new resources for new syllabus (1 Viewer)

[tywebb]

is awful for how shallow it is.

what i find shallow is in the proof topic u get to prove heaps of things but never use those results ever again for the rest of your life.

u are told by the teacher the things u proved are oos so u are not allowed to use it.

a simple example is proving the AM-QM inequality. It can be done easily within the scope of the syllabus.

but then u are told don't u dare ever use the AM-QM inequality for anything because it is oos! (and i have seen some hsc questions where it can be used if one were allowed to)

this is ridiculous and antithetic to how maths actually works.

 

[tywebb]

what it amounts to is this:

real maths: prove things so that u can use them to do many other things

school maths: prove things so that u never use them ever again and if u dare disobey u will be punished for doing oos.

 

[coolcat6778]

I just checked out this stupid textbook called Mastering Mathematics as I've never heard of it before, and oh my god it's so fucking shit.

Are you a textbook, or a stupid fill in the blank primary school ahh worksheet?

If I were a person who bought this textbook, I would be pissed off to find out that it doesn't even teach me the content. I would have just used past hsc papers and thsc if I wanted questions, ya dumb fuck (the author of this book).

 

[Flatuitous]

stop i actually hated php and i dont get it

it's legit the most obvious thing ever

if i have 3 holes and i have 4 pigeons, obviously i can't fit 1 pigeon into each hole

it was so simple my teacher couldn't even explain it and lwk js said it was logical

 

[Flatuitous]

I just checked out this stupid textbook called Mastering Mathematics as I've never heard of it before, and oh my god it's so fucking shit.

Are you a textbook, or a stupid fill in the blank primary school ahh worksheet?

If I were a person who bought this textbook, I would be pissed off to find out that it doesn't even teach me the content. I would have just used past hsc papers and thsc if I wanted questions, ya dumb fuck (the author of this book).

View attachment 51831

That's because it works best as a practice questions textbook

It doesn't teach you things like cambridge does, it goes straight into questions
Very good complementary as a teacher teaches you content and gives questions from MM (as mine does)

the mastering maths textbook has amazing questions in there ranging from easy to hard

 

[Flatuitous]

with the formal introduction of the cauchy-schwarz inequality as we transition from current syllabus to new one one might reenvision inequalities as in the following example



rephrase it for current syllabus

Spoiler: answer

A nice trick that works is also

a^3/b + b^3/c + c^3/a >= ab + bc + ac

Consider
a^3/b + b^3/c + bc >= 3ab
b^3/c + c^3/a + ac >= 3bc
c^3/a + a^3/b + ab >= 3ac

Summing up, we achieve the wanted result

 

[Flatuitous]

Why would they remove eulers form? It’s intuitive for understanding how args and moduli work when doing operations with complex numbers

because of questions like i^i and sin(x) = 2

 

[Flatuitous]

sorry for the necropost, guys

 

[Dzeeshr]

because of questions like i^i and sin(x) = 2

What do you mean?

 

[coolcat6778]

maybe because cisgender(x) is the best looking format.

 

[jane1820]

it's legit the most obvious thing ever

if i have 3 holes and i have 4 pigeons, obviously i can't fit 1 pigeon into each hole

it was so simple my teacher couldn't even explain it and lwk js said it was logical

yeah im just stupid

(i got every php q right even without understanding what i was doing)

 

[Flatuitous]

What do you mean?

e^ix is defined in the 2017 hsc syllabus
but things like Ln(z) are not

To find a value of i^i, we set out
i = e^(ipi/2 +/- 2kpi)
We're just gonna consider the principal argument for this one
i = e^(ipi/2)
i^i = (e^ipi/2)^i
= e^(i^2 pi/2)
= e^(-pi/2)

So we've found a solution
but when did you ever learn that (e^(ipi/2))^i = e^(i^2 pi/2)

Things like (a^b)^c for complex value of a, b, c are not well defined for hsc

Consider this:
We've learnt de moivre's theorem
(e^itheta)^n = e^(nitheta) for integer values of n

What about rational?
Let's say (e^ix)^(1/2) = e^(ix/2) holds
Now consider x = 2pi and you'll see how the problem arises

What about irrational?
See here:

Desmos | Graphing Calculator

www.desmos.com

Set n = sqrt(2)

What about imaginary?

We stray further down the rabbit hole when we introduced euler's form into the syllabus

 

[Flatuitous]

yeah im just stupid

We love a self-aware queen

 

[jane1820]

We love a self-aware queen

So you love me

 

[Flatuitous]

So you love me

no

 

[Dzeeshr]

e^ix is defined in the 2017 hsc syllabus
but things like Ln(z) are not

To find a value of i^i, we set out
i = e^(ipi/2 +/- 2kpi)
We're just gonna consider the principal argument for this one
i = e^(ipi/2)
i^i = (e^ipi/2)^i
= e^(i^2 pi/2)
= e^(-pi/2)

So we've found a solution
but when did you ever learn that (e^(ipi/2))^i = e^(i^2 pi/2)

Things like (a^b)^c for complex value of a, b, c are not well defined for hsc

Consider this:
We've learnt de moivre's theorem
(e^itheta)^n = e^(nitheta) for integer values of n

What about rational?
Let's say (e^ix)^(1/2) = e^(ix/2) holds
Now consider x = 2pi and you'll see how the problem arises

What about irrational?
See here:

Desmos | Graphing Calculator

www.desmos.com

Set n = sqrt(2)

What about imaginary?

We stray further down the rabbit hole when we introduced euler's form into the syllabus

Ohhhhh I see what you are saying, took me a while. So if you push eulers form a bit further you see it breaks down, its not defined fully only for simple integer cases and such. I like your way of thinking. Thanks for the explanation

 

[Flatuitous]

Ohhhhh I see what you are saying, took me a while. So if you push eulers form a bit further you see it breaks down, its not defined fully only for simple integer cases and such. I like your way of thinking. Thanks for the explanation

Precisely!

 

[Dzeeshr]

Precisely!

I have my ext2 test tomorrow, proofs and complex numbers, any advice?

 

[Flatuitous]

I have my ext2 test tomorrow, proofs and complex numbers, any advice?

What's your situation looking like?

Are you comfortable with your content?

Is it just a little extra revision you need?

If so, I would recommend just flicking through mcq for a bit of extra practice without working your head too much

 

[jane1820]

fetus was robbed of a state rank ong