People themselves all the time when taking a mathematics course "When will I ever use this?" or "How is this applicable to me in my daily life?" As I see it both are valid questions just as a mechanic would ask if he would use a certain tool he is about to buy. You are buying mathematic knowledge with time (and brain energy - but that is not a scarce resource as far as I know). The question is what is math really about - in one word?
As I see it mathematics is about predicting events from existing data. 'Where is that ball going to 'land' in relation to the earth?' or 'when will that train arrive?' are questions that demand a predictive answer. Within the margin of error equal to the measurement tool you are using and the premise you set you can predict anything. Theoretically if you had a measuring tool that was perfect and a set of laws that applied to all energy and matter, you could predict time itself - in other words... see into the future. Since we do not live in a clean room nor are the laws of physics perfect (the laws start to break down below a certain microscopic point) we will have to rely on statical probabilities and data sets collections to predict our future to a wide varying degree of error.
I have observed something about math that would help people better understand the mechanism by which it operates.
Math can be broken up into three parts:
1. Data Set
They are all interconnected. In a graph you can see graphically a rough idea of what kind of equation is used and from what 'family' that equation is from. In a data set you create an equation that equal in accuracy as how many points you have. Then the equation is a complex set of symbols and numbers that represent a simple function in this statement: "If I input this number I get this different number."
As my analogy to the mechanic is a rough one, it is the only analogy that describes math in it's syntax. You look at what tools you need to predict some event, location, length or volume (to varying degrees of accuracy) and choose accordingly. Do you need calculus for everyday life? Well, depends on if you are a rocket scientist or a mechanic. One uses it in it's detail and the other uses it in rough application.
Here are some simple mnemonics for mathematics:
A frowning graph is an even negative one.
A happy graph is one that just got even (The graph of X^(even) = a 'u' or 'n' shape)
It's super to be odd. (The graph of X^(odd) = an S shape)
Why can't i exist? Because it's imaginary.
An inflection point is where you gravity stops or starts taking over when skiing the slope and becomes a mountain or valley in it's derivative.
If a graph is X^(even) then both lines creating the graph will be be pointing up or down.
If a graph is X^(odd) then one line will point up and the other down.
If a graph is X^(fraction) then it's graph looks like a cannon ball shot without gravity to pull it down.
If a graph is X^(negative whole number) then there will be two lines mirroring each other. (Essentially 1/X^(number))
If a graph is X^(negative fraction) then it's graph looks like a marble dropped from a building but the marble hovers over the ground - getting closer and closer to the ground but NEVER landing.
These are some things I learned from being a calculus and algebra tutor. I hope it helped.