[Tests + Stats Released] SFA's 2021 Orange Mathematics Competition (OMC) 10/12

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70 posts

#1 h Jan 12, 2021, 5:00 AM • 36 Y

Y by son7, jacoporizzo, Pleaseletmewin, fukano_2, JustinLee2017, 606234, math31415926535, winnertakeover, Jerry122805, Monkey_king1, ab456, RedFireTruck, MathJams, ImSh95, RJ5303707, v4913, sotpidot, amazingxin777, vsamc, 618173, fidgetboss_4000, Ha_ha_ha, john0512, bowenying24, SuperJJ, superagh, centslordm, aops98888, russellk, skyscraper, nikitadas, megarnie, rayford, KLBBC, Mango247, Mango247

Hello AoPS!

After a successful mock contest with the OMC 8, STEAM For All is excited to announce its first ever

OMC 10/12

The virtual Orange Mathematics Competition (OMC) 10/12, is a Mock American Mathematics Competition (AMC) 10/12 with questions written by STEAM for All volunteers! Our problem writers and testsolvers consist of a two-time MOPper, a two-time USAJMO qualifier, and plenty of AIME qualifiers.

The mock contest offers two entirely free online math contests, the OMC 10 and the OMC 12. Students may only take one exam, and students in grades 10 and below are eligible for the OMC 10 while students in grades 12 and below are eligible for the OMC 12. It is a wonderful opportunity for students to engage in a practice test with fun, original questions, listen to experienced competitors explain solutions to the most difficult questions on the exam, and finish off with an awards ceremony to recognize some of the top scoring students!

Register at https://www.steamforall.org/omc-10-12. Registration ends on Thursday, January 21st, 2021 at 12 PM PST.

The competition will be held on Saturday, January 23rd, 2021 from 4 - 6:30PM PST. The general schedule will be as follows (note that all times below are in PST):
4:00 - 4:15 PM: Introduction
4:15 - 5:30 PM: OMC 10/12 Competition
5:30 - 6:15 PM: Problem Review Session
6:15 - 6:30 PM: Awards and Closing Ceremony

FAQ

As for sample problems, here are a few problems from our problem writers that came up on previous contests! Feel free to discuss any of them in this thread.
Sample Problems

More Questions? Contact us at info@steamforall.org or ask in this thread!

We hope that you join us for the upcoming tournament!

Test Links:

OMC 10: https://drive.google.com/file/d/1UVlvprEDwY_l9zTGV7VqW_Ymz1FYQ7Uk/view?usp=sharing

OMC 12: https://drive.google.com/file/d/1SVWk3bJUsMUQR9RUQ1P6YBsIXcHS1uYn/view?usp=sharing

Statistics attached.

Attachments:

OMC_12_Statistics.pdf (82kb)

OMC_10_Statistics.pdf (83kb)

This post has been edited 9 times. Last edited by ilovemath04, Jan 25, 2021, 11:37 PM

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Pleaseletmewin

1574 posts

Pleaseletmewin

#2 h Jan 12, 2021, 5:02 AM • 7 Y

Y by ImSh95, RedFireTruck, Ha_ha_ha, v4913, russellk, Mango247, Mango247

Wow, I'm definitely signing up for this!

As I know some of the test writers personally, I can tell everyone without a doubt they are more than qualified to write this mock.
I highly encourage people to do this mock as it will be great practice for the upcoming AMC's

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reniebeanbean

16 posts

reniebeanbean

#3 h Jan 12, 2021, 5:03 AM • 5 Y

Y by ImSh95, RedFireTruck, Ha_ha_ha, v4913, russellk

wow, can't wait to join! :-D

SfA's events are always so well-planned out and SHEESH MOPPER PROBLEM WRITER :blush:

sniped

This post has been edited 1 time. Last edited by reniebeanbean, Jan 12, 2021, 5:04 AM
Reason: default emotes uglee

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JustinLee2017

1703 posts

JustinLee2017

#4 h Jan 12, 2021, 5:03 AM • 4 Y

Y by ImSh95, RedFireTruck, v4913, russellk

@3below, oh ok. Sorry I briefly skimmed and saw "mock contest" so I thought to move.

