Tuesday, 30 May 2017

SMO 2017 (Junior Section) Answers

SMO 2017 Junior Round 2 List

Cut off for Rd 2 ~16

SMO 2017 Junior Questions
SMO 2017 Junior solutions by a group of Year 1 students from NUS High is here

You can find past year SMO papers (2005-2013, Round 1 and 2 with full solutions) here.

For more SMO Junior Special Round practice, you may download the All Soviet Union Math Competition 1961-1987 here (note that only the first 99 questions have solutions included).

SMO 2017 (Junior Section) Answers

1. A
2. E
3. D
4. A
5. D
6. A
7. B
8. C
9. C
10. B
11. 7 (assuming interior angles are integers)
12. 277
13. 22
14. 85
15. 1
16. 18
17. 2017
18. 10
19. 49
20. 1144
21. 2
22. 71
23. 24
24. 1442
25. 4033
26. 61
27. 18
28. 677
29. 5
30. 16
31. 2016
32. 2
33. 79
34. 60
35. 8

90 comments:

PSJH said...

Qn 2 should be E.

Anonymous said...

Agreed, q2 should be E

Mather said...

Q2 is e and is getting 27 questions correct a bad thing?

Anonymous said...

27 questions? Wow I'm so impressed!!!

Anonymous said...

Can anyone help explain why qn 8 is c

Anonymous said...

Question 21 should be 4

LL said...

Q21

http://www.wolframalpha.com/input/?i=(x%5E2-((x%2B1)%2F2)%5E2)%2F(((x%2B1)%2F2)%5E2-1)%3D(sqrt(3)%2B1)%2F(3-sqrt(3))

AD/BC=3+2sqrt(3)

http://www.wolframalpha.com/input/?i=(4%2B2sqrt(3))%2F(3%2B2sqrt(3))*sqrt(3)

LL said...

Q8
5,17,19
5,5,5
17,17,17
19,19,19
5,17,17
5,19,19
17,19,19
19,17,17
total:8

Kairav Makhija said...

is 16 a good mark

Kairav Makhija said...

q20 should be 1068

R777 said...

Q20) a = 13, b = 1, c = 88
a^2 + bc = 169 + 88 = 257
ab + bc = 13 + 88 = 101
Thus, abc = 13 × 88 = 1144 and NOT 1068.

Anonymous said...

yes 21 should be 4

Anonymous said...

How do you do qn 17? ... I got 2019 + 2*sqrt(2017)

Anonymous said...

What do your think is the cut off point for round 2 this year?

Anonymous said...

How to do Q16

Anonymous said...

14

Anonymous said...

How many marks is needed for bronze based on previous years?

Anonymous said...

How much is needed to score honorable mention this year? Is 5 enough?

Anonymous said...

Is 5 to 6 enough for honorable mention?

Anonymous said...

I dun think so. based on previous years is 6 and this year's paper is easier

Anonymous said...

Wait could someone explain q8

Anonymous said...

Could someone help me with Q16

Anonymous said...

Why isn't q8 E? And why isn't q4 C?

Anonymous said...

Why isn't q4 C and q8 E?

Anonymous said...

Should number 25 be 4035 instead?

Anonymous said...

No. For Q25, the inequality holds when x ranges from -2015 to 2017 (including 0) so there are 4033 solutions

Anonymous said...

Shouldn't question 13 be 27?

Anonymous said...

1+4+4+8+9+22=6×8

Thi Phuong Tran said...
This comment has been removed by the author.
Anonymous said...

LL, 5,5,5 and 17,17,17 are congruent, hence counted as one.
Ans =10 where you can extend the length using one or more rods. Taking in mind restrictions of only once.

Anonymous said...

Agreed.That was my reasoning too

Smo Noob said...

I realised that 15 is the cut off for last year smo junior round 2 based on the comments in last year's post. With a score of 14 for round 1, will i be able to make it into round 2?

Anonymous said...

Possibly, but this year's paper was easier than last year. There is a chance though

Anonymous said...

What will i get if i get around 6 to 7?Will i be able to get honourable mention?

Anonymous said...

Depends. Most of time 7 to 8 should give honorable

Anonymous said...

For Q14 I made a calculation error:
sqrt 5 × sqrt 5 =25
So I got 425 :(

Anonymous said...

Also, Q8 is C
Because 5 5 17 and 5 5 19 doesn't work
So the answer is 10-2

Anonymous said...

And I put 58 for Q34 because I forgot that 35/175, 70/175 .... 140/175 repeated.

SMO noob said...

so is q8 C or E?

Anonymous said...

How much is needed for silver based on previous years?Around 12 to 13?

Anonymous said...

Could someone help explain question 25? Thanks.

Anonymous said...

