One-way ANOVA (analysis of variance) is typically used when you have a categorical independent variable (with two or more categories) and a normally distributed continuous dependent variable (DV). It allows you to test for differences in the mean of the DV across the levels of the independent variable. So, in your case, it would allow you to test the hypothesis that for a particular obstacle variable, students who encountered that obstacle had a different mean exam score than students who did not.
You can read about the assumptions of this test and how to deal with situations when one or more of those assumptions is not met here: https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.phphere
There. There was also a previous question about ANOVA assumptions: Checking ANOVA assumptionshere.