This post has been edited 1 time. Last edited by JustinLee2017, Jan 12, 2021, 5:07 AM

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PruneJames

39 posts

PruneJames

#5 h Jan 12, 2021, 5:04 AM • 4 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk

So excited! Stem For All's competitions are always very well written

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bfan0805

271 posts

bfan0805

#6 h Jan 12, 2021, 5:05 AM • 5 Y

Y by RedFireTruck, Ha_ha_ha, ImSh95, v4913, russellk

Sheesh, definitely signing up. Thank you ilovemath04 for letting us know!!

This post has been edited 1 time. Last edited by bfan0805, Jan 12, 2021, 5:09 AM

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Pleaseletmewin

1574 posts

Pleaseletmewin

#7 h Jan 12, 2021, 5:06 AM • 5 Y

Y by RedFireTruck, Ha_ha_ha, ImSh95, v4913, russellk

JustinLee2017 wrote:

Move to Mock Contest forum

This is an actual contest and has a scheduled date and time, so it should stay in C&P.

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Random_Person_921

470 posts

Random_Person_921

#8 h Jan 12, 2021, 5:07 AM • 6 Y

Y by RedFireTruck, Ha_ha_ha, ImSh95, v4913, russellk, jacoporizzo

Wow! This looks very high quality! I will sign up.

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brmorgan82

96 posts

brmorgan82

#9 h Jan 12, 2021, 5:16 AM • 6 Y

Y by RedFireTruck, Ha_ha_ha, MtnDu, v4913, niam, russellk

Hey AoPS Community and Friends,

I would definitely recommend this contest. I personally helped write and test-solve this contest (along with a few of my friends), and I believe that it truly is a high quality contest.

Hopefully this helps you,
Br Morgan

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math31415926535

5617 posts

math31415926535

#10 h Jan 12, 2021, 5:21 AM • 6 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk, Mango247, Mango247

I am definitely signing up.

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winnertakeover

1179 posts

winnertakeover

#11 h Jan 12, 2021, 5:25 AM • 4 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk

Hi, this seems like a great test! I can't wait to take it!

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math31415926535

5617 posts

math31415926535

#12 h Jan 12, 2021, 5:34 AM • 4 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk

will there be proctoring in the test?

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ab456

220 posts

ab456

#13 h Jan 12, 2021, 6:41 AM • 4 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk

This is going to be a really good test; I know the two-time USAJMO qualifier and the two-time MOPper personally, and both are very good mathematicians.

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HungryProblem_Solver1

469 posts

HungryProblem_Solver1

#14 h Jan 12, 2021, 6:44 AM • 5 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk, Mango247

Steam is run by kids? Wow never knew that. Impressive!

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ilovemath04

70 posts

ilovemath04

#15 h Jan 12, 2021, 8:13 AM • 4 Y

Y by RedFireTruck, Ha_ha_ha, v4913, russellk

math31415926535 wrote:

will there be proctoring in the test?

Yes, there will be proctoring in breakout rooms in the Zoom call. More details will come on the mock competition date.

ritvikaops wrote:

Steam is run by kids? Wow never knew that. Impressive!

Yes, STEAM for All is completely run by student volunteers!

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WarriorKid

4133 posts

WarriorKid

#201 h Feb 1, 2021, 2:11 PM • 3 Y

Y by pbj2006, Ha_ha_ha, Randy_Lee

never even heard of that until now

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math31415926535

5617 posts

math31415926535

#204 h Feb 2, 2021, 5:42 AM

Y by

On problem 21 of the OMC 10 I don't really understand the solution. In the solution it said thus, our answer is simply $(1+3+...+2^{2020}-1)+(1+3+...+2^{2019}-1)+...+(2^{1}-1). I don't really understand this part, how did they come up with this conclusion?

And also it would be nice if you guys had video solutions to these problems.

