Math League News (#2) 12/98

Future Contests High School Contest dates are Jan. 6, Feb. 3, Mar. 10, and Apr. 7. Our annual Algebra Course I Contest is held in April. A registration form is enclosed. If circumstances (such as vacations, school closings, or special testing days) require it, our rules permit you to give the contest on another date (preferably early)-but scores must still be mailed by Friday of the official contest week. If scores are late for due cause, please attach a brief explanation. We reserve the right to consider as unofficial late scores lacking such an explanation.

Which Calculators Are Allowed? Stephen Zenk pointed out that our rules were inconsistent about calculator usage. We have now made them consistent. Thanks! Let us clarify: A calculator with a QWERTY keyboard, such as the TI-92, is not allowed on our contests.

Rescheduling A Contest and Mailing Results If circumstances (such as school closings, or special testing days) require it, our rules permit you to give the contest on another date; and we request that you schedule the contest for the previous week so we get your results on time. You should mail the scores by Friday of the official contest week. If scores are late for due cause, please attach a brief explanation. Late scores unaccompanied by an explanation of due cause are not normally accepted.

Regional Groupings We sometimes receive requests about regional groupings. Within guidelines, we try, when possible, to honor such requests for the next school year.

Student Cumulative Scores Although completion of the Cumulative Column is optional, we list (and consider official) only cumulative scores reported in this column. A student whose cumulative scores are incorrect (or don't appear regularly in the Cumulative Column) may lose eligibility for recognition by the League.

What Do We Print in the Newsletter? Our policy is to print every solution and comment we receive, space permitting, when we prepare our newsletter. But we prepare the newsletter before we prepare the score report, so slow mail (a big problem in December!) means we don't get to print some comments. Finally, when space is tight, we may mention that "so-and-so sent an alternate solution" even though we don't have room to print it.

General Comments About Contest #2 Cheryl Armstrong said "My students felt this was a challenge." Ted Heavenrich thought the wording was "unfriendly to the weaker students." He said our definition of reversible in 2-1 would have been clearer if we had referred to a pair of positive integers. Peter Gressis said "Great test as usual." Jerry Lamb said "This was a really terrific contest. The last two problems were really good." Ross Arseneau said "This was the first time I used internet scoring. I like it!" Dave Farber said "This was another good contest for teaching students some more math."

Problem 2-3: Comments Dave Farber said that students could have gotten the correct answer by taking a specific case. When k = 1, the numbers are 2, 4, 8, and 16, the median is 6, and median/smallest = 6/2 = 3. Ted Heavenrich said said this was tough to read. How about The median of {2k, 2k+1, 2k+2, 2k+3} is the arithmetic mean of the two middle numbers. If k is a positive integer, what is the result, in simplest form, of dividing this median by the smallest of the four numbers?

Problem 2-4: Rewording Suggestions Several advisors said that this credit card problem was the favorite of most of the students. Advisor Peter Gressis suggested a revised wording for clarification. We like his suggestion:

After my 16-digit credit card number was written below (one digit per box), some digits were erased. If the sum of the digits in any four consecutive boxes was 24, what was the sum of the seven digits between the two 9's shown?


Problem 2-5: Comments and Alt Sol'n By the quadratic formula, Dave Farber got t ³ -1 and (t < 1 or t > 6). Ted Heavenrich thought that most students solved this by trial and error.

Problem 2-6: Comments Ted Heavenrich felt 2-6 "was a very nice problem." One student wrote that she "was very dissatisfied with [#2-6]. You claim that the linear dimensions of an object cubed equal its volume and the linear dimensions squared equal its surface area." Our claim was different. We said that in similar figures, "the areas vary directly as the cubes of the corresponding linear dimensions, and the volumes vary directly as the cubes of these same dimensions." One or both of these concepts is tested every year on the Math SAT I test. Our claim is correct. Advisors Tim Butler and Dave Farber sent in alternate solutions.

Statistics / Contest #2

Problem #, % Correct (top 5 each school)

2-1    91%2-4    94%
2-2    90%2-5    26%
2-3    72%2-6    35%