MAT!
-ICOUNTS
1996--97
I National Competition H
Target Round
Problems 1 and 2
Name
School
State
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO
This round of the competition consists o‘f, eight problems.
They presented to you in pairs. Work on one pair of
will be
the problems will be completed and answers will be collected
‘
before the next pair is distributed. The time limit for each
set of two problems is six minutes. The first pair of problems
is on the other side of this sheet. When told to do so, turn
the page over and read silently as the problems are read
aloudr l?encfls are to be drwvn.vvhfle the protflerns are being
read. When instructed to begin, pick up your pencil and
begin Working. Record your final answer in the designated
space on the problem sheet. All answers must be complete,
legible, and simplified to lowest terms. This round assumes
the use of calculators, and calculations may also be done on
scratch paper, but no other aids are allowed. If you complete
the problems before time is called, use the time remaining
t on .
_
Total Correct S<:orer’s Initials
l\/IATHCOUNTS is acooperative project of the National Society of Professional Engineers, the CNA lnsurance
Companies, The Dow Chemical Company Foundation, the General Motors Foundation, Texas lnstruments
Foundation, the National Council of Teachers of Mathematics, and the National Aeronautics
Incorporated, 3l\/I
i
'
and Space Administration.
-_.___,__.__,.___________,l
1. How many square units are in the area of the region 1.
determined by the system of inequalities? Express your
answer as a decimal.
$ y 3 4
—-
3: 2 -~1
m 3 3
y 2 --4
y 3 5
2. A thin rectangular piece of tin is 12 inches long and 8 inches ‘[0
wide. A thin square piece of metal with side length 1.5 inches
is cut from each corner, and the tin is folded to form an open
rectangular box. How many cubic inches are in the volume
of the box? Express your answer as a decimal to the nearest
tenth.
‘xi
MATE-ICOUNTS
1996-87
National Competition I
~
:.%&»“I<€«'$>§5x~ Target Round
Problems 3 and 4
’
Name __
School
State
.
A
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO
“\ '.I7()‘ta1 Correct S<:ore:"s h1itia.}s
MATHCOUNTS is <:oopera.tive project of the National Society of Profe?ssi<>na1 Engineers, the CNA Insurance
ex
Companies, The Dow Chemical Company Foundation, the General Motors Foundatioxu, Texas Instruments
Incorporated, 3M Foundation, the National Council of Teachers of Math<-amaticts, etxnd the National Aeronautics
and Space Administration.
,,.
3. A hollow piece of cylindrical pipe has an outside radius of 3.
1.7 inches and an inside radius of 1.5 inches. T he pipe is
3 feet long. How many square inches are in the total surface
area of the pipe? Express your answer as a decimal to the
nearest tenth.
4. The 25 students in a history class took a test and had an 4.
overall of 82 percent. Given that the mean score
mean score
of the 12 boys in the class was 75 percent, What was the
mean score of the girls in the class? Express your answer
rounded to the nearest tenth of a percent.
W
‘.g¥a»—-¢u'fi,><ze"no MATI-ICOUNTS
.,‘-”W_b4» National
1996-97
Competition I
._yw
Target Round
:“_q.,- Problems 5 and 6
,.4A<_
..
Flange
School
State
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO
Total Correct Sco:‘o;”'s Initials
MATHCOUNTS is a (:o<.>p:;mLive project; of the l\T€’Ll:vl‘.)lJ.<.Ll f3«;>ciety of‘Proi.\;_-..:alo1‘1exl l§l;lOL..l tllc: CNA In.~3ur;;mce
Companies, The Dow Chemical Company Foundation, the General Motors FoL1r1cla.tion, Texas Instruments
Incorporated, 3M Founclation, the National Council of Teachers of Mathenmtics, and the National Aeronautics
and Space Adrrxirxistration.
5. An integer between 0 and 5000 inclusive is selected at random 5.
and is found to be a perfect cube. What is the probability
that it is also a perfect fourth power? Express your answer
as a common fraction.
6. Pedro stood at the center of a circular field that had a radius 6.
of 120 feet. He walked due north halfway to the circle. He
then turned and walked due east halfway to the circle. He
turned again and walked due south halfway to the circle.
Finally, he turned and walked due west halfway to the circle.
When he stopped, how many feet was Pedro from the center
of thecircle‘? Express your answer to the nearest; foot.
w‘_,. u“’—~
_.%,g—
.
MATHCOUNTS
1996-97
I National Competition I
Target Round
Problems 7 and 8
N ame
School
State
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO
Total Correct Scorer’s Initiais
MATHCOUNTS is a. <fi(')(,)}‘)6F’1"’r"‘\UV() pro‘jc<:,t of the Nzxtional Society of Profe-zssiorxaol Eng;inee1‘s. f:ho CNA hnsurance
Companies, The Dow Choznical Company Foundation, the General Motors Foundation, Texas I11strumen't.s
Im:c;rp<3ra*;:e::<"i? RM Fosmdafiozz. the National Counci} of Teachers of Mathematicts, and the National A€I‘<3I}£111iiCS
'
and Space AdminisIzrzmion.
4v
I‘fi<hl> :.u«,
7. Of 6000 apples harvested, every tl1ir<.l apple was too small, 1.
every fourth apple was too green, and every tenth apple was
bruised. The remaining apples were perfect. How many
perfect apples were harvested?
8. A circular garden is surrounded by a sidewalk with a uniform 8.
Width of 25 feet. The total area of the sidewalk equals the
total area of the garden. How many feet are in the diameter
of the garden‘? Round your answer to the nearest whole
number.
