1.
Eighth Grade Test - Excellence in Mathematics Contest - 2004
The bar graph shows the grades of
8th Graders
students from two Algebra I classes.
A. 70%
B. 75%
8
C. 77.5%
D. 80%
4
E. 82.5%
2.
9th Graders
Number of Students
12
What percent of these students
received an A, B, or C?
0
A
B
To attend Zan’s graduation from Williams College, Rick drove
D
C
Grades
F
1
of the 1260-mile drive on Monday and
3
60% of the remaining distance on Tuesday. To reach Williams College on Wednesday, how many miles
must Rick drive?
A. 84
3.
B. 168
C. 252
D. 336
E. 504
E
ABDE is a rectangle and BCD is an equilateral triangle.
What is the measure of angle CDE?
D
C
A. 75o
4.
B. 105o
6.
B. 2
E. 150o
A
B
C. 5
D. 14
E. 15
What fraction of this square is shaded?
A.
1
3
B.
1
4
D.
5
32
E.
7
32
C.
3
16
If building a road costs $175 per square meter, what is the cost to construct a 40-kilometer stretch of this road
that is 10 meters wide?
A. $70 thousand
7.
D. 135o
Kilroy incorrectly converted 4.35 minutes to 4 minutes and 35 seconds.
By how many seconds was he in error?
A. 0
5.
C. 120o
B. $700 thousand
C. $7 million
D. $70 million
E. $700 million
Write any two-digit whole number. Create a four-digit number by writing one “9” in front of your number
and one “9” behind your number. Add your two-digit and four-digit numbers and divide the sum by 11.
From that answer, subtract your original two-digit number and then divide that result by 21.
What is the final answer?
A. 17
B. 25
C. 39
D. 52
-1-
E. None of these
8.
Eighth Grade Test - Excellence in Mathematics Contest - 2004
In a 10-kilometer race, a runner averaged 3.5 minutes per km for the first 2 kilometers. She crossed the finish
line with a total time of 41 minutes. For the final 8 km, how many minutes per km did she average?
A. 3.5
9.
B. 3.75
D. 4.25
E. 4.5
How many hundreds are there in one trillion?
A. 10 million
10.
C. 4
B. 100 million
C. 1000 million
D. 10 billion
E. 100 billion
What is the product of the 12th and 13th prime numbers?
A. 1147
B. 1443
C. 1517
D. 1591
E. 1763
11.
Create seven equations (three horizontal and four vertical)
by placing any one of the four basic operations:
 +, -, ×, ÷  in each of the ten blank boxes.
If the value of each symbol is:
$1 for +; $2 for - ; $4 for
;
and $8 for  ;
what is the total value of the ten symbols used?
A. $28
12.
B. $36
D. $40
14
-32
=
-40
0.4
5
0.5
=
4
=
=
=
15
9
-16
=
-10
E. $47
B. $225 billion
C. $2,250 billion
D. $22.5 million
The colors of the five rings shown are Blue, Green, Red, Purple, and Yellow,
not necessarily in that order. Given:
 The Blue ring does not intersect the Green Ring
1
 The Purple ring intersects only the Blue Ring
 The Red ring is to the right of the Green Ring
and is on the same horizontal level as the Green Ring
A. 1
B. 2
C. 3
D. 4
E. $225 million
3
5
4
2
Which ring is colored Yellow?
14.
=
The Congressional Budget Office projects that total US debt will increase from 6.2 trillion dollars in 2002 to
8.9 trillion dollars in 2014. What is the projected average annual increase in debt for this 12-year period?
A. $22.5 billion
13.
C. $37
6
E. 5
A positive integer less than or equal to 50 is randomly selected. What is the probability that the number
selected is a multiple of 5 but not a multiple of 3?
A. 10%
B. 14%
C. 16%
D. 18%
-2-
E. 20%
15.
Eighth Grade Test - Excellence in Mathematics Contest - 2004
A square has sides of 20 cm. As shown, two congruent circles are tangent to each other and are tangent to the
square. In square centimeters, what is the area of the shaded region outside the circles? Round to the nearest
tenth.
A. 85.8
16.
B. 242.9
B. 43
E. 55
D. 240
E. 480
C. 26,460
D. 33,075
E. 41,344
An equilateral triangle and a square have equal perimeters.
If the length of one side of the triangle is 14 cm, what is the area of the square?
B. 56 cm2
C. 100.25 cm2
D. 110.25 cm2
If x   12 , determine the sum of these three numbers: 80  x ; x2 ; and
B. –132
C. –4
E. 196 cm2
x
.
0.15
D. 132
E. 156
-8, -3, 0, 7, 10 , select three different numbers for A, B, and C. What is the greatest
possible value of A  B  C ?
From the set
A. 70
22.
C. 160
B. 8,148
A. –156
21.
D. 51
For the next seven years, the St. Louis Cardinals will pay Albert Pujols an average of 14.7 million dollars per
year. Twenty-five $20-bills weigh 0.9 ounces. If Albert were to insist on being paid in $20-bills, how many
pounds would the $14.7 million weigh? Round to the nearest pound.
A. 42 cm2
20.
C. 47
B. 120
A. 1,654
19.
E. 337.2
At Perry’s Produce Packers, each parer pares a pair of pears every 6 minutes.
How many pears do two sets of triplets pare in a pair of hours?
A. 60
18.
D. 321.5
If x2 + y2 = 392 and x and y are positive integers, what is the sum x+y?
A. 39
17.
C. 289.4
-9,
B. 72
C. 75
D. 76
When this network of six squares is folded into a cube,
what is the sum of the numbers on the three faces which include vertex V?
