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Thursday, May 8, 2025

2024/2025 Mathcounts, AMCs, AIMEs Competition Preparation Strategies

Hi, Thanks for visiting my blog.

E-mail me at thelinscorner@gmail.com if you want to learn with me.  :) :) :) 

Currently I'm running different levels of problem solving lessons, and it's lots of fun learning along with students from different states/countries. 

So many students are not learning smart.

Problem solving is really fun (and a lot of the times very hard, yes).

Good questions are intriguing and delicious, so come join our vibrant community and have the pleasure of finding things out on your own.


There is no overnight success.

My other blogs :


thelinscorner  : Standardized test preps, books, links/videos for life-time learning

Take care and have fun learning.

Don't forget other equally interesting activities/contests, which engage your creativity  and imagination. 

Some also require team work. Go for those and have fun !! 

Don't just do math.  


Before going full throttle mode for competition math, please spend some time reading this
well- thought-out article from BOGTRO at AoPS "Learn How to Learn".

It will save you tons of time and numerous, unnecessary hours without a clear goal, better method in mind.

Less is more. My best students make steady, very satisfactory progress in much less time than those
counterparts who spent double, triple, or even more multiple times of prep with little to show.

It's all about "deliberate practices", "tenacity", and most of all, "the pleasure of finding things out on your own".

Take care and have fun problem solving.

I have been coaching students for many years. By now, I know to achieve stellar performance you need :
Grit (from TED talk), not only that but self-awareness (so you can fairly evaluate your own progress) and a nurturing-caring environment. (Parents need to be engaged as well.)
               
Thanks a lot !!  Mrs. Lin

"Work Smart !!" , "Deliberate practices that target your weakness ", " Relax and get fully rested.", "Pace your time well", "Every point is the same so let go of some questions first; you can always go back to them if time permits."

"It's tremendous efforts preparing for a major event on top of mounting homework and if you are the ones who want to try that, not your parents and you work diligently towards your goal, good for you !!"

"Have fun, Mathcounts changes lives, because at middle school level at least, it's one of those rare occasions that the challenges are hard, especially at the state and national level."

Now, here are the links to get you started: 

Of course use my blog.  Whenever I have time I analyze students' errors and try to find better ways (the most elegant solutions or the Harvey method I hope) to tackle a problem. Use the search button to help you target your weakness area.

Last year's Mathcounts competition problems and answer key


For state/national prep, find your weakness and work on the problems backwards, from the hardest to the easiest. 

Here are some other links/sites that are the best.

Mathcounts Mini : At the very least, finish watching and understanding most of the questions from 2010 till now and work on the follow-up sheets, since detailed solutions are provided along with some more challenging problems.

For those who are aiming for the state/national competition, you can skip the warm-up and go directly to "The Problems" used on the video as well as work on the harder problems afterward.

Art of Problem Solving 

The best place to ask for help on challenging math problems. 
Some of the best students/coaches/teachers are there to help you better your problem solving skills.

                                                             Do Not Rush !!

Awesome site!!
       
For concepts reviewing, try the following three links.
 
Mathcounts Toolbox
 
Coach Monks's Mathcounts Playbook
 
You really need to understand how each concept works for the review sheets to be useful.

To my exasperation, I have kids who mix up the formulas without gaining a true understanding and appreciation of how an elegant, seemingly simple formula can answer myriads of questions.

You don't need a lot of formulas, handbook questions, or test questions to excel.

You simply need to know how the concepts work and apply that knowledge to different problems/situations.

Hope this is helpful!!

Wednesday, May 7, 2025

Ay reflection notes

Ay

 5/7 

1) Reviewed the attached problems and solutions and I understand them well
2) Attempted the 2024 AMC 12A in 60 minutes. I attempted #1 to #19 and got them all correct.
I had a headache after that so I couldn't attempt the rest of the questions. Skipped  -#20 to #25
Not sure how many I could have actually done.


Sunday, May 4, 2025

An, a 7th grader sample student reflection note, or report

from a 7th grader  A. 

2025 chapter test 

total 34 correct
21-30 wrong on sprint

8th was wrong on target
Sent from my iPhone

2024 chapter test
Sprint Round
2 Q19 Algebra Silly mistake Didn't set up the equation correctly Underline important parts of the question
3 Q23 Geometry Didn't know how to do it Learn how to do it
4 Q25 Geometry Didn't know how to do it Learn how to do it
5 Q26 Algebra Didn't know how to do it Learn how to do it
6 Q27 Time, Rate, Distance Didn't know how to do it Learn how to do it
7 Q28 Number Theory Didn't know how to do it Learn how to do it
8 Q29 Probability Silly mistake Didn't count all possible scenarios Learn how to do a faster way to solve these probability problems
9 Q30 Geometry Didn't know how to do it Learn how to do it
10 Target
11 Q5 Alegbra Wasn't sure on how to do it. Learn how to do it
12 Q6 Number Theory Didn't know how to do it Learn how to do it
13 Q8 Number Theory Wasn't sure on how to do it. Learn how to do it
14
15 Total score: 32

Sent from my iPhone

Friday, May 2, 2025

Ar. Student reflection notes to keep track of progress

 from a 9th grader Ar. 

