2012 Year 9 &10 Mathematics Marathon (6 Viewers)

Demento1 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

kazemagic said:
Ikr, its 9:30 already. Should enjoy a game of LoL

russ3l said:
how much shit do you do in the holidays!? :O

I occasionally get quite busy during the holidays, especially on particular mornings and afternoons. You guys should add me on LoL. It's Demento1 (exact same username), however let's get back on topic guys.

Here's another interesting question which I stumbled upon, when ruffling through the papers on my shelf and I thought it might test some avid year 10 students:

If 935712 × N is a perfect cube for some positive integer N, ﬁnd the minimum value of N.

Hint: Find the primes which multiply to make 935712.

qwerty44 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Demento1 said:
I occasionally get quite busy during the holidays, especially on particular mornings and afternoons. You guys should add me on LoL. It's Demento1 (exact same username), however let's get back on topic guys.

Here's another interesting question which I stumbled upon, when ruffling through the papers on my shelf and I thought it might test some avid year 10 students:

If 935712 × N is a perfect cube for some positive integer N, ﬁnd the minimum value of N.

Good question. Also realised your source of questions

Demento1 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

qwerty44 said:
Good question. Also realised your source of questions

Haha, no doubt from an AIMO paper I found on the shelf in my room. Also, it's best not to look at the solutions before giving it a go. No point reading the solutions without understanding. Though I'd be happy to explain the answer.

qwerty44 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Demento1 said:
Haha, no doubt from an AIMO paper I found on the shelf in my room. Also, it's best not to look at the solutions before giving it a go. No point reading the solutions without understanding. Though I'd be happy to explain the answer.

That's true. Some people read solutions and think they understand, but when you give them a similar question, they have no idea.

Demento1 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

qwerty44 said:
That's true. Some people read solutions and think they understand, but when you give them a similar question, they have no idea.

Exactly. You can rote learn to some extent, although a question of application generally throws off an average student.

twinklegal19 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Demento1 said:
Exactly. You can rote learn to some extent, although a question of application generally throws off an average student.

inb4 Rivalry comes to debate about this

russ3l · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

ymcaec said:
Simplify the following algebraic fractions:
$$1. $\left ( 1 + \frac{45}{x-8} -\frac{26}{x-6} \right ) \left ( 3 - \frac{65}{x+7} +\frac{8}{x-2} \right )\\ $2. $\left ( 2 - \frac{3n}{m} +\frac{9n^2-2m^2}{m^2+2mn} \right ) \div \left ( \frac{1}{m} - \frac{1}{m-2n- \frac{4n^2}{m+n}} \right )\\$3. $\frac{1}{x + \frac{1}{x+2}} \times \frac{1}{x + \frac{1}{x-2}} \div \frac{x-\frac{4}{x}}{x^2 - 2 + \frac{1}{x^2}}$

does anyone know how to do no.3?

Fawun · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

ymcaec said:
Simplify the following algebraic fractions:
$$1. $\left ( 1 + \frac{45}{x-8} -\frac{26}{x-6} \right ) \left ( 3 - \frac{65}{x+7} +\frac{8}{x-2} \right )\\ $2. $\left ( 2 - \frac{3n}{m} +\frac{9n^2-2m^2}{m^2+2mn} \right ) \div \left ( \frac{1}{m} - \frac{1}{m-2n- \frac{4n^2}{m+n}} \right )\\ $3. $\frac{1}{x + \frac{1}{x+2}} \times \frac{1}{x + \frac{1}{x-2}} \div \frac{x-\frac{4}{x}}{x^2 - 2 + \frac{1}{x^2}}$

Is it bad if I don't know how to do any of them?

bleakarcher · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

russ3l said:
does anyone know how to do no.3?

I just tried it and got 1/x

Peeik · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Fawun said:
Is it bad if I don't know how to do any of them?

