How Many Formulas?

Date: 11/25/2002 at 19:42:46
From: Rebecca
Subject: Math

Hey,

I have a question. I am in pre-algebra and I just want to know, How 
many formulas do you actually have to learn? And does it ever get 
easy?

Another questian. I am planning on taking PRE ALG, alg1, and then 
BUSINESS MATH (not alg 2). Is this going to affect me in any way in 
my life? Will I be dumb?

Thanks,
Rebecca

Date: 11/26/2002 at 01:40:37
From: Doctor Ian
Subject: Re: Math

Hi Rebecca,

There's no limit to the number of formulas in math, because people are
making up new ones all the time. 

However, you don't have to know very many of them. Here are just about 
all the formulas that I've memorized:

  1. area of a rectangle = length * width

  2. area of a circle = pi * radius^2

  3. volume of a prism = area of base * height

  4. sin^2 + cos^2 = 1

     (This is really just a version of the Pythagorean Theorem.)

  5. The quadratic formula, 

           -b +/- sqrt(b^2 - 4ac)
       x = ----------------------  whenever ax^2 + bx + c = 0
                    2a

  6. The derivative of e^x is e^x.

  7. The derivative of ax^n is anx^(n-1).

Along with some definitions (e.g., exponents, and the sine, cosine, 
and tangent functions), I think that's about it. (Don't worry too much 
if you don't understand what they all mean. The important point is 
that there aren't very many of them.) 

There are lots more formulas than this. But if when you learn about a 
new formula, you make sure that you _understand_ why it works, then 
you don't have to remember it, because you can figure it out again 
later if you need it.  

(For example, you can turn any parallelogram into a rectangle by
cutting a piece from one side and moving it to the other. So I can
figure out that the area of a parallelogram is the same as the area of
the rectangle that has the same base and height. And you can make any
triangle by cutting a parallelogram in half. So I can figure out that
the area of a triangle is half the area of the corresponding
parallelogram, which is the same as the area of the corresponding
rectangle.  See how it works?)

As for your other question, not taking algebra won't make you 'dumb'.
But it will make it somewhat easier for other people to take advantage 
of you by using statistics, graphing tricks, and so on. And you may 
find later that you're unable to pursue certain careers because you 
won't know enough math to learn about them. 

But certainly there are lots of happy, productive, well-adjusted, and
perfectly intelligent adults who couldn't solve an algebra problem if
their lives depended on it. Fortunately for them, hardly anyone's
life ever depends on it. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/