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2008 AMC 8 Problems - AoPSWiki
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美国数学竞赛 AMC8 真题
Art of Problem Solving
2008 AMC 8 Problems
Contents
From AoPSWiki
1 Problem 12 Problem 23 Problem 34 Problem 45 Problem 56 Problem 67 Problem 78 Problem
89 Problem 910 Problem 1011 Problem 1112 Problem 1213 Problem 1314 Problem 1415
Problem 1516 Problem 1617 Problem 1718 Problem 1819 Problem 1920 Problem 2021 Problem
2122 Problem 22
23 Problem
2324 Problem 2425 Problem
2526 See Also
Problem 1
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Susan had 50 dollars to spend at the carnival. She spent 12 dollars on food and twice
as mHow m
any dollars did she have left to spend?
uch on rides.Solution
Problem 2
The ten-letter code
represents the ten digits , in order. What 4-digit number is
represented by the code word
?
Solution
Problem 3
If February is a month that contains Friday the
, what day of the week is February 1?
http://doc.xuehai.net/ba988a6986540aeecba11b29e.htmlSolution
Problem 4
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In the figure, the outer equilateral triangle has area
, the inner equilateral triangle has area , and the
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1/5
three trapezoids are congruent. What is the area of one of the trapezoids?
WikiGo
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Solution
Problem 5
Barney Schwinn notices that the odomsameter on his bicycle reads odome forward and
backward. After riding , a palindrome, because it reads theeter shows another
palindrom
e, . What was his average speed in m
more hours that day and://doc.xuehai.net/ba988a6986540aeecba11b29e.htmlpar
the next, he notices that theiles per hour?
Solution
Problem 6
In the figure, what is the ratio of the area of the gray squares to the area of the
white squares?
Solution
Problem 7
If
, what is
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?
Solution
Problem 8
Candy sales from the Boosters Club from January through April are shown. What were
the average sales permonth in dollars?
Solution
Problem 9
In
Tycoon Tammy invested
dollars for two years. During the the first year her investment suffereda
loss, but
during the second year the remaining investm
ent showed a
gain. Over the two-yearperiod, what was the change in Tammy's investm
ent?
Solution
Problem 10
The average age of the
A is
people in Room
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. The average age of the
people in Room B is . If the
thttp://doc.xuehai.net/ba988a6986540aeecba11b29e.htmlwo groups are combined, what
is the average age of all the people?
Solution
Problem 11
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2/5
Each of the and a cat. Twenty students have a dog and
students in the eighth grade
at Lincoln Middle School has one dog or one cat or both a dog
and a cat?
students have a cat. How many students have both a dog
Solution
Problem 12
A ball is dropped fromfalling and bouncing to
a height of
of the height it reached
in the previous bounce. On which bounce will it not rise to meters. On its first bounce
it rises to a height of
a height of
meters. It keeps
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meters?
Solution
Problem 13
Mr. Harman needs to know the combined weight in pounds of three boxes he wants to
mail. However, the
only
available
scale
is
not
accurate
for
weights
less
than
pohttp://doc.xuehai.net/ba988a6986540aeecba11b29e.htmlunds or m
ore than
pounds. So theboxes are weighed in pairs in every possible way. The results
are
,
and
pounds. What is thecom
bined weight in pounds of the three boxes?
Solution
Problem 14
Three one of each letter. If , three , and three
is placed in the upper left corner, how m are placed in the nine spaces so that each
row and columany arrangem
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ents are possible?
n contain
Solution
Problem 15
In Theresa's first
basketball games, she scored
and
points. In her ninth game, she
scored fewer than in her tenth gam
also an integer. What is the product of the nume, she scored fewer than
points and
her points-per-gam points and her points-per-game average for the nine gamber of
points she scored in the ninth and tenth gam
e average for the es was an integer. Sim games?
es washttp://doc.xuehai.net/ba988a6986540aeecba11b29e.html
ilarlySolution
Problem 16
A shape is created by joining seven unit cubes, as shown. What is the ratio of the
volumthe surface area in square units?
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e in cubic units toSolution
www.artofproblemsolving.com/Wiki/index.php/2008_AMC_8_Problems3/5
Problem 17
Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths
and a perim
eter of
units. All of her students calculate the area of the rectangle they draw.
What is the difference betweenthe largest and smallest possible areas of the
rectangles?
Solution
Problem 18
Two circles that share the sam
path shown, starting at
and ending at e center have radii
. How m
any m
eters and eters does the aardvark run?
meters. An aardvark runs along the
Solution
m
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Problem 19
Eight points are spaced aroundhttp://doc.xuehai.net/ba988a6986540aeecba11b29e.html
at intervals of one unit around a points are chosen at random. What is the probability
that the two points are one unit apart?
square, as shown. Two of the
Solution
Problem 20
The students in Mr. Neatkin's class took a penm
anship test. Two-thirds of the boys and of the girlspassed the test, and an equal
numnumber of students in the class?
ber of boys and girls passed the test. What is the minim
um possibleSolution
Problem 21
Jerry cuts a wedge from
closest to the volume of his wedge in cubic centim a -cm cylinder of bologna as shown
by the dashed curve. Which answer choice iseters?
Solution
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Problem 22
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4/5
For how m
any positive integer values of
are both
and
three-digit whole num
bers?
Solutihttp://doc.xuehai.net/ba988a6986540aeecba11b29e.htmlon
Problem 23
In square square
?
,
and
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. What is the ratio of the area of
to the area of
Solution
Problem 24
Ten tiles numWhat is the probability that the product of the numbered
through
are turned face down. One tile is turned up at random
bers on the tile and the die will be a square?
, and a die is rolled.Solution
Problem 25
Margie's winning art design is shown. The smradius increasing by 2 inches.
Approximately what percent of the design is black?
allest circle has radius 2 inches, with each successive circle's
Solution
See Also
2008 AMC 8 (Problems ? Resources)
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Preceded byFollowed by2007 AMC 82009 AMC 8
1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 ? 8 ? 9 ? 10 ? 11 ? 12 ? 13 ? 14 ? 15 ? 16 ? 17 ? 18 ? 19 ?
20
? 21 ? 22 ? 23 ? 24 ? 25
http://doc.xuehai.net/ba988a6986540aeecba11b29e.htmlAMC 8
AMC 8 Problems and SolutionsMathematics competition resources
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