HSC 2013 Maths Marathon (archive) (1 Viewer)

bedpotato · Oct 18, 2013

Re: HSC 2013 2U Marathon

Menomaths said:
I understood up until there

The last line is like saying:

x = y + 1

and you want to make y the subject,
so y = x - 1

Same concept applies above.

mahmoudali · Oct 18, 2013

Re: HSC 2013 2U Marathon

Sy123 said:
Its like saying

$\frac{d}{dx} \sin x = \cos x$

THEREFORE

$\int \cos x = \sin x + c$

we are just reversing what we've done, in this case I re-arranged the integrals

$\frac{d}{dx} x\ln x = \ln x + 1$

integrate both sides

$x\ln x = \int (\ln x + 1) \ dx$

$x \ln x = \int \ln x \ dx + \int 1 \ dx$

$x \ln x = \int \ln x \ dx + x$

$\therefore \ \ x \ln x - x= \int \ln x$

edit great why cant i write in his quote

Shazer2 · Oct 18, 2013

Re: HSC 2013 2U Marathon

braintic said:
Oh dear. Four days to get this out of your system.

Yeah it was a pretty stupid mistake.

SophxMusic · Oct 18, 2013

Hey just a quick question...
When writing answers what form do they usually want it in?
For example, probability could be a fraction or a decimal, integral could be in terms of pi or an approximate decimal, equations of a line could be in gradient intercept or general form etc..
Obviously if they ask for a specific form or an exact answer you would know, but if they don't specify can you lose marks for having the answer in a different form?
In a lot of past exams they have put the gradient intercept form as the answer but I'm assuming I would still be marked right if I had the correct general form unless they specified, is this right?

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mahmoudali · Oct 18, 2013

Re: HSC 2013 2U Marathon

SophxMusic said:
Hey just a quick question...
When writing answers what form do they usually want it in?
For example, probability could be a fraction or a decimal, integral could be in terms of pi or an approximate decimal, equations of a line could be in gradient intercept or general form etc..
Obviously if they ask for a specific form or an exact answer you would know, but if they don't specify can you lose marks for having the answer in a different form?
In a lot of past exams they have put the gradient intercept form as the answer but I'm assuming I would still be marked right if I had the correct general form unless they specified, is this right?

Sent from my iPhone using Tapatalk - now Free

for integrals leave in exact form (easier for marker to mark it)
probability it doesnt even mattere
i'd say leave any approximation methods (Simpsons rule or trapeziodal rule) in decimals.
exact values for trig, integrals, annuities ect are better so you can use in case there is a second part to the qustion

Menomaths · Oct 18, 2013

Re: HSC 2013 2U Marathon

Help please, I'm mathematically retarded

nerdasdasd · Oct 18, 2013

HSC 2013 2U Marathon

^ do a tree diagram to see the probable lots ... But they will be 1. Legal/not legal / not legal, 2. Not legal / legal/ not legal , 3. Not legal/ not legal/ legal.

RealiseNothing · Oct 18, 2013

Re: HSC 2013 2U Marathon

B

Menomaths · Oct 18, 2013

Re: HSC 2013 2U Marathon

nerdasdasd said:
^ do a tree diagram to see the probable lots ... But they will be 1. Legal/not legal / not legal, 2. Not legal / legal/ not legal , 3. Not legal/ not legal/ legal.

Oh right, takes too long to draw the diagram so I visualized it and it works, thanks

edit: is there an easier way to work it out like P(E) or something?

Menomaths · Oct 18, 2013

Re: HSC 2013 2U Marathon

$By first writing the function y=7^x$ $in logarithmic form, show that the derivative is ln7\times7^x$ $\fbox{2}$

RealiseNothing · Oct 18, 2013

Re: HSC 2013 2U Marathon

Menomaths said:
Oh right, takes too long to draw the diagram so I visualized it and it works, thanks

edit: is there an easier way to work it out like P(E) or something?

$\frac{4}{5} \times \frac{1}{5} \times \frac{1}{5} \times 3$

Menomaths · Oct 18, 2013

Re: HSC 2013 2U Marathon

RealiseNothing said:
$\frac{4}{5} \times \frac{1}{5} \times \frac{1}{5} \times 3$

Yeah that's what I did

Youi_ · Oct 18, 2013

Re: HSC 2013 2U Marathon

Menomaths said:
$By first writing the function y=7^x$ $in logarithmic form, show that the derivative is ln7\times7^x$ $\fbox{2}$

$y=7^x$$

$\ln(y)=\ln(7)^x = e^{ln(y)} =e^{xln(7)}$

$y= e^{xln(7)} \ \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}=\ln 7 \star e^{xln(7)}$

$\therefore y'=\ln 7 \star 7^x$

ColdLipstick · Oct 18, 2013

Re: HSC 2013 2U Marathon

Another Q by me ^.^

Carrotsticks · Oct 18, 2013

Re: HSC 2013 2U Marathon

ColdLipstick said:
Another Q by me ^.^

2011 HSC 2U Q9 (d) =)

You seem to enjoy writing questions. Very few students do that, good to see. The forum has about 2-3 other regulars (HSC Students) who also write questions.

Shazer2 · Oct 18, 2013

Re: HSC 2013 2U Marathon

I'd write questions if I had the knowledge!

Youi_ · Oct 18, 2013

Re: HSC 2013 2U Marathon

Carrotsticks said:
2011 HSC 2U Q9 (d) =)

View attachment 28803

You seem to enjoy writing questions. Very few students do that, good to see. The forum has about 2-3 other regulars (HSC Students) who also write questions.

why is it n>= 1 shouldn't it be n>=0 since $\sqrt{0} + \sqrt{0+1} = 1$ ? or is there more to it?

anthony_wheels · Oct 18, 2013

Re: HSC 2013 2U Marathon

ColdLipstick said:
Another Q by me ^.^

I know it's a very 'shonky' proof/deduction lol... How could I improve it?

RealiseNothing · Oct 18, 2013

Re: HSC 2013 2U Marathon

Youi_ said:
why is it n>= 1 shouldn't it be n>=0 since $\sqrt{0} + \sqrt{0+1} = 1$ ? or is there more to it?

It doesn't matter, you could do either. The person who wrote the question just specified $n \geq 1$ .

RealiseNothing · Oct 18, 2013

Re: HSC 2013 2U Marathon

Prove that:

$\log_{a+b}(ab) < 2$

For $a>b>1$

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