Last fall, for example, nearly 12 percent of first-year U.C.S.D. undergraduates were not qualified to take pre-calculus, a low-level class, up from only 0.5 percent in 2020. “The key problem is that many of the students coming in do not know algebra,” said Mina Aganagic, a Berkeley physics professor. More than half of entering Berkeley students who took a math placement test incorrectly answered basic questions (such as solving for x in x²> 4).