Well, she is going to find out sooner or later right? Or does she not read your report cards? Or meet with your teachers?
I understand you don't want to disappoint her, but you need to get better grades for yourself, not for her. If you have any hope of going to college, you need to learn better study habits now. Take responsibility for your actions and the choices you make - how can you say it is "partly" your fault for not getting the work done? Who or what else is to blame? If you keep up with the homework on a daily basis, you will get practice solving algebra problems and will be better prepared for tests because you will have mastered the material and fully understand it. If you are having trouble, it is up to you to go the teacher, stay after school if you have to, and have him/her explain it and go over it and give you extra help until you got it down. In college, nobody comes to you when you are failing a class and warns you and starts giving you chances to get your grade up - you just fail and that's it. You cannot expect to fall behind and then think you can catch up a few days before the test - understanding concepts later on depends on building on what is taught first.
Be honest with your mom and then tell her what you plan to do about this so you can end up with a passing final grade and not have something like this happen again. I am assuming you are in high school, so grades now do count toward grade point average, which colleges look at when it is application time. Stay after school if necessary, go to the teacher for help, and spend more time on your homework and studies so you get it down. Your friend may have passed doing the same amount of work, but either he understands it better, or he's better at keeping up with it. Your mother may be upset, but it also doesn't sound like you really tried your best. I didn't always get great grades either in school, but if my parents knew and could see that I had made my best effort, they were never disappointed.