A. 19
B. 25
C. 37
D. 41
E. 49
E. 79
V
1
2
4
8
16
23.
Evaluate
A. 2
 1 3  5  7  9  11 13  15 17 19 
256 

 38  34  30  26  22 18 14 10  6  2 
B. 1
C. 0.5
D. 0.25
-3-
E. 0.125
32
24.
Eighth Grade Test - Excellence in Mathematics Contest - 2004
In the last time trial on the way to victory in the 2003 Tour de France, Lance Armstrong rode 30.4 miles in 54
minutes and 19 seconds. To the nearest tenth, what was his average speed in miles per hour?
A. 24.7
25.
B. 26.4
How many whole numbers are between
A. 16
26.
B. 17
402  262 and
C. 42
E. 33.6
402  262 ?
D. 43
E. 716
B. 0
C. 300
D. 400
E. 500
At 3:00 pm while driving on highway US 2 towards Oakton and Trenary, Karela sees the sign: “Oakton 37
miles; Trenary 57 miles.” At 3:15 pm, Karela sees another sign and notices that Trenary is now twice as
far ahead as Oakton. What was Karela’s average speed between 3:00 pm and 3:15 pm?
A. 60 mph
28.
D. 31.2
The edges of a cube are 10 cm. All of the edges of a cube are reassembled to form a square. In square
centimeters, compute the difference: (Area of square) – (Surface area of cube).
A. –200
27.
C. 28.9
B. 62 mph
C. 64 mph
D. 65 mph
Six cups numbered 1 through 6 must be placed on the six squares
labeled 1 through 6, one per square, according to these rules:



The number on a cup never matches the number in the square
Cup #3 is on a square adjacent to and right of Cup #1
Cup #6 is on a square adjacent to and below Cup #4
E. 68 mph
1
2
3
4
5
6
According to these rules, Cup #2 must be placed in which square?
A. 1
29.
C. 4
D. 5
E. 6
Scott’s seven math test scores are all whole numbers. After his first five tests, the arithmetic mean of his
scores was 74 and the median was 73. The score on his 6th test was higher than any of his previous five
scores and the score on his 7th test was two points higher than his score on the 6th test. After all seven tests,
the arithmetic mean had risen to 76 and the median score was 75.
What is the lowest possible score on any of Scott’s seven tests?
A. 68
30.
B. 3
B. 69
C. 70
D. 71
Fortunately, Big Guy stayed awake long enough for me
to complete this sketch.
How many triangles are in this drawing of Big Guy?
A. 12
B. 14
C. 15
D. 16
E. 18
-4-
E. 72
Eighth Grade Test - Excellence in Mathematics Contest - 2004
31.
S2
As indicated, ABC and ADC are right angles.
A
If AC = 14 cm, what is the sum of the areas of the
four squares S1, S2, S3, and S4 ?
32.
A. 380
B. 392
D. 416
E. 424
S3
14
C. 400
C
S1
B
S4
If you write out the natural numbers one, two, three, four, five, … , and stop when you get to sixty, how
many times have you written the letter “f”?
A. 32
33.
D
B. 33
C. 41
D. 42
In this triangle of six numbers, the value of each number in row two
and in row three equals the positive difference between the two
numbers immediately above it.
For example, C equals B-A or A-B, whichever is positive.
E. 43
A
B
C
Replace the letters A through E with the numbers 1 through 5 (once each)
in a way that follows the above rule.
6
D
E
What does C equal?
A. 1
34.
C. 3
D. 4
E. 5
Tan Ho read eight consecutive pages of a book. If the sum of the eight page numbers is 1124, what is the
product of the page numbers on the first and last of the eight pages?
A. 19,728
35.
B. 2
B. 19,860
C. 19,448
D. 20,010
E. 20,468
Let N = 999,999,…,999,998 where N has fifty 9’s followed by one 8.
What is the sum of the digits of N2 ?
A. 450
36.
B. 451
C. 460
D. 469
E. 916
In a game against the Detroit Red Wings, the St. Louis Blues have an equal chance of scoring 0, 1, or 2 goals.
In that game, the Detroit Red Wings have an equal chance of scoring 0, 1, 2, or 3 goals. What is the
probability that the St. Louis Blues will win the game? (Note: Tie games are allowed in hockey.)
A.
1
6
B.
1
4
C.
1
3
D.
-5-
1
2
E.
5
12
Eighth Grade Test - Excellence in Mathematics Contest - 2004
37.
February 29, 2004 was on a Sunday. What is the next year that February 29 will be on a Sunday?
A. 2016
38.
B. 2020
D. 2028
E. 2032
Note: 7+241+83+569 is a sum of prime numbers that uses each of the digits 1 through 9 exactly once.
What is the least possible sum of primes that uses each digit 1 through 9 exactly once?
A. 207
39.
C. 2024
B. 218
C. 225
D. 228
E. 252
This network of eight equilateral triangles can be folded to form a regular octahedron.
A
B
C
5
D
9
3
E
To construct a Magic Octahedron, replace the letters A, B, C, D, and E with the numbers 2, 4, 6, 7, and 8
(without repetition) so that the sum of the four numbers on the four faces that share each vertex has the same
sum S.
On your Magic Octahedron, what does B+D equal?
A. 6
40.
B. 7
C. 8
D. 9
What is the maximum number of non-overlapping
1x2 rectangles that can be placed on the checkerboard shown?
(Note: the edges of the rectangles lie on the gridlines and
cannot protrude beyond the checkerboard.)
A. 19
B. 20
D. 22
E. 23
C. 21
-6-
E. 10