HSC 2013 MX2 Marathon (archive) (2 Viewers)

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HeroicPandas

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Re: HSC 2013 4U Marathon



without equating coefficients
 
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GoldyOrNugget

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Re: HSC 2013 4U Marathon

Sy your summation of products of triangular numbers & sines question is raping me. Hint plz? :) so far I've been working with Re( (z+z^2+...+z^n) + 2(z^2 + ... + z^n) + ... + n(z^n) ), then simplified that with geometric series, but it's not getting anywhere.
 

Sy123

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Re: HSC 2013 4U Marathon

Sy your summation of products of triangular numbers & sines question is raping me. Hint plz? :) so far I've been working with Re( (z+z^2+...+z^n) + 2(z^2 + ... + z^n) + ... + n(z^n) ), then simplified that with geometric series, but it's not getting anywhere.
You got this right?





Then differentiation :)
 

Magical Kebab

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Re: HSC 2013 4U Marathon

A bag contains 12 red marbles and 12 yellow marbles. Six marbles are selected
at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles 1 are red. Give your answer correct to two decimal places.
(ii) Hence, or otherwise, calculate the probability that more than three 2 of the selected marbles are red. Give your answer correct to two
decimal places.
 

RivalryofTroll

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Re: HSC 2013 4U Marathon

If the polynomial:
x^3 + 3px^2 + 3qx + r = 0 has a double root. Show that the double roots must be (pq-r)/(2q-p^2).
 
O

Omed62

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Re: HSC 2013 4U Marathon

HEY GUYS!

PERFECT EXAM QUESTIONS!! Right here.

Guys see the below solutions, feel free to correct it, with full worked out solutions.

Practice Question: PROBABILITY:

I will start...

Q1. In how many ways can three groups of three numerals be chosen without replacement from the nine numerals 1,2,3,4,5,6,7,8,9 ?

9!/3!x3!x3!=?

Q2. In how many ways can a group of three letters be chosen without replacement from the nine letters of the world AUSTRALIA?

9C3= 84

PRACTICE QUESTIONS: COMPLEX Numbers:

Q1. In an Argand diagram the vectors OP and OQ represent the complex numbers z and w repectively such that Triangle OPQ is equilateral.
What is an expression for z^2 +w^2.



I planned to keep on posting questions to help other students for their upcoming half yearly exams, so please make sure you post your answers.
 

Immortalp00n

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Re: HSC 2013 4U Marathon

awesome initiative there fagmed62, keep us posted with the questions !!~~~@@@!!!
 
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Re: HSC 2013 4U Marathon

HEY GUYS!

PERFECT EXAM QUESTIONS!! Right here.

Guys see the below solutions, feel free to correct it, with full worked out solutions.

Practice Question: PROBABILITY:

I will start...

Q1. In how many ways can three groups of three numerals be chosen without replacement from the nine numerals 1,2,3,4,5,6,7,8,9 ?

9!/3!x3!x3!=?

Q2. In how many ways can a group of three letters be chosen without replacement from the nine letters of the world AUSTRALIA?

9C3= 84

PRACTICE QUESTIONS: COMPLEX Numbers:

Q1. In an Argand diagram the vectors OP and OQ represent the complex numbers z and w repectively such that Triangle OPQ is equilateral.
What is an expression for z^2 +w^2.



I planned to keep on posting questions to help other students for their upcoming half yearly exams, so please make sure you post your answers.
http://community.boredofstudies.org/showthread.php?t=298062

nice word for word copied questions...
 
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HeroicPandas

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Re: HSC 2013 4U Marathon

A bag contains 12 red marbles and 12 yellow marbles. Six marbles are selected
at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles 1 are red. Give your answer correct to two decimal places.
(ii) Hence, or otherwise, calculate the probability that more than three 2 of the selected marbles are red. Give your answer correct to two
decimal places.
do u do 4U?

