What would you have to know to be an engineer?

Pick an Engineering Discipline and look at a College that offers it. See what classes are recommended.

If you can't decide a discipline, or if you would like to make your decision by what classes you must take; there is a core group of college classes that are common for any type of Engineering. They are a starting point and you need to be prepared to take them. Unless you are a higher math whiz, take a Pre-Calculus class to prepare. Calculus uses Trigonometry and Algebra; but it is very different from them.
These classes include: Calculus (3 classes), Analytical Geometry, Differential Equations, Statistics, Computer Programming (to include a higher level language), Chemistry, Statics, Dynamics, Thermodynamics, Property of Materials, Physics (3 classes including Optics and Theoretical). Some of these include a Lab class, which is separate from the lecture class.
These are usually taken in the first 2 years and are mandatory.

From then on, you take classes needed for your major (Aerospace, Biomedical, Chemical, Civil, Computer, Electrical, Environmental, Mechanical, etc.) Your last year you may choose your electives from those recommended for your emphasis; for example: Digital Communications to specialize in designing Communications Systems if you are in Electrical Engineering.

Your classes form a foundation, common to other engineers. You will have the understanding of the terminology used and will need it when you interview for an internship or job.

Well a very good question which not many students ask.

I have written a detailed post on what you must know before you start preparing for an Engineering.

Read the post.

This post explains four things:-

1.Introduction

2.List of colleges you are aiming

3.Engineering Entrance Exams

4.Books to Refer

WHAT TO KNOW ABOUT ENGINEERING AS A PROFESSION
Doing a Little Research
If you think you might want to be an engineer, it's useful to begin finding out about the field and gaining some exposure to real, live, practicing engineers. According to College Board, there are more than 30 college engineering majors, including the following:

Aeronautical/aerospace
Agricultural
Architectural
Bioengineering
Chemical
Civil
Computer
Construction
Electrical
Environmental
Industrial
Manufacturing
Marine, navel and ocean
Materials
Mechanical
Metallurgical and mining
Nuclear engineering

You need a good background in math and sciences, although good writing skills are also needed to convey your ideas, thoughts and progress to others. If you a curious, and want to find a better way of doing things, you will make a good engineer. There are many fields in engineering ,so if you are curious about mining, machines, automobiles, chemistry , electrical or electronics there are programs geared to those specialties.

To be prepared for engineering school you need to be good in math and sciences.