Closing her eyes, 17-year-old Kim Boyd polishes off a quadratic equation faster than a speeding abacus. Just like she said she could.

"It's very easy," she says afterwards, smiling. "I get into the numbers and relax with them."

Eastern High School's Keith Landfair, another 17-year-old of the same ilk, amuses himself with physics problems and dreams of possible early admission to the Massachusetts Institute of Technology.

Just who are these whiz kids?

The snappy, ebullient Boyd, the sheltered only child of educators, lives in Upper Northwest Washington's Gold Coast, and is a student at D.C.'s School Without Walls. She is also studying at Howard University with hopes of entering the school's combined six-year bachelor of arts/medical doctor degree program. If she stays on schedule, she will be a physician by age 24.

Landfair, a quiet, reserved Southeast Washington youth who like fencing, collects Marvel Comics and reads physics journals for fun, is studying applied computers and calculus at George Washington University.

He lives with his mother, Sadye Russell, a retired nurse's assistant. His father Slim died in 1973.

Russell says her son is the only one of her three children she would define as exceptional. "The girls," she says of Keith's older sisters, "just made it through."

Keith and Kim are among the 92 students, who are currently enrolled in the D.C. public schools' High School College Internship Program. HI/SCIP, as it is called, provides an opportunity for highly motivated students to complete their senior year in high school and freshman year in college at the same time. As an added bonus, the college tuition is free.

Begun in 1975, HI/SCIP is the brainchild of Evelyn R. Marshall, a former teacher and guidance counselor in the D.C. public school system, who now serves as the program's director.

Marshall undertook the program because she thought the schools did not offer enough challenge to sustain a high level of motivation among bright students. She had followed the careers of 700 youngsters who entered the D.C. schools as freshmen, and was alarmed to learn that only 292 remained in the system long enough to graduate.

"I saw that we had nothing to offer them in the 12th grade except tennis-shoe tying, basket-weaving and prom preparation," Marshall recalled, stretching the point, "And I realized that we could and should be doing more."

Convinced that some students would benefit from beginning the college experience early. Marshall sold her plan to public school administrators, and then to officials at Howard and the former Washington Technical Institute. She proposed allowing selected students to take college courses for academic credit without charge. The schools would cover tuition, and the students' only responsibility would be for books and incidental items.

Today, six colleges and universities -- Georgetown, George Washington, Howard and Southeastern universities, the University of the District of Columbia and Mount Vernon College -- participate in the program.

The annual budget for HI/SCIP, excluding administrative costs for Marshall and an assistant, is $10,000. The universities contribute a total of $167,000 each year. Students must meet the admissions requirements of the college they choose, and they must meet general HI/SCIP guidelines.

In order to qualify, students must haave complete three years each of high school mathematics and English, two or three years of laboratory science, two years of social studies, and also have what Marshall describesd as "good" electives. A course in Latin, for example, would be a plus.

"It takes a very special kind of student to be a part of HI/SCIP," said Marshall, who does the recruiting. "When I talk to the kids, I let them know right away that this isn't a plaything."

Students are recommended for HI/SCIP by their high school counselors. Marshall then schedules a meeting with them and their parents before a final decision is made.

School Superintendent Vincent E. Reed has high praise for HI/SCIP.

Reed calls the program "one of the greatest things we've got going for us in the public school system." He believes HI/SCIP not only gives students a chance to expand their knowledge, but also offers junior high school students an objective.

"And, of course," he adds, "you can't ignore the financial benefits. I don't think that any family with college-age children would turn down a free first year at any of the institutions that participate in the program."

At the college level, school administrators are equally pleased with HI/SCIP. Clarence Lee, associate dean of Howard's College of Liberal Arts, says that HI/SCIP students have done "extremely well."

"We've been very pleased with them. Ninety-five percent of the youngsters have remained at Howard, and of course, we like that. But beyond that, I like the program because it's a breath of fresh air for many young people who would be trapped by the school system, spending that valuable last year taking superficial courses and wasting time."

Samuel Harvey, director of minority affairs at Georgetown, describes the HI/SCIP students as "the cream of the crop. They are highly motvated, studious and achievement oriented, and the program allows them to test themselves out in advance. I have a message for Evelyn (Marshall) -- Send me more. Send me more."

Kim Boyd and Keith Landfair are the first to point out that the D.C. schools contain many more students like themselves. Though they veil their accomplishments in modestly, their parents are openly proud.

In a room lined with trophies and certificates documenting Kim's achievements, her father, Henry Boyd, a teacher at Southeast's Kramer Junior High School, beams as strains of Beethoven fill the air.

"We're not going to push her into anything," he says while Kim plays.

But her mother, Queen, a counselor at Southwest's Randall Junior High School, hastens to add that they expect their daughter to be "the very best at whatever she wants to do.

"Kim is a hard worker," Mrs. Boyd continues. "But any child can achieve if he works hard and has strong family support. Kim is the main focus of our lives."

Across town, Keith Landfair has collected his share of certificates, too, although an insouciant attitude toward such things keeps him from putting them on display.

But like the Boyds, his mother's pride is obvious.

"I suppose we did something right," she says. "It was so important to me. I missed my education because my parents didn't encourage me, and I wanted it to be different for him."

Keith says he would like to obtain a master's degree in physics, find a consulting job which would allow him to travel extensively in this country and Europe, and eventually open his own business.

"I know it sounds like a lot," he says shyly, "but I also know that I can do it. . . One thing about HI/SCIP, it really improves your opinion of yourself."