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:

Qn 2 should be E.

Agreed, q2 should be E

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

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

Can anyone help explain why qn 8 is c

Question 21 should be 4

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)

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

is 16 a good mark

q20 should be 1068

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.

yes 21 should be 4

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

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

How to do Q16

14

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

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

Is 5 to 6 enough for honorable mention?

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

Wait could someone explain q8

Could someone help me with Q16

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

Why isn't q4 C and q8 E?

Should number 25 be 4035 instead?

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

Shouldn't question 13 be 27?

1+4+4+8+9+22=6×8

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.

Agreed.That was my reasoning too

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?

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

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

Depends. Most of time 7 to 8 should give honorable

For Q14 I made a calculation error:

sqrt 5 × sqrt 5 =25

So I got 425 :(

Also, Q8 is C

Because 5 5 17 and 5 5 19 doesn't work

So the answer is 10-2

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

so is q8 C or E?

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

Could someone help explain question 25? Thanks.

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)

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

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.

@smo guy wow!You confirm second round

What school are you btw?

@anonymous

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

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

Is 22 or 23 enough to get a Gold?

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

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

what is usually cut-off for silver?

what can 16 get me

A silver maybe?

Is it possible to get silver without going second round?

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

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.

SUBSTITUDE X = -1

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.

All the world: 10% (500/5000)

Vietnam: 55% (76/139)

Impressive, right :))

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/

So is question 8 C or E?

Ng Bee Yong, thank you very much.

Heard that the 2nd round results are out.

Anyone knows what is the cut-off points?

Where are the second round results posted

I heard from teacher

the results are not out

i checked the singapore maths society website

Guys the results are out!!!

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

What is cut-off?

16 got me in!

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

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

16 got me to second round

Anyone got lower than 16 still went second round?

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

No.Silver

ok thank you

Thanks for your reply!!

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

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

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

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

i got 16

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

Yes should be

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

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

so cutoff is 16?

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

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

Is listing or guess and check allowed for round 2

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