• Congratulations to the Class of 2024 on your results!
    Let us know how you went here
    Got a question about your uni preferences? Ask us here

HSC 2015 MX1 Marathon (archive) (1 Viewer)

Status
Not open for further replies.

davidgoes4wce

Well-Known Member
Joined
Jun 29, 2014
Messages
1,877
Location
Sydney, New South Wales
Gender
Male
HSC
N/A
Re: HSC 2015 3U Marathon

Induction Question from El Hosri Paper 2



Its worth 3 marks, someone critique my working out and let me know what they would give out of 3. I have tried to blend in the explanations from Kinney Lewis' videos and Fitzpatrick textbook explanation when writing my answer.
 

rand_althor

Active Member
Joined
May 16, 2015
Messages
554
Gender
Male
HSC
2015
Re: HSC 2015 3U Marathon

Induction Question from El Hosri Paper 2



Its worth 3 marks, someone critique my working out and let me know what they would give out of 3. I have tried to blend in the explanations from Kinney Lewis' videos and Fitzpatrick textbook explanation when writing my answer.
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.
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: HSC 2015 3U Marathon

What he has done is technically correct because his the statements in his steps are biconditional, which basically mean they go both ways. He should have made this clearer by adding signs between the steps. Even though this is correct though, I think it is despised or not approved of by markers sometimes...it is safest in the HSC to just reverse his steps lol.
 

rand_althor

Active Member
Joined
May 16, 2015
Messages
554
Gender
Male
HSC
2015
Re: HSC 2015 3U Marathon

What he has done is technically correct because his the statements in his steps are biconditional, which basically mean they go both ways. He should have made this clearer by adding signs between the steps. Even though this is correct though, I think it is despised or not approved of by markers sometimes...it is safest in the HSC to just reverse his steps lol.
What do you mean 'reverse his steps'? Start from k>0?
 

davidgoes4wce

Well-Known Member
Joined
Jun 29, 2014
Messages
1,877
Location
Sydney, New South Wales
Gender
Male
HSC
N/A
Re: HSC 2015 3U Marathon

Induction is like an essay, I think I have watched and read about 5 different methods when evaluating the 'inequality induction'.

All slight variations but I like Kinney-Lewis way of explanation (you can view it on Youtube) and Fitzpatrick for divisibility and sums/products.

For all you current HSCers, I just did a quick check in previous years, the inequality induction has popped up 3 times in the past 17 years.
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: HSC 2015 3U Marathon

Would you give that full marks Integrand? (out of 3). I think inequality is the trickiest of the main 4 induction types (divisiblity, series, sums/products, inequalities)
Well I probably would, but I'm fairly sure a lot of markers wouldn't, so it is safest for HSC purposes to write it differently.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Re: HSC 2015 3U Marathon

Bruh... how can it be so hard to understand theres the curve y=|x| and theres a circle in squished between the two lines...
I don't associate gravity with the cartesian plane. So EXCUSE ME if I keep HS physics and HS mathematics separated.
 

dan964

what
Joined
Jun 3, 2014
Messages
3,479
Location
South of here
Gender
Male
HSC
2014
Uni Grad
2019
Re: HSC 2015 3U Marathon

Induction is like an essay, I think I have watched and read about 5 different methods when evaluating the 'inequality induction'.

All slight variations but I like Kinney-Lewis way of explanation (you can view it on Youtube) and Fitzpatrick for divisibility and sums/products.

For all you current HSCers, I just did a quick check in previous years, the inequality induction has popped up 3 times in the past 17 years.
Induction: View attachment Mathematical Induction.pdf
Excuse the light writing in sections (I used aqua pen i think)
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: HSC 2015 3U Marathon

It may have been the first time I have heard of the 'inductive hypothesis', that to me sounds like the 'Assumed step' in this process.
Yes, the thing you assume is called the inductive hypothesis (or inductive assumption, etc.).
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top