Looking for solutions (2 Viewers)

[Carrotsticks]

Haha that paper is from The Brain. Math Man wrote it.

 

[deswa1]

this one is not the hardest MX2 paper, I have a more crzay oneView attachment 25848View attachment 25849View attachment 25850

Wow- that looks nice. Do you happen to have a copy of the whole paper?

And thanks Carrot for your solution. That's way better set out than what I did

 

[nightweaver066]

this one is not the hardest MX2 paper, I have a more crzay oneView attachment 25848View attachment 25849View attachment 25850

Want that paper!

 

[asianese]

Note that Q3c) in the paper MathMan wrote is outside the syllabus =)

 

[RealiseNothing]

Haha that paper is from The Brain. Math Man wrote it.

I remember at the first library meat spiral was talking about that paper to you lol.

 

[Carrotsticks]

Note that Q3c) in the paper MathMan wrote is outside the syllabus =)

Correct. Fundamental Theorem of Calculus (this question uses the 1st part of it, since there are two) is outside the syllabus.

Probably should have stated something like:

You may assume without proof that



If f(t) is continuous in the interval [a,b] and x E [a,b].

 

[Nooblet94]

Has anyone got a copy of the full paper? I would love to give it a go.

 

[Carrotsticks]

I do, but I will ask Math Man if he's willing to distribute it.

 

[seanieg89]

Correct. Fundamental Theorem of Calculus (this question uses the 1st part of it, since there are two) is outside the syllabus.

Probably should have stated something like:

You may assume without proof that



If f(t) is continuous in the interval [a,b] and x E [a,b].

The question also uses differentiation under the integral to obtain an expression for B'(t), out of syllabus and not always valid.

 

[Nooblet94]

I do, but I will ask Math Man if he's willing to distribute it.

Okay, thanks!

 

[math man]

View attachment holiday_test 2.zip

Yeh i learnt after test that 3 (c) was not in syllabus anymore, but still such a trivial question.
I know Q5 the FTC part was too difficult, but i had shown my students it before and how to use
it a while ago, i was tossing whether or not to put the formula there, but i was in an evil mood so
i didn't. Otherwise the rest of q5 was very doable. Also mc and q1-4 were fairly decent, more of
a std paper those parts were.

Edit: note this test more suited my students as i gave questions on things i have taught them specifically,
such as collapsing sums, riemann upper/lower sums, convergence

 

[nightweaver066]

View attachment 25855

Yeh i learnt after test that 3 (c) was not in syllabus anymore, but still such a trivial question.
I know Q5 the FTC part was too difficult, but i had shown my students it before and how to use
it a while ago, i was tossing whether or not to put the formula there, but i was in an evil mood so
i didn't. Otherwise the rest of q5 was very doable. Also mc and q1-4 were fairly decent, more of
a std paper those parts were.

Will have some fun tonight.

Thanks

 

[math man]

The average for the test was 50, which is the highest average i have ever had on a paper i wrote,
and the top mark was 71.5.

 

[Nooblet94]

View attachment 25855

Yeh i learnt after test that 3 (c) was not in syllabus anymore, but still such a trivial question.
I know Q5 the FTC part was too difficult, but i had shown my students it before and how to use
it a while ago, i was tossing whether or not to put the formula there, but i was in an evil mood so
i didn't. Otherwise the rest of q5 was very doable. Also mc and q1-4 were fairly decent, more of
a std paper those parts were.

Edit: note this test more suited my students as i gave questions on things i have taught them specifically,
such as collapsing sums, riemann upper/lower sums, convergence

Thank you so much! I shall be having some fun tomorrow morning

 

[nightweaver066]

The average for the test was 50, which is the highest average i have ever had on a paper i wrote,
and the top mark was 71.5.

If possible, could you put up the solutions as well so we could mark it? lol

Clearly you've eased up a bit on the difficulty without realising it

Need to make them more challenging.

 

[math man]

If possible, could you put up the solutions as well so we could mark it? lol

Clearly you've eased up a bit on the difficulty without realising it

Need to make them more challenging.

im only giving solutions to ppl who had to endure the test under exam conditions, but dw
next holiday test will be the worst yet

 

[Trebla]

I had a look through the paper and then did question 8. I found it surprisingly easy in comparison to the rest of the paper. It was as easy, if not easier than some of the earlier questions IMO.



I'm pretty sure your proof for (iii) is circular. You're assuming the result from (ii) is true, but in part (ii) you assume what you're proving in (iii).

Also, for finding the expression for g(x) in part (ii) can't you just replace the n's in with n+1 rather than having to go through the whole process of differentiating and then integrating? You get the same result.

I don't think there is a circular argument. My structure for (iii) is probably not what you would write in an exam but I'm just highlighting the connection between (ii) and (iii). The point of part (ii) was in fact to show the inductive step. I don't see where any assumption of (iii) came in at all in my proof for part (ii). Part (ii) is basically saying suppose that

call this (1)

then we can prove that

call this (2)

hence

call this (3)

So we're effectively saying IF (1) holds so does (2) hence (3)


If you look at the inductive step of (iii) carefully, it's saying assume



then prove



i.e. Prove if (1) holds then (3) holds which is the same thing you proved in part (ii) through equation (2). So you could rewrite the entire proof in full if you want but you'll effectively be repeating yourself from (ii).

The whole replacement of n with n + 1 was not the intention of part (ii) (though that is probably the flaw in the question) and it is not exactly a 'proof'. Also, doing it that way defeats its intention which was to help you with the inductive step in part (iii).

 

[deswa1]

The average for the test was 50, which is the highest average i have ever had on a paper i wrote,
and the top mark was 71.5.

So 71.5 is the mark to beat lol. The test looks really solid though- will attempt tomorrow or Wed.

 

[Fus Ro Dah]

lol at the warning. To be honest, I don't think this paper truly reflects the abilities needed to get a State Rank because it requires methods outside the syllabus. Although some things in the HSC Examination are out of syllabus and not necessarily taught at schools or in textbooks, they are always intuitive things that can be deduced by an observant student. The 'FMC #1' however is not intuitive at all and a rigourous proof for it isn't exactly simple. Even the simple 'proof' uses things outside the syllabus like the MVT and Newton's Quotient. I like question 5 (a) because of the result. I presume you're meant to use polynomial long division? Otherwise you can just use Cauchy's Integral

 

[seanieg89]

lol at the warning. To be honest, I don't think this paper truly reflects the abilities needed to get a State Rank because it requires methods outside the syllabus. Although some things in the HSC Examination are out of syllabus and not necessarily taught at schools or in textbooks, they are always intuitive things that can be deduced by an observant student. The 'FMC #1' however is not intuitive at all and a rigourous proof for it isn't exactly simple. Even the simple 'proof' uses things outside the syllabus like the MVT and Newton's Quotient. I like question 5 (a) because of the result. I presume you're meant to use polynomial long division? Otherwise you can just use Cauchy's Integral

Write the numerator as the sum of two polynomials, one with a factor of (x^2-1), another with a factor of (x^2+1). It falls apart from there.