HSC 2015 MX1 Marathon (archive) (1 Viewer)

[Drsoccerball]

Re: HSC 2015 3U Marathon

So you haven't done Ext 1 Projectile Motion yet?

He's still in year 11 I doubt he has.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

I tried to model my Induction for inequalities answer following the Kinney-Lewis textbook. This is how Kinney explains it:

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

I'm not sure if your proof for n=k+1 is correct. You say you want to prove , but you haven't really done so. I think what you should do is say RTP , and then say "Consider the difference". Then simplify, show that the expression (you end up with ) is >0, and then go back to what you started with to show and hence . If I'm wrong someone please correct me.

I also think you made a good point in this question. I should state' consider the difference' or like the explanation Kinney has assigned a letter 'E' to represent the differences.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

In how many ways can 2 men, 2 women and 2 boys be arranged in a row if the two boys are to remain together? A) 40 B) 60 C) 120 D) 240

 

[rand_althor]

Re: HSC 2015 3U Marathon

In how many ways can 2 men, 2 women and 2 boys be arranged in a row if the two boys are to remain together? A) 40 B) 60 C) 120 D) 240

Is it D? We have M M W W B B. If we consider the boys to be one group. we have M M W W BB, which can be arranged 5! ways. The boys can be arranged 2! ways. So we have 5!2!=240.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Is it D? We have M M W W B B. If we consider the boys to be one group. we have M M W W BB, which can be arranged 5! ways. The boys can be arranged 2! ways. So we have 5!2!=240.

The answer is different if it was 2 identical black balls, 2 identical white balls and 2 identical magneta balls ?

 

[InteGrand]

Re: HSC 2015 3U Marathon

The answer is different if it was 2 identical black balls, 2 identical white balls and 2 identical magneta balls ?

Yes, because in this case the items of same colour are identical. In the case with people, people in the same "class" (i.e. man, woman, or boy) are not identical.

 

[braintic]

Re: HSC 2015 3U Marathon

The answer is different if it was 2 identical black balls, 2 identical white balls and 2 identical magneta balls ?

Assuming you mean that the two black balls must be adjacent, you are essentially creating a 5-letter word from the letters W, W, M, M and BB.
So the count would be 5!/(2!2!)

 

[braintic]

Re: HSC 2015 3U Marathon

In how many ways can 5 men, 5 women, 5 girls and 3 boys be arranged in a line if all the children must be together, but no two boys can be adjacent?

 

[kawaiipotato]

Re: HSC 2015 3U Marathon

In how many ways can 5 men, 5 women, 5 girls and 3 boys be arranged in a line if all the children must be together, but no two boys can be adjacent?

Arrange the girls first = 5!
Ways for boys to slip between the girls = 6P3
Arranging everyone, with the children as one item = 11!
Total = 5! * 6P3* 11! = 5.7x10^11 ... a very large number

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon



A) n=2 B) n=3 C) n=4 D) n=5

I know the rule for nPr= n!/(n-r)! , someone give me a kick start to this question. When I do it I have 'n terms' cancelling with each other.

 

[InteGrand]

Re: HSC 2015 3U Marathon

A) n=2 B) n=3 C) n=4 D) n=5

I know the rule for nPr= n!/(n-r)! , someone give me a kick start to this question. When I do it I have 'n terms' cancelling with each other.

Just sub. in values of n in the options (trial and error).

 

[braintic]

Re: HSC 2015 3U Marathon

Arrange the girls first = 5!
Ways for boys to slip between the girls = 6P3
Arranging everyone, with the children as one item = 11!
Total = 5! * 6P3* 11! = 5.7x10^11 ... a very large number

It's also possible to do it by arranging the boys first, but it requires a bit more thought.

 

[rand_althor]

Re: HSC 2015 3U Marathon

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Just sub. in values of n in the options (trial and error).

Im ashamed to say I still can't get the answer after your hint.

 

[braintic]

Re: HSC 2015 3U Marathon

Im ashamed to say I still can't get the answer after your hint.

What is the answer supposed to be? Because I get no solution.

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

Im ashamed to say I still can't get the answer after your hint.

just use your calculator and sub them in and see if theyre equal................

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

What is the answer supposed to be? Because I get no solution.

The answer is n=3

From Kinney-Lewis videos:

https://www.youtube.com/watch?v=hQlEigQ5ieI

 

[InteGrand]

Re: HSC 2015 3U Marathon

Im ashamed to say I still can't get the answer after your hint.

If none of the options work, there is something wrong with the question, maybe a typo. You can try solving for n too by rewriting each side in terms of factorials; if there is no solution, there is something wrong with the question most likely.

 

[InteGrand]

Re: HSC 2015 3U Marathon

The answer is n=3

From Kinney-Lewis videos:

https://www.youtube.com/watch?v=hQlEigQ5ieI

By direct substitution and evaluation, we can see that n = 3 does not work. Maybe the 6 in the RHS was meant to be a 2.