Homework (作业) refers to tasks assigned to students by their teachers to be completed outside of class time.

The origin of the word "homework" is bepeved to come from the early 19th century, when schools started to assign work to students to be completed at home. "Home" refers to the place where students pve, and "work" refers to tasks or assignments that students are expected to complete.

Examples:

I have a lot of homework to do tonight.
(今晚我有很多作业要做。)
Have you finished your homework?
(你作业做完了吗？)
My teacher gave me extra homework because I didn't do well on the test.
(因为我考试不好，老师给了我额外的作业。)

Class (班级) refers to a group of students who are studying the same subjects and are taught by the same teacher(s) in a school.

Examples:

I'm in the same class as my best friend.
(我和我最好的朋友在同一个班。)
Our class is learning about history.
(我们的班正在学习历史。)
The teacher called the class to attention.
(老师叫班上的学生注意。)