Math Exams

Learning Objectives

  • Compare pre- and post-test-taking strategies for quantitative courses against those for other courses

Preparing for Your Math Exam

Facing a math exam soon? You may want to consider the four sensory modalities in Fleming’s Learning Styles model:

  1. Visual learning
  2. Auditory learning
  3. Read/write learning
  4. Kinesthetic learning

You can use the understanding you have of your own learning style to your advantage as you prepare for a math exam. Keep in mind you may have more than one style of learning, and that the more you think about own learning process, the better off you’ll be as a student. It takes time to know yourself as a learner.


Visual learners make sense of the world through pictures and images. They learn well when lesson plans incorporate photos, videos, or visual maps. A visual learner may describe their understanding as images or pictures rather than with words, and are drawn to design and spatially focused.

If you learn with pictures and images, you may benefit from creating drawings related to each concept. Diagrams and visual cues can help visual learners make important connections between concepts. Mind maps may also be a helpful tool for further solidifying your understanding of how mathematical concepts are connected. Additionally, if you are visual, you could color code your notes and study materials.hands drawing physics problem with a pen on paper

Auditory Learners

Aural learners are best equipped to understand and store information absorbed via sound and music. Their ears are particularly adept at deconstructing and parsing heavy mixes of tones. They will often do better with books on tape versus printed versions.

Many aural learners enjoy listening to music. Playing pleasant music in the background while learning mathematics can evoke positive emotions and stir up a bit of energy while you are working. Just make sure that the music is not overly distracting or played too loud. In addition, musical minded people can try to organize formulas and operations into musical patterns or rhymes. Coming up with a rhyme or melody to remember the quadratic equation may be more effective than simply attempting to remember the visual image of the formula. It may also help to find someone who will listen to you explain what you are learning or studying.

Read/ Write

Read/ Write learners may prefer learning with words –  both with speech and writing. If you are a read/ write learner you may soak up knowledge through various mediums centered around language. If you prefer learning this way, try sitting down after class to rewrite your notes. Translating a mathematical expression, graph, or equation into words may also help. If you learn from reading and writing, keeping a homework journal may be very beneficial to you.


Physical learners learn best by touch and movement. A lot of superb athletes tend to fall into this category as physical processes and activities seem to sync well with their learning and memorizing capabilities.

For physical learners, studying may seem like torture, but if you are committed to it, there are ways. If you tend to learn best when active, it is important for you to stay in motion while studying. This could involve squeezing a stress ball while working, or simply taking a break every 20 or 30 minutes to walk around the room. Hands on models are terrific as well when applicable. If there is a tangible learning device that you can actually touch and interact with, all the better.

As you work through problems to study for your exam, use this decision tree to help you optimize your time.

A flow tree for the query Can I Do This Type of Question? If yes, go on to the next concept or question. Begin. Can I do this type of question? If no, read the relevant material in your text and notes. Can you try the question now? If no, read the solution, or write it out. If you still can't try the question, ask for help. If help is unavailable, make note of the problem and move on. If you can try the question, try it and check if you got it right. If you did, go on to the next concept or question. If you didn't, read the relevant material in your text and notes and try again. Begin. Can I do this type of question? If no, read the relevant material in your text and notes. If you can try the question now, try it and check it. If you didn't get it right, read the relevant material again and repeat. If you did get the question right, go on to the next concept or question. Begin. Can I do this type of question? If maybe, try the question and check if you got it right. If you did not get it right, read the relevant material in your text and notes, then try the question. If you did get it right, go on to the next concept or question.

Group Study

Some learners prefer to learn in groups surrounded by other people. If you thrive in social environments, you may benefit from working in teams to complete homework assignments and prep for exams. This kind of activity can can often charge your energy levels and can create a supportive network of caring classmates. It is imperative that at least one person in the group be willing and able to keep the group on track and focused; otherwise your study session will turn into social hour.

If you plan to study in a group, try preparing an agenda before you get together. Your agenda could include a summary of the topics you will review, and a few problems for each topic that you want to try to work out together. Beware of the “attention seeker” when you are part of a study group. Try to share the work of solving problems or answering each other’s questions. All of you will get much more our of the experience.

