美国数学竞赛mathcount技巧中英对照

2023年12月31日发(作者：数学试卷开头的卷首语)

美国数学竞赛mathcount技巧中英对照

1. Read each problem carefully and multiple times

I cannot stress this point enough. This is the single most

important part of MATHCOUNTS for a great number of students,

myself included. Misreading the problem is likely one of the

leading causes, if not the leading cause, of incorrect answers.

Personally, I would have made Nationals in 7th grade had I read

some key words correct (\"smallest\" instead of \"largest\", \"first\"

instead of \"last\", etc.). I also would likely have made National CD

had I managed to read \"Positive\" on the final Target question.

2. Manage your time

This falls second on the list of importance, just below

misreading. Note that poor time management will likely hamper

your ability to read carefully (and multiple times), which will likely

lead to even more time wasted. Know when to \"give up\" on a

problem in favor of easier questions. They\'re all worth the same.

3. Do all the questions

Difficulty is extremely difficult to gauge (heh) in general, but

even more so when the problems are all roughly the same

difficulty level. Don\'t be intimidated by the question number -

many times a #26 will be a giveaway question, while #14 will be

one of the more difficult problems. You should aim to at least

read through all of the questions (carefully!) and to make a

serious attempt on most of them.

4. Organize your work

In MATHCOUNTS, you will likely spend a lot of time checking

your answers, something that will be much harder to do if your

paper is messy and disorganized. The method that you choose

will be up to you, but my recommended method is to either

section off your paper before the test begins, or to section off

your paper as you complete problems. Write down all non-trivial

steps - you\'ll use these for reference. You should include

computation, either to the side or in the problem, as this is where

you\'ll do most of your checking.

5. Do problems multiple ways

Most problems will have several valid approaches to the

answer. In most cases, one approach will immediately jump out

to you, and you will follow it to the answer. A great way to check

your answer is to do the problem in another way, even if it\'s just

slightly different. For example, if you do 5(3+5) as 5*3+5*5 and

5*8, you\'ll be significantly less likely to make a computation error.

Similarly, if use similar triangles and Power of a Point, getting the

same answer, you can be

reasonably sure your answer is correct (but if they\'re different,

time to find out why!). When using a second method, you

shouldn\'t know what answer you\'re trying to achieve - you may

consciously or subconsciously force yourself to get that answer.

6. Make assumptions

This is a very dangerous, but potentially rewarding technique.

Mostly used for time-saving (and especially in CD), what looks

like it\'s true usually is. Rely on your intuition - it\'s usually a very

powerful tool. A combination of practice and experience gives

you an intuition that can easily outweigh the time needed for a

rigorous solution. This isn\'t to say guess; rather to make educated

guesses.

For example, take 2011 Chapter Target #8. From experience,

I was able to immediately guess that the b in was 2 ( is highly

associated with 45-degree angles and squares), which

immediately led to (there\'s no other possible answer that makes

it between 0 and 1). This gives the correct answer of 3 without

any effort, on a relatively difficult problem (for chapter).

Disclaimer: Only use this technique when necessary. If you

have time, focus on checking problems you used this method on

FIRST, before checking others.

7. Don\'t check in order

It\'s usually a waste of time to check from #1 to #30 in that

order. You\'ll end up using your precious time checking problems

that are almost certainly correct instead of checking those that

need it. Make a mark on your paper next to the question number

signifying that you are unsure of your answer. Make a seperate

mark if you arrived at the answer without a rigorous solution (see

tip 6). Focus on checking these first. After that, focus on checking

problems that you aren\'t 100% sure of, then go to the easier

problems. I also made notes of problems that were essentially

just computation, because I always made computational errors

on early problems. You may decide that you need marks for

certain issues that you typically encounter, which is also fine.

8. CD - Buzz in before you know the answer

Another dangerous but rewarding technique, only do so if

you know you can get the answer within 3 seconds. For example,

if you know that the answer is 15*16, that would be a good time

to buzz in. Countdown is also an important time to utilize tip 6 -

use your intution! With only 45 second per problem, and the

\"race\" element, you need to be very fast in order to pick up your

points. For example, this question: If , compute n, from the 2011

State CD

round, was one that I instantly recognized as a question I

could solve within 3 seconds (btw, so did my opponent). I

instantly buzzed in (before I knew the answer!), gave the correct

answer of 5, and ended up winning my next match to make

Nationals. Had I not buzzed in when I did, my opponent would

have (he was going for his buzzer as well), and I would have

missed out. In this case, the extra few milliseconds were

incredibly important.

9. Take it easy

Finally, don\'t dwell on your results, good or bad, however

cliche that sounds. Poor results do not really indicate much in a

competition like MATHCOUNTS, where the difference between a

national winner and a person just missing out on State CD is

generally very small. It comes down to tiny speed tricks that

makes one person just a little bit faster than the other guy, which

can be enough. I know it won\'t feel like it at the time, but you\'re

the lucky ones. As middle schoolers, you have so much time left

to improve, both math-wise and competition-wise (yes, they can

be seperate things). If you get 11th written at State (which I did

in 7th grade), or 5th CD (which my friend did last year at States

[because I beat him]), you\'ll be originally crushed, but in the end,

it really makes so little difference. Both me and my friend do

decently at math now, failures at MATHCOUNTS.

