The elementary mathematics (arithmetics and elementary geometry) is needed to be used by all people but babies, for everyday life circumstances such as shopping, banking, driving or sports. Other advanced parts of mathematics are essential for some jobs. Though, many of the most advanced areas of mathematics (such as topology, Lp spaces...) have been poorly used elsewhere in the applied sciences.
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we use discrete mathematics in industry and business
Pure Mathematics is the branch of mathematics that deals only with mathematics and how it works - it is the HOW of mathematics. It is abstracted from the real world and provides the "tool box" of mathematics; it includes things like calculus. Applied mathematics is the branch of mathematics which applies the techniques of Pure Mathematics to the real world - it is the WHERE of mathematics; it includes things like mechanics. Pure Mathematics teaches you HOW to integrate, Applied mathematics teaches you WHERE to use integration.
In a mathematics exam.
Not all... some don't need mathamatics..
All of them use it now.