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)
13 comments:
27. 33? 16+16+1
i used wolfram and found 2 solutions, 16+16=32. What is your 1?
Isn't answer for q16 50 and not 140?
yeah oops x,y=0 doesnt work argh
ya Q16 ans is 50
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
Q21?
But the identity in the question is cos50/(1-sin50) and not cos50/(1+sin50)
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...
@Anon, tan(230-160) = tan(50-160), so x = 50.
Must you get a silver to go to round 2?
Still waiting for the namelist.....
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How to do question 29
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