At the high school level you need the materials covered in Tiers 1 through 5. You will need to understand the concepts and tools. It is important you learn to use a scientific calculator (I recommend the TI 30Xa), and Wolfram Alpha, WA. WA is a modern tool that makes solving problems from algebra, calculus, analytical geometry, linear algebra, and much more, very easy. Indeed, with WA you can solve problems impossible without such a tool.
Then in post-secondary schools you will learn to use specialized tools for various STEM subjects.
For example, I imagine an architect will need to learn how to use a CAD system. Also, there will be specialized architect tools I am sure. In fact, there will probably be tools in five years that don’t even exist today. You will always be learning to use more powerful tools as technology progresses.
A civil engineer will also learn specialized tools. For example, you will need to learn to use a spectrum analyzer to analyze vibration frequencies and identify natural resonance frequencies. This is critical in building structures of all types. The same is true in all engineering fields. Each field will have its own specialized tools.
What you should master in high school are the fundamental concepts of algebra, analytical geometry, geometry, trigonometry, complex numbers, calculus, and if you have time differential equations and linear algebra. These are all basic math concepts and tools used in virtually all STEM subjects. The TI 30Xa and WA are great places to start. You can also begin to master spread sheets too.
What you want from high school math is enough math to launch into science and engineering subjects immediately after you matriculate to a good post-secondary school of any type. You want to begin to take advanced courses in your desired field ASAP.
This means you need to really understand calculus, linear algebra, and differential equations before you enter college.
International students often do since they are given special classes and math programs. Remember we are competing with the best of the best from foreign countries. They are separated from the ordinary students and given special teachers and training.
This is something that only very rich students or students in an unusually good special high school can get in the U.S. However, this is not longer the situation. You can now enroll any student anywhere in a modern math curriculum. Triad Math is one such example.