In this case an "extra class" refers to an addtional class perhaps because Dave is not good at Maths. Hence he may need extra classes for addtional support.

According According to the context Alexa crossing mean that a person is taking an extra time to study because he couldn’t undersell well the subject. And that would help him in the exam.

In North American English, "course" is a series of lectures on a topic such as statistics. "Class" can mean a course or a single lecture. In the text, the woman said she had had to miss some classes. Here, the meaning is that she missed some lectures. In the text, Dave said he was taking an extra class in statistics. Here, the meaning is that he is taking an extra course (one more course than usual). Some students take extra courses to graduate earlier (to graduate in three years instead of four years). Other students fail a course and then repeat it as an extra course to avoid delaying their graduation.