I couldn't go all out studying for my test this time.
I couldn't give it my all studying for my test this time.
この場合、次のような言い方ができますよ。
ーI couldn't go all out studying for my test this time.
「今回の試験で全力を尽くせなかった」
go all out で「全力を尽くす・本気を出す」
ーI couldn't give it my all studying for my test this time.
「今回の試験で全力を尽くせなかった」
to give it one's all でも「全力を尽くす」と言えます。
ご参考まで！
カナダ 
