Helpful checks to avoid mistakes in problems

• Level of difficulty: if a derivation becomes too messy, it is quite likely to be wrong - the problems are developed to correspond to your abilities, available time, material given in lectures and textbooks, etc. - go back and check!
  


• When taking determined integrals: do not forget to substitute integration limits - the integration variable should not appear in the result for such an integral (until the notations for the variable and the limit coincide).
  


• When dealing with derivatives: remember that derivative of a function is zero in its minima and maxima - so you may not always need to actually solve differential equation(s).
  


• Consistent units: when adding two values - their units should be the same; the arguments of algebraic functions (exp, sin, etc.) should be unitless; at any stage - the units of values should make sense, so that, e.g., distance is not in m⁴, etc.
  


• Appearance of results: compare what they predict with what you would expect in terms of common sense - say, whether the answer behaves reasonably with changing variables in the obtained expression.
  


• Memorising expressions: sometimes it may be easier to know the origins of an expression and the idea of how it is obtained - then you do not have to remember the expression itself but can readily produce it.