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STEP Prep Thread 2016 (Mark. II)
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 1301
 15062016 09:45

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 1302
 15062016 09:51
Spoiler:Wordy mostly done solution to 7 (haven't looked for an example but whatever, screw examples)Show
S U T = set of odd integers
S ∩ T = empty set (cannot leave two different remainders)
Proving the closure under multiplication of S is trivial, just express numbers in terms of 4k + 1 for nonnegative integer k
As for disproving close under multiplication of T, just take 3 in T, then 3^2 = 9 which is not in T
For part iii, if none of its prime factors are in T, then they are all in S (since S U T = set of odd integers, and all prime factors must be odd as otherwise we'll have an even number in T). But then the product is in S, not in T, contradiction as T is a product of powers of its prime factors
for iv a), you can go the "handwavey" route/intuitive route but I dunno how permissible that would be. Basically you can first inductively show using modular arithmetic or whatever you want that any product of an odd number of integers in T is itself in T, while any product of an even number of integers in T is in S. an integer in T that is not Tprime can be expressed as the product of two or more integers in T, so wee see it must be expressible as the product of an odd number of integers in T. Then we apply the same logic to each of the factors in such a product, and eventually this process stops as it is finite (and the final product must be of an odd number of the fellas since it is in T). I thought I had something more rigorous but realised it assumed a little bit much, maybe come back to this if I care enough but that's the gist.. 
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 1303
 15062016 09:54
how many marks for doing 1 full, 2 full but missing the constant, 3 full, 4 and getting a circle center 0,0 and radius 1/k by missing the constant again but otherwise full, 10 did all up to finding the value of lamda, where i got bogged down in algebra and but said how to ding lamda then sub back in into the equation for lamba and e to find e, then 11 i did all except find the value of cos2a where i got bogged down again but i showed how to find the max distance by pythag that was like hsec2a or something then subbed my value of cos2a...
thanks i really dont have much idea how they are marked especially thepartials 
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 1304
 15062016 09:54
(Original post by 13 1 20 8 42)
Spoiler:Wordy mostly done solution to 7 (haven't looked for an example but whatever, screw examples)Show
S U T = set of odd integers
S ∩ T = empty set (cannot leave two different remainders)
Proving the closure under multiplication of S is trivial, just express numbers in terms of 4k + 1 for nonnegative integer k
As for disproving close under multiplication of T, just take 3 in T, then 3^2 = 9 which is not in T
For part iii, if none of its prime factors are in T, then they are all in S (since S U T = set of odd integers, and all prime factors must be odd as otherwise we'll have an even number in T). But then the product is in S, not in T, contradiction as T is a product of powers of its prime factors
for iv a), you can go the "handwavey" route/intuitive route but I dunno how permissible that would be. Basically you can first inductively show using modular arithmetic or whatever you want that any product of an odd number of integers in T is itself in T, while any product of an even number of integers in T is in S. an integer in T that is not Tprime can be expressed as the product of two or more integers in T, so wee see it must be expressible as the product of an odd number of integers in T. Then we apply the same logic to each of the factors in such a product, and eventually this process stops as it is finite (and the final product must be of an odd number of the fellas since it is in T). I thought I had something more rigorous but realised it assumed a little bit much, maybe come back to this if I care enough but that's the gist..
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 1305
 15062016 09:56
(Original post by drandy76)
Pretty much what I did, except I didn't know what the notation meant for the first part
Posted from TSR Mobile 
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 1306
 15062016 09:56
(Original post by johnthedog)
would quite like one of them fancy polls to gauge how hard the paper was compared to previous years.
Posted from TSR MobilePost rating:1 
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 1307
 15062016 09:56
(Original post by Duke Glacia)
ur opinions on this paper ?
Everything else I got wrong/didn't do was just being being 5x dumber than usual. 
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 1308
 15062016 09:58
(Original post by IrrationalRoot)
Did badly but nice paper. No idea how to do the second part of the circles Q I'll admit.