Positive Mental Habits for Testing

  • Define and repeat a positive mantra like “I have all the tools I need to do well on this test,” or “I am capable of answering all the questions on this test.”
  • Avoid over-thinking—your gut reaction is usually right. Math teachers grade innumerable tests where students erased the right answer.
  • No amount of positive self-talk can make up for not being prepared. Give yourself lots of time and practice so you don’t feel stressed.
  • Stop studying at least 30 minutes before your test, and let your brain rest.
  • Before your exam try to laugh or get some light exercise; read a funny book or comic.
  • If others are commiserating before the exam about how hard it will be, don’t join in. Remove yourself from self-doubt and negative talk.
  • Before the exam—visualize yourself taking the test and knowing how to answer the questions and feeling good about your performance. Repeat this activity as much as possible. It works!
  • Make mini exams for yourself. Take homework problems that were not assigned and give yourself an allotted amount of time to do them. Getting good at something happens from practicing the mechanics of the motions frequently.

Math Test-Taking Strategies

Just as it is important to think about how you spend your study time (in addition to actually doing the studying), it is important to think about what strategies you will use when you take a test (in addition to actually doing the problems on the test). Good test-taking strategy can make a big difference in your grade.

  • First, look over the entire test to identify problems you definitely know how to do right away, and those you expect to have to think about.
  • Do the problems in the order that suits you. Start with the problems that you know for sure you can do. This builds confidence and means you don’t miss any sure points just because you run out of time. Then try the problems you think you can figure out, with more time. Finally, try the ones you are least sure about.
  • Time is of the essence—work as quickly and continuously as you can while still writing legibly and showing all your work. If you get stuck on a problem, move on to another one. You can come back later, and something you do on another problem might help inspire you when you return to one you skipped.
  • Work by the clock. On a 50 minute, 100 point test, you have about 5 minutes for a 10 point question. Starting with the easy questions will probably put you ahead of the clock. When you work on a harder problem, spend the allotted time (e.g., 5 minutes) on that question, and if you have not almost finished it, go on to another problem. Do not spend 20 minutes on a problem which will yield few or no points when there are other problems still to try.
  • Show all your work: make it as easy as possible for the Instructor to see how much you do know. Try to write a well-reasoned solution. If your answer is incorrect, the Instructor will assign partial credit based on the work you show.
  • Never waste time erasing! Just draw a line through the work you want ignored and move on. Not only does erasing waste precious time, but you may discover later that you erased something useful (and maybe worth partial credit if you cannot complete the problem).
  • For a multiple-step problem with limited space on the page—you can put your answer on another sheet to avoid needing to erase. Outline your answer and indicate where the solution can be found.
  • Don’t give up on a several-part problem just because you can’t do the first part. Attempt the other part(s). If the actual solution depends on the first part, at least explain how you would move through each step. Read the questions carefully, and do all parts of each problem.
  • If you finish early, check every problem—that means rework everything from scratch. Does each answer make sense given the context of the problem?

After You Get Your Results

Your instructor passed back your first math exam and you are devastated.  You thought you did so well preparing, you kept up with assignments, and came to every class. Why did you get a C−? You may feel like you have failed, but this is an opportunity take charge of your education! You have been given several opportunities by getting a C− on your exam.

Don’t throw away any tests, even if you are upset about your grade. It is very important to take an inventory of the errors you made on each question.   Use the following inventory to assess your mistakes.

The Six Types of Test-Taking Errors

  1. Carelessness. You lost focus on the question and made a silly error (like changing a sign or inventing a new rule of algebra).
  2. Directions. You skipped over or misunderstood directions and as a result you did the problem incorrectly.
  3. Concept. You did not understand the properties or principles required to work the problem.
  4. Application. You understood the concepts involved, but did not apply them correctly in the context of the specific problem presented.
  5. Nerves. You made errors in judgment due to the pressure of the test-taking environment. These include not completing the problem to the last step, changing a correct answer to an incorrect answer, getting stuck on one problem and spending too much time on it, rushing through the easiest parts of the test and making careless mistakes, leaving answers blank (no partial credit), or leaving early and not checking all of your answers.
  6. Preparation. You studied the wrong material, or did not spend enough time studying the relevant topics.

Identifying what kinds of error you made will help you focus your strategy for study and preparation for the next exam.  You can develop a plan for how to prevent similar types of errors, once you know where to concentrate your efforts.


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