The problem was fairly easy for Arthur Nam, a 17-year-old geometry student at Warren High School in Downey.
"A plane 15 centimeters from the center of a sphere cuts the sphere in a circle of radius 8 centimeters. Find the diameter of the sphere."
Thirty-four centimeters, of course.
Nam answered that problem and 28 others correctly--he missed only one--to lead Warren High to victory in the geometry division of the 1989 National Mathematics League competition. More than 430 schools from across the country entered the geometry division, said league director Diane Riley, who released the final results earlier this week.
"Personally, this competition was easy," said Nam, who one day would like to be a researcher or a professor.
But the first-place finish was no mean feat, according to Riley. The contest problems are more advanced than those that would be presented in the average high school geometry course, she said. The league, an organization of math teachers, has run the contest for the last six years to stimulate interest in mathematics. "The schools that participate are the top schools in the country," she said.
The competition consisted of five, 30-minute tests, with six geometry problems per test. It was given by teachers and administrators at participating high schools. School personnel used answer keys to grade the tests, and then reported the scores to the National Mathematics League. The top five scores in each round represent a school's overall score. The league relies on an honor system, counting on school officials to report accurate scores.
Twenty-eight Warren High students had perfect scores on the first test, but so did at least five students from 72 other schools. Warren and South Pasadena High were tied for first place with perfect scores after the second round, according to the league.
The Warren High students had a rougher time with the third test. The top five scorers missed four problems for a combined mark of 26 points out of a possible 30. Nevertheless, Warren High held the lead after three rounds. Vestavia Hills High of Birmingham, Ala., and Grissom High of Huntsville, Ala., were in second and third places.
One of the two problems Jane Kang missed during the competition was on the third test. She is Warren's second-highest scorer.
"They test your thinking. You have to think about everything you learned and gather data," said Kang, a 16-year-old who says she plans to study science in college.
Warren was one of four schools with perfect scores in the fourth round. At that point, Vestavia, last year's geometry division winner, was in second place trailing by four points. Warren sealed the victory when its top five scorers correctly answered all the problems on the fifth test. Runner-up Vestavia also had a perfect score on the last test. Stevenson High of Prairie View, Ill., came in third, with Grissom High and Berkeley Preparatory School of Tampa, Fla., tied for fourth place.
Six students finished with perfect scores, while five, including Nam, missed only one. Riley estimated that more than 10,000 students of different ages participated in the geometry competition. To compete, a student must be enrolled in a geometry class.
Warren will receive a plaque for the victory and the top students will receive ribbons. It was the first time the Downey school participated in the competition, said Dianne Camacho, Downey Unified School District's mentor math teacher.
About 100 Warren High students took one or all of the tests, she said.
No Organized Preparation
Camacho, who teaches honors geometry and other math courses, said she was proud of the students for winning. But perhaps more important, Camacho said, was that the competition enabled her to further sharpen her students' skills.
"After the exam, I put the (missed) question on the board and said 'What would you do?' " Camacho said. "Sometimes they'd say: 'That's easy. Why didn't I think of that?' "
Camacho attributed the school's success to hard work by instructors and students in their math classes. The students had no school-organized preparation outside of class, she said.
Camacho also credited a testing program, in which the district has participated for the past five years. The program, offered through the University of California and the California State University and Colleges system, uses testing to identify students' weaknesses and enable teachers to provide better instruction.
"I think it's helped us a lot," Camacho said.
Nam said he benefited from outside math work with his father, a physicist who would make up problems for his son. He also said he was helped by years of schooling in Korea, where advanced math is taught at an earlier age than it is in the United States.
"By the time you go to high school you're in calculus," Nam said.
Warren's top scorers had something else in common--they said they enjoy math.
"Math is challenging," said Chang Kim, 14, who missed three problems during the competition. She wants to be a doctor.
Warren High also participated in the National Mathematics League's math analysis division, which required students to work 30 problems over five tests. The school finished 14th among 269 schools that entered the division, Riley said. Twenty-five students participated, Camacho said.
In addition to geometry and math analysis, the league stages competitions in sixth-grade math, pre-algebra, algebra 1 and algebra 2.
"I think next year we're going to try to (participate) in all the levels if we can," Camacho said.
The Downey Unified School District has been working to improve its math program in recent years. It began offering advanced placement calculus three years ago. Twenty-two district students took calculus during the 1986-87 school year. Last year, 27 students took calculus, and this year, 32 students are enrolled, Camacho said.