A Brooklyn middle-school boss gave students a leg up on tough city and state exams — by cheating, whistleblowers told The Post.

Adrienne Spencer, principal of Parkside Preparatory Academy since 2003, is accused of handing out embargoed exams to teachers, who then used them to coach kids before they took the tests.

“I know what she was trying to do was unethical,” said Addam Amauri Jones, a Spanish teacher at the Prospect-Lefferts Gardens school who claimed his refusal to take part in cheating on a citywide Spanish exam cost him his job.

The Department of Education dismissed the cheating allegations as unfounded, despite smoking-gun evidence: One teacher took time-stamped photos of “practice” questions which appeared on the official exam days later.

Shrink-wrapped state math exam booklets for grades 3 to 8 were delivered by testing vendor Questar on April 10 to 12 — more than two weeks before the exams were given citywide May 1 to 3, records show.

School staffers are forbidden to open the test booklets until the day of the exams. But Spencer had them unwrapped ahead of time, staffers contend.

To disguise the alleged scheme, Spencer had teachers physically cut up the test questions and paste them onto their own “practice tests,” said guidance counselor Ebony Valentine.

But it went further. Valentine was summoned to a classroom last year on May 2 as students in grades 6 to 8 were taking the state math exams.

“One student during the actual test pulled out the ‘practice paper’ and was copying the answers onto his actual test,” said Valentine. When she confronted the boy, he stuffed the papers in his book bag.

Valentine said she reported it immediately to an assistant principal. “Nobody came upstairs to the classroom. Nobody asked the child to take the copy out of his book bag. No one asked me what I saw.”

Valentine and special-ed teacher Greer Pope reported the alleged wrongdoing to the DOE’s Office of Special Investigations last July. It wasn’t until August that OSI investigator Doug Goroway contacted them.

“He said to me, ‘This is very serious,'” Pope said Goroway told her.

Pope said she showed the investigator her photos of stapled sheets, the top dated “4/30/19,” with questions that showed up later on the May 2 exam.

The sheets, reviewed by The Post, include at least five math problems among the actual test questions and multiple-choice answers.

After learning that Pope took the photos, Spencer had an assistant principal remove a cell phone from an aide’s purse, thinking it was Pope’s phone, several staffers recalled.

“She was looking for my phone. She knew I had the pictures,” Pope said.

The administrators asked a tech-savvy staffer to examine photos in the aide’s phone, Pope said.

Parkside teacher Patricia Washington, a union delegate, told investigators that the aide saw the principal and assistant principal looking at her photos, and complained to her about the incident, Washington told The Post.

In addition, on May 9, days after the test, Pope emailed a union representative, saying another math teacher “had the unreleased questions for the math test, which she taught to the students before the exam.” Pope got no response, she said.

Spencer did not respond to emailed questions.

DOE spokeswoman Danielle Filson said the cheating allegations against Spencer have “absolutely no merit,” and cheating accusations against the student were “unsubstantiated.”

Filson dismissed the photos provided by Pope, saying some might have been taken after the test questions were released in June. But Pope produced copies showing the photos all time-stamped during school hours on April 30, two days before the test. The DOE gave no response to that evidence.

Parkside Prep serves 476 students, 91 percent black and Hispanic, and 89 percent low-income. Last year, 24 percent of kids in grades 6 to 8 passed the state math exams, up from 22 percent the year before.

Jones, a Spanish teacher the school hired through a DOE vendor, SmartStart Education, said Spencer tried to get him to rig the 2019 citywide Spanish Comprehensive Exam, one of the tests that can fulfill high-school graduation requirements.

Last April, two months before the test, Spencer met with Jones and handed him a copy of an exam. She told him to “cut it into pieces,” sort the questions by type, put them in legal-sized envelopes — then start using them as practice tests for students, a tape-recording of the exchange shows.

“You begin the testing and give it back to me,” Spencer says on the tape, referring to the envelopes.

Jones tells Spencer, “I was doing my own version of some of those (questions), so they’re not exactly the …”

“No, no, no. You got to use what they give us,” Spencer replies.

Spencer fired Jones on May 3 without giving a reason, he said. He now teaches at a charter school.

Spencer also terminated Pope, who lacked tenure, on Sept. 3, and brought disciplinary charges against Valentine, who was tossed in a DOE “rubber room” pending a hearing.

Queens City Councilman Robert Holden, who met last month with staff of Brooklyn US Attorney Richard Donoghue to discuss unfettered grade fraud in city schools, called for an independent probe.

“This is a clear-cut case of the DOE’s lack of oversight where bending the rules to cheat is in the principal’s interest. It puts them in a better light. It jacks up their numbers, but it’s such an abuse of power,” Holden said. “We can’t trust the DOE to investigate themselves.”