For Q25
x^2+2015x+1<2017x+2017^2
x^2-2x+1-2017^2<0
x^2-2x-(2016)(2018)<0
(x-2018)(x+2016)<0

I can't explain this next part but you can visualise it as a quadratic graph with equation y=(x-2018)(x+2016) which is a u-shaped quadratic graph (opening upwards) with roots 2018 and -2016. There will be a region of the graph below the x axis which satisfies
(x-2018)(x+2016)<0. If you draw it out yourself you get this:

-2016<x<2018

So integers -2015 to 2017 satisfy the inequality and the number of integers is 2017+2015+1=4033. Take note that the inequality is not inclusive (a.k.a -2016 and 2018 are not included)

Hopefully this helped because I'm honestly not that great at explaining these type of questions.

@SMO noob From my explanation above 5,5,17 and 5,5,19 do not work so the answer for Q8 is 10-2=8 (C)

Smo noob said...

@anonymous your explanation sounds good!You must have did pretty well in Smo.How much did you get?

SMO Guy said...

I should start giving myself a username :)

I didn't record all my answers but from what I recorded I got 22...could have gotten higher if I didn't make careless mistakes on Q14 and Q34.

Anonymous said...

@smo guy wow!You confirm second round
What school are you btw?

SMO Guy said...

@anonymous
I'll probably just say I'm not from NUS High, school doesn't really matter :)

Isuckatmath said...

What can 13 get me?I know it probably won't take me to second round but can i get silver or bronze?

Anonymous said...

Is 22 or 23 enough to get a Gold?

Isuckatmath said...

You can enter second round and probably have to get a few marks there to boost your chances of getting gold

Anonymous said...

Probably a gold and if you do well in round 2, you may even get into SIMO team.

Anonymous said...

what is usually cut-off for silver?

Kairav Makhija said...

what can 16 get me

SMO Guy said...

A silver maybe?

Anonymous said...

Is it possible to get silver without going second round?

Smo noob said...

Yes it ia possible but you have to score like 1 or 2 mark below the cut off for round 2 i think.

Anonymous said...

Hi! We're students from NUS High M17106 and we know that some of you might require solutions.
Solutions are not in Popular or any other bookstore, so we're here to provide you with them.

http://nushs-smo-junior-2017-sol.blogspot.sg

Here's a link to get to the solutions.

Unknown said...

SUBSTITUDE X = -1

Đặng Kim Oanh said...

Hello, I am from Vietnam. It is surprising for me to go to Singapo for round 2 of SMO. But now,I don't have any document& exam to learn.I hope you will help me and upload the exams of SMO for me.Sorry, because my English is not good.Thank you so much.

Anonymous said...

All the world: 10% (500/5000)
Vietnam: 55% (76/139)
Impressive, right :))

Ng Bee Yong said...

Kim Oanh, download past year papers (2005-2013 both Rd 1 and 2) from below:
https://www.intereseducation.com/resources/smo-problems-with-answers-and-solutions-singapore-mathematical-olympiad/

Anonymous said...

So is question 8 C or E?

Đặng Kim Oanh said...

Ng Bee Yong, thank you very much.

Anonymous said...

Heard that the 2nd round results are out.
Anyone knows what is the cut-off points?

Anonymous said...

Where are the second round results posted

Anonymous said...

I heard from teacher

Kairav Makhija said...

the results are not out
i checked the singapore maths society website

Anonymous said...

Guys the results are out!!!

Anonymous said...

http://sms.math.nus.edu.sg/Competitions/SMO2017/SMO%20Junior%20R2.pdf

What is cut-off?

Anonymous said...

16 got me in!

Anonymous said...

Will we be able to know if we got silver, bronze or honorable mention?

Anonymous said...

After the second round. The results for gold, silver, bronze, etc will be shown together

Anonymous said...

16 got me to second round

Anonymous said...

Anyone got lower than 16 still went second round?

Anonymous said...

if we get into round 2 will we get gold (if we do badly for r2)

SMO noob said...

No.Silver

Anonymous said...

ok thank you

Anonymous said...

Thanks for your reply!!

Smo noob said...

@Anon how much did you get to go round 2?

Anonymous said...

What is the cut-off point to get into round 2 this year?

Anonymous said...

Lets say cut-off is 16. If i get 14, do i still stand a chance of getting silver?

Kairav Makhija said...

if i do not attend round 2 will i get at least silver

Kairav Makhija said...

i got 16

SMO noob said...

Yes.Anyone who got 15 can share whether they got into second round?

Anonymous said...

Yes should be

Anonymous said...

are all of students who got away to round 2, attend or no, certainly got medal?

smo noob said...

You would get definitely a silver at least if you go to round2.

Anonymous said...

so cutoff is 16?

Anonymous said...

For the second round, is each question worth only 1 mark?

Anonymous said...

For round 2, each question is worth 10 marks. However, solutions are required.

Anonymous said...

Is listing or guess and check allowed for round 2