How can you learn Math's formula?

Question

Perhaps this is a weird question, but I had a really though time when I was in college. So much so that I dropped from it.

It wasnt only in maths, but also in other subjects with formula or equations.

There was sometimes that we have to learn by memory some formulas. And I didn't know how to read them.

So, how do you do it?

P.S.: I will try to put an example as soon as possible.

Answer 1

This is partly a failure of the way math is taught in America. Unfortunately, we are very results-oriented (i.e. scores on multiple choice tests) with respect to education - it's easy to get better results with less effort in the short-term by pushing a memorization approach, but in the long term this is doomed to fail as ever-more formulas, dependent on formulas previous, stack up as one goes from algebra to precalculus to calculus.

If you have a good feel for the underlying concepts, you can often re-derive what you need when you need it. A great example: as a tutor I strongly discourage my algebra / pre-calculus students from memorizing the distance formula:

If $P = (x_1, y_1)$ and $Q = (x_2, y_2)$ are points in the plane, then the distance between $P$ and $Q$ is given by $d(P,Q) = \sqrt{(y_1-y_2)^2 + (x_1 - x_2)^2}$

Generally, at some point previous, they will have learned this famous fact:

If you have a right triangle whose legs have lengths $a$ and $b$ and whose hypotenuse has length $c$, then the equality $a^2 + b^2 = c^2$ holds.

If you already know this, then the distance formula follows by considering the right triangle:

Another example is the quadratic formula:

If $ax^2 + bx + c = 0$, then $\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In most courses where this is taught, one also learns about the method of completing the square. Alas, what is often not mentioned is that you can get the mess of a formula above by simply completing the square on a quadratic equation with general coefficients (see here).

Answer 2

You should understand the derivation of formula and practice the questions related to it. Many tricks or mnemonics have also been created to memorize the formulas. But I would recommend you to invent your own tricks.However you should use them only for memorizing. After you have memorized the formulas, not use tricks to recall formulas while solving the questions as it will make you slow.

For instance, consider the following formula:

$ cos A − cos B = -2 sin(\frac {A+B} 2)\cdot sin(\frac {A-B} 2) $

I used the following trick. My friends find this trick useless (may be you too). But, it worked for me.

$c-c=-2ss$

Note that I have not used the trick for the terms inside the brackets because $(\frac {A+B} 2)$ and $(\frac {A-B} 2)$ are common for all sum to product trigonometric identities.

You may also visit blog.artofmemory.com for memory tips.

Hope it helped you.