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I think you should definitely know the general trend that electronegativity increases as you go to the right across a period and up a group. This way you can roughly determine what kind of dipole moment may appear in a molecule. The only time I think we would need to have an electronegativity chart is if we are asked to determine if a certain bond is covalent or ionic by calculating the exact electronegativity difference. (Difference > 2 means ionic, Difference <1.5 means covalent). If such a problem is asked, I'm fairly sure the relevant chart or at least the values for each element will be given.
We may be given electronegativity numbers for some of the elements involved in the problem if any do arise in the midterm, however, it would probably be in your best interest to generally know the trends for electronegativity, and other periodic trends as well. In the case of electronegativity, it goes up from left to right and goes down from top to bottom. Generally the rightmost elements are most electronegative as it is easier to gain an electron than lose one, energetically. The electronegativity decreases down the group as the radius increases, meaning that the pull of the nucleus becomes more shielded, making it harder for electrons to be attracted.
We will not be given an electronegativity chart, but we won't need to know them very accurately or precisely. You just need to know whether it increases or decreases down a period and down a group, similar to how you should know the trends of ionization energy, electron affinity, and atomic radius.
Adding on, I think it would also be helpful to just know which elements are generally a lot more electronegative and the electronegativity values of the most electronegative elements like F, N, O, and Cl.
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