BURLINGTON—The YouTube clip shows her in the stands with her Brestyan’s clubmates at the 2008 US gymnastics championships at Agganis Arena, answering the Grant’s Tomb question posed by John Macready, the roving emcee and former Olympian.

Where will the Beijing Olympics be held?

“I kind of stuttered,’’ Alexandra Raisman remembered. “I got nervous.’’

Maybe Raisman would be in the Games one day, Macready suggested.

“I remember her saying, ‘Next year I’ll be down on the floor,’ ’’ her mother Lynn said.

Not only was her driven daughter on the floor in 2009, she qualified for the national team. In 2010, the Needham native made the world squad and came home with a silver medal. Last year, she won worlds gold as the de facto leader of a rookie bunch and vaulted into the front rank of contenders for the US team for this summer’s Games in London.

“It’s kind of unbelievable where she came from,’’ said her mother.

If the 17-year-old Raisman stays healthy—no guarantee in a mid-air sport with no safety nets—she has an excellent chance to earn a place on the most difficult women’s Olympic team to make in domestic history.

Besides her gold-medal teammates—all-round champion Jordyn Wieber, McKayla Maroney, Sabrina Vega, Gabrielle Douglas, and Beijing medalist and clubmate Alicia Sacramone—all but one member of the 2008 team is back, most notably Nastia Liukin and Shawn Johnson, who finished 1-2 in the all-around.

The talent pool is so deep that the squad named to last summer’s Pan American Games, where USA Gymnastics usually sends the junior varsity, included three former world champions in Johnson, Chellsie Memmel, and Bridget Sloan.

“It’s going to be a really big challenge because there are so many newcomers and so many of the girls from the 2008 Olympics,’’ Raisman acknowledged. “It’s going to be a fight to get on that team, but whoever is on it, it’s going to be an amazing team.’’

Yet Raisman has the résumé to earn a place at Olympus, particularly with the team roster reduced from six to five. She competed in three of the four events (all but uneven bars) in the ’11 worlds team competition, finished fourth in the all-around and balance beam, and earned a bronze on the floor.

“I don’t like to have favorites, but I always want to differentiate between the girls who have the dedication,’’ said national team coordinator Martha Karolyi. “I see Aly as one of the important components of the Olympic team if everything continues to go in the same direction.’’

Unlike the last two Olympic teams, this one will be determined at the June trials in San Jose instead of at a subsequent Texas boot camp. So the shortened calendar means that everybody will have to be in top form a month before the Games.

“You need to be ready,’’ said Mihai Brestyan, the Romanian emigre who also coaches Sacramone, who is rehabbing from Achilles’ tendon surgery but expects to be in the chase. “Today the flag is up, you have to jump. You need to be ready at any time.’’

It was impractical for Raisman to juggle academics and gymnastics, which caused her to miss 50 days of school last year.

“Running to school, running to the gym, running back,’’ said Lynn. “A lot of running.’’

So Raisman is doing her senior year online at Needham High, getting much of her work done on weekends.

“I’m still going to go to the prom and graduation,’’ she said, “so I kind of get the best of both worlds.’’

Raisman spends at least seven hours in the gym four days a week—double sessions at 8:30 a.m. and 5 p.m.—plus three-hour morning workouts on Wednesday and Saturday.

“She knows she has the possibility to get a medal in the Olympic Games, but for everything you want to do, you need to make a sacrifice,’’ said Brestyan. “It’s one chance.’’

High school can be done by mouse pad, and college can wait. If Raisman makes it to London, she’ll be on tour for three months after the Games, which will delay her enrolling at a university.

“Definitely I want to go to college,’’ she said. “I don’t know where yet. I’ll take a year off and then I’ll figure out where I want to go. But I’m definitely going to go and be able to experience being a normal kid for once.’’

When Raisman does enroll, it will be only as a student. By signing with the Octagon sports management firm last autumn and turning professional, she passed up a gymnastics scholarship.