Alexander attended Boys' High School in Brooklyn, graduating in 1906. He then went to Harvard University, graduating cum laude in history and government in 1910.
While in high school, Fred played both lacrosse and ice hockey where he won his letters in both sports, and was elected captain his senior year of both the lacrosse and hockey teams. Additionally, Fred was a baseball player, a member of the rifle team, and participated in all other types of sports.
At Harvard, Fred was captain of his freshman team, then on to three years of varsity play, winning letters all three years and was elected captain his senior year of the 1910 team. The 1908 team won the Intercollegiate Championship, the 1909 team tied for the championship, and the 1910 team won the Northern Intercollegiate Championship. Fred's normal position was center, but on occasion he played every position, including goalie.
After leaving Harvard, Fred played 12 years for the Boston Lacrosse Club and was captain of the 1923 team. Fred not only played for Harvard, but also did most of the coaching of the teams and also helped coach the Rindge Tech High School in Cambridge in 1909. After graduating from Harvard, Fred taught math and physics at Framingham High School, and then went into business with the L.S. Drake, Co. in Massachusetts, where he worked until 1928, becoming one of the vice-presidents and factory managers. Fred then moved to the Johnson-Appleby Co., where he was factory superintendent and salesman until 1951.