Wednesday, 3 June 2015

SMO 2015 (Senior Section) Answers


SMO 2015 Senior Questions

SMO 2015 Senior Round 2 cut off (~17)

SMO 2015 (Senior Section) Answers

1. B
2. B
3. B
4. A
5. D
6. E
7. D
8. C
9. C
10. A
11. 4
12. 960
13. 9
14. 11
15. 6
16. 50
17. 2016
18. 1225
19. 18
20. 4
21. 87
22. 100
23. 4
24. 5
25. 13
26. 21978
27. 32
28. 25
29. 6
30. 12
31. 28
32. 5
33. 1728
34. 509
35. 20

Initial answers are provided by Clarence Chew.

SMO (Senior) Previous Years' Cut-off Points (Inclusive of Round 2 scores)
2014 Scores were not revealed to schools and students
2013 Gold (13), Silver (8), Bronze (6), HM (5), Round 2 (~8), Top 30 (~26)
2012 Gold (24), Silver (11), Bronze (8), HM (7), Round 2 (11)
2011 Gold (21), Silver (15), Bronze (10), HM (9), Round 2 (~15), Top 30 (27)
2010 Gold (26), Silver (10), Bronze (7), HM (6)
2009 Gold (19-23), Silver (10), Bronze (7), HM (6)
2008 Gold (27-28), Silver (15), Bronze (10), HM (9)
2007 Gold (29-30), Silver (16), Bronze (12), HM (10)
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13 comments:

  1. Anonymous3 June 2015 at 13:33

    27. 33? 16+16+1

    ReplyDelete
  2. LL3 June 2015 at 13:36

    i used wolfram and found 2 solutions, 16+16=32. What is your 1?

    ReplyDelete
  3. Anonymous3 June 2015 at 13:46

    Isn't answer for q16 50 and not 140?

    ReplyDelete
  4. Anonymous3 June 2015 at 14:57

    yeah oops x,y=0 doesnt work argh

    ReplyDelete
  5. Anonymous3 June 2015 at 17:35

    ya Q16 ans is 50

    ReplyDelete
  6. Clarence Chew3 June 2015 at 17:48

    The answer for Q16 is 180. (I messed up on the tan identity tan(a)tan(90-a)=1). Proof:

    We need to show that:
    tan20 = cos50/(1+sin50)
    cos50/(1+sin50)=sin40/(1+cos40)=2sin20cos20/(2cos^2(20))=sin20/cos20=tan20

    ReplyDelete
    Replies
    1. Anonymous3 June 2015 at 18:50

      But the identity in the question is cos50/(1-sin50) and not cos50/(1+sin50)

      Delete
  7. Anonymous3 June 2015 at 17:57

    Q21?

    ReplyDelete
  8. Anonymous4 June 2015 at 12:09

    Shouldnt Q16 be 230?

    This is how I do it:
    tan x= sin x/cos x
    sin x/cos x = cos 50/ (1 - sin 50)
    Imply sin x = cos x cos 50 + sin x sin 50
    = sin 140 - x (by identity)
    If and only if x = 70.
    70 + 160 = 230

    But I did not do it correctly in the competition as I was very careless to calculate 90 + 50 = 130... Argh...

    ReplyDelete
  9. Skittles Pony6 June 2015 at 00:08

    @Anon, tan(230-160) = tan(50-160), so x = 50.

    ReplyDelete
  10. Anonymous17 June 2015 at 07:39

    Must you get a silver to go to round 2?
    Still waiting for the namelist.....

    ReplyDelete
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    ReplyDelete
  12. Anonymous31 October 2018 at 22:34

    How to do question 29

    ReplyDelete