Although Bobby Rydell didn't appear in the movie, his song "Swingin' School" was part of the soundtrack. It entered the Billboard Top 40 on May 16, 1960 (3 weeks before Duane Eddy & the Rebels' version of the title song), and stayed for 8 weeks, peaking at #5.
Based on an early review of the movie in the September, 1959 issue of Stardust Magazine (Vol. 1, No. 1) ...apparently the working title was the same as the John Farris novel, HARRISON HIGH, on which it was based (no mention of BECAUSE THEY'RE YOUNG). The review also mentioned that Dick Clark's character was that of the principal, not a teacher.
The title song was not written by John Williams, but rather Don Costa, with lyrics by Aaron Schröder and Wally Gold. The song "Because They're Young" was released by Duane Eddy and became one of the rare all-instrumental hits of the era, going to number 4 on the American charts in the summer of 1960. The combination of Duane Eddy's "twang" guitar style and string orchestration was a different one for Eddy and it ironically became the biggest hit of his career. Eddy's version of the title song was not the version used in the movie; an anonymous orchestra played the instrumental version over the opening credits, and James Darren sang the vocal version. Duane Eddy and the Rebels performed "Shazam" in the movie. Darren didn't hit it big as a singer until a year and a half after this movie came out, when he hit the top 10 with "Goodbye Cruel World."