A student writes notes in the Advanced Placement Physics class at Woodrow Wilson High School in Washington, in this file photo from February 2014. (Charles Dharapak/AP)

1. How does the America’s Most Challenging High Schools list work?

We take the total number of Advanced Placement, International Baccalaureate and Cambridge tests given at a school each year and divide by the number of seniors who graduated in May or June. I call this formula the Challenge Index. With a few exceptions, public schools that achieved a ratio of at least 1.00, meaning they had as many tests in 2016 as they had graduates, were put on the national list. We rank the schools in order of that ratio, with the highest, 26.25, this year achieved by BASIS Phoenix, part of a charter school network that has ranked high on this list for years.

I think 1.00 is a modest standard. A school can reach that level if only half of its students take one AP, IB or Cambridge test in their junior year and one in their senior year. But this year, just 12 percent of the approximately 22,000 U.S. public high schools managed to reach that standard and earn placement on our list. The top 220 schools are in the top 1 percent nationally, the top 440 in the top 2 percent, and so on.

America’s Most Challenging High Schools 2017

2. Why do you count only the number of tests given, and not how well the students do on the tests?

Some schools brag about their high passing rates on AP or IB, meaning the percentage of test-takers who scored 3, 4 or 5 on the 5-point AP exam or 4, 5, 6 or 7 on the 7-point IB exam. Passing scores make students eligible for credit at many colleges and universities.

I decided not to count passing rates in this way because I found that many high schools kept those rates artificially high by allowing only top students to take the courses. AP, IB and Cambridge are important because they give average students a chance to experience the trauma of heavy college reading lists and long, analytical college examinations. Research has found that even low-performing students who got a 2 on an AP test did significantly better in college than similar students who did not take AP.

We also give readers a sense of how well each school’s students are doing on the tests by posting the Equity and Excellence rate, which is the percentage of all graduating seniors, including those who never took an AP course, who had at least one score of 3 or above on at least one AP test sometime in high school. The nonprofit College Board, which oversees the AP program, invented this metric. It found that the average Equity and Excellence rate in 2016 was 21.9 percent.

3. Why don’t I see famous public high schools such as Stuyvesant in New York City or Thomas Jefferson in Fairfax County on the list?

We do not include any magnet or charter high school that draws such a high concentration of top students that its average SAT or ACT score exceeds the highest average for any normal-enrollment school in the country. This year, that meant such schools had to have an average SAT score below 1362 or an average ACT score below 29.0 to be included on the main list.

The Challenge Index is designed to identify schools that have done the best job in persuading average students to take college-level courses and tests. It does not work with schools that have no, or almost no, average students. We put those schools on our Public Elites list.

4. If I think my school qualifies for the list but I don’t see it there, what should I do?

Email Jay Mathews at jay.mathews@washpost.com. If we find that the school qualifies, we will add it to the list.