Ough, I remeber this kind of feeling as a kid. I was always really good at testing for reading and writing.... but I was bad at math, so it balanced out a bit. (Until later I had to get diagnosed with dyscalcula)
God that mom sucks, how hard would it be to say something "I'll give you both some cookies if you promise study together next time" rather than make your daughter feel inferior and punished in front of her friend