Download Grade 8th Test

Eighth Grade Test - Excellence in Mathematics Contest - 2001
1.
Nettie buys 600 roses at $0.40 each. She is able to sell 80% of them at $8.90 per dozen. But at the
end of the day, she sells the rest for $3.00 per dozen. What profit does she make?
A. $60
2.
B. $82
4.
B. 64
1,000,000,000
B.
100,000,000
D.
100,000
E.
10,000
E. 120
C.
10,000,000
1
6
B.
1
8
C.
1
4
D.
1
12
E.
1
3
Each school bus can hold 44 passengers. How many school busses are needed to transport 334
students and 28 adults as passengers?
B. 7.6
C. 8
D. 8.2
E. 9
On a cube, what is the sum of the number of vertices, edges, and faces?
18
B. 20
C.
22
D.
24
E.
26
A contractor agrees to pave a rectangular 80 foot by 140 foot parking lot for $1.25 per square foot
and to fence in all four sides of the parking lot for $18.50 per foot. What is the total cost of this
project?
A.
8.
D. 112
While at Montoni’s Pizza, you eat half of a large pizza. When you arrive home, you eat half of the
remaining pizza and put the rest in the refrigerator. At midnight, you eat one-third of the remainder.
What fraction of the pizza is left?
A.
7.
C. 96
A.
A. 7
6.
E. $180
One million divided by one one-hundredth equals
A.
5.
D. $146
What is the sum of all of the whole number factors of 56?
A. 48
3.
C. $124
$12,820
B.
$15,550
C.
$17,760
D.
$22,140
E.
$24,680
In the sequence: 0, 1, 2, 5, 12, 29, ……; each number equals twice the previous number plus the
number before that. For example, 29 = 2(12) + 5 . If 29 is the 6th number in this sequence, what is
the 12th number in the sequence?
A.
5741
B. 5920
C. 5981
-1-
D.
6032
E.
6152
Eighth Grade Test - Excellence in Mathematics Contest - 2001
9.
The area of the 48 contiguous states can be approximated by a 3000 mile by 1000 mile rectangle.
The population of these 48 states is about 265 million. Using this data, which of the following is
closest to the population density of these 48 states in “people per square mile”?
A. 50
10.
B. 2
A. 85
E. 8
1
% will eventually play Major League
5
1
% of 42,500?
5
B. 110
C. 212.5
D. 2125
E. 8500
B. 15.2o
C. 15.8o
D. 19.8o
E. 21.4o
B. 5.6%
C. 5.9%
D. 6.2%
E. 36.9%
In the arithmetic sequence: 11, 41, 71, … , what is the first non-prime integer?
A. 121
15.
D. 6
8 gallons make one Firkin of Ale
9 gallons make one Firkin of Beer
2 Firkins make one Kilderkin
2 Kilderkins make one Barrel
2 Barrels make one Puncheon
Before conference swim championships, Suzanne’s best time in the 200 yard butterfly race was
2 minutes, 23 seconds. In the conference championships, she won 10th place by swimming the
200 yard butterfly in 2 minutes, 15 seconds. What per cent decrease is that, rounded to the nearest
tenth of a per cent?
A. 3.6%
14.
C. 4
E. 130
The formula for converting between Fahrenheit and Celsius temperatures is: F = 1.8C + 32 .
If the temperature in Montreal increased from 6o Celsius in the morning to 17o Celsius in the
afternoon, what was the increase in temperature in degrees Fahrenheit?
A. 12.4o
13.
D. 110
Among the 42,500 men playing college baseball, about
baseball. What is
12.
C. 90
“The Scholar’s Arithmetic”, written in 1815 by
Daniel Adams, included this conversion table.
How many more gallons are in one Puncheon
of Beer than in one Puncheon of Ale?
A. 0
11.
B. 70
B. 131
C. 151
D. 161
E. 221
All nineteen whole numbers between the prime numbers 887 and 907 are composite numbers. How
many of these nineteen numbers are NOT divisible by 2, 3, or 5?
A. 3
B. 4
C. 5
-2-
D. 6
E. 7
Eighth Grade Test - Excellence in Mathematics Contest - 2001
16.
Calculate the mean A and the median B of this set of fifteen automobile speeds collected by a police
officer: 72; 80; 62; 71; 71; 64; 65; 73; 66; 78; 81; 66; 64; 77; 66 .
What does A – B equal?
A. -2.6
17.
B. -0.6
B. 654
C. 42
D. 43
E. 44
B. $40
C.
$42.50
D. $52.50
E. $60
2
of her money.
5
What is the ratio of her “amount remaining” to her “amount spent”?
2
3
B.
3
2
C.
5
2
D.
3
5
E.
5
3
For a clock with an hour hand and a minute hand, how fast is the hour hand rotating in degrees per
minute?
0.5
B.
1
C.
2
D.
3
E.
6
If M is a whole number, which one of these five numbers could equal 6M + 1 ?
A. 512
23.
E. 788
Charla has spent
A.
22.
D. 756
One share of Zicronite stock was worth $40 in 1995. During the next five consecutive years it
changed by: increased 50%; decreased 50%; increased 50%; decreased 50%; increased 50%.
What was its value in 2000?
A.
21.
C. 728
B. 41
A. $33.75
20.
E. 4.4
0.AB represents a 2-digit decimal number. A and B each can be any digit 0 through 9, possibly the
1
3
same. How many such numbers satisfy:
 0.AB  ?
3
4
A. 40
19.
D. 1.4
The sum of two perfect cubes is 2060. What is their positive difference?
A. 602
18.
