Ninth Grade Test - Excellence in Mathematics Contest - 2004
1.
To attend Zan’s graduation from Williams College, Rick drove
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
2.
B. 90o
E. 504
D. 120o
A
E. 135o
C. 5
D. 14
E. 15
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?
B. $700 thousand
C. $7 million
D. $70 million
B. 25
C. 39
D. 52
E. None of these
Given sets A = {2, 3, 4, 6}; B = {1, 2, 3} ; C = {3, 4, 5, 6},
place the elements into the correct regions of this Venn diagram.
A. 8
B. 10
R
D. 14
P
E. 19
Q
C
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
8.
C. 13
B
A
What is the SUM of all numbers in the regions labeled P, Q, and R?
7.
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
6.
C. 105o
B. 2
A. $70 thousand
5.
D. 336
Kilroy incorrectly converted 4.35 minutes to 4 minutes and 35 seconds.
By how many seconds was he in error?
A. 0
4.
C. 252
Which of the following is closest to the measure of angle A?
A. 75o
3.
B. 168
B. 3.75
C. 4
D. 4.25
E. 4.5
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
B. $225 billion
C. $2,250 billion
-1-
D. $22.5 million
E. $225 million
9.
Ninth Grade Test - Excellence in Mathematics Contest - 2004
Anna walked along the two sides of a 30 m by 50 m rectangular field. Beth took a shortcut by walking along
the diagonal of the field. Compared to Anna’s route, what percent shorter was Beth’s route? Round to the
nearest percent.
A. 12%
10.
B. 18%
B. 4
E. All of these answers: 3, 4, 5, and 6, are possible.
C. 160
D. 240
B. 8,148
C. 26,460
E. 480
D. 33,075
If x   12 , determine the sum of these three numbers: 80  x ; x2 ; and
B. –132
C. –4
E. 41,344
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
15.
D. 6
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. –156
14.
C. 5
B. 120
A. 1,654
13.
E. 27%
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
12.
D. 24%
The number of intersection points of a circle and a triangle CANNOT be:
A. 3
11.
C. 21%
If A  B 
A. –5
-9,
B. 72
C. 75
D. 76
E. 79
D. 3
E. 5
BA
, what is the value of 4  (20  8) ?
2
B. –1
C. 1
V
16.
When this network of six squares is folded into a cube,
what is the sum of the numbers on all faces which include vertex V?
A. 19
17.
C. 37
D. 41
E. 49
2
4
8
16
32
A set consists of fifteen consecutive odd integers. The median of these fifteen numbers is N.
What is the greatest number in this set?
A. N+7
18.
B. 25
1
Evaluate
A. 2
B. N+13
C. N+14
D. N+15
E. N+16
 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
-2-
E. 0.125
19.
Ninth Grade Test - Excellence in Mathematics Contest - 2004
If ABC is a right triangle and ABD  xo ,
A
what is the measure of angle CAB?
A. x– 90o
B. 90o– x
C. 180o– x
xO
D. x + 90o
20.
How many whole numbers are between
A. 16
21.
B. 17
402  262 and
D
B
C
402  262 ?
C. 42
D. 43
E. 716
The radioactivity of a polluted site decreases by 40% every three years. If the radioactivity was 500 μrem in
1989, what is its level in 2004? Round to the nearest hundredth.
A. 0.24 μrem
22.
E. x
B. 5.12 μrem
C. 23.33 μrem
D. 38.88 μrem
E. 64. 8 μrem
An equilateral triangle and a regular hexagon have equal perimeters.
What is the ratio of the area of the hexagon to the area of the triangle?
A. 1
B.
3
2
C. 2
D.
9
4
E. 3
y
23.
Write the equation of the line shown
in the form: ax + by = c.
40
Given that a, b, and c are integers; that there is no
factor common to a, b, and c; and that c is positive;
what is the sum a+b+c?
20
0
24.
A. 52
B. 58
D. 68
E. 116
C. 62
x
0
4
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
According to these rules, Cup #2 must be placed in which square?
A. 1
25.
B. 3
C. 4
D. 5
8
12
1
2
3
4
5
6
E. 6
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
B. 26.4
C. 28.9
D. 31.2
-3-
E. 33.6
26.
