Tuesday, September 16, 2025

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.


There is no overnight success.

My other blogs :

thelinscorner  : Standardized test preps (ONLY the hardest problems), 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.

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!!

Saturday, September 13, 2025

2017 AMC 12 B Reflection Notes from H

2017 AMC 12B — Practice Log

Quick reflections and timing notes.
Q1–Q23: all correct ✅ Q22: time sink ⏳ Q24–Q25: not answered ❌

Notable Questions

  • #13: Took me a while; need to keep practicing Burnside's lemma/technique. (note to self: revisit topic & drill)
  • #22: Became a time sink. Pause sooner; sketch structure, estimate difficulty, and decide quickly whether to skip.
  • #24: Didn’t understand the question—unclear how to set up the average. Re-read carefully; translate wording to variables first.
  • #25: Ran out of time.

Process & Timing Notes

  • Not enough time at the end—was able to draw the diagram but didn’t complete the setup.
  • For average/setup questions: define variables immediately, write the equation before computing.
  • When a problem starts ballooning (>3–4 minutes without structure), mark and move.

Follow-Up Plan

    Thursday, September 11, 2025

    Dimentional Change Questions III: Similar Shapes

    There are numerous similar triangle questions on Mathcounts.

    Here are the basics:



    If two triangles are similar, their corresponding angles are congruent and their corresponding sides will have the same ratio or proportion.

    Δ ABC and ΔDEF are similar. \(\frac{AB}{DE}\) = \(\frac{AC}{DF}\) = \(\frac{BC}{EF}\)= their height ratio = their perimeter ratio.







    Once you know the linear ratio, you can just square the linear ratio to get the area ratio and cube the linear ratio to get the volume ratio. 

    Practice Similarity of Triangles here.  Read the notes as well as work on the practice problems.  There is instant feedback online. 

    Other practice sheets on Similar Triangles                                                        


    Many students have trouble solving this problem when the two similar triangles are superimposed. 

    Just make sure you are comparing smaller triangular base with larger triangular base and smaller triangular side with corresponding larger triangular side, etc... In this case:
    \(\frac{BC}{DE}\)= \(\frac{AB}{AD}\) = \(\frac{AC}{AE}\)




    Questions to ponder (Solutions below)


    #1: Find the area ratio of Δ ABC to trapezoid BCDE to DEGF to FGIH. You can easily get those ratios using similar triangle properties. All the points are equally spaced and line \(\overline{BC}\)// \(\overline{DE}\) // \(\overline{FG}\) // \(\overline{HI}\). 



    #2: Find the volume of the cone ABC to Frustum BCDE to DEGF to FGIH. Again, you can use the similar cone, dimensional change property to easily get those ratios.Same conditions as the previous question.




    Answer key: 

    #1:

     #2:


Monday, September 1, 2025

9/1/2025 Student Reflection Note from H

2018 AMC 12A Notes 🎉

😊 Only 2 Wrong — Great Job!

Wrong

  • 22: Not sure how to express √abi cleanly.
        Couldn’t manage complex numbers or split the area into 4 pieces.
  • 25: Was able to get the powers of 10 and simplify, but not the final casework step.

Right

15, 16, 17, 18, 19, 20, 21, 23, 24

8/31/2015 Student reflection notes from H

2019 AMC 12B Notes

Problems 20–25 → Wrong

  • 20: Tried coordinate bash but didn’t realize AOBX is cyclic.
  • 21: Very close, but made a mistake in casework.
  • 22: No idea how to estimate.
  • 24: Confusing — unsure how to approach.
  • 25: Imaginary numbers solution was smart.
        Also homothety solution was smart too.

Problems 15–19, 23 → Right