C. -4.4
B. 513
C. 514
D. 515
E. 517
Two pitchers of the same size contain pure orange juice. One pitcher is 1/3 full and the other pitcher
is 2/5 full. Each pitcher is then filled with water. The contents of both pitchers are poured into one
large container. What is the fraction of pure orange juice in the large container?
A.
1
8
B.
1
3
C.
-3-
3
8
D.
11
30
E.
11
15
Eighth Grade Test - Excellence in Mathematics Contest - 2001
24.
A rectangular birthday cake measures 12 inches by 24 inches and is 3 inches thick. A thin layer of
frosting is placed on the top and the four sides.
What per cent of the frosting is on the top of the cake? Round to the nearest per cent.
A. 39%
25.
C. 60%
D. 62%
E. 67%
Experts say that the first four moves in a chess game can be played in 197,299 different ways. If it
takes 10 seconds to make four moves, how long would it take to try every possible set of four
moves? Round to the nearest hour.
A. 5 hours
26.
B. 57%
B. 55 hours
C. 505 hours
D. 548 hours
1
and C = 4 or –1, then four different numbers
2
What is the sum of those four numbers?
If B = -2 or
A. 3
B.
3
2
C. 
15
8
D.
E. 5481 hours
B
can be formed.
C
9
8
17
8
E.
A
27.
A rectangular placemat is decorated with
six congruent semi-circles. AB = 20 cm.
What is the total area of the decorated placemat?
B
Round to the nearest square centimeter.
A. 988
28.
B. 1342
C. 1742
D. 1918
One half of a fair circular spinner is divided into six congruent
sectors and these sectors are labeled 1 through 6. The other
half of the spinner is divided into three congruent sectors and
these sectors are labeled 7, 8, and 9. If the spinner is spun once,
what is the probability that the number spun is odd?
A.
1
2
B.
5
9
C.
E. 2685
1
2
7
3
8
4
7
12
9
5
6
D.
29.
2
3
E.
3
4
In a game of darts, 2, 5, 8, or 11 points can be earned with each toss of one dart.
What is the fewest number of darts needed to earn exactly 100 points?
A. 9
B. 10
C. 11
-4-
D. 12
E. More than 12
Eighth Grade Test - Excellence in Mathematics Contest - 2001
30.
Of 80 8th grade students in a school, 55% are girls. Of the girls, 1/4 are left-handers while 1/3 of the
boys are left-handers. If the principal randomly selects one student from the 8 th grade class, what is
the probability that the student is a left-handed boy?
A. 1/3
31.
33.
C. 1/5
The first digit of the decimal expansion of
A. 4
32.
B. 1/4
B. 2
D. 1/6
E. 3/20
1
is “1”. What is the 2001st digit?
7
C. 8
D. 5
E. 7
In a solid cube, 9 cm on a side, a 3 cm by 3 cm square hole is drilled perpendicular
through the center of each face to the opposite face. What is the volume,
in cubic centimeters, of the remaining piece?
A. 486
B. 513
D. 540
E. 594
C. 532
A, B, and C each can be any digit 0 through 9, possibly the same. The seven digit whole
number: 20ABC01 is a perfect square. What is the middle digit, B?
A. 1
B. 3
C. 5
D. 7
E. 9
296 m
34.
35.
What is the area in square meters of this
trapezoid with right angles at points B and C?
(The drawing is not to scale.)
A. 65,120
B. 75,040
D. 79,328
E. 93,536
316 m
220 m
C. 77,642
B
C
A fair tetrahedral die has four faces and four vertices. Each vertex is numbered and each vertex is
equally likely to "land up". You have two such dice.
On die #1, the vertices are labeled: 1, 2, 3, and 4.
On die #2, the vertices are labeled: 2, 3, 4, and 5.
When these two dice are rolled, the probability that the sum of the two "up" vertices is 7 is:
A.
1/16
B. 1/8
C. 3/16
-5-
D. 1/4
E. 3/8
Eighth Grade Test - Excellence in Mathematics Contest - 2001
36.
The date of the second Thursday of a month is a prime number.
Of the following three dates:
I. 23rd
II.
28th
III. 30th
the last Sunday of the month could be:
A. III only
37.
B. I or III, only
D. I or II, only
E. I, II, or III
On a digital clock, during any 12 hour period, for how many minutes does at least one “9” appear?
A. 60
38.
C. II or III, only
B. 96
C. 126
D. 132
E. 180
A
Each end of this rectangular box is a 1 m by 1 m square.
The other four faces are 1 m by 2 m rectangles.
A spider can crawl one meter in one minute.
If the spider walks on the faces and/or edges of the box,
what is the minimum amount of time for the spider to get from
vertex A to vertex B? Round to the nearest hundredth of a minute.
2.8
A. 3
B. 3.16
C. 3.24
D. 3.41
E. 4
B
39.
A one inch thick stack of paper contains 200 sheets of paper. A large, thin piece of this paper is
folded in half (two thicknesses), then folded in half again (four thicknesses), and so on.
If Marge could fold this paper in half 35 times, how thick would be the folded paper?
A. Less than 1 foot
B. Between 1 foot and 1 yard
D. Between 1 mile and 10 miles
40.
C. Between 1 yard and 1 mile
E. More than 10 miles
A teacher asked Garfield to calculate five 10-digit perfect square numbers. After a lot of arithmetic,
Garfield turned a list of the following five numbers (see below), but he made two mistakes. First, he
spilled milk on the paper so that the middle six digits of each number were impossible to read.
Second, he made an error in calculating one of the five numbers and that number is not a perfect
square. Don’t cry over spilled milk, but determine which of these five 10-digit numbers is NOT a
perfect square.
A.
B.
C.
D.
E.
3150352384
2384271241
4878184372
5184864036
8983248400
-6-