By 1987/1988 our public school in Texas was doing summer prep for the PSAT as an experimental program and we were advised to take the SAT once in spring of junior year and once in the fall of senior year. The ACT was something you only took if you were applying to schools in certain states.
I believe I took the PSAT/NMSQ the first year that they combined the tests - 1971 as posted upthread. I was cross because with a little practice I’d probably have done better. My PSAT score 68/69 or thereabouts and was only good enough for commended. My SAT scores were 730/740 (unrecenter the verbal would be an 800 today, math the same), and they would have been enough for NMS. We did not study for either test.
I used to think my kids were so much educated than me, but then I remember I was 16 when I graduated while my oldest had just turned 19. So I’m feeling pretty good about only having four APs and lower scores. 
Our school (private) made everyone take the SAT twice. Once spring junior year, once fall senior year. We all had to take subject tests too, and we took them fall senior year instead of in the spring when the material was fresh. Even my friend who got a 750/750 the first round (plenty for her first choice Swarthmore) had to take it again much to her annoyance. She got a 790/710 the second time. We were amused the total was exactly the same.
That is so funny because I live in Texas and our local school district has a summer PSAT prep thing for kids who scored decently well on the 10th grade PSAT.