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Great Study habits

1. Read the book and notes before class, summarize the lecture after class, work through the homework and then look at old exam questions on the topic.

2. Use pencil and paper when doing your homework.

3. Write up the full solutions to your homework when you are done, so that you will have them for review.

4. Summarize each section as you go through it so that you can review easily. Try to pull out general principles, understand concepts and make sure you can reconstruct the main formulas. Make sure you know the conditions necessary for a theorem to apply.

5. Read your book and do your homework prior to the tutorial and try old exam questions on the sections covered in the tutorial.

6. Before an exam take the practice exam under the same conditions as the exam is given, namely make sure you have no cheat sheets, books, solutions, calculators etc... Also pay attention to the time allowed and time yourself appropriately.

7. Take your practice exam 4 or 5 days prior to the exam, so that you will have enough time to fix your weaknesses.

8. On exam day make sure you do not spend too much time on a problem. If you get stuck, move on and come back to the problem later if you have time.

9. Get help when you need it.

10. Make a list of the questions you are having trouble with, sometimes formulating the question is the biggest problem.

11. Carry a one page summary of the material covered so far in your backpack, so that you can review easily.

12. When you find you do not remember/understand something(even if it is trigonometry or algebra), look it up and reread that section.

13. Look at homework as an exercise to build basic skills and look at tutorials as an opportunity to get practice on the next level of problems(worksheets) and an opportunity to practice in exam taking conditions (on your quizzes).

14. Always try to integrate new material with what you have learned before.

15. Try to see where calculus is applied in your other subjevcts, Physics, Economics, Chemistry,... Try to get past the differences in notation and see how the concepts are used. Seeing these connections means you will have less memorization to do in other subjects.

More Great Study Habits

1. Keep in mind that old knowledge often has to be relearned in a new context.

2. Know what distrascts you (e.g. noise, Facebook, etc...) and avoid it if you wish to concentrate.

3. Know what helps you to relax. On the morning of the exam, it may be better to listen to some music or stretch or do something that helps you relax rather than a final hour of cramming.

4. Try to figure out what helps you learn, listening, pictures, experiments and use it to your advantage. (This is not unrelated to what distracts you).

5. Keep in mind that if you want to learn soccer, you do not watch your coach paly soccer, you must practice to learn the skills involved. Similarly, you must try problems yourself to learn mathematics. The more you challenge yourself, the more you learn

6. Just as in learnng a sport, some activities are designed to build foundational skills and some are designed to fine tune your skills or to teach you to put together your basic skills to solve more complex problems. In this course, the basics are learned and practiced by doing homework, more complex challenges are given in the form of old exam questions and worksheets at tutorials. On exam day you meet a large complex challenge in the form of solving problems from a large chunk of material without props or references. You should do the groundwork in accquiring the basic skills way ahead of the exam and spend the week before your exam putting the basics together in a big picture and practicing more complex problems.

7. Work in groups if that helps you learn, but keep in mind when practicing for exams that you will be solving problems on your own and also practice for that.

8. Remember that a big part of mathematics involves solving problems using the basic methods and ideas. Look up problem solving skills on the internet. You will find that it often helps to draw a picture, identifying variables, rewrite the problem in a different form etc... .


Common Misconceptions

1. "My intellegence quota is fixed and I cannot increase my (understanding of mathemtics)/(performance on math exams) with work."

This attitude often leads people to turn away from a challenge instead of getting down to work. It is through challenges that our knowledge grows and it is precisely when we do not understand something that we have the opportunity to learn and explore the unknown. Mathematics by its nature requires you to be comfortable with solving problems, so this attitude causes great difficulty for math students.

This attitude also hinders students from learning how to learn. There are many ways of improving performance on exams and incresing efficiency in problem solving by changing study habits or paying attention to personal learning habits and organization.

2. "I studied calculus in high school, I know everything already, and this will be an easy course."

Most students have to work hard in Calculus 1, even if they have studied calculus in high school. There are many aspects to calculus and many levels at which it acn be studied. If you have already studied calculus, you may encounter the same results and formulas, but we may explore them at a greater level of detail and apply them to more complex problems. In particular the problems we look at may require material from many sections to solve. When studying theorems, we think not just about situations where the result applies, but also where it does not apply. We emphasize a complete knowledge of the basic concepts, such as limits and derivatives, so that they can be applied to data as well as to well known functions. We expect that you will be able to apply the basic skills from algebra, trigonometry and precalculus. We expect students to retain material learned in each section for further use and application and we expect students to develop an understanding of the big picture by constantly reviewing their knowledge from early sections.


3. "I did all of the homework and got it right and now I am ready for the exam."

By completing the homework, you learn the basic skills section by section, exam questions are more complex and exam taking conditions are more challenging. There are three major differences between online homework and doing exam questions on exam day. The first is that there are many props and hints available to you as you do the online homework which will not be available on exam day. The second is that the online homework is always directly related to the section in which it appears and exam questions usually involve concepts from many sections. The third major difference is that on exam day, you will have to solve questions on a large amount of material at once, whereas while doing homework you are concentrating on one or two sections on which you have recently had a lecture. To prepare for the exam, you must first do your homework, then test yourself on old exam questions. In the tutorial you will take a quiz on old exam questions without props or calculators and have a chance to solve more complex problems on a worksheet. For your exam review, you should summarize the main concepts and formulas from each section. Memorize what you need to memorize, but also seek out general principles so that you need to memorize less. If you are weak on trigonometry or algebra, make sure you review these topics way ahead of the first exam. Before the exam you need to take a practice exam without any props or hints. Give yourself enough time to fix any weaknesses you find.

4. "I did really well on the first exam, so I can take it easy because this course is going to be easy for me."

Sadly it is very common for students to get an A on exam 1 and as a result reduce their study efforts in the period between exam 1 and exam 2, resulting in a much lower grade on exam 2.

5. "I am not going to need my algebra, trigonometry, or precalculus in a calculus exam"

We do not explicitly test algebra, precalculus and trigonometry on calculus exams, but we do assume that you know and can apply your knowledge of these subjects to solve problems. Problems on exams often require use of these subjects in the steps towards the solution. A mistake in one of these areas may lead to the wrong answer and you may thus lose all of the points on a multiple choice question because of this. If you feel that your knowledge is weak in one of these areas, you should review that area using Chapter 1 and the appendices of the Book. Also there are some review assignments on these topics available in the online homework system.

6. "I do not need the material from exam 1 for exam 2 or exam 3"

The material covered before exam 1 is the foundational material for the material covered on exam 2 which in turn is foundational for the material covered in exam 3. Just as algebra, trigonometry and precalculus build a foundation for calculus, the material in Calculus 1 is part of the foundation for Calculus 2 etc.. So you are expected to retain material when you learn it. Because of the nature of memory, you will probably have to review material a number of times thrioughout the semester in order to commit it to long term memory. The final is comprehensive and does require that you know all of the material at once.