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# STEP Prep Thread 2016 (Mark. II)

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1. Question about inequalities: when they ask you to prove/show that a given inequality is true, is it acceptable to start with that inequality and manipulate til you get something that is definitely true and then say that therefore the initial inequality is true? I know its probably the opposite way round to what you're supposed to do but I can never spot which other inequality I'm supposed to use so can only do it this way, however it does kind of feel like cheating starting with the thing they've asked you to prove.
2. (Original post by smartalan73)
Question about inequalities: when they ask you to prove/show that a given inequality is true, is it acceptable to start with that inequality and manipulate til you get something that is definitely true and then say that therefore the initial inequality is true? I know its probably the opposite way round to what you're supposed to do but I can never spot which other inequality I'm supposed to use so can only do it this way, however it does kind of feel like cheating starting with the thing they've asked you to prove.
Only if you then cross out your work and do it in reverse. That is: all your steps must be reversible.
3. (Original post by Zacken)
Only if you then cross out your work and do it in reverse. That is: all your steps must be reversible.
If the steps are reversible, you can just add 'if and only if' signs, or you just explain that the steps are reversible, no?
4. (Original post by Zacken)
Only if you then cross out your work and do it in reverse. That is: all your steps must be reversible.
or put the <- signs in.
5. (Original post by Insight314)
Did you guys know that you can't take your STEP exams in your usual exam hall but have to take them in a separate room by yourself or at least that is how it is in my school. I prefer it this way to be honest. Oh, and make sure you bring photo ID with you. Also, you are allowed to use a timer for your STEP exams.

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I was hoping for it to be this way but Ill be doing them in the main exam hall still... all on my own
6. IrrationalRoot Also dont suppose u know of any more resources about the (ir)rational root theorem. Zain linked to a nice part Ia q which uses it very briefly but id like to find out more
7. (Original post by EnglishMuon)
IrrationalRoot Also dont suppose u know of any more resources about the (ir)rational root theorem. Zain linked to a nice part Ia q which uses it very briefly but id like to find out more
I learnt about it from a textbook, but don't know of any other resources sorry. Any reason you're interested? I thought it was not particularly deep.
8. Just to make sure, we can't quote things like Descartes' rule of signs in STEP can we?
9. (Original post by EnglishMuon)
IrrationalRoot Also dont suppose u know of any more resources about the (ir)rational root theorem. Zain linked to a nice part Ia q which uses it very briefly but id like to find out more
Have you seen the wikipedia article on it? They have a nice technique linked and explained called Horner's method. Might want to look that up.
10. (Original post by smartalan73)
Question about inequalities: when they ask you to prove/show that a given inequality is true, is it acceptable to start with that inequality and manipulate til you get something that is definitely true and then say that therefore the initial inequality is true? I know its probably the opposite way round to what you're supposed to do but I can never spot which other inequality I'm supposed to use so can only do it this way, however it does kind of feel like cheating starting with the thing they've asked you to prove.

We have and squaring gives . But is definitely true and so we must have .

Notice how showing that a statement leading to a true statement does not necessarily imply that the initial statement is true. False statements can imply true statements.
11. (Original post by IrrationalRoot)
I learnt about it from a textbook, but don't know of any other resources sorry. Any reason you're interested? I thought it was not particularly deep.
Nah it was in a dream i had last night for some reason, but i would like to know more Thanks anyway

(Original post by Zacken)
Have you seen the wikipedia article on it? They have a nice technique linked and explained called Horner's method. Might want to look that up.
ooh ok i did briefly go over that page but cant remember reading about that. Ill look at it again, thanks.
12. (Original post by EricPiphany)
If the steps are reversible, you can just add 'if and only if' signs, or you just explain that the steps are reversible, no?
(Original post by physicsmaths)
or put the <- signs in.
Yeah, you can. But it's usually considered very ugly and any analysis professor/supervisor would glare at you if you did that. Normally if you can't see what to do you would assume the result held, worked backwards and see that every step is reversible and then write the proof properly in the proper direction for it to look clean.
13. (Original post by EnglishMuon)
Nah it was in a dream i had last night for some reason, but i would like to know more Thanks anyway

ooh ok i did briefly go over that page but cant remember reading about that. Ill look at it again, thanks.
Lol you dream about maths? I bet you're like Ramanujan and get all your ideas given to you by the gods in your dreams, no wonder you're so good XD.
14. (Original post by IrrationalRoot)
Lol you dream about maths? I bet you're like Ramanujan and get all your ideas given to you by the gods in your dreams, no wonder you're so good XD.
lol im not that good XD Although i have made progress on a couple of BMO problems when trying to sleep. I guess its the only time when everythings quiet and I can concentrate properly
15. (Original post by EnglishMuon)
lol im not that good XD Although i have made progress on a couple of BMO problems when trying to sleep. I guess its the only time when everythings quiet and I can concentrate properly
Protip: sleep during your STEP exam
16. (Original post by Zacken)
Protip: sleep during your STEP exam
haha maybe Ill probably end up sleeping after the exam and pointing out all my errors to myself
17. (Original post by EnglishMuon)
haha maybe Ill probably end up sleeping after the exam and pointing out all my errors to myself
Ouch, yeah, that's not going to be a fun time. It'll take a day before solutions are up on TSR.
18. (Original post by Zacken)
Ouch, yeah, that's not going to be a fun time. It'll take a day before solutions are up on TSR.
I can ask my school for the question paper, scan it and upload it on here after the exam if you guys have trouble asking your exam centre about it.

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19. (Original post by Insight314)
I can ask my school for the question paper, scan it and upload it on here after the exam if you guys have trouble asking your exam centre about it.

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That'd be great.

(You shouldn't upload it till 24 hours after the exam, though)
20. (Original post by Zacken)
That'd be great.

(You shouldn't upload it till 24 hours after the exam, though)
All right, gonna make sure not to upload before that. If I have time I am also planning on going through the solutions with one of the maths teachers in my school (super good at maths, PhD and everything) so that would be cool.

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