Page 23 - Calculus Workbook For Dummies

Chapter 1

Getting Down the Basics:

Algebra and Geometry

In This Chapter

Fussing with fractions
Brushing up on basic algebra
Getting square with geometry

know, I know. This is a calculus workbook, so what’s with the algebra and geometry? Don’t
Iworry, I’m not going to waste too many precious pages with algebra and geometry, but
these topics are essential for calculus. You can no more do calculus without algebra than you
can write French poetry without French. And basic geometry (but not geometry proofs —
hooray!) is critically important because much of calculus involves real-world problems that
include angles, slopes, shapes, and so on. So in this chapter — and in Chapter 2 on functions
and trigonometry — I give you some quick problems to help you brush up on your skills. If
you’ve already got these topics down pat, skip on over to Chapter 3.

If you miss some questions and don’t quite understand why, go back to your old textbooks
or check out the great pre-calc review in Calculus For Dummies. Getting these basics down
pat is really important.

Fraction Frustration

Many, many math students hate fractions. Maybe the concepts didn’t completely click when
they first learned them and so fractions then became a nagging frustration in every subse-
quent math course.

But you can’t do calculus without a good grasp of fractions. For example, the very definition
of the derivative is based on a fraction called the difference quotient. And, on top of that, the
dy
symbol for the derivative, , is a fraction. So, if you’re a bit rusty with fractions, get up to
dx
speed with the following problems ASAP — or else!

Q. Solve $ c = ? Q. Solve a ' c = ?
a
b d b d
A. ac To multiply fractions, you multiply A. a ' c = a d = ad To divide fractions, you
$
bd b d b c bc
straight across. You do not cross-multiply! flip the second one, then multiply.