If the polynomial:
x^3 + 3px^2 + 3qx + r = 0 has a double root. Show that the double roots must be (pq-r)/(2q-p^2).
I got
 

HeroicPandas

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Re: HSC 2013 4U Marathon

Q1. In an Argand diagram the vectors OP and OQ represent the complex numbers z and w repectively such that Triangle OPQ is equilateral.
What is an expression for z^2 +w^2.
z^2 + w^2 = 0 using rotation
 

GoldyOrNugget

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Re: HSC 2013 4U Marathon

HEY GUYS!

PERFECT EXAM QUESTIONS!! Right here.

Guys see the below solutions, feel free to correct it, with full worked out solutions.

Practice Question: PROBABILITY:

I will start...

Q1. In how many ways can three groups of three numerals be chosen without replacement from the nine numerals 1,2,3,4,5,6,7,8,9 ?

9!/3!x3!x3!=?

Q2. In how many ways can a group of three letters be chosen without replacement from the nine letters of the world AUSTRALIA?

9C3= 84

PRACTICE QUESTIONS: COMPLEX Numbers:

Q1. In an Argand diagram the vectors OP and OQ represent the complex numbers z and w repectively such that Triangle OPQ is equilateral.
What is an expression for z^2 +w^2.



I planned to keep on posting questions to help other students for their upcoming half yearly exams, so please make sure you post your answers.

this guy...
 

GoldyOrNugget

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Re: HSC 2013 4U Marathon

HEY GUYS!

PERFECT EXAM QUESTIONS!! Right here.

Guys see the below solutions, feel free to correct it, with full worked out solutions.

Practice Question: PROBABILITY:

I will start...

Q1. In how many ways can three groups of three numerals be chosen without replacement from the nine numerals 1,2,3,4,5,6,7,8,9 ?

9!/3!x3!x3!=?

Q2. In how many ways can a group of three letters be chosen without replacement from the nine letters of the world AUSTRALIA?

9C3= 84

PRACTICE QUESTIONS: COMPLEX Numbers:

Q1. In an Argand diagram the vectors OP and OQ represent the complex numbers z and w repectively such that Triangle OPQ is equilateral.
What is an expression for z^2 +w^2.



I planned to keep on posting questions to help other students for their upcoming half yearly exams, so please make sure you post your answers.

this guy...
 

SpiralFlex

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Re: HSC 2013 4U Marathon

Has anyone done integration yet? Don't wanna post anything you guys haven't done. Actually this is quite appropriate, I think it's around Q14 level















Note: You are NOT allowed to use the mean value theorem for part a) only HSC methods. However a hint would be to use integration.
 
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RealiseNothing

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Re: HSC 2013 4U Marathon

PRACTICE QUESTIONS: COMPLEX Numbers:

Q1. In an Argand diagram the vectors OP and OQ represent the complex numbers z and w repectively such that Triangle OPQ is equilateral.
What is an expression for z^2 +w^2.
Ok first we want to know what this looks like, it is an argand diagram with complex numbers and .

Now since it is an equilateral triangle, due to all sides being the same length. Hence

Now let , then by substitution we get:



So we end up with:



A really big thanks to your contributions for helping me and other students for our upcoming half yearlies!

I'm really looking forward to future questions that you have to offer!
 
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cutemouse

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Re: HSC 2013 4U Marathon

Actually, my bad. It's actually correct. Stop trolling bleakarcher :p Sorry, it's been a while since I've done complex numbers.
 
O

Omed62

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Re: HSC 2013 4U Marathon

Ok first we want to know what this looks like, it is an argand diagram with complex numbers and .

Now since it is an equilateral triangle, due to all sides being the same length. Hence

Now let , then by substitution we get:



So we end up with:



A really big thanks to your contributions for helping me and other students for our upcoming half yearlies!

I'm really looking forward to future questions that you have to offer!
Thanks RealiseNothing, your one of the best guys out their, so nice and keen on helping students.

I hope god be with you always... lol could you please answer the probability questions... please
 
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