Told my history professor I was really worried about my final grade the day of my final. Told him being in college was so here wrecking and the pressure to do well was so overwhelming that it's a wonder I could even remember my name to put on the heading of the paper. He chuckled and said not to worry about it. Got an A in the class. It was partially bs, partially true. I'd studied, but knew I missed some questions. Dude was cool. Doesn't hurt if you participated in class discussions.
My junior year in philosophy. Sent my professor an email early in the semester saying I would miss class because I had to take my new born daughter to the hospital. Every time I missed class, I said it was because of my daughter. Did well on all my assignments, but my school had a strict attendance policy where you receive an F if you missed more than 4 days of class. End of the semester rolls around. Professor tells me I missed 11 classes (I didn't like night classes). Says he's gonna have to fail me despite the B I had without the attendance issue. Told him I understood and accepted responsibility for my actions. Then he asks how my daughter was doing. Had a talk with him about how being a new parent is difficult, especially at my age and being in school. Talked for about 30 minutes and we didn't even bring back up the grade. Turns out he let me keep my B. I have no kids.
Sometimes you just gotta talk to professors. They're people too. Some are cool, some aren't. For 1 percentage point I would go all out but it shouldn't eem be that hard.
But like someone else said, don't ask for it. Ask if you can do anything (ie revised homework assignment, paper, quiz, etc) before the deadline to get the extra point.