SMO 2020 Open Questions
SMO 2020 (Open Section) Answers
1. 0
2. 2030
3. 12
4. 27
5. 70
6. 945
7. 50
8. 4
9. 43
10. 8
11. 4097
12. 1010
13. 5120
14. 0
15. 4039
16. 12
17. 8800
18. 2017
19. 41
20. 140
21. 704
22. 165
23. 838
24. 1600
25. 290
52 comments:
Hi may I ask where are the answers for 23 and 25?
Hi I if I score 9/25 what can I get?
Why isn't q18 2019?
try k=3
should question 13 be 20*15*17 instead of 20*16*16 because an arithmetic progression needs to have the common ratio different from 0
Can 4/25 get HM?
should question 13 be 20*15*17 instead of 20*16*16 because an arithmetic progression needs to have the common ratio different from 0
to the person who said this, AP does not need to have non-zero common difference. 1,1,1,1,1,... is in AP
I got 2 for qn 14 though...
Got 1qn right
I think qn 22 is not 165......
You should also consider the situation when r=0, this leads to another 55 n (11 chose 2)
so in total there's 165+55 = 210 n before 2020......
2020 in binary is 11111100100 with 11 digits. 11C3 already takes into account r=0.
Shouldn't qn 16 be 13? I got p>12, so the smallest positive value of p is 13。
Shouldn't the answer for qn1 be 2020 instead of 0??
For qn16, p >= 12. When p = 12, z = 2x, sub in those values will give an infinite no of solutions for y
For qn1, if x is a root then -x is also a root
for q6, i got my points of intersection between the lines as (7,4,4), (1,2,3) and (4,5,6), which leads to my area being 12 but this won't give me the answer.. could anyone help me with where i might've gone wrong?
isnt qn16’s answer 13?
oops pls ignore this i was very careless
I got 15 out of 25. Will I get a gold or a silver?
I got 8/25 but could have gotten 10/25 bec of carelessness. What can I get with this score?
Estimated cut offs for bronze, silver and gold?
I also got 13
Can 10/ 25 get me a bronze?
what was the comment that got deleted?
I got 15 out of 25. Will I get a gold or a silver?
I think you will get silver, but there is also a chance that you get gold.
I wish you all the best.
Any idea what is the cut off for open this year? Higher or lower than last year?
Insider information:
HM - >6
Bronze - >10
Silver - >13
Gold - >16
The comment that I deleted was just me miscounting my score
Hi, can I ask is there a chance 9 gets me Silver?
There is 2 roots 2020 and - 2020 so when u add them together it becomes 0.
Will 12 get me sliver?
i dont understand why q12 is 1010, shouldnt it be 2020?
Expected cutoffs:
Gold >20
Silver>14
Bronze>10
HM > 5
can 9 get me a bronze
q12: put a -1 in (1,2),(3,4), etc till (2019,2020). you only need one -1 for every two rows and columns
Can someone explain q23 pls?
Q23
max S = floor(n^2/4), min S = n - 1
Guess that everything in between is possible, then solve for n
hello, can someone explain Q15?
I need help wif qn 7
can 23/25 get into smo junior team?
can13getsilver？
are results out
alao wonderÔ¾‸Ô¾
Anyone knows the cut off?
I think cutoff for gold is 15 as I got gold and my friend who got 14 got silver
thank u！！
CUTOFFS FOR SMO OPEN 2020:
Gold: 15
Silver: 11
Bronze: 8
HM: 6
Information from mathematics teacher
Cutoffs are identical to that for SMO OPEN 2019 (with round 2)
Comments on Q7:
Set a = b, f(0) = 0. Set a = -b, f(-a) = -f(a). Replace b with -b, (f(a)-f(b))/(a-b) = f(a^2-b^2)/(a^2-b^2). Let b approach a, then the LHS becomes f'(a) whereas the RHS approaches some constant independently of the choice of a, i.e. f is linear.
I would like to see a more elegant proof on the linearity of f though.
yes! I got full marks again
anyone can tell me how to do question 21
There is another root 1/2020 and -1/2020 but this cancels out too
U find the length of each side, then u find it is an right angle triangle
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