Can you get a Z/T score from a given confidence interval without a table on a TI-84?

Hello, I'm studying for my final stats exam, and I'm hitting a bit of a road bump. I can get the corresponding z or t score of a given confidence interval when I'm looking at a table, but we will apparently not be getting a table on the final exam. I'm pretty confused as to how I'm supposed to find a z or t score without a table, when I'm not given all of the information to do the typical z or t score equation, i.e. z=x-u/sd.

For example, say I'm given the confidence level, the standard deviation, the sample size, and the fact that it's an upper/lower/two tailed test, and I'm meant to find the critical value. How would I go about doing that without a table? I've memorized most of the common z scores at this point in the semester, but the t scores are a complete no-go for me, especially since they go 4 decimal places compared to z's two.

I'm not being given a sample mean, so I can't run it through the z-test. Is there another way I'm missing, or should I just try and memorize the more common values and hope for the best?