Preparing for /Taking /Analyzing returned
FOR PROBLEM-SOLVING TESTS
- Review notes
and text - list the major concepts and formulas that have been
those topics/problems that were emphasized. Note why they were
- The single
best way to prepare for problem-solving tests is to solve
problems - lots of them. Work problems not previously
- Analyze all
problems you work:
concepts, formulas, and rules did I apply?
methods did I use?
- How did I
- Have I seen
this problem before?
- Is it
similar to or dissimilar from other problems I've
- How does my
solution compare with the examples from the book and
- Could this
problem be worked another way? Can I simplify what I
- In your own
words, next to each problem-solving step, explain what you did
- Look for
fundamental problem types. Usually a course has approximately 5
fundamental groups of problems - make sure you can recognize
what they are.
working problems out of sequence. For example, work a problem
from Chapter 7, then one from Chapter 5, then one from Chapter
10. This randomness will allow you to see how different
problems relate to each other and will simulate the test-taking
- Work with a
time limit - aim to solve as many problems as you will have on
the test within the test time limit (i.e., 30 problems in 50
- Make up a
practice test. Possibly you might cut/paste/xerox a test from
your homework problems.
starting the test, turn it over and jot down all the formulas,
relationships, definitions, etc., that you are trying to keep
current in memory.
- Look the whole
test over, skimming the questions and developing a general plan
for your work. If any thoughts come to you immediately as you
look at a problem, note these down in the margin.
- Plan your
time. Allow more time for high point value problems: Reserve
time at the end of the period to review your work and to handle
- Start with the
easier problems, the ones for which you can specify a solution
method quickly. This will reduce anxiety and facilitate clear
- For the more
absolutely sure that you understand the posed problem: Mark
key words, identify the givens and unknowns in your own
words, sketch a diagram or picture of the problem,
anticipate the form and characteristics of the solution
(e.g., it has to be an integer, the solution is an algebraic
- Make a
note, in symbols, diagrams, graphs or tables of all the
- For complex
problems, list all the formulas you consider might be
relevant to the solution, then decide which you will need to
- If you have no
possible, write out an equation to express the relationships
among all the givens and unknowns, accounting for all the
data and facts of the problem.
- Think back
to similar practice problems to select a solution
- Solve a
simpler form of the problem if dealing with complex
configurations OR substitute simple numbers for unknowns to
reduce the amount of abstract thinking required.
- Break the
problem into a series of smaller problems and work each
part, thus building up to a solution.
- Guess an
answer and check it. Possibly the checking process will
suggest a solution method.
- If all else
fails, mark it to come back to later and work another problem.
You may find clues in subsequent problems.
- For all
problems, easy and difficult:
- Once you
have the solution method, follow it carefully. Check each
step for consistency in notation. Document all your work so
that it may be read easily; write legibly.
your solutions. Check your answers against the original
problem to make sure they fit.
- Try all test
problems. If your mind goes blank, relax for a moment and
contemplate the problem OR mark it to come back
- If you run out
of time and still have some problems left, try to gain at least
partial credit by setting the problem up in a solution plan
(even if you can't follow through on calculations).
RETURNED PROBLEM-SOLVING TESTS
- Read the
comments and suggestions.
- Locate the
source of the test: Did the problems come from the lectures,
the textbook, or the homework?
- Note any
transformations - how were the problems changed from those in
the notes, text, and homework?
- Detemine the
source of your errors:
- Were your
errors due to carelessness? For example, did you fail to
carry a negative sign from one step to another?
- Did you
misread questions? For example, did you fail to account for
all the given data in your solution method?
- Did you
consistently miss the same kind of problem?
- Could you
produce the formulas, or did you remember them
- Were you
unable to finish the test because you ran out of
- Were you
unable to solve problems because you had not practiced doing
- Did you have a
difficult time during the test because you were too anxious to
focus on the questions?