Wednesday, 30 May 2012

SMO 2012 (Open Section) Answers

SMO 2012 Open Special Round Participants List
COP for Special Round - 8, about 8.9% (~138/1549 participants) selected

SMO 2012 (Open) Questions
Solutions to some questions can be found in AoPS 2012 SMO (Open) Discussion topic by goran
1. 121
2. 7986
3. 4
4. 3333
5. 62
6. 3015
7. 38
8. 76
9. 4
10. 2015
11. 22
12. 2
13. 86
14. 337
15. 2011
16. 10 (*19)
17. 584
18. 25
19. 1
20. 21
21. 2500
22. 20121
23. 0
24. 2013
25. 1
*Answers updated on 1 Sep 2012, after checking the Solution Book

SMO (Open) Previous Years' Cut-off Points (Inclusive of Round 2 scores)
Update: 2012 Gold (21), Silver (8), Bronze (6), HM (5), Round 2(8)
2011 Gold (18), Silver (9), Bronze (6), HM (5), Round 2 (9)
2010 Gold (38), Silver (9), Bronze (6), HM (5)
2009 Gold (27-29), Silver (9), Bronze (6), HM (5)
2008 Gold (27), Silver (11), Bronze (10), HM (6)
2007 Gold (19-20), Silver (9), Bronze (6), HM (5)
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10 comments:

  1. Anonymous30 May 2012 at 18:01

    I got 2 for question 3. I thought it was really similar to one of the questions in this year's SMO senior

    ReplyDelete
  2. Anonymous30 May 2012 at 23:35

    I only got 5 correct... Should have fill up all those didn't attempt with 0... Then I will get two more correct lol...

    ReplyDelete
  3. wdmsg31 May 2012 at 14:28

    Q3:
    let P(x)=xf(x)-2,the degree of P(x) is 2013, it has roots x=1,2,...2013.
    hence, P(X)=xf(x)-2=a(x-1)(x-2)...(x-2013),letting x=0,a=2/2013!, xf(x)=a(x-1)(x-2)...(x-2013)+2,so 2014f(2014)=2+2=4

    ReplyDelete
  4. Lee Zheng Han31 May 2012 at 15:14

    Wait... isn't the for question 16 13?
    13 - 4 ⌊∛13⌋ = 5...

    ReplyDelete
  5. Anonymous31 May 2012 at 16:11

    How many ans should I get to stand a chance for round 2 Open section?

    ReplyDelete
  6. Anonymous31 May 2012 at 16:22

    If i got 10, can i get in round 2?

    ReplyDelete
  7. Goran2 June 2012 at 21:29

    Solutions of questions from SMO 2012 Open
    http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481905&p=2700878#p2700878

    ReplyDelete
  8. Unknown6 June 2012 at 17:19

    Question 3 similar to a last year junior question.

    ReplyDelete
  9. Anonymous6 June 2018 at 14:53

    Sorry for the necro, but the answer for question 16 is indeed 10. The solution book itself does imply that the answer is 10, and the "19" is just an erratum.

    ReplyDelete