The best strategy for preparing for a problem-solving exam is to practise problems throughout the semester. To help you be efficient and systematic when you work on problems, try these strategies:
Problem solving takes time
Take the time to fully work out the lengthy questions – don’t give up!
The more you work on a problem, the better you will understand it
Have an eye for details
What is the question asking?
Make an effort to fully understand every aspect of the problem you are working on
Identify the knowns and unknowns
Based on what you know, what might be a logical response?
Write down all of the data that is given to you in the problem, then write down what you need to find out
Draw diagrams or flow charts, or make summaries
In order to organize given information, arrange everything in a systematic way that you can easily see
It may help you to find the path to solve the problem
Break the problem into parts (if possible)
Small parts are easier to work with and often lead to the information necessary for the next step in the equation
Try to link information together
Think about how the information or “knowns” in the problem are related to the equations and concepts you’ve studied
Check your answer for logic or calculation errors
Based on the question, does your answer make sense?
Preparing for Problem-Based Exams
Problem-solving exams come in a variety of forms, from multiple choice to short answer to long calculations. In all of these cases, prepare for the exam with particular emphasis on the following points:
Practise, practise, practise!
The more problems and the more types of problems you solve, the better prepared you’ll be
Divide the study material into sections
Based on similarities such as concepts, equations, or the type of math required
Pay attention to problems and examples emphasized in class, the text, and assignments, especially those that appear in more than one of these places
When studying a section, note the important equations
Although it’s important to know how to use an equation, knowing when to use it is just as critical
Look for connections between concepts and equations and note how to choose the correct equation in complex practice problems
Study questions out of order
Problems on exams rarely appear in the order the course was taught and may combine concepts taught at different points in the semester
Practise questions out of order, look for links between concepts, and seek out combination questions
Generate your own test questions with a study group or partner
Make sure you create complex problems which incorporate multiple course concepts
Compare the questions in a mock or old exam with those presented in lecture, problem sets, and the text
Note where the majority of exam questions come from (text, lecture, or assignments) and how the exam questions differ from previous problems
To get the most out of a practice exam, write it under exam conditions – in a quiet area, with a time limit and close your books!
Review previous tests, quizzes, or midterm exams
Sometimes similar questions will appear on the next exam, particularly if many students in the class got it wrong
Your previous errors will also indicate concepts and question types that you may need to work on
Writing the Exam
When you are writing the exam, here are a few tips and strategies to help you do your best:
Dump the details
Find a blank page on your exam and write down equations, concepts, and constants that you have memorized before starting the exam
Look over the entire exam before beginning and budget your time according to how much each question is worth
Do the questions you know how to answer first to warm up your brain and calm exam nerves
The easier questions can provide helpful hints on how to solve harder problems later on
Skip difficult problems and move on
You don’t want to lose marks somewhere else because you spent a lot of time trying to solve one question
Read the questions carefully and rephrase them in your own words
This may help you to understand what the question is asking and remind you how you solved similar problems in the past
Keep track of all units
Convert values to keep the units consistent
Also, be aware of +/- signs
Limit the rounding of numbers in intermediate steps until the final answer has been reached
Present numerical answers with the correct number of significant figures and always write down the units
Clearly mark assumptions, if they are necessary, and place them at or near the beginning of the solution whenever possible
Look at your final answer
Does your answer sound reasonable, logical, and well-organized?
If not, go back and check your work, but don’t get hung up on a difficult problem, and stick to your time limits
Review at the end
If possible, try to give yourself a couple of minutes at the end to check all the answers
Exception: Some Engineering professors allow 'assumptions' to be made on exams
In these cases, the professor will deliberately leave out pertinent or required information, which you must then assume
Assume carefully! Make your assumptions reasonable and within “typical” or “conventional” values, depending on the situation
Above all, ask your professor if assumptions are allowed before you make any
Analyzing Your Performance
After a midterm is returned, or after completing an practice exam, consider the suggestions below to figure out how to improve your performance on the next exam.
Read and consider comments and suggestions from the professor or TA that marked the exam
These are usually intended to help you improve
How were the problems different from those given in the text, lecture, or homework? Identify how you can change what or how you study
Determine the source of your errors
Different types of errors warrant different approaches to studying
Consult Error Analysis for more information about common types of errors and suggestions for how to deal with them
Berkeley Student Learning Center. Taking Problem-solving Tests, part of Study and Success Strategies.
Fogler, Scott H., & LeBlanc, Steven E. (2007). Strategies for Creative Problem Solving.
Whimbey, A., & Lochhead, J. (1986). Problem Solving & Comprehension, 4th Edition. London: Lawrence Erlbaum Associates.
Woodcock, D. (2000). The A Thru E Approach to Problem Solving in Chemistry.