As Montgomery County digs into the possible causes of widespread failure on high school math final exams, school leaders have released an informal survey that shows a striking gap in the way students study for the biggest test of the semester.

Slightly more than half of the 600 students who took the survey said they studied one hour or less for the final tests. At the same time, 27 percent put in two to four hours of studying, and 11 percent labored for five hours or more preparing for the exams, the survey showed.

The figures are another hint of underlying problems as school leaders in Montgomery County try to get to the bottom of high failure rates on high school final exams, particularly in math.

Data revealed this past spring showed that a majority of the 30,000 students enrolled in seven high school math courses in Montgomery had failed their most recent finals, touching off alarm among parents in the well-regarded school system.

Superintendent Joshua P. Starr created a math work group to investigate reasons for the poor performance. The group, including school and community leaders, is scheduled to make recommendations by early November.

Among information provided to the work group was the survey, which was optional and taken as students completed June exams at Rockville High School, which has been a focal point of the issue. Rockville High educators came up with the survey as a way to better understand the student perspective, according to a Montgomery County schools spokesman.

Complaints about failing grades bubbled up at Rockville High last school year, and in late April, its PTSA president, Dylan Presman, obtained systemwide data on the problem. He shared the figures with other parent leaders, and many called for immediate action.

Several waves of data have been released since then, most recently figures from June, which showed that 71 percent of high school students countywide flunked their geometry final exams and that 68 percent did not pass the exam for Algebra 1.

Parents and educators have offered ideas about why exam grades are so low, suggesting that it could be attributed to a misalignment between the test and what is taught in the classroom, a push to move students ahead in math before they are ready, grading policies and student absences, and a lack of student support.

Many also have suggested that some exam-takers don’t try hard because their course grades are settled by the time exams are given, even though exams can be worth 25 percent of a student’s overall grade. For example, students with C’s for their quarter grades would still get a C even if they fail the final. Students consult an archived online table of grading scenarios as they consider how much to study or whether they should study at all.

The new survey did not ask specifically about that issue, but it asked about the length of time a student studied and about intensity. Nearly 57 percent of students at Rockville High said they had studied “hard” for their math final.

More than 40 percent of students said they had not studied hard — and half of that group attributed it to already knowing they would not do well. Thirty percent of those who had not studied hard said it was because they spent more time studying for another test.

More than 38 percent said the final exam was more difficult than other tests given during the semester.

Rockville parent Lee Tiffany said his son studied for many hours but got results that did not match his classroom performance. To Tiffany, the test must be flawed. He asks: Why not curve the test if so many students are doing so poorly?

“When you have students who study hard, work hard and are getting good grades all through the semester . . . there’s something really wrong,” he said.

Tom Loveless, a Brookings Institution scholar who studies student achievement, pointed out that a majority of students say they both studied hard and studied an hour or less, suggesting that at least some believe it’s possible to achieve a lot in very little time.

He wondered whether all students know what it takes to prepare for a two-hour final exam. The exam review materials posted online suggest studying is important, he said.

“Those review packets are pretty difficult,” Loveless said. “I just wonder how many of these students know what it means to study hard.”

In other findings, two-thirds of students said teachers had prepared them for the exam during prep week. More than 80 percent said their teacher had covered all or most of the curriculum and the material on the exam.

As the school day ended at Rockville High one recent day, several 10th-graders said that they had not studied for exams for long stretches the previous year, but to some extent they said that reflected the mind-set they had in middle school.

Ronald Lagos, 15, recalled that for his geometry final, he studied perhaps 15 minutes but said he felt he had kept up with the subject throughout the course. “I don’t study at the last minute; I study the whole year,” he said.

Ronald passed the exam, he said. One of Ronald’s friends, 14, was not as fortunate, saying that he did not pay full attention in class.

Dwayne Henry, 15, studied longer than his friends for his honors geometry final last year, he said. But then he gave some thought to his study methods. “I don’t think I know the proper way,” he said.

Board of Education member Michael A. Durso said he found the Rockville results interesting, but he questioned how they could be generalized across Montgomery’s 25 high schools. He said he would support a survey of student experiences across the system.