Ninth Grade Test - Excellence in Mathematics Contest - 2004
ABDE is a rectangle and BCD is an equilateral triangle.
C
A robot, Automon, is programmed to move only in the
direction of its arrow and to rotate clockwise only as it makes a turn.
What is the minimum number of degrees that Automon must rotate
to travel from A to E, via B, C, and D?
27.
A. 780o
B. 810o
D. 870o
E. 900o
D
B
C. 840o
Automon
E
A
Fortunately, Big Guy stayed awake long enough for me
to complete this sketch.
How many triangles are in this drawing of Big Guy?
A. 13
28.
B. 14
C. 15
D. 16
E. 18
Rectangle PQRS is divided into square A and rectangles B, C, and D as shown.
The area of rectangle B is twice the area of square A.
The area of rectangle D is three times the area of rectangle B.
If the area of A is x2, what is the perimeter of rectangle PQRS?
A. 7x
B. 12x
C. 13x
D. 14x
Q
P
E. 16x
A
B
C
D
S
R
29.
Two lifeguard stations on a long, straight beach are 4 km apart. Using radar, a boat’s captain determines that
the boat is 7 km from one station and 9 km from the other. To the nearest tenth of a kilometer, how far is the
boat from the beach?
A. 5.0
30.
C. 5.7
D. 6.0
E. 6.7
Point P is the center of a circle with radius 30 cm. Square ABCD has vertices A and B on the circle and point
P on side CD. In square centimeters, what is the area of the square?
A. 720
31.
B. 5.5
B. 840
C. 900
D. 1125
E. 1200
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
B. 451
C. 460
D. 469
-4-
E. 916
Ninth Grade Test - Excellence in Mathematics Contest - 2004
32.
Line segment AB is one side of an n-sided regular polygon inscribed in circle C.
C
If angle B is six times as large as angle C, how many sides does the polygon have?
A. 8
B. 12
C. 20
D. 24
E. 26
A
33.
S2
As indicated, ABC and ADC are right angles.
B
D
A
If AC = 14 cm, what is the sum of the areas of the
four squares S1, S2, S3, and S4 ?
34.
A. 380
B. 392
D. 416
E. 424
S3
14
C. 400
C
S1
B
S4
Four villages, A, B, C, and D lie at the corners of a square with AB = 20 miles. To connect the four villages
by roads, an engineer suggests the design in Figure 1. Dr. Edwards, a mathematician, states that the Steiner
design in Figure 2 will require the least total length of roads. In Figure 2, AE = EB = DF = FC and the
measure of angles AEB and DFC is 120o. To the nearest tenth of a mile, how much shorter is the total length
of roads in Dr. Edwards’ design than in the engineer’s design?
A
A
B
B
E
F
D
D
C
Figure 1
A. 0.5
35.
C
Figure 2
B. 0.7
C. 1.1
D. 1.6
E. 1.9
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
Ninth Grade Test - Excellence in Mathematics Contest - 2004
36.
Let L(n) be the least common multiple of all natural numbers from 1 to n. For example, L(4) = 12 because 12
is the least common multiple of 1,2, 3, and 4. Calculate:
37.
A. 9,676,800
B. 14,515,200
D. 58,060,800
E. 87,091,200
C. 29,030,400
Let L(n) be the least common multiple of all natural numbers from 1 to n. If x is the least value of n such
that L(x) = L(x+1) = L(x+2), what is the value of L(x)?
A. 2,520
38.
17!
L(17)
B. 27,720
C. 55,440
D. 360,360
E. 720,720
A
The six faces of the triangular dipyramid, shown, are equilateral triangles.
The triangle BCD divides the shape into two congruent tetrahedra.
The network of six equilateral triangles, below, can be folded
into a triangular dipyramid. Of the following five choices
of sets of three vertices, which would form the triangle
that divides the shape into two congruent tetrahedra?
D
C
B
F
E
A.
F, G, L
B.
H, I, M
C.
G, H, I
D.
H, K, L
E.
F, I, K
H
G
L
K
39.
J
M
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
40.
I
B. 69
C. 70
D. 71
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. 72