"Speak up and speak out," Mayor Marion Barry exhorted the political science students at H.D. Woodson High School yesterday. "Ask me any question, no matter how trivial you think it may be."

A youth in a tan sweater and striped shirt popped up to ask the first question: "What effect has the grand jury investigation into Pride and Mary Treadwell Barry's ex-wife had on your political career?"

"That's a heavy question, but a good question," said Barry, shaking his head and smiling broadly at the youth.

Then Barry launched into his usual response to questions about the federal probe of P.I. Properties Inc., a real estate spinoff of Youth Pride Inc., the self-help organization that Barry cofounded. The probe has not involved any allegation of wrongdoing by the mayor, and Treadwell has denied any wrongdoing. "I'm not going to be indicted . . . I have a letter from the U.S. prosecutor's office clearing me ," Barry said. "I don't expect it to have any effect on my political career."

Barry spent yesterday teaching classes at Woodson High, to find out "what's on young people's minds." He got an earful.

While the mayor wanted to talk about how the D.C. government runs, why there should be a national Martin Luther King Day, and to promote his annual Youth Leadership Institute, the students wanted to know why he has proposed cutting the schools' budget request, how many summer jobs there will be and what he would do for the city if elected to a second term.

In between responses, Barry, who has not yet declared formally for reelection, seized the opportunity to tell the students that his administration has created 7,500 new housing units and 6,000 more jobs for adults, urged the 18-year-olds to register to vote, and reminded some teachers that he would be looking for their support next November.

Barry got a royal welcome at Woodson, located at 55th and Eads streets NE, not far from the Prince George's County border. Modern, seven-story Woodson has long been a showcase for the school system with its escalators, elevators and indoor swimming pool. The school's standardized test scores are also better than those of most city high schools.

Barry said he picked Woodson because it is his neighborhood high school. "I'm not campaigning," Barry said. "I go visit schools all the time."

Though Barry has given pep talks and commencement speeches at city schools, this was the first time he came to teach. He took off his suit jacket and rolled up his sleeves to teach a chemistry class in the morning, drilling the students on various compounds like sulfuric acid and sulfur dioxide.

Barry has bachelor's and master's degrees in chemistry, but admittedly hadn't "opened a chemistry book in 10 years."

After chemistry, the mayor ate lunch, as students crowded around his table to seek his autograph and city funds to buy trophies for their football team.

At the afternoon political science class, Barry found to his disappointment that none of the students knew who represents Ward 7--where Woodson is located--on the school board, how many members are on the school board or who is the board's current president.

A few knew how many members there are on the City Council, and several knew that H.R. Crawford represents Ward 7 on that body and that Arrington Dixon is the council's president.

There were 13 students in the class who were 18 years old, and Barry asked those who were registered to vote to stand up. Only four stood. "If you vote," Barry explained, "you can say to so-and-so, 'I voted for you and I don't like what you're doing.' A politician will generally listen more to someone who did vote."

Though the students were caught unprepared to answer many of Barry's questions, they were well prepared with questions of their own for him--including, who did he think would give him the stiffest campaign challenge.

"I'm the man to beat. I'm the strongest. I'm the best," Barry responded, flashing a wide, confident grin.