[okkk]

To try find the substitutions the trick is often to try match up the powers. For example, if I was like prove that a^4+b^4+c^4>abc(a+b+c), you see the 4th power so instantly you're thinking along the lines of Am-Gm for four. Then, you see three terms on the LHS and you notice that on the RHS you've got a^2bc, so a is twice the power. Therefore a good guess would be Am-Gm for a^4+a^4+b^4+c^4≥4a^2bc. And you'll find that this works out if you to it for b and c and add them together. Like fr it's tricky but there are some hints in the question itself and it helps you narrow it down to like a couple guesses. Idk if this helps

 

[jklol]

yea nah i getcha, like for this one AM-GM inequality that was in my trial paper that was just insane and even now I can't seem to get it, i tried letting and but got stuck, to this day idk how to do it lmao

 

[aim for 95+]

yea nah i getcha, like for this one AM-GM inequality that was in my trial paper that was just insane and even now I can't seem to get it, i tried letting and but got stuck, to this day idk how to do it lmao

I thought I was getting stronger until I met SBHS, Q14, 15 and 16‘s Kind regards

 

[Anounymouse352]

yea nah i getcha, like for this one AM-GM inequality that was in my trial paper that was just insane and even now I can't seem to get it, i tried letting and but got stuck, to this day idk how to do it lmao

Hope this helps

 

[d1zzyohs]

My problem with inequalities is how examiners expect you to just brute force all the possibilites of AM-GM a thousand times until one niche interpretation of their question works. It isn't a test of mathematical ability and maturity, but rather feels like a question which expects rote learning.
Something like recursive integration, is cool because you can figure out what to do by parts by your knowledge of derivatives and integrals. AM-GM inequalities are often random and just stupid.

But I guess I can't change anything. Time to study for inequalities

 

[Run hard@thehsc]

My problem with inequalities is how examiners expect you to just brute force all the possibilites of AM-GM a thousand times until one niche interpretation of their question works. It isn't a test of mathematical ability and maturity, but rather feels like a question which expects rote learning.
Something like recursive integration, is cool because you can figure out what to do by parts by your knowledge of derivatives and integrals. AM-GM inequalities are often random and just stupid.

But I guess I can't change anything. Time to study for inequalities

True. Recursive integration is relaxing ngl .

 

[jklol]

View attachment 36609
Hope this helps

WOW that is a very nice result thanks big man

 

[yanujw]

I think they're going to test a geometrically-derived inequality this year. It's quite obscure but nonetheless a part of the syllabus and makes for some unique questions.

 

[tgone]

I think they're going to test a geometrically-derived inequality this year. It's quite obscure but nonetheless a part of the syllabus and makes for some unique questions.

here's a fun one from our assignment in T4:


it can be done fairly straightforward algebraically as well, but suppose the question asks for a geometric proof... enjoy

 

[okkk]

here's a fun one from our assignment in T4:
View attachment 36612

i imagine it can be done fairly straightforward algebraically as well, but suppose the question asks for a geometric proof... enjoy

Yeah the algebraic way is really straightforward, you do Am-Gm for 2 to get x^2+(y^2+z^2)≥2xsqrt(y^2+z^2) and y^2+(x^2+z^2)≥2ysqrt(x^2+z^2) then you just add then together. I don't really know what "geometric" proof you're supposed to provide given that the RHS is not a curve in 3d space we can sketch, are you supposed to just find suitable vectors or smth and take their lengths?

 

[tgone]

Yeah the algebraic way is really straightforward, you do Am-Gm for 2 to get x^2+(y^2+z^2)≥2xsqrt(y^2+z^2) and

hence why I asked for geometric haha

 

[tgone]

Yeah the algebraic way is really straightforward, you do Am-Gm for 2 to get x^2+(y^2+z^2)≥2xsqrt(y^2+z^2) and y^2+(x^2+z^2)≥2ysqrt(x^2+z^2) then you just add then together. I don't really know what "geometric" proof you're supposed to provide given that the RHS is not a curve in 3d space we can sketch, are you supposed to just find suitable vectors or smth and take their lengths?

what does remind you of

 

[okkk]

what does remind you of

The length of the vector (0,y,z) or like a semi circle equation, idk how that's gonna help though

 

[tgone]

The length of the vector (0,y,z) or like a semi circle equation, idk how that's gonna help though

the geometric way is essentially a more convoluted version of the easy algebraic way, you just get to draw a nice triangle instead of immediate substitution lmao

edit: in fact, its exactly the same working out as the algebraic way... just imagine the teachers decided to include an extra mark to test the geometric proofs syllabus point

 

[okkk]

the geometric way is essentially a more convoluted version of the easy algebraic way, you just get to draw a nice triangle instead of immediate substitution lmao

edit: in fact, its exactly the same working out as the algebraic way... just imagine the teachers decided to include an extra mark to test the geometric proofs syllabus point

As in draw a triangle to prove Am-Gm for 2? Got scammed. Normally all the geometrical proofs I see are all functions and areas under the curve tbh