SMO 2019 Open Rd 2 Namelist
SMO 2019 Open Rd 2 Questions
SMO 2019 Open Questions
SMO 2019 (Open Section) Answers
1. 39
2. 0
3. 49
4. 4041
5. 505
6. 0
7. 0
8. 30
9. 9
10. 750
11. 37
12. 196
13. 4
14. 83210
15. 21
16. 299
17. 24
18. 5
19. 2020
20. 26
21. 1
22. 2
23. 2010
24. 1347
25. 99048
61 comments:
"No, q25 is obviously 4 it's so epic!"
Q22 should be 2 - the probability evaluates to 3/8.
Opinions on whether this was better or worse than 2018 / past years?
In my opinion, worse.
Much worse.
Note that B can be closer to O than A - in this scenario the triangle inequality has a 1/2 chance of holding.
Agreement with the above comment
I'm dying I did so badly... single digit score
bruh
For Q22, isn't the answer 99999? My Y6 senior said so.....
That’s impossible because probability cannot be more than 1
What do you think will be the cut off?
hi can i ask what's the fraction for q16
It's 48/251.
I find the answers for questions 2, 6 and 7 very interesting.
Hmm
Guys, I think I got 5, so does this mean I get honourable mention?
I got 6 last year and got HM
Can 11 get me anything?
Q9 should be 7, because a = 8, b = 1, and the problem asks form b-a, not b+a
Anyone has a guess for the score to enter the second round ?
b = 8, and a = -1, since a ≤ x ≤ b.
Hence the answer is b - a = 9.
anyone knows the construction for q13, i only have 6,15,21 and 21,14,35 which give an answer of 3
can some explain why 21:1?
if n=1, (e^1/1)/1 is already 2 so how can summation limit be 1
Imo the phrasing is quite ambiguous
The answer should be 4 but it wont be that easy?
q22 should be 4. Imagine a graph of cubic square of 0≤x≤1，0≤y≤1，the equation holds when 1. x＜1/2andy＞1/2andy-x＜1/2， 2. x＞1/2andy＜1/2and x-y＜1/2.
The area satisfied is 1/4
Isnt 48/251 bigger than 386/2019?
Oh nvm i read the qn wrongly
Was this harder than last year or easier? What about cut-offs?
Indignation as he asked his very trustworthy invigilator which told him it was only 1 letter and not 1 of each letter
Hello, what are the points for HM, bronze, silver, gold and round 2? Thanks
My guess:
HM 5-6
Bronze 7-8
Silver 9+
Round 2 11-12
for q13, one construction is 1, 23, 56, 78.
Basically the consecutive differences can be 2p, 3p, 2p, where p is some prime larger than 7.
This year, the questions are all atypical. Very strange..
It decreases when n increases. You can imagine it as a series of n rectangles, each with width 1/n on the graph of y=e^x from 0 to 1. The sum of the areas of the rectangles (an overestimation) is the expression you want to find, and it approaches the area under the graph when n goes to infinity. So its just the definite integral of e^x from 0 to 1, giving e-1.
Based on past experiences, do you guys think 9 will get anything?
Q22, answer seems to be 4
Shouldn't 23 be 2020?
Ever seen the 2009-2011 papers?
Hi, can I ask how did you solve Q25? I've been trying to solve it but haven't had any success :( would appreciate any help! Thanks!
question 2 should be c, last year's smo papers second question was the same as this one
What will 9 get me? Bronze or honourable mention?
Bronze
round 2 list is out https://sms.math.nus.edu.sg/Competitions/SMO2019/R2Open-2019.pdf
You guys mind sharing how much yall got?
What’s the cut off this year?
When will we know whether we got any award?
I got 13 and got it, can’t believe it myself haha
Anyone got in with 11
I got 11, didn't make it sadly. I wonder if 12 makes the cutoff.
12 is the cut off. My friend got 12 and got in
does anyone know when we'll know our results??
Question 25 hint: for most colourings of the top two rows, the top two rows will completely determine the colouring of the rest of the rows.
See also SMO Senior 2014, question 27
Hi guys, anyone know how to do question 12? I have been trying but unfortunately I couldn't get the answer. I tried using quadratic mean ≥ arithmetic mean, as well as power mean and Cauchy Schwarz inequality but it doesn't help me solve the question in any way nor does it help me move forward. The only lead I have is that the square of a number is positive, so 960498 is the sum of 99 positive square numbers, but idk how to move forward from here. Also is x1,x2,..,x99 supposed to be integers or reals? Because it doesn't mention anywhere in the question.
@Praveen there's no need for inequalities. A level statistics knowledge is sufficient. Also, they're reals.
How do you use A Level Statistics? I mean like the first thing I get is that the mean of 99 numbers is 98. What do I do now for the sum of the squares?
@Praveen Using the sum of squares, you can deduce that the variance is also 98. For all the numbers to have the mean 98 and variance 98 with x1 being as large as possible, the other numbers x2, x3, ..., x99 must contribute as little to the variance as possible, i.e. they have to be equal. You can use the mean of 98 to figure out what x2, x3, ... are equal to in terms of x1, then use the sum of squares to figure out what x1 itself is.
Btw, if you don't want to use statistics, Cauchy-Schwarz works too. See http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481764
One can easily use Cauchy Schwarz Inequality to get 196
Can upload round 2 question asap thanks
Will 7 in round 1 of open get me a bronze.
You can check results are out to schools
Where are SMO 2020 Open Answers
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