Everything else I got wrong/didn't do was just being being 5x dumber than usual. 
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 1309
 15062016 09:59
(Original post by Duke Glacia)
predicted grade boundries ? 
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 1310
 15062016 10:02
(Original post by 13 1 20 8 42)
Spoiler:Wordy mostly done solution to 7 (haven't looked for an example but whatever, screw examples)Show
S U T = set of odd integers
S ∩ T = empty set (cannot leave two different remainders)
Proving the closure under multiplication of S is trivial, just express numbers in terms of 4k + 1 for nonnegative integer k
As for disproving close under multiplication of T, just take 3 in T, then 3^2 = 9 which is not in T
For part iii, if none of its prime factors are in T, then they are all in S (since S U T = set of odd integers, and all prime factors must be odd as otherwise we'll have an even number in T). But then the product is in S, not in T, contradiction as T is a product of powers of its prime factors
for iv a), you can go the "handwavey" route/intuitive route but I dunno how permissible that would be. Basically you can first inductively show using modular arithmetic or whatever you want that any product of an odd number of integers in T is itself in T, while any product of an even number of integers in T is in S. an integer in T that is not Tprime can be expressed as the product of two or more integers in T, so wee see it must be expressible as the product of an odd number of integers in T. Then we apply the same logic to each of the factors in such a product, and eventually this process stops as it is finite (and the final product must be of an odd number of the fellas since it is in T). I thought I had something more rigorous but realised it assumed a little bit much, maybe come back to this if I care enough but that's the gist..
Posted from TSR Mobile 
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 1311
 15062016 10:08
(Original post by LukaVendov)
how many marks for doing 1 full, 2 full but missing the constant, 3 full, 4 and getting a circle center 0,0 and radius 1/k by missing the constant again but otherwise full, 10 did all up to finding the value of lamda, where i got bogged down in algebra and but said how to ding lamda then sub back in into the equation for lamba and e to find e, then 11 i did all except find the value of cos2a where i got bogged down again but i showed how to find the max distance by pythag that was like hsec2a or something then subbed my value of cos2a...
thanks i really dont have much idea how they are marked especially thepartials 
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 1312
 15062016 10:12
(Original post by Ecasx)
For iv)a), you could say this. Suppose t (not 1) in T is not Tprime. Then express t as a product of integers in T (excluding 1). Decompose each integer in the product until t is written as a product of Tprime integers (cannot be decomposed further). In this state let t = t1 * t2 * ... * tm. Now, the product of two 3 mod 4 integers is congruent to 1 mod 4. So if m is even, then t = 1 mod 4, a contradiction. Therefore m is odd.
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(A wellordering principle method for instance like the one used for integers in general)Post rating:1 
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 1313
 15062016 10:16
(Original post by shamika)
EDIT: if someone can let me know when the paper has been uploaded that'd be great
I'm afraid that I didn't do very well but the boundaries are going to be really high. 
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 1314
 15062016 10:21
Can we only use pencil ?
step central page : They should write their answers in hard pencil or pen.
Can we only use pencil only in graphs ?
Also is HB2 (regular pencils) considered to be hard ? 
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 1315
 15062016 10:24
Don't care about step I bring on ii tomorrow

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 1316
 15062016 10:29
Spoiler:ShowLooks like it was a nice paper*Spoiler:Show* = Dun kill me if it wasn't! 
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 1317
 15062016 10:31
(Original post by Vesniep)
Can we only use pencil ?
step central page : They should write their answers in hard pencil or pen.
Can we only use pencil only in graphs ?
Also is HB2 (regular pencils) considered to be hard ?
It's just to ensure your answers are (and remain) legible.
Posted from TSR Mobile 
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 1318
 15062016 10:33
(Original post by johnthedog)
oh for **** ******** ****** ************ sake 
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 1319
 15062016 10:38
shamika whats ur opinion on the paper ?

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 1320
 15062016 10:49
(Original post by 13 1 20 8 42)
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Updated: August 26, 2016
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