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%
|