What are some good shortcuts for undergrad-level math and below?

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Professors often set exam times based on their own completion rates, which can make it challenging for students to finish on time. Effective shortcuts include using specific methods for simplifying complex equations, such as partial fractions, and focusing on problems that can be solved quickly before tackling more difficult ones. Utilizing resources like Schaum's outlines can aid in understanding and efficiency. Calculators like the TI-89 can help with simplification and integration, but it's important to balance their use with manual problem-solving skills. Mastering these strategies can significantly improve performance in undergraduate-level math.
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My professors say that they determine how much time they give to students based on the amount of time it takes them to complete their own test. Suffice to say, lately, I'm never been able to finish on time.

What are some good shortcuts I can use?

I learned about this shortcut: http://www.maa.org/sites/default/files/0746834248847.di020749.02p0056u.pdf and I was wondering if you can share some of your tips. That shortcut method is great. It makes complex partial fractions so much less tedious! I love it. :)
 
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Personally, I just try to reduce/simplify whatever the equation is to something I know how to work with. That way I don't have to remember how to solve each type of equation/integral. A schaum's outline is also great to have on hand. Do the problems you know you can do quickly, first. Then go back and try to work through the rest.

Also, I used to use a TI-89 platinum or something calculator. I could type in equations and have it simplify or do indefinite integrals and it would show me the resulting equations. Use it sparingly though, as you do need to at least know how to do things by hand, even if it takes you some time. And you'll likely need to show your work anyways.
 
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