Eighth Grade Test - Excellence in Mathematics Contest - 2000
1.
A basketball team has won seven of its first fifteen games. How many wins in their next ten games will
raise their winning percentage for the season to 60%?
A.
2.

A.
2
B.
5
2

12
3

13
12
3.
6
C.
7
C.

D.
8
E.
D.
1
4
E.
9
equals
B.

7
12
1
3
A
1
3
B
The length of line segment AB is approximately
A.
4.
If 2
A.
7.
25 mm
C.
3 cm
0.8
B.
0.78
C.
13
17
D.
$0.14
B.
$0.35
C.
$0.41
8 cm
E.
0.5 m
0.93
E.
0.62
650 miles
B.
660 miles
C.
670 miles
Make a correct addition problem by replacing
each of the variables: A, B, and C with a digit.
A.
D.
$0.48
E.
$0.51
1
3
inches on a map represents 300 miles, what distance does 5
inches represent?
2
4
7
B.
8
C.
D.
680 miles
E.
690 miles
E.
11
43A2
35B
+ C627
-------------------8293
The sum A+B+C equals
8.
D.
The peel of a banana weighs 1/8 of the total weight of the banana. If you buy 3.5 kg of bananas at one kg
for $1.10, how much are you paying for the peels?
(Round to the nearest cent.)
A.
6.
B.
If these five numbers were placed in a list from smallest to largest, the middle number would be
A.
5.
6 mm
9
D.
10
A $20 dollar bill is 15 cm long. If five million dollars worth of $20 bills were laid end-to-end, their
length would be
A.
3.75 km
B.
37.5 km
C.
75 km D.
1
750 km
E.
None of these
Eighth Grade Test - Excellence in Mathematics Contest - 2000
9.
A
B
-4 -3
-2 -1
0
1
2
A and B represent points on this number line.
A.
10.
2
3
B.
-1
C.
4
D.
1
C.
-3
D.
-1
2
3
E.
3
E.
33
5
6
If x = -3 , -5x - 2x2 equals
A.
11.
4
3
4
B - A equals
-33
B.
-31
A painter has finished painting 2/3 of a room by 2:00 PM and 3/4 of the same room by 2:30 PM. At this
rate, when does he finish painting the room?
A.
3:30 PM
B.
4:00 PM
C.
4:30 PM
D.
5:00 PM
E.
5:30 PM
12.
Shannon and Suzanne average 68 miles per hour on a 390 mile automobile drive.
If they start at 8:40 AM, when do they complete their drive?
(Round to the nearest minute.)
A.
2:14 PM
B. 2:24 PM
C. 2:40 PM
D. 2:41 PM
E. 3:14 PM
13.
If it takes Jeremy 18 hours to dig a 2 meter by 2 meter by 2 meter hole, how many hours would it take
three men (each working at the same rate as Jeremy) to dig a 4 meter by 4 meter by 4 meter hole?
A.
14.
3.75
9 - 9 x 9 + 92
A.
16.
B.
If Kelly walks
A.
15.
12
-66
18
C.
24
D.
36
E.
48
3
of a mile in 12 minutes, what is her walking speed in miles per hour?
4
2
2
B.
4
C.
5
D.
E.
3
6
3
3

