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Thousands of city students who passed their high school completion exams last year will receive a rude awakening once they get to college: They’ll have to retake high school math — if they get into college at all.

New analysis of students’ scores by Harvard testing expert Daniel Koretz shows that many students who passed these exams have essentially been lied to about their skill level. While a score of 65 on a Regents exam technically means the student is proficient, students actually need to score above a 75 or an 80 on the English and math tests in order to have a chance of getting into college and doing well once they’re in.

The percentage of New York City students who fell in this dangerous range of scoring between a 65 and a 75 or 80 was very high in 2009, when the most recent data was available. At that time, 51 percent of students scored in this range in algebra and 32 in English.

Though their scores should have meant they were competent in algebra and English, they actually mean these students are likely to score too low on their SATs to get into college. If they do get in, they face a high probability of being required to take remedial classes.

“The word ‘proficient’ should tell you something, and right now that is not the case on our state tests,” said David Steiner, the state education commissioner.

Students who score below an 80 on the math Regents have a 28 percent chance of scoring above 500 on the math SAT. If they get below a 75 on the English Regents, they stand a 19 percent chance of getting above a 500 on the reading SAT.

The City University of New York enrolls all incoming students who score a 75 or below on their Regents in remedial classes.

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