There\'s a lot more to life than it.

第1条：仔细、多次读题

这点再怎么强调也不过分这是MATHCOUNTS最重要的一条技巧，不仅对学生，也包括我自己。误解了题意如果不是回答错误的主要原因，也是主要原因之一。从我个人来说，我本来7年级就可以参加全国比赛，如果我将一些关键词读对（“最小”读成“最大”，“首先”读成“最后”等）我也可能获得全国CD的胜利，如果我能够细心读到在最后一道Target问题中“正”。

第2条：安排好时间

这是第二重要的，仅次于仔细、多次读题注意时间安排不佳，会

妨碍你仔细（并多次）读题，并可能使你学浪费更多的时间。知道何时“放弃”一道难题，而先去解决较容易的题目。因为这些题目的价值是一样的。

第3条：阅读所有题目

虽然通常测量困难程度是极难的（？），但是在处于一个难度水平的众多问题去分辨困难程度就更难了。不要被题号吓倒了——许多情况下26题可能是需要放弃的题目，但14题却可能更难。你应该安排将所有题目至少通读一遍所有（仔细地！）然后再解决其中的大部分。

第4条：组织你的工作

MATHCOUNTS中，你可能会花很多时去检查你的答案，如果你的试卷混乱并且没有组织，检查出错误会困难得多你选择的方法取决于你自己，但我推荐的方

法是在考试前将你的稿纸分区，或者在你完成一个题目后将稿纸分区。写下所有非细节性步骤——你会利用这些来作参考。你应该将计算包括在内，要么在题目旁边，要么在做题过程中，因为这是你大部分检查工作。

第5条：多种方法解题

大部分问题有好几种有效的解题途径。大多情况下，你会立刻想到其中的一种方法，并依此解题。一个很好的方法是利用另一种方法来检查你的答案，哪怕它只是稍有不同。举例来说，如果你将5(3+5)以5*3+5*5和5*8来计算，你会明显降低计算错误的可能。同样，如果利用相似三角形和点的幂得到了相同的答案，就几乎可以确信答案是正确的。（但如果不相同，就要找出原因了）当利用第二种方法，你不应该知道你试图得到的答案——因为你可能会有意识地或下意识地强迫自己去得到那个答案

第6条：假设

假设的确有风险，但不能否认它的潜在价值。大部分省时间的方法（特别是COUNTDOWN),就是利用直觉。依赖你的直觉——它通常是一个非常强大的武器。实践和经验的结合会赋予你直觉，它能比

严谨的解法更轻松地节省时间。但这不是瞎猜，而是有根据地推测。

例如，2011年chapter Target第8题，依据经验，我能立即猜测到b在是2（是与45度角和平方高度相关），这可立即得出（在0-1之间不可能

有其它可能的答案）。在这样一个相对较难的题目中（chapter)直觉毫不费力地给你正确的答案。

免责声明：仅在必要时利用这个技巧。如果有时间，应该先集中注意力检查你用直觉解题的答案。

第7条：不要按顺序检查

从第1题到30题这样按顺序检查常常是浪费时间。这到头来只会使你将宝贵的时间用来检查那些回答几乎正确的题目，而不是需要检查的题目。在稿纸上对题号做上显示你对答案不确定标记，如果你不是通过严谨步骤得到答案的话，需要做一种不同的标记。（见技巧6）首先集中检查这些题。然后，检查那些你不是百分之百确定的题目，再才是相对容易的题目。我也对那些纯粹计算的题目做标记，因为我总是在开始的题目上犯计算的错误。你也可以决定标记哪些题目。

第8条：CD，在知道答案前抢按电铃

这是另一个有风险但却有价值的技巧，只有当你能够在3秒内得到答案时你才能运用这个技巧。例如，如果你知道答案是15*16，这时就可以按电铃了。Countdown 也是一个重要的利用你直觉的机会，见技巧6。45秒每题，并且“竞速”，你需要非常迅速地去获得你的答案。例如这个问题：

如果，计算n，来自2011年州CD，我立刻意识到

我能在3秒内解题。（顺便提一下，我的对手也是这样）。我立刻按电铃（在我知道答案前）给出了正确答案5,结束了CD，使我能够参加下一个国家级的比赛。

如果我当时不按铃，我的对手可能会按铃，我就可能会错过机会。这种情况下，哪怕多仅仅几毫秒也是非常重要的。

第9条：放松

最后，不要在乎你的结果，不管是好是坏，虽然这听起来是陈词

滥调。在Mathcount 这样的比赛中结果不好并不意味着什么，一个国家级的胜利者与在州CD中被淘汰的选手差异通常非常小。这归结一些细微但能提高速度的技巧，可以使你比其它人快那么一点点，这就够了。我知道那时的感觉可能就不同了，但你是幸运者。作为初中生，还有很多需要学习改善之处，包括数学的智慧和竞赛的智慧（的确，它们是不同的）。