Problem-Solving Exams

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Problem-Solving Strategies

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?
    Organizing Information

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

References

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.