If you are in year 10 then it's not that bad (although a 5.3 should be more than capable).....if you are in year 11 then you "should" be able to do it.

nightweaver066 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

russ3l said:
does anyone know how to do no.3?

With 3. , focus on the expression with the divide sign in front of it.

Notice the bottom is a perfect square, and if you put the two terms at the top together under a common denominator and factorise it (difference of two squares), you find things work nicely.

Fawun · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Peeik said:
If you are in year 10 then it's not that bad (although a 5.3 should be more than capable).....if you are in year 11 then you "should" be able to do it.

Well I'm in 5.3 and in year 10 :L I was also an accelerant so i'm going to take that it is bad haha. The only idea that I have for the third question is to change the division sign into a multiplication sign and reciprocate the fraction and that's it. To be honest, I don't even think that's what you're suppose to do LOL

ymcaec · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

bleakarcher said:
I just tried it and got 1/x

yep $\frac{1}{x}$ is the answer

ymcaec · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Demento1 said:
I occasionally get quite busy during the holidays, especially on particular mornings and afternoons. You guys should add me on LoL. It's Demento1 (exact same username), however let's get back on topic guys.

Here's another interesting question which I stumbled upon, when ruffling through the papers on my shelf and I thought it might test some avid year 10 students:

If 935712 × N is a perfect cube for some positive integer N, ﬁnd the minimum value of N.

Hint: Find the primes which multiply to make 935712.

The hint is really helpful

$$By drawing a factor tree - $935712=2^5\times3^4\times19^2\\\\$To make each power a multiple of 3 (so when times together it is a cube), I need to times (at least) $2^1 \times 3^2\times19^1 = 342\\\therefore$ Minimum value of N $ = 342$

RivalryofTroll · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

twinklegal19 said:
inb4 Rivalry comes to debate about this

I have no comments on Demento's statement.

Rote-learning has it's advantage of memory retention but one major fatal flaw is: anything unexpected thrown at you will throw you off indeed.

Tips to Years 9 & 10: Learn to look beyond your typical questions in a textbook and do more problem solving questions or challenging questions. (I didn't do this in my younger years and now I suffer from not being able to interpret lengthy/wordy questions)

bleakarcher · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

RivalryofTroll said:
I have no comments on Demento's statement.

Rote-learning has it's advantage of memory retention but one major fatal flaw is: anything unexpected thrown at you will throw you off indeed.

Tips to Years 9 & 10: Learn to look beyond your typical questions in a textbook and do more problem solving questions or challenging questions. (I didn't do this in my younger years and now I suffer from not being able to interpret lengthy/wordy questions)

Weren't you interested in the more stimulating problems? I know I was.

iBibah · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

1. If triangle PQR has side lengths 80, 60 and 40, then the shortest height is K times the longest height. Find the value of K.
2. A regular hexagon in inscribed in a circle or radius R. The length of the shortest diagonal is $9\sqrt3$ , find R.

twinklegal19 · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Here's a probability question for you guys

Bag A contains 4 green marbles and 4 red marbles. Bag B contains 3 green marbles and 1 red marble. Two marbles are drawn at random from Bag A and placed in Bag B. Two marbles are then drawn from Bag B.

Calculate the probability that two marbles drawn from Bag B are of different colours.

Demento1 · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

twinklegal19 said:
Here's a probability question for you guys

Bag A contains 4 green marbles and 4 red marbles. Bag B contains 3 green marbles and 1 red marble. Two marbles are drawn at random from Bag A and placed in Bag B. Two marbles are then drawn from Bag B.

Calculate the probability that two marbles drawn from Bag B are of different colours.

Will take the time to read the Q. Not sure exactly as to what method I would use to solve it as of yet, but I'm hoping it will hit me soon.

twinklegal19 · Jul 3, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Demento1 said:
Will take the time to read the Q. Not sure exactly as to what method I would use to solve it as of yet, but I'm hoping it will hit me soon.

A tree diagram might help

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