Eighth Grade Test - Excellence in Mathematics Contest - 2007
1.
The title of this competition is the “The 10th Prime Contest”. What is the 10th prime number?
A. 23
2.
C. 29
D. 31
E. 37
A 2.5 pound fish costs $8.50. At the same unit cost, how much does a 1.5 pound fish cost?
A. $5.10
3.
B. 27
B. $5.20
C. $5.30
D. $5.40
E. $5.50
In feet and inches, the heights of five students are:
49; 411; 47; 54; 47
In inches, what is the positive difference between the mean and the median of these five heights?
A. 0.6
4.
B. 35%
E. 53%
B. 2.4
B. 15
C. 38%
C. 2.8
D. 3
E. 3.2
C. 26
D. 37
E. 87
The sum of three consecutive prime numbers is:
A. Always an even number
C. Always a multiple of 3
E. None of the above
8.
E. 3
Sharon’s age is 11 years more than a perfect cube and 11 years less than a perfect square. What
is the least number of years until her age is a perfect cube?
A. 11
7.
D. 1.4
The weight of a box with 30 identical chocolates is 21 ounces. When 6 chocolates are removed
and eaten, the weight of the box and remaining chocolates is 17.4 ounces. In ounces, what is the
weight of the empty box?
A. 2.2
6.
C. 1
A target consists of four concentric squares of side
lengths 1, 3, 5, and 7. What per cent of the target is shaded?
Round to the nearest percent.
A. 33%
D. 43%
5.
B. 0.8
B. Always an odd number
D. Never a multiple of 3
In 2006, poor Pluto was demoted and is no longer classified as a “planet”. Assume that Pluto and
the Earth are both spheres and that the diameter of Pluto is 2296 km while the diameter of the
Earth is 12756 km. The volume of a sphere of radius R is given by: V 
4
R 3 .
3
Approximately what is the ratio of the volume of Earth to the volume of Pluto?
A. 5.6
9.
B. 31
C. 171
D. 243
E. 1321
Find the largest 3-digit multiple of 9 which does not contain the digit 9.
What is the product of its three digits?
A. 72
B. 75
C. 76
D. 128
E. 256
Eighth Grade Test - Excellence in Mathematics Contest - 2007
10.
If x = –12, evaluate:
A. –12
11.
12.
A. 100o
B. 120o
D. 260o
E. 280o
C. 220o
C
B. –4
C. 7
D. –7
E. –11
B. 103
C. 106
D. 109
E. 1012
B. x2
C. x3
D. x4
E. x5
B. 7/3
C. 7/5
D. 17/3
E. 7
B. 26¢
C. 27¢
D. 28¢
E. 29¢
The Davis’ house had 1200 square feet of living space before they added-on a 20 foot by 15 foot
rectangular room. By what percent had their amount of living space increased?
B. 10%
C. 12.5%
D. 20%
E. 25%
The product of three whole numbers is 48 (two of the numbers used could be the same).
What is the least possible sum of these three numbers?
A. 11
19.
A
With exactly 8 coins, each a penny, a nickel, or a dime, their total value CANNOT be:
A. 2.9%
18.
B

What is the sum of the reciprocals of 3, 3/5, and 0.2?
A. 25¢
17.
E. 12
If x = –0.5, which is the least of these five numbers?
A. 5/2
16.
D. 6
2
Let T=1 trillion, H= 1 thousand, M = 1 million, and B = 1 billion. What is the value of MB2 ?
TH
A. x
15.
C. –4
The first four elements of a sequence are: 7, 11, 4, –7,… Each new element is obtained by
subtracting the 2nd to last element from the last element. For example, the 4th element is –7
because: 4 – 11 = –7. What is the 2007th element of this sequence?
A. 1
14.
B. –6
Angle θ measures the amount of counter-clockwise rotation
in degrees from Ray AB to Ray AC. Select the best estimate of θ.
A. 4
13.
x2
.
24  x
B. 12
C. 13
D. 14
E. 15
The area of right triangle ABC is 130 square centimeters. To the
B
nearest tenth of a centimeter, what is the perimeter of triangle ABC?
A. 48.2
D. 61.3
B. 56.9
E. 66
C. 57.4
C
20 cm
A
Eighth Grade Test - Excellence in Mathematics Contest - 2007
20.
In the time that the minute hand of a clock rotates 300 degrees, how many degrees has the hour
hand rotated?
A. 16
21.
B. 20
D. 25
E. 30
For the given square, what is ratio of the area of the larger circumscribed circle to the area of the
smaller inscribed circle?
B. 4
C.
2
E. Cannot be determined
A. 2
D. 
22.
C. 24
You have an 800 ml container which is 75% full of anti-freeze. You have a second 800 ml
container which is 75% full of a mix that is 50% anti-freeze and 50% water. Assume that each
container is well-mixed at all times. You perform the following two steps.
Step 1: You fill the first container with fluid from the second container.
Step 2: You then fill the second container with fluid from the first container.
After these two steps, what is the percent of anti-freeze in the second container?