9
equals
B.
-45
C.
-18
D.
288
B.
306
D.
320
E.
336
E.
27
24 cm
(The figure is not drawn to scale.)
The area, in square centimeters,
of the shaded region is
A.
3
5 cm
C. 314
18 cm
10 cm
6 cm
2
9 cm
Eighth Grade Test - Excellence in Mathematics Contest - 2000
17.
18.
Frank bought a dog one day for $2.50 and spent one hour per day for nine days trying to sell it. Food for
the dog cost him 25 cents, and he spent a total of four hours in cleaning and caring for the dog. He sold
the dog for $3.75. How much did he profit per hour for the time spent on the whole transaction?
(Round to the nearest cent.) (Thorndike Arithmetics - Book Three, Edward Lee Thorndike, 1917, P. 51)
A.
8 cents/hour
B.
10 cents/hour
D.
14 cents/hour
E.
29 cents/hour
23.
3
16
C.
15
16
D.
1
8
E.
7
8
-5
-1/2
One
B.
1/2
Two
0.8
C.
Three
E.
Five
5
D.
Four
r
2
B.
2r
C.
r
D.
r 2
E.
r 2
4
A number x is doubled, the result is increased by 6, then that result is halved.
The final answer is 36.
A number y is divided by 3, the result is decreased by 6, then that result is tripled.
The final answer is 36.
The sum x + y equals
A.
22.
B.
AB is the diameter of a circle of radius r with center C. Triangle DAB is an isosceles triangle with DA =
DB. The area of the circle equals the area of the triangle DAB. DC equals
A.
21.
9
64
For HOW MANY of these five values for x is x3 < x ?
A.
20.
11 cents/hour
A city park is rectangular with a length of 3/4 mile and a width of 330 yards. The area of the park is
what fraction of one square mile?
(1 mile = 1760 yards)
A.
19.
C.
52
B.
57
C.
66
D.
82
E.
87
E.
35
Martha owns a large square garden. A contractor builds
a fence around the garden and builds two divider fences
parallel to the ends, as shown.
If the contractor uses 480 meters of fence, what is the
area enclosed (in square meters)?
A.
6,400
B.
14,400
D.
40,000
E.
57,600
2000
A.
C.
25,600
is the sum of 40 consecutive odd integers. The smallest of these is
9
B.
11
C.
27
D.
3
29
Eighth Grade Test - Excellence in Mathematics Contest - 2000
24.
A package of 20 plastic forks costs $0.39 . A package of 24 plastic knives costs $0.45 .
If you wish to purchase the same number of forks and knives,
what is the least amount that you could spend?
A.
25.
B.
$4.20
C.
$4.59
D.
$5.34
E.
$9.18
You have eight United States coins worth exactly $0.92 .
(Consider only the current coins: penny, nickel, dime, quarter, and half-dollar.)
HOW MANY different combinations of coins are possible?
A.
26.
$3.36
One
B.
Two
C.
Three
D.
Four
E.
More than four
The three circles are tangent to the rectangle and to each other.
The length of the rectangle is 24 cm.
The area, in square centimeters, of the shaded region is
(Round to the nearest tenth.)
A.
41.2
B.
56.6
C.
D.
116.6
E.
Cannot be determined
24 cm
84.6
Problems #27 and #28 each use the following information.
The new American Mathematics Competition consists of 25 questions.
The scoring rules are:
Each correct answer:
+6
Each wrong answer:
0
Each answer left blank: +2
27.
The score of a student who answers 16 questions with 12 correct and 4 wrong answers is
A.
28.
74
B.
80
C.
84
D.
90
E.
Five
E.
96
A student has N correct answers and receives a score of 102.
The number of possible values of N is
A.
One
B.
Three
C.
Four
D.
More than five
**********************************************
29.
D
MATH is a rectangle. DH = HT.
The area of triangle DHT is 8 .
The area of triangle AHT is 3 .
The area of triangle MAD is
M
A.
4.5
B.
5
D.
6.5
E.
11
C.
A
5.5
4
H
T
Eighth Grade Test - Excellence in Mathematics Contest - 2000
30.
-10,
-7,
-4,
0,
2,
5
From these five numbers select three different numbers for x, y, and z in order to make this expression,
x(y - z), as large as possible
What is the largest possible value of x(y - z)?
A.
31.
B.
85
C.
90
D.
105
E.
120
Example: The "sum of digits" of 1656 is 1+6+5+6 = 18 .
HOW MANY whole numbers from 1 to 2000 have their "sum of digits" equal to 25?
A.
32.
60
10
B.
12
C.
13
D.
15
E.
16
Suzanne's birthday is tomorrow (March 19). Suzanne's father, Rick, has his birthday on April 1 (no
fooling!). On March 18, 1999, Rick was three times as old as Suzanne. Today (March 18, 2000), Rick
is 32 years older than Suzanne. (In this problem, all "ages" are whole numbers.)
What will be the sum of their ages on April 2, 2000?
A.
33.
64 years
B.
65 years
C.
66 years
The radius of circle C is 20 cm.
A 120o sector is removed from circle C.
Segments AC and BC are taped to form
a cone with Vertex C.
34.
120o
B
A.
559
B.
628
D.
838
E.
Cannot be determined
9
D.
12
E.
13
C.
C
20
20
A, B
A
B
D
B.
68 years
656
x + y equals
8
E.
C
The number 9 has been placed into one of the small
triangles. Place the digits 1 through 8, inclusive,
into the other eight small triangles so that the sum of the
four numbers in each of these three triangles:
ADE, BFH, and CGI, is equal to 21.
A.
67 years
A
What is the area of the base of the cone?
(Round to the nearest square centimeter.)
C.
D.
C
x
D
11
F
G
5
y
E
9
G
9
H
I
Eighth Grade Test - Excellence in Mathematics Contest - 2000
35.
ABCD was a square sheet of paper, 6 cm
on a side. As shown, corner D was folded
to point F on the diagonal BD. The area of
triangle EFG equals the area of the shaded
L-shaped polygon: ABCGFE.
A
B
E
F
The length of BF, in centimeters, is
(Round to the nearest tenth.)
36.
A.
1.4 cm
B.
1.6 cm
D.
2.0 cm
E.
2.2 cm
C.
1.8 cm
A
Triangle ABC is an isosceles right triangle with
AB = BC = 2 cm .
Arc BPD is the arc of a circle with center at C.
Arc BQD is the arc of a circle with center at A.
(The diagram is not drawn to scale.)
37.
38.
0.78
B.
1.00
C.
Q
1.14
3 N . What does N equal?
A.
80
B.
C.
119
D.
1.32
E.
1.57
D.
239
E.
359
E.
27
In this multiplication problem, replace each letter
with a digit chosen from 0 through 9, inclusive. M  0 .
Replace identical letters with the same number.
Different letters represent different numbers.
The sum
A.
20
C
B
1
of 9120 equals
3
40
D
P
The area, in square centimeters (rounded to the
nearest hundredth), of the shaded region BPQ is
A.
C
G
D
MEGSL
x 4
------------LSGEM
M+E+G+S+L equals
B.
22
C.
23
D.
6
26
Eighth Grade Test - Excellence in Mathematics Contest - 2000
Problems #39 and #40 each use the following diagram.
1
3
2
39.
7
9
6
4
8
Always following the direction of the arrows, the number of distinct paths from 1 to 9 is
A.
40.
5
32
B.
34
C.
36
D.
38
E.
40
D.
630
E.
640
If the above pattern were continued up to 15,
the number of distinct paths from 1 to 15 would be
A.
600
B.
610
C.
620
7