Stuyvesant High School students haven’t learned their lesson.

Five years after a nationally publicized cheating scandal led to the principal’s ouster and the suspension of a dozen kids, academic dishonesty is rampant at the city’s educational crown jewel, students say.

“You could call Stuyvesant a meritocracy. Your worth is kind of judged on your academic success. Everyone here is pushing for the Ivies,” freshman Matthew Qiu, 15, told The Post. “Some kids do it by studying. Other kids don’t want to put in the effort or they aren’t able to, so they cheat.”

A survey by the student newspaper, The Spectator, found a stunning 83 percent of 329 responding students admitted they cheated at the elite institution.

“We all are just helping each other out. Stuyvesant breeds a culture of cheating, and you’re honestly stupid to not take advantage of it,” one student told The Spectator.

Cheating is most common among students in their third year, the most academically challenging because the grades count heavily on college applications, the December survey found. A whopping 97 percent of juniors said they had engaged in academic dishonesty, while 56 percent of freshman said they had already cheated after just four months in the school.

Students interviewed outside the downtown school last week weren’t surprised by the survey results.

“This school has a competitive environment, so some kids feel like they have to [cheat] in order to succeed,” Qiu said. “There is this bar. You are always trying to be on top, to be the best.”

“For some people, the pressure can be so much that they’ll take the risk even a second or third time after being caught cheating,” said junior Rafsan Zaman, 17.

Stuy’s brainy kids hold the city’s highest average SAT scores — 1450 (out of 1600). It’s the city’s most coveted high school, accepting only 926 of nearly 23,000 eighth graders who applied to get in last year. Admission is based solely on a test given for eight “specialized” city high schools.

Last spring, Stuy administrators caught students sharing Spanish homework answers in a Facebook group with nearly 100 students, senior Rafsan Hamid, a member, told The Post.

The Facebook group was started as a way to discuss the class and homework, Hamid said, but it turned into a cheating ring. Students would submit their homework to the Vista Higher Learning Central site, an online homework submission portal, which kicked back instantaneous answers. Kids then took photos of assignments with the correct answers filled in, and posted them for classmates to copy.

A whistleblower student eventually alerted Spanish teacher Abigail Carpenter and the school administration launched a probe, The Spectator reported. Several students who orchestrated the scheme received zeros on some assignments.

Hamid said the Spanish department’s assistant principal lectured each class, then teachers began giving pop quizzes on homework and made tests harder. No students were suspended. The Facebook group has since been shut down.

Carpenter, who resigned this month, is no stranger to cheating at Stuy. She was a proctor for the statewide Regents exams in 2012, when 71 Stuyvesant students had their scores tossed for sharing cellphone photos of a test.

Carpenter told investigators she didn’t see any hanky panky. Longtime principal Stanley Teitel, who was accused of hiding the wrongdoing, was fired over the scandal and a dozen students were suspended.

According to the recent survey, 73 percent of students said they have copied someone else’s homework, and 58 percent said they’ve cheated on a test more than once.

A 15-year-old sophomore told the Post that students memorize the sequence of correct True/False answers on tests and share them with friends in later classes who have yet to take the tests.

Seventy-six percent of students in the survey said their teachers have taken steps to stop cheating, but only 10 percent said they’ve been busted.

For years, the school has tamped down on plagiarism by requiring students to submit papers via Turnitin, a website that scans work for passages that appear in publications on the Internet.

But that didn’t stop one of junior Rafsan Zaman’s friends from plagiarizing two papers — once in freshman year and again in sophomore year — which led to the pal’s suspension, he said.

The school notifies parents of students caught cheating, according to Stuyvesant’s academic dishonesty policy, and the kids are also “subject to suspension,” which can be reported to colleges.

Despite the consequences, students are defiant.

“It’s not academic dishonesty if you don’t get caught,” one said.

That attitude alarms David Bloomfield, a Brooklyn College and CUNY Grad Center education professor.

“Cheating seems to have achieved a degree of social acceptance, where the kids feel pressure to not get caught, rather than to live up to high ethical standards,” he said. “That’s a responsibility for the school to teach.”

Principal Eric Contreras said in a statement to the Post, “We hold students to high academic integrity standards and have a strict policy in place that is reviewed with students at the start of each school year.”