Hello Mrs. Lin, 4/25

I hope you are well.
Sorry for sending this a bit late, but I wanted to share my reflection for what I have done this week. I first looked over the problems we did in class. I had some issue with the last problem-I am still not 100 percent on that one. I was hoping if you could please re-explain this in class, that would be helpful. I also looked over the formula sheet. While doing some of the AMC problems you gave, I tried to really focus on the first 7 problems. I was hoping we could go over some quicker ways to think on problems 3, 5, and 6 on the AMC 10 2023 A.
Sorry for sending this late.
Thank you,

Thank you Mrs. Lin. 5/2
I wanted to share my reflection for this week. I reviewed all of the problems we went through during class, and I really understood everything. I continued doing problems from the AMC 10 2023 A test, and I redid problems 3, 5, 7. Those were the problems I struggled with last week, so I reviewed those. I also tried to go on by doing problems 7 to 13, but it took me a while to do those and I didn’t get those correct. I went back to problems 1 through 7, except for the B test.
Thank you,


Hello Mrs. Lin, 5/11
I wanted to share my reflection from this week.
I felt good about all the problems we did in class, but I wanted to just quickly go over the last problem once more. I had a question on that one. I started a new test (2022 AMC 10 A), and did questions 1-10. I was hoping to go over questions 5, 7, 8, and 10. 

Monday, February 17, 2025

Harder Mathcounts State/AMC Questions

2012 Mathcounts State Sprint #30: In rectangle ABCD, shown here, point M is the midpoint of side BC, and point N lies on CD such that DN:NC = 1:4. Segment BN intersects AM and AC at points R and S, respectively. If NS:SR:RB = x:y:z, where x, y and z are positive integers, what is the minimum possible value of x + y + z? 

Solution I :


¯AB:¯NC=5:4 [given]

Triangle ASB is similar to triangle CSN (AAA)

¯NS:¯SB=4:5

Let ¯NS=4a,¯SB=5a.






Draw a parallel line to ¯NC from M and mark the interception to ¯BNas T.

 ¯MT:¯NC = 1 to 2. [ΔBMT and ΔBCN are similar triangles ]

¯NT=¯TB=4a+5a2=4.5a

¯ST=0.5a

 ¯MT:¯AB = 2 to 5
[Previously we know  ¯MT:¯NC = 1 to 2 or 2 to 4 and  ¯NC:¯AB=4:5 so the ratio of the two lines  ¯MT:¯AB is 2 to 5.]


¯TB=4.5a  [from previous conclusion]

Using 5 to 2 line ratio [similar triangles ΔARB and ΔMRT , you get ¯BR=57×4.5a=22.5a7 and ¯RT=27×4.5a=9a7

Thus, x : y : z = 4a : 12a+9a7 : 22.5a7 = 56 : 25 : 45

x + y + z = 126

Solution II : 
From Mathcounts Mini: Similar Triangles and Proportional Reasoning

Solution III: 
Using similar triangles ARB and CRN , you have xy+z=59.
9x = 5y + 5z ---- equation I

Using similar triangles ASB and CSN and you have x+yz=54.
4x + 4y = 5z  ---- equation II

Plug in (4x + 4y) for 5z on equation I and you have 9x = 5y + (4x + 4y) ; 5x = 9y ; x = 95y
Plug in x = 95y to equation II and you have z  =  5625y

x : y : z = 95y  : y  :  5625y =  45 y :  25y  :  56y

45 + 25 + 56 = 126


























Solution IV : Yes, there is another way that I've found even faster, saved for my private students. :D 

Solution V : from Abhinav, one of my students solving another similar question : 

Two other similar questions from 2016 AMC A, B tests : 

2016 AMC 10 A, #19 : Solution from Abhinav 






2016 AMC 10 B #19 : Solution from Abhinav 





The Grid Technique in Solving Harder Mathcounts Counting Problems : from Vinjai



The following notes are from Vinjai, a student I met online. He graciously shares and offers the tips here on how to tackle those harder Mathcounts counting problems. 

The point of the grid is to create a bijection in a problem that makes it easier to solve. Since the grid just represents a combination, it can be adapted to work with any problem whose answer is a combination.

For example, take an instance of the classic 'stars and bars' problem (also known as 'balls and urns', 'sticks and stones', etc.):
Q: How many ways are there to pick an ordered triple (a, b, c) of nonnegative integers such that a+b+c = 8? (The answer is 10C2 or 45 ways.)
Solution I: 
This problem is traditionally solved by thinking of ordering 8 stars and 2 bars. An example is:
* * * |    | * * * * *
  ^       ^       ^
  a       b       c
This corresponds to a = 3, b = 0, c = 5.

Solution II: 
But this can also be done using the grid technique:




The red path corresponds to the same arrangement: a = 3, b = 0, c = 5. The increase corresponds to the value: a goes from 0 to 3 (that is an increase of 3), b goes from 3 to 3 (that is an increase of 0), and c goes from 3 to 8 (that is an increase of 5). So a = 3, b = 0, c = 5.

Likewise, using a clever 1-1 correspondence, you can map practically any problem with an answer of nCk to fit the grid method. The major advantage of this is that it is an easier way to think about the problem (just like the example I gave may be easier to follow than the original stars and bars approach, and the example I gave in class with the dice can also be thought of in a more numerical sense).