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 (

instead of

have made National CD had I managed to read

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

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

be very fast in order to pick up your points. For example, this question:

If

,

compute

n,

from

the

2011

State

CD