The Washington Post’s America’s Most Challenging High Schools list is designed to recognize schools that challenge average students. These top-performing schools, listed in alphabetical order, were excluded from the list because, despite their exceptional quality, their admission rules and standardized test scores indicate they have few or no average students. Non-neighborhood schools with SAT or ACT averages above the highest averages for neighborhood schools nationally are placed on this list. Our sampling of private schools is exempt from this rule so that readers can see how they compare to schools on the main list.

BASIS Scottsdale (Scottsdale, Ariz.)

This charter school, founded by Olga Block and Michael Block, has been in the top 10 of our main list. As has happened with a few other charters, it has become so popular with the parents of high-achieving students that its average SAT and ACT scores now exceed our limit, and it must be moved to this list. The BASIS method sets very high standards and is spreading to other cities.

Bergen County Academies (Hackensack, N.J.)

The seven, career-focused academies have an extended school day.

Biotechnology High School (Freehold, N.J.)

The demanding program started in 2005, with two large research rooms and four state-of-the-art science labs; most of the senior class earns International Baccalaureate diplomas.

Bronx High School of Science (New York)

One of the most famous schools in America, it has a richly talented, ethnically diverse student body.

Davidson Academy of Nevada (Reno, Nev.)

The tiny school opened in 2006 on the campus of the University of Nevada at Reno as a “university school for profoundly gifted students” under a state law.

Early College at Guilford (Greensboro, N.C.)

At the state’s first early college high school, 11th- and 12th-graders take courses at Guilford College and graduate with a high school diploma and up to two years of college credit.

Gatton Academy of Mathematics and Science (Bowling Green, Ky.)

Juniors and seniors from across the state are selected by scores, grades and essays to live in a residence hall at Western Kentucky University, earning college credit as well as completing high school.

High Technology High School (Lincroft, N.J.)

The school, which opened in 1991, uses the increasingly popular High Tech High name for magnets emphasizing hands-on learning. It is run by Monmouth County and Brookdale Community College.

Hunter College High School (New York)

One of the city’s legendary public high schools, it has a program for seventh- through 12th-graders administered by Hunter College. It was an all-girls school until 1972.

Illinois Mathematics and Science Academy (Aurora, Ill.)

“Wayne’s World,” the Mike Myers “Saturday Night Live” sketch and film, is not Aurora’s only claim to fame. IMSA is a state-funded boarding school. It takes 10th- through 12th-graders and has a strong mentoring program.

International Academy (Bloomfield Hills, Mich.)

The magnet school for 20 Oakland County school districts has three campuses. All students take the International Baccalaureate diploma program.

International Community School (Kirkland, Wash.)

Students are selected through a lottery to attend this school focusing on international awareness. It is one of the few elite public schools without a selective admissions system. Instead, as happens sometimes, the lottery participants self-select into an academic powerhouse.

Louisiana School for Math, Science and the Arts (Natchitoches, La.)

Sophomores, juniors and seniors who survive the tough admissions process live at the boarding school, which was established by the state legislature in 1982.

Maggie L. Walker Governor’s School for Government and International Studies (Richmond)

Unlike the math-science orientation of most of the public elites, the focus of this school is on world cultures and building students’ leadership skills.

North Carolina School of Science and Mathematics (Durham, N.C.)

This school, established in 1980 in an abandoned hospital, started the small but interesting trend of state-created boarding schools drawing bright and ambitious high schoolers from across the state.

Northside College Prep (Chicago)

Opened in 1999, the selective magnet school was the first new high school in Chicago in 20 years. It has 1,100 students whose academic classes are at the honors and AP levels only.

Oklahoma School of Science and Mathematics (Oklahoma City)

The state-funded boarding school teaches all courses at the university level.

South Carolina Governor’s School for Science and Mathematics (Hartsville, S.C.)

Another state boarding school, this one is for 11th- and 12th-graders from across the state.

Stuyvesant High School (New York)

It has been teaching the city’s most academically ambitious students for several generations. It offers about 55 AP courses every semester and has many courses above that level.

Thomas Jefferson High School for Science and Technology (Fairfax County)

It is the most selective public high school in the United States and draws mostly from the affluent households of Northern Virginia.

Union County Magnet High School (Scotch Plains, N.J.)

This selective-admission school focuses on science, math and technology.

University Laboratory High School (Urbana, Ill.)

Admission to this day school on the University of Illinois campus is competitive. The school makes good use of its higher-education environment.

Whitney High School (Cerritos, Calif.)

Like Jefferson, this suburban version of the New York City super-schools has a highly competitive admissions system. Unlike students at the state boarding schools, those at Whitney go home at nights.

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