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How do I study efficiently for math?

First of all, studying should just be a review...you shouldn't be doing all your homework for the first time just before a test...you will learn the material much better if you keep up with your homework throughout the course. While it may be obvious that doing your homework is definitely important, HOW you do your homework is also key! 

How to Complete Homework

To do your homework, begin by reviewing your lecture notes and trying all the examples in the lecture notes on a separate sheet of paper and comparing your answers. If you find that the section is unclear, you can read up on it in your textbook. Once you feel confident with the material in the lecture, move onto the homework questions. If you have a solutions manual, KEEP IT CLOSED while attempting the homework. Attempt all homework that the professor suggests one section at a time. Perhaps even give yourself a time limit just like you would have during a test (say, 10 minutes per question)...if you can't get the question within this time, go on to the next one, but indicate somehow (e.g., with an asterisk) that you struggled with this one, so it can be one of the first ones you retry when studying for the test. Compare your answers with the answers in the solutions manual. If you find that you’re doing all of the questions wrong, start from scratch by going back to the lecture notes and textbook. You probably missed some key concepts. You can also use other resources that your professor may have suggested (e.g., certain webpages or web resources). 

Things to Avoid

Many students encounter the problem of getting the wrong answer when trying it, then looking in the solutions manual and understanding the answer there. It’s tempting to tell yourself that you understand once you see the solution, but in fact, in most cases, the problem lies in the beginning. If you need to see the solution to understand how to do a certain problem, then you probably don’t understand the section, and certainly won't be able to complete a similar question on a test. Go back to the lecture notes and textbook. 

Studying for Tests

When studying for a quiz or test, it’s best to review all material given within the course. Start off by reviewing all lecture material that will be covered on the quiz/test. Some find it useful to separate their studying by sticking to one section at a time. For example, if you know your test is based on Sections 1.1 through 1.6 of your textbook, start off with section 1.1. You can then go back and redo some of the lecture and homework questions that you struggled with when you first completed the homework. Once you’ve finished this for each section that the quiz/test is based on, you should never stop there. A lot of students get confident with their math skills once they understand a certain section. Keep in mind that you’ve just been doing a bunch of questions in the same section, so you’re getting the hang of it. When you’re in a test, the professor isn’t going to tell you which section the question came from. The best way to work around this is to test yourself with a mock test. Get or design sample tests and take several practice tests. Get a friend to pick some random questions from each section, mix them all up on a piece of paper, and test your knowledge of all sections that will be covered on the test. Be sure to time yourself to see if you can finish in the allotted time. 

Additional Study Tips

Many students wonder what more can be done besides reading through all the lecture material and doing the homework. One great idea is to make yourself a short study guide, summarizing the key points of each section as you work through the course...this will help you make sense of what's important, and will be a valuable resource to reread before the test/exam. Another idea? Create study groups! Some students find it helpful to study with others; this may motivate you and some students might pick out some things that you may have missed. Also, in many first-year courses, you will have a tutorial which is a place to go and ask a teaching assistant (TA) any questions that may still be unclear for you. Take advantage of these! The TAs are there to help you through the course, so come prepared, having attempted all your homework, and participate by asking and answering questions. Also, the professor usually has office hours directly related to the course being taught. Take advantage of these as well! The professor wants you to succeed and do well, and will be very happy to see that you’re making an effort with their course. 

Preparing for Math Exams: 
 

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