I’m a chemistry major in the college of chemistry and I was considering exempting out of calculus 1A and 1B. I took Calculus BC as a junior and got a 5 but since it will have been two years ago by the time I start classes I’m not sure if I will remember a lot of the information. So does math 53 and 54 build on concepts taught in 1A and 1B or are they their own stand alone material.
53 builds on 1B. 54 is standalone for the most part.
Math 53 obviously depends on single variable calculus.
The differential equations in Math 54 require single variable calculus knowledge. Math 1B also includes some introductory differential equations material that may not be present in other high school or college calculus courses, but may be assumed in Math 54 (i.e. you may have to study that on your own). See the bottom of https://math.berkeley.edu/courses/choosing/ap-exams . Math course outlines are at https://math.berkeley.edu/courses/choosing/lowerdivcourses .
You can try old Math 1A and 1B final exams to check your knowledge: https://tbp.berkeley.edu/courses/math/