SAY farewell to vocabulary flashcards with arcane words like “compendious,” “membranous,” “mendacious,” “pugnacious,” “depreciatory,” “redolent,” “treacly” and “jettison.” In the new SAT, to be unveiled in 2015, David Coleman, president of the College Board, wants to get rid of obscure words that are . . . just SAT words, and replace them with more common words like “synthesis,” “distill” and “transform,” used in context as they will be in college and in life.

And the math? “There are a few things that matter disproportionately, like proportional reasoning, linear equations and linear functions,” Mr. Coleman said. “Those are the kinds of things we’re going to concentrate on.”

“And it shouldn’t just be about picking the right answer,” he said. “It should be about being able to explain, and see, the applications of this math.”

Big changes are coming to the nation’s two competing admissions tests.

Mr. Coleman, who became president last October, is intent on rethinking the SAT to make it an instrument that meshes with what students are learning in their classrooms. Meanwhile, the ACT, which has always been more curriculum-based, is the first of the two to move into the digital age. In adapting its test for the computer, ACT Inc. is tiptoeing past the fill-in-the-bubble Scantron sheets toward more creative, hands-on questions.