A. 50%
23.
 and
B. 62.5%
C. 66 2/3 %
are two distinct operations from the set:
D. 68.75%
E. 75%
, , ,  .
If 9  6  45 , what is the value of 6  3 ?
2
A. 3/16
24.
25.
A. 6
B. 10
D. 14
E. 16
C. 12
D. 15
C. 112
E. 20
1
1
1
1
How many different numbers can be expressed as the sum of exactly three different numbers
from the set {1, 2, 3, 9, 10}?
B. 7
C. 8
D. 9
E. 10
The first four terms of a sequence are: 2, 3, 6, 18, … where each term is the product of the
previous two terms. If the 10th term is written 2 p 3q , what is the sum p+q?
A. 55
27.
B. 6
8
From a solid wooden cube of side length 2, a tetrahedron with slant
lengths 1 (as shown) is cut from EACH of the eight vertices of
the cube. One such tetrahedron is shown in the diagram.
How many faces does the remaining solid have?
A. 6
26.
12
6
B. 68
C. 89
D. 96
E. 144
With 84 m of fence, Matt enclosed a square corral for his horse.
With his 84 m of fence, Nick built a rectangular corral which was twice as long as wide.
What is the ratio of the area of Matt’s corral to the area of Nick’s corral?
A. 1:1
B. 2:1
C. 3:2
D. 7:6
E. 9:8
Eighth Grade Test - Excellence in Mathematics Contest - 2007
28.
A
Two fair spinners are divided into thirds and labeled as shown.
If each spinner is spun once, what is the probability
that Spinner B shows the larger number?
3
1
A. 5/9
B. 2/3
D. 8/9
E. 1
C. 7/9
B
4
2
5
6
A
29.
ABC is an isosceles right triangle and ACD is a quarter-circle.
If CD = 45 cm, what is the area in square centimeters of region ABCD?
Round to the nearest square centimeter.
A. 1083
D. 2217
B. 2603
E. 2435
C. 4193
B
C
30.
0
A
2
B
3
On this number line, what is the sum A+B?
A. 5/12
31.
D. 1/3
E. 7/12
B. 4π
C. π2
D. 2π2
E. 4π2
In 1990, the average age of Tad and his older sister was 6. In 2002, the average age of Tad, his
older sister, and their twin brothers was 13. In what year were the twin brothers born?
A. 1993
33.
C. 2/3
The circumference of a smaller circle equals the radius of a larger circle. What is the ratio of the
area of the larger circle to the area of the smaller circle?
A. 2π
32.
B. 1/2
B. 1994
C. 1998
D. 1999
E. 2000
For an adult weight W in pounds and height H in inches, the Body Mass Index or BMI is given
by the formula: BMI  703*
W
. If Brian is 5 foot 10 inches tall, to reduce his BMI from 28.2
H2
to 24.0, how many pounds must Brian lose? Round to the nearest pound.
A. 21
34.
C. 25
D. 27
E. 29
C. –142
D. 142
E. –20
Convert 12021 from base –3 to base 10.
A. –22
35.
B. 23
B. 22
The latitude of St. Louis is 38o35 North. Suzanne is studying in Uppsala, Sweden, at latitude
59o52 North. Assume that the Earth is a sphere with radius 3960 miles.
How many miles further north of the equator is Uppsala than St. Louis?
A. 1463
B. 1471
C. 2446
D. 2926
E. 2942
D
Eighth Grade Test - Excellence in Mathematics Contest - 2007
36.
The Sonderman’s and the Bozek’s own cottages 2400 feet apart at opposite ends of a lake. At
9:00 AM, Amy and Dan Sonderman begin canoeing to Bozek’s cottage. A while later, Brian
Bozek begins swimming to Sonderman’s cottage. When they meet in the lake, Amy and Dan
have paddled twice as fast as Brian swam and have paddled twice as many minutes.
How far has Brian swum?
A. 480 feet
B. 600 feet
E. Insufficient information is given
37.
C. 800 feet
D. 1200 feet
In this addition problem, each letter represents a different digit
from 0 through 9.
Compute the sum L+I+V.
38.
A. 13
B. 15
D. 17
E. 20
40.
I
L
+
I
V
I
L
L
C. 16
In this 2x4 grid of dots, the dots are 1 cm apart both
horizontally and vertically. Using three dots of the grid
as the vertices of a triangle, how many distinct
non-congruent triangles can be drawn?
A. 5
D. 8
39.
L
B. 6
E. More than 8
1 cm
C. 7
1 cm
In this Magic Square, the sum of the three numbers
in each row and in each column is the same.
What is the value of B–C?
A. 5
B. –5
D. –9
E. Cannot be determined
C. 9
A
B
8
B
13
–3
E
8
C
D
F
Place the numbers: 4, 6, 7, 8, and 9, (without repetition) in the five regions marked A, B, C, D,
and E so that each sum of the numbers in the three regions between each pair of short and long
arrows (namely: A+1+D; A+B+2; 3+E+C; and 5+E+D) equals the same number S.
What is the value of C+D?
A
A. 13
B. 14
D. 16
E. 17
C. 15
1
B
2
D
C
5
E
3