Attachments:

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ilovemath04

70 posts

ilovemath04

#205 h Feb 2, 2021, 8:31 AM • 1 Y

Y by SK_pi3145

@above

Essentially what we're doing is doing casework based on the power of $2$ that divides the numerator. Thus, we would group the numbers as follows:

$0$ powers of $2$ : $1,3,5, \cdots, 2^{2020}-1$
$1$ power of $2$ : $2,6,10,\cdots,2^{2020}-2$
...
$2019$ powers of $2$ : $2^{2019}$

Now, you can see that because the denominator has a huge power of $2$ , all powers of $2$ in the numerator of any fraction will have canceled out, so only the odd factors matter. So basically, if we ignore all the powers of $2$ , it becomes

$0$ powers of $2$ : $1,3,5, \cdots, 2^{2020}-1$
$1$ power of $2$ : $1,3,5,\cdots,2^{2019}-1$
...
$2019$ powers of $2$ : $1$

Now, note that these are all sums of consecutive odd numbers, which we know add up to perfect squares. Thus, our sum just collapses down to $(2^{2019})^2+(2^{2018})^2+\cdots+(2^{0})^2$ , from where you can continue with the official solution.

Regarding the second question, unfortunately, we won't be having video solutions.

This post has been edited 1 time. Last edited by ilovemath04, Feb 2, 2021, 8:31 AM

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henryqi

98 posts

henryqi

#206 h Feb 3, 2021, 5:16 AM

Y by

noooooooooooooo i got 75 ughhhhhhhhhhhhhhhhhh

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Facejo

2847 posts

Facejo

#207 h Oct 17, 2021, 11:00 PM

Y by

Where is the answer key?

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artgag33

96 posts

artgag33

#208 h Oct 17, 2021, 11:12 PM

Y by

Facejo wrote:

Where is the answer key?

here: https://c3aeae64-b3d0-473f-8447-b60fd55684ac.filesusr.com/ugd/e6d77e_59cb2dec76a74b6fb7abaa6792063f64.pdf

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Facejo

2847 posts

Facejo

#209 h Oct 17, 2021, 11:14 PM

Y by

artgag33 wrote:

Facejo wrote:

Where is the answer key?

here: https://c3aeae64-b3d0-473f-8447-b60fd55684ac.filesusr.com/ugd/e6d77e_59cb2dec76a74b6fb7abaa6792063f64.pdf

FTFY, but thanks

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phamryd000

19 posts

phamryd000

#210 h Oct 24, 2021, 7:03 PM • 1 Y

Y by Lilathebee

I just mocked this and scored a 76.5. How do my chances for qualifying for AIME look for the AMC 12B this year?

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mm999aops

2634 posts

mm999aops

#211 h Oct 24, 2021, 7:10 PM

Y by

hm im ngl in a real amc12 the chance would be perhaps 0.1% but I dont know the dif (like how hard OMC is compared to normal AMC12)

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math31415926535

5617 posts

math31415926535

#212 h Oct 24, 2021, 7:28 PM

Y by

phamryd000 wrote:

I just mocked this and scored a 76.5. How do my chances for qualifying for AIME look for the AMC 12B this year?

I think its pretty good, as OMC is a lot harder than normal amc 12.

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phamryd000

19 posts

phamryd000

#213 h Oct 24, 2021, 7:43 PM • 1 Y

Y by Lilathebee

mm999aops wrote:

hm im ngl in a real amc12 the chance would be perhaps 0.1% but I dont know the dif (like how hard OMC is compared to normal AMC12)

If you look at the statistics for this particular mock test, they have the AIME cutoff at 78 points but I'm not so sure how that would translate into a real AIME cutoff

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JenniferChenyingNi

2 posts

JenniferChenyingNi

#214 h Oct 31, 2021, 4:01 PM

Y by

Monkey_king1 wrote:

Yeah, a solution document will be provided, we are working on it right now. Scores will be sent out today hopefully!

Where can I access the solution document?

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asdf334

7579 posts

asdf334

#215 h Oct 31, 2021, 4:25 PM

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who else thought stats for this years omc was released

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Overlord123

799 posts

Overlord123

#216 h Oct 31, 2021, 4:29 PM

Y by

this test must be extremely hard if moppers, mc nats cdr, and amc 10 dhr people got between 90 and 105 on the amc 10

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ASnooby

99 posts

ASnooby

#217 h Aug 19, 2022, 2:10 AM • 1 Y

Y by Mango247

How do my chances look for AMC 12 later this year with a 78 on the mock 12? got 3 problems wrong.
got 4 wrong because I thought the wording was "on the circle", got 5 wrong because I drew an octagon, and got 7 wrong because I am bad and forgot $x^2$ .

edit: also p13 is based off an ARML preparation problem

This post has been edited 1 time. Last edited by ASnooby, Aug 19, 2022, 2:11 AM

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