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On the Chem 14A website, there is a link titled constants and equations.. this is what will be given to us, everything else other than a periodic table is what we would have to know. As far as wavelength I think either is okay as long as the question does not specify but remember in terms of the equations you would use the unit m.
If you recall from test 1, we were given a cover sheet of constants and equations. I know that same cover sheet is being provided for test 2 and test 3, but I am not positive about the midterm/final. As for the units, as long as the question does not specify, you are free to use whichever. nm are usually more practical.
In short, no we are not expected to memorize the formulas since we will be provided a formula and constant sheet for all exams. However, we will be expected to know which formula to use and how to appropriately manipulate the formula for the given question. (i.e. p*c = ((h*c)/λ) ----> p = (h/λ) or E = h*v = h(c/λ)). And the preferred units for wavelength will be dependent on what units are asked for in the question.