[bakuninsbart]

> In math you can't often solve a more advanced problem such as Calculus problem without understanding the more foundational math such as algebra, fractions, etc.

This is true to a good degree, but maybe a bit less so than you believe. Trigonometry is a topic that only clicked for me after finishing my uni calculus curriculum, I didn't get a great grade, but got by with a technique similar to how we handle complex numbers: Instead of giving up after being unable to solve an eg. weird chain of sin, arccos etc. functions, just declare it to be u(x) and do the calculus bits around it. In the last step substitute the actual function back in and you have an incomplete, yet technically correct solution.

[conwy]

I know what you mean, in fact I remember earlier on when I started the course, I had wanted to use these kinds of substitution techniques, etc. and thought I could finish the course in a few days. Boy was I wrong!

These techniques definitely won't work in a tough online multiple-choice test (of the kind I'm getting) where they deliberately sprinkle in subtle quirks to deceive you, which would require very disciplined algebra, fractions, powers, etc. to identify.