Math League News (#4) 3/00

New Calculator Rule Our contests say that neither a TI-89 nor a TI-92 is permitted. That rule has changed. Since Contest 2, we have allowed any calculator without a QWERTY keyboard.

Future Contests and Rescheduling Contests  Contest dates are Mar. 7 and Apr. 11. Our annual Algebra Course I Contest is in mid-April. If circumstances (such as vacations, school closings or special testing days) require it, we permit you to give the contest on another date. If your scores are late, please attach a brief explanation, or the scores may be considered unofficial.

What Do We Publish?  Wonder why a solution you sent wasn't mentioned? We discuss everything we have at the time we write the newsletter. But the newsletter is the first thing we prepare, so we may use your score report yet not use your solution. We try to be efficient! Sorry to those whose solutions were too "late" to use in our newsletter.

Contest Books Make A Great Resource  Have you bought our books for your math team? Collections of past contests are a great way to work with your team. We've enclosed a flyer so that you may order books from us.

Calculator Issues  Advisor Alaine Gorfinkle wrote "I realize that when you wrote this year's contests, you did it thinking that the TI89 would not be allowed. However, when you allowed the calculator beginning with contest #2, an unfair advantage was given to those who use the TI89 . . . [and] I think that either you should not allow the TI89 (or any equivalent calculator) or try to design questions not trivialized by the technology." We agree! We prepare the contests with technology in mind. We made the rule change after an quick review of the questions. We failed to note the impact of technology on #4-6. (See discussion of #4-6, below.)

General Comments About Contest #4  B Heckler said that contest 4 was "my favorite contest so far." Melinda Michael said "Thanks for a great contest."

Problem 4-1: Comment  Dave Farber said none of his freshman solved #4-1 correctly.

Problem 4-2: Comment  Student Callie Reger pointed out that kg are units of mass, not units of weight.

Problem 4-3: Alt. Solution and an Appeal (Denied)  B. Heckler used the idea that the locus of the vertex of the right angle of all right triangles whose hypotenuse is the segment of the x-axis form (0,0) to (10,0) is the graph of (x-5)2+y2 = 52. Substituting y = 4 and solving, we get x = 2 or x = 8. One advisor wrote "I had several students answer (8,4) instead of 8. They clearly solved the question correctly, but were careless when answering. Can this answer be accepted for credit?" This and similar appeals were denied. The question asked for the value of x, and x is not the ordered pair (8,4), so credit cannot be given for (8,4).

 Problem 4-4: Alternate Solution Advisors Dennis Swirtz and Jim Feenstra both said that, since the length of the interval from -10/3 to 1 is 1 - (-10/3) = 13/3, and the midpoint of that interval is (1 + -10/3)/2 = -7/6, the inequality is |x-(-7/6)| less than or equal to 13/6, which is the same as |6x+7| less than or equal to 13.

Problem 4-5: Appeals (Accepted and Denied)  Appeals that "the squirrel may have moved 62.5 m, but it had run only 17.5 m, much as a person walking on a train does not actually walk the distance the train travels" were denied. Had the squirrel retained its position atop the log, never moving forward, the squirrel would have to have traveled 60 m just to avoid being crushed by the weight of the log. Moving forward requires an even further distance to be traveled by the squirrel. In fact, if the log had been dragged without rolling, then 17.5 m would have been correct. The rolling of the log requires additional running to stay on top. Appeals for "17.5 m relative to the log" or "62.5 m relative to the field" were also denied. These do not answer the question asked. Several appeals claimed that, somehow, the squirrel was really traveling 120 m, twice the apparent distance downhill. These were also denied by our appeals judge, Prof. Brian Conrad, Mathematics Dept., Harvard University. An appeal for Root(602 + 17.52) was accepted, since it is mathematically exactly equivalent to our answer.

Problem 4-6: Comments and Alt Solutions  Ben Wearn said he no longer teaches root sum and product theorems and disliked the question. Students Laura Mendez, J. Sam Alexander, and James Lu found the real x-intercepts and used successive synthetic divisions to get a second degree quotient which could be solved. Student Glenn Willen used the graph to determine a fact about the complex roots (Yes, it can be done.) Ken Welsh, Alaine Gorfinkle, Jerry Detweiler, Dr. Daniel J. Heath, Dennis Gwirtz, William Yager, Catherine Steele, James Derkson, and R. Morewood were disappointed that anyone with a TI85, TI86, or TI89 could just use the polynomial solver.

Statistics / Contest #4

Prob #, % Correct (top 5 each school)

4-1    87%

4-4    35%

4-2    96%

4-5    62%

4-3    91%

4-6    43%