Problem Patterns
Four habits that apply regardless of which module a problem comes from.
Every physics problem implicitly assumes a model: point particle versus extended body, ideal gas versus real gas, non-relativistic versus relativistic. Stating that choice explicitly — and knowing where it breaks down — prevents applying a formula outside the regime where it holds.
Exploiting a problem's symmetry — spherical, cylindrical, translational, time-reversal — before writing any equation often eliminates most of the algebra. A field problem with spherical symmetry needs Gauss's law and almost no integration; the same field computed by brute-force integration takes far more effort for the same answer.
A correct result should behave sensibly in extreme or special cases: does it reduce to a known simpler formula when a parameter goes to zero or infinity? Does it match an expected symmetric special case? A formula that fails an obvious limit is wrong, however correct the algebra leading to it looked.
Checking that a final answer has the expected dimensions catches the majority of algebra slips in under a minute, well before comparing to a numerical answer.