Eighth Grade Test - Excellence in Mathematics Contest - 1999
1.Which one of these five numbers is closest to 4.7 ?
A. 4.5 B. 4.8 C. 4.62 D.4.7264 E. 4.68834
2.The sum of all whole number factors of 48 is
A. 75 B. 105 C. 108 D. 112E.124
3.A high school with 425 students (16% African-American) closes. All of the students join a high school whose student body of 1250 students was 44% African-American. Rounded to the nearest per cent, the per cent of African-American students in the high school after the merger is
A. 30% B. 34% C. 37% D. 49%E.60%
4.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
John's daughter, Mackenzie, has a set of wood carvings of the 26 capital letters of the alphabet. Each solid wooden letter is painted red on one side and blue on the other side. How many of the letters can be turned over (and rotated if necessary) so that the letter looks correct red side up or blue side up?
A. 10 B. 12 C. 13 D. 15 E. 18
5.Which is the SMALLEST of these five numbers?
A.B.C.D.E.
6.In basketball, a player can score 1-point (free throw), 2-points, or 3-points on a shot. The table shows the number of each type of shot that a team attempted in one game and the per cent of each shot made.
1-point shots 2-point shots 3-point shots
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Shots Attempted253516
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Per Cent Made76%40%25%
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How many points did the team score in this game?
A.37B.42C.48D.57E.59
7.In which list are the three numbers arranged from smallest to largest?
A.B.C.
D.E.
8.A taxi driver charges a flat rate of $2.00 plus $0.10 per mile.
If you include a 20% tip, what do you pay for a 16.5 mile trip?
A.$19.80B.$21.80C.$23.76D.$26.16E.$26.88
9.The prime factorization of 2000 can be written 2000 = 2x 5y .
The sum x + y equals
A. 6 B. 7 C. 8 D. 9E.10
10.Suzanne buys bagels for $6.60 per dozen. She spends $16.50 for the bagels and then sells all of them for $23.70 . What is her average profit per bagel?
A. $0.24 B. $0.30 C. $0.36D. $0.40 E. $0.42
11.A circle with radius 16 cm is inscribed in a square.
Rounded to the nearest square centimeter,
the area of the shaded region is
A.3 B. 55 C.74 D. 137 E. 220
12.A 27-year old mother has a 5-year old daughter.
In how many years will the mother be three times as old as her daughter?
A. 4 B. 6 C. 9 D. 15E.None of these
13.For what value of x does: 1 + x + x + 8 + 13 + x3 + x3 + 83 = 1998 ?
A. 3 B. 5 C. 7 D. 8E.9
14.Among the 500 spectators at a basketball game, 30% were not students. Among the students, 30% were sophomores. Among the sophomores, 60% were boys. How many female sophomores were spectators at the game?
A.18 B. 27 C. 42 D. 54 E. 63
15.A manager wants to hire a good problem solver to work at her computer store for just four weeks. When Terry applies, the manager offers him, "I will pay you $0.01 on Day 1, $0.02 on Day 2, $0.04 on Day 3, $0.08 on Day 4, and so on, doubling your pay each day." Terry laughed and walked out. How much would Terry have earned on Day 20 alone?
A. $0.40 B.$10.24 C. $1,024 D. $5,242.88 E. $10,485.76
16.A math teacher buys three sport coats and six ties. He teaches Monday through Friday. Starting on a Monday, he wears a different combination of new sport coat and new tie each day that he teaches. On which day of the week does he wear his last new combination?
A. Monday B. TuesdayC. Wednesday D. Thursday E.Friday
17.A small