Math League News (#5) 3/99

Which Calculators Are NOT Allowed? Our contests do not permit the TI-89 or any calculator with a QWERTY keyboard, such as the TI-92.

Future Contest Dates and our Algebra Contest Our final contest is Apr. 13. This is year 6 of April's Algebra Course I Contest. To participate, write for information.

Rescheduling A Contest & Mailing Results If you have school closings or testing days, our rules allow an alternate contest date. We prefer the previous week so we get results on time. Mail scores by Friday of the official contest week. If scores are late for due cause, attach a brief explanation. Late scores unaccompanied by such an explanation are not normally accepted.

Next Year's Contest Dates will be held on these Tuesdays: Oct. 26, Nov. 30, Jan. 11, Feb. 8, Mar. 7, and Apr. 11. We also sponsor contests for grades 4, 5, 6, 7, 8 and Algebra Course I.

End-of-Year Awards Engraving of awards begins Apr. 26. We give awards to the 2 schools and 2 students with the highest totals in the entire League and to the school with the highest score in each region. Winning schools must postmark their results by Apr. 16. Results postmarked later cannot be used to determine winners. Completion of the cumulative column is optional, but student awards are based only on scores regularly listed in that column. (Student certificates of merit were enclosed with Contest 5.)

General Comments About Contest 5 Linda Sadler said "This was more difficult than the other contests this year." Ted Heavenrich said "A good contest! Certainly more challenging than the last one." Jim Beam was surprised his school "didn't have several perfect papers" since none of the problems seemed especially difficult." Dwight Williams said contest 5 had "a good variety of questions." Joe Holbrook called it "A good competition." Dylan wrote that he had averaged 3 or 4 last year, but was averaging 5's this year. He thought we should make the questions more difficult. Dave Stouffer said "Thanks for another set of well-balanced questions which require a student to have a reasonable command of the fundamentals and the capacity to read a problem for exactly what it says and not what the student wants it to say." Karen Holmes said "we are enjoying the monthly competitions although we did not fare well on contest 5." Suzanne Moll said "This contest was harder, but the students enjoyed it. Most scores were low, and there were not too many 4's." Cathy Heideman said "Thanks for all the great questions! Contest 5 was a real challenge for my students." Sheryl Cabral wrote "This is our first year, and my students and I are very excited about it. The problems are challenging but accessible, and all participants understand the solutions when we go over them." Student Allen Piscitello said he has been taking our contests since 5th grade. As a freshman, he got only 2 or 3 right on each HS contest. As a senior, he has gotten all but 1 of the first 30 correct. Congratulations, Allen! Elizabeth Kannegaard said her students thought the League "has gotten a wee bit too easy this year. We enjoyed our lower scores and beefier questions." Irene Stein said "Thanks for a great year so far." Mary Lynn Mallen said "What an unusual contest. More students got #6 right than #4 or #5. Good problems, though." Jerry Detweiler asked "What happened to the order of difficulty 6, 5, 4, 3, 2, 1?"

Problem 5-1: Comments Brenda Mason said this was the worst her students had done on a #1 question. One advisor said that many of her students thought that, in the ordered pair (a,b), a and b were distinct, She felt "problem #1 was poorly written."

Problem 5-3: Alternate Solutions Travis Bower said "Another way: use a clock as a model. Subtract opposite numbers, then double." For example, there are 2(9-3) = 12 numbers on a clock. There are 2(99-19) = 160 students. Dave Farber doubled the # from 19 to 98, inclusive, to get 2(98-19+1) = 160.

Problem 5-4: Comments And An Appeal (Denied) Dwight Williams, Lorna TenEyck, Leo Polovets, Jerry Detweiler, J. Shaw, and Ken Brien, all noticed what Mary Lynn Mallen noticed: "In #4, most kids treated the problem as if the domain were the natural numbers." Sheryl Cabral said "I believe that teaching our students precision in vocabulary is essential, but I'd rather do it somewhere other than on a contest." Numerous appeals sought credit for an answer of 3/9 or 3/10, based on treating the domain as the natural numbers. The appeal was denied by Prof. Brian Conrad of Harvard University's Math Department. R. Whirl asked "Is the probability [1,3]/(0,10) really 2/10, since the interval 1£x£3 includes both endpoints, while 0<x<10 includes neither?" The answer is "yes." Since a single point has no dimension, it has no length. Its presence or absence has no effect on the length of an interval. This topic is called geometric probability. The number of possible outcomes is infinite, so you can't compute the ratio (favorable #)/(total #) Instead you must use ratios of lengths (or sometimes ratios of areas). Jim Beam and Bruce White independently said it would have been clearer to have used the words positive real number in the question statement. Thanks for a great suggestion!

Problem 5-5: Appeals (Denied) Numerous appeals claimed that, since 10n and log10n are inverses, the correct answer is 1, not 6. Dwayne Cameron, Kim Albertazzi, Elizabeth Kannegaard, Mary Lynn Mallen, Clarence Tabar, Ted Heavenrich, and Suzanne Moll explained the reason: many people mistakenly treated only the outer brackets (not the inner ones) as greatest integer symbols. Tabar was unhappy that some kids could do the problem on a calculator. "Does the best calculator win?" he wondered.

Problem 5-6: Comment Ted Butler & Linda Sadler said the following solution led many students to the right answer using wrong reasoning: Area = 49 = 72, so r = 7 and arclength = 14. David Sutleff & Dave Farber sent the same alternate solution.

Statistics / Contest #5

Problem #, % Correct (top 5 each school)

5-1    82%5-4    33%
5-2    70%5-5    34%
5-3    81%5-6    44%