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Study tips for Math 184 Section 106 November 10, 2015 1 How did you study for the midterm? Make a list of what you did to study for the midterm: Compare this to the following list: • Worked through the suggested textbook problems, workshops and webworks, • Worked through all practice and actual quizzes, • Memorized all definitions, theorems, and rules/laws e.g. continuity, rules or differentiation, intermediate value theorem, etc., • Used the “learning goals” to structure my studying and make sure there were no gaps in my knowledge. 1 2 How to structure your learning: Through the rest of the semester you should do the following on a weekly basis: 1. Every Friday review the learning objectives along with your notes. Identify where in the notes different goals are addressed. This is crucial to digesting the new information – you should have been doing this all along but now it’s really really important since many of you also need to allocate some time to learning older material. This is a good time to: • Make flashcards for definitions and formulas. • Address anything you were confused by during lecture by coming to office hours or using piazza. • Work the suggested problems (at least several of them). 2. Keep up with Webwork, workshop, studying for quizzes, etc. Note that the midterm problems were nearly identical to problems from webwork. 3. Allocate some time, (3 hours at least if you failed the midterm) to understanding older material, use the general guidelines above. As a starting point, go back to your quizzes, webworks, workshops, and the midterm and make sure you can solve all of the problems you’ve seen before. You must start doing this now since it will be WAY too much to deal with the week before the final exam. 3 General guidelines • Study actively not passively – don’t just read a passage from the textbook or your notes, make sure you re-enforce the ideas you’re consuming them by working through a practice problem or checking that you understand each step in a worked example. • Self-test your skills using old webworks, workshop problems, and quizzes from our course. Do you remember how to do the problems from webwork number 2? Make sure by re-doing each and every 2 problem trying not to use your text, notes, etc. Since you’ve done them before they won’t take as long this time but you’ll reinforce your understanding and be able to answer similar problems much more easily on an exam. You’ll also identify your weaknesses so you can address them. Related to this, do not assume that after following someone through an example you can duplicate the solution unless you actually test yourself. So, a review session where someone works problems for 5 hours while you watch is of deceptively little value – your 5 hours would be better spent trying to work the problems yourself and then using office hours or piazza if you get stuck. • Review the learning goals – these are the topics we’ve covered each week in the course and what we expect students to know at the end of the course. As you glance over them, ask if you’ve met these goals. For instance in week 3 we had the goal: “ state the definition of the derivative and use it to compute the derivative of a given function in simple cases.” To satisfy this goal, you should have memorized the definition of the derivative and worked problems where we use the definition to find limits explicitly. If you can correctly work all of the suggested problems I guarantee you will get a spectacular mark on the final exam. Key words are important. If a learning goal states ”define...”, ”know the...”, ”be able to explain...”, or ”be able to state the...” then you should memorize something, e.g. the definition of continuity or the intermediate value theorem. Vaguer words like ”compare and contrast..” might mean you should be aware of examples or counterexamples. For instance, “explain using sketches of appropriate functions the relationship between continuity and differentiability.” means you should know that diff. implies cont. but not the other way around. You should have in mind a counterexample such as |x| to illustrate that a function can be cont. but not diff. • Treat studying like training for a sport. Can you run a marathon tomorrow? Probably not. If you train for the next three days will you be able to run one in five days? Probably not. It’s the same with learning. You should be thinking today about the final exam. Also, 3 in sports, taking a week off means losing fitness. In math, taking a week off means you have twice as much to learn the following week. So be diligent and study regularly. Review the learning goals on a weekly basis. • Don’t squander learning opportunities. Every problem you work has value. If you copy a friend’s approach to a webwork problem without struggling with it yourself you will not understand it. So, what was the point of doing it at all? Focus on the long term objective of acing the final exam and treat each exercise as if it will improve your mark (because it likely will). • Practice, practice, practice! 4