"To believe" (pisteuo) in John's Gospel is more than to believe something or someone. Rather, it means to believe in God and also in Jesus. This means trusting and following them wholeheartedly. By the way, in this Gospel "to believe" occurs more than 80 hundred times while there is no occurrence of the word faith at all. Faith is expressed in all verbal forms. John takes 80-90% of the total occurrences of "to believe" expressions among the four Gospels. In John, trusting God requires to trust his Son. To trust his Son means to hear him and abide in his teaching. So he says like this in John 8:31-32: "Then Jesus said to the Jews who had believed in him, ‘If you continue in my word, you are truly my disciples; and you will know the truth, and the truth will make you free.’"
Similarly, he also says in 10:37-38: "If I am not doing the works of my Father, then do not believe me. But if I do them, even though you do not believe me, believe the works, so that you may know and understand* that the Father is in me and I am in the Father.’"
John 14.11 also strikes a similar chord: "Believe me that I am in the Father and the Father is in me; but if you do not, then believe me because of the works themselves."
"Believe" in John (59 matches):
1:7, 50; 3:12, 18; 4:21, 42, 48; 5:38, 44, 46; 6:29f, 36, 40, 64, 69; 8:24, 45; 9:18, 35, 38; 10:25f, 37; 11:15, 25, 42, 48; 12:36f, 39; 13:19; 14:1, 10, 29; 16:9, 30; 17:20f; 19:35; 20:25, 27, 29, 31
"Believed" in John (24 matches):
1:12; 2:11, 22-23; 3:18; 4:39, 41, 50, 53; 5:46; 7:5, 31, 48; 8:30-31; 10:42; 11:40, 45; 12:38, 42; 16:27; 17:8; 20:8, 29