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Pre-Calculus For Dummies, 2nd Edition by Elleyne Kase, Yang Kuang PhD

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Chapter 17

Ten Habits to Quit Before Calculus

In This Chapter

arrow Recognizing all the bad habits

arrow Remembering all the correct habits

You’ve come this far in math, for which you deserve high praise. But we can say with confidence that only 1 percent of you have few to no bad math habits. We wrote this chapter on breaking bad math habits in hopes that you’ll recognize a mistake that you commonly make and resolve to not make it anymore. The 1 percent of you who are perfect can now leave the building!

Operating Out of Order

Don’t fall for the trap that many students do by performing operations in order from left to right. For instance, 2 – 6 · 3 doesn’t become –4 · 3, or –12. You’ll reach those incorrect answers if you forget to do the multiplication first. Focus on following the order of PEMDAS every time, all the time:

Parentheses (and other grouping devices)

Exponents

Multiplication and Division from left to right

Addition and Subtraction from left to right

Don’t ever go out of order, and that’s an order!

Squaring without FOILing

Always remember to FOIL. Here’s a common mistake we see: (x + 3)2 = x2 + 9. Why is that wrong? Because you forgot that to square something means to multiply it times itself. Foiled again! Here’s the correct process: (x + 3)2 = (x + 3)(x + 3). You should reach ...

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