2025/2026 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.

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Testimonials from my students/parents.   :) 

My other blogs :

thelinscorner  : Standardized test preps (ONLY the hardest problems), books, links/videos for life-time learning

Studentsspeak Magazine  (featuring students' independent projects)

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.  

11 Qualities Google Looks For In Job Candidates 

In Chinese : 《專題報導》亞裔尖子生 職場難出頭？

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.

Newest 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!!

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. 

5/17 no notes 

5/24

This week I reviewed the SAT problems we went over in class. If you could please give me some of those harder SAT problems going forward for homework that would be great. I thought that they were good practice. 

I didn’t have a ton of time this week for AMC work, because I have finals for many classes coming up. However, I did do some problems from the 2016 AMC 10 A. 

I had some trouble with problems 11, 12 and 9. If we could please go over those that would be great Sorry about the late reflection again.

5/31

Hi Mrs. Lin,

I wanted to send you my reflection for this week. I re-did the AMC 10 2016 A test, including the problems from last week. I also did problems 13 to 20. I had questions on 13, 17, 18, and 20.

Thanks,

6/28 

Hello Mrs. Lin,

I hope you are doing well.

This week, I redid the problems from last class, and reviewed the formula sheet on geometry. I worked on problems 1-15 on the AMC 10 A from 2017. I had some trouble with questions 9, 12, and 15. 

Talk soon,

H. a 10th grader student reflection notes

 6/17/2025 2010 AMC 12A

6/26/2025 2010 AMC 12 B

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

June 3, 2025 

2023 chapter

Sprint

Q20 time understood question but couldn't think of a solution learn how to do it Total score: 33

Q26 radicals calculation error I made a calculation error either adding or converting the radicals double check the calculation

Q27 3-D Geometry didn't know how to do it. learn how to do it

1. Q28 counting didn't know how to do it. learn how to do it
   Q30 probability didn't know how to do it. learn how to do it
   Target
   Q4 geometry had an idea but it did not work learn how to do it
   Q6 probability didn't know how to do it learn how to do it
   Q7 2-D+3-D geometry had an idea but it did not work learn how to do it
   Q8 probability had an idea but it did not work learn how to do it
   Team
   Q4 combinatorics didn't know how to do it learn how to do it
   Q7 counting and geometry didn't know how to do it learn how to do it
   Q8 geometry didn't know how to create a picture that suits this problem learn how to do use imagination to help create a picture that suits this problem
   Q9 probability had an idea but it did not work learn how to do it
   Q10 counting silly mistake didn't read the question right underline important phrases
   
   

2.   June 29, 2025

3. 2021 state sprint
   20/30
   
   Q14 Probability silly mistake I included one but I wasn't supposed to When it says inclusive only count the highest number from 1 to H.
   Q18 Geometry silly mistake Instead of 6^2 I put 4^2 which messed up the answer First always label the given side lengths then find the unknown side lengths
   Q19 Number theory had the right number but my thought process wasn't right For these type of problems first find the number by subtracting the remainder then find the number of divisors then subtract by the amount of the divisors that cannot have that remainder and that is your answer
   Q22 Algebra didn't know how to this problem Learn how to do this problem a fast way and accurate way
   Q24 Algebra didn't know how to this problem Learn how to do this problem a fast way and accurate way
   Q25 Probability Had an idea got close but it didn't work Learn how to do this problem a fast way and accurate way
   Q27 Number theory didn't know how to this problem Learn how to do this problem a fast way and accurate way
   Q28 Counting Had an idea but it didn't work Learn how to do this problem a fast way and accurate way
   Q29 geometry Had an idea got close but it didn't work Learn how to do this problem a fast way and accurate way
   Q30 Algebra didn't know how to this problem Learn how to do this problem a fast way and accurate way

2015 Mathcounts National sprint #22 level 1 +

 

2015 Mathcounts National sprint #22

If six people randomly sit down at a table with six chairs, and they do not notice that there are name tags marking assigned seats, what is the probability that exactly three of them sit in the seat he or she was assigned? Express your answer as a common fraction.

Try this yourself first (extremely), then scroll down for solutions.

Method 1-Elementary Counting

Choose the three people who sit correctly: \( \binom{6}{3}=20 \).
The remaining three must all sit incorrectly. A quick check (or listing) shows only two ways: \((A\,B\,C)\) or \((A\,C\,B)\).
Total favourable seatings \(=20\times2=40\); total seatings \(=6!\).
Therefore \( P=\dfrac{40}{720}=\boxed{\tfrac{1}{18}} \).

Method 2 – Derangement formula

Pick the three fixed seats: \( \binom{6}{3}=20 \). Derange the other three: \( !3 = 2 \).
Again \( 20\times2 = 40 \) good seatings, so \[ P \;=\; \frac{20\cdot!3}{6!} \;=\; \boxed{\tfrac{1}{18}} . \]

Derange the remaining 3 people. The number of derangements of 3 items is \[ D_3 \;=\; 3!\left(1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!}\right) \;=\; 6\left(1 - 1 + \frac{1}{2} - \frac{1}{6}\right) \;=\; 2. \]