Michael Crystal was the captain of the Princeton Regional High School math team, he took multivariable calculus and matrix and linear algebra at Princeton University, he tutored other students in math, and he wrote a book - all during his senior year in high school.
The book, ''SAT Success,'' is the result of what coauthors Joan Davenport Carris and Michael Crystal believe is possible - improving Standard Achievement Test (SAT) scores. Ms. Carris, an author and teacher, wrote the verbal section of the book, and Michael wrote the math section.
''Preparation helps a lot more when you're toward the lower end,'' says Michael, presently a student at Massachusetts Institute of Technology, ''the person who just wants to break over a 700 will have a harder time.''
Michael made up more than 100 questions in the text, and after a while he began ''thinking SAT.''
''Everywhere I went,'' he says, ''I was thinking of SAT problems - like there are three boys in a room and four girls, now how could this be an SAT problem. . . .''
Ms. Carris and Michael designed their book as closely as possible to pattern the real SAT test. When writing the sample tests, Michael says he followed SAT tests.
''I got more than ideas from the SAT tests, I made sure that in Problem 2, if it was decimals, my Problem 2 was decimals; . . . we're trying to test as closely as you can,'' Michael says.
In his book, ''SAT Success,'' Michael Crystal suggests the following for the thousands of high school students preparing to take SAT tests.
* Learn about the test you'll be taking. Read all you can find in the guidance office, plus the ACT or PSAT and SAT booklets so that you know what to expect. Ask questions of your sadder-but-wiser friends.
* Write on the test in any way that helps you solve the problems. Draw pictures whenever they will help.
* Check problem number and answer sheet number and be sure they're the same. In other words, ''Don't fall off the trolley.''
* Avoid last-minute, eleventh-hour reviews, because they're apt to make you jittery.
* Celebrate the night after the test.