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1.
Read the problem carefully.
2.
Make sure you understand
the situation that is described.
3.
Make sure you understand
what information is provided,
and what the question is asking.
4.
For many problems,
drawing a clearly labeled
picture is very helpful.
1.
First focus on the
objective. What do you need
to know in order to answer
the question?
2.
Then look at the given
information. How can you use
that information to get what
you need to know to answer
the question?
3.
If you do not see a
clear logical path leading
from the given information
to the solution, just try
something. Look at
the given information and
think about what you can find
from it, even if it is not
what the question is asking
for. Often you will find another
piece of information that
you can then use to answer
the question.
You
need to express mathematically
the logical connections between
the given information and
the answer you are seeking.
This involves:
1.
Assigning variable
names to the unknown quantities.
The letter x is always
popular, but it is a good
idea to use something that
reminds you what it represents,
such as d for distance
or t for time. The
trickiest part of assigning
variables is that you want
to use a minimum number of
different variables (just
one if possible). If you know
how two quantities are related,
then you can express them
both with just one variable.
For example, if Jim is two
years older than John is,
you might let x stand
for John’s age and (x + 2)
stand for Jim’s age.
2.
Translate English into
Math. Mathematics is a language,
one that is particularly well
suited to describing logical
relationships. English, on
the other hand, is much less
precise. The next page is
a table of English phrases
and their corresponding mathematical
meanings, but don’t take it
too literally. The meaning
of English words has to be
taken in context.
Now you just have to solve
the equation(s) for the unknown(s).
Remember to answer the question
that the problem asks.
Think about your answer.
Does your answer come out
in the correct units? Is it
reasonable? If you made a
mistake somewhere, chances
are your answer will not just
be a little bit off, but will
be completely ridiculous |
