## Friday, March 7, 2014

### 2014 Mathcounts Competition Preparation Strategies

You can now discuss this year's Mathcounts school and chapter questions.

Here is the link from Mathcounts.org.

Good Luck !! NY, MI, OH, IL, CT state !!!!!

Have Fun, that's the most important ! You are going to meet some other kindred spirits in the state and later at the same college or at work. No kidding !!

Stay focused if your state competition is on Mar. 8th.

Thanks a lot for your kind remarks in the comments. If you want to join my weekly problem solving group lessons, e-mail me at thelinscorner@gmail.com.

Please don't plan for the last-minute prep. Like I mentioned before, my students who love problem solving never stop learning when the ____ season ends and that is the reason they excel.

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.

Mathcounts official website : last year's competition problems and answer key

This year's handbook questions.
Near the end of the handbook, there is a page called  problem index (page 82 and 83 for 2013-2014 handbook).
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.

Register for Alcumus and start using the great tool to practice deliberately.
Change the setting based on the levels of your proficiency of different topics.                                                                     Do Not Rush !!

Awesome site!!

For concepts reviewing, try the following three links.

Mathcounts Bible

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.

## Thursday, March 6, 2014

### 2012 Harder Mathcounts State Target Questions

Check out Mathcounts here -- the best competition math program for middle schoolers up to the
state and national level.

# 6: A semicircle and a circle are placed inside a square with sides of length 4 cm, as shown. The circle is tangent to two adjacent sides of the square and to the semicircle. The diameter of the semicircle is a side of the square. In centimeters, what is the radius of the circle? Express your answer as a decimal to the nearest hundredth. [2012 Mathcounts State Target #6]

#6:  Solution:
Using Pythagorean theory: (2 + r)2 = (4-r)2 + ( 2- r)2
4 + 4r + r2 = 16 - 8r + r2 + 4 - 4r + r2
r2 - 16 r + 16 = 0
You have 8 ± 4√ 3
Only 8 - 4 3 = 1.07 works

There is a Mathcounts Mini #34 on the same question. Check that out !!

The above question looks very similar to this year's AMC-10 B #22, so try that one.
(cover the answer choices so it's more like Mathcounts)

2014 AMC-10 B problems  : Try #22

#8: In one roll of four standard, six-sided dice, what is the probability of rolling exactly three different numbers? Express your answer as a common fraction. [2012 Mathcounts State Target #8]

Solution I : Permutation method
If order matters, there are 6 * 5 * 4 * 1 ways to choose the number, 1 being the same number as one of the previous one.
Let's say if you choose 3 1 4 1.

Now for the placement of those 4 numbers on the 4 different dice. There are 4C2 ways to place where the two "1" will
be positioned so the answer is : $$\dfrac {6\times 5\times 4\times 1\times 4C2} {6^{4}}$$ = $$\dfrac{5}{9}$$
Solution II:  Combination method

There are 6C3 = 20 ways to choose the three numbers.

There are 3 ways that the number can be repeated. [For example: If you choose 1, 2, and 3, the fourth number could be 1, 2 or 3.]

There are
$\frac{4!}{2!}= 12$ ways to arrange the chosen 4 numbers.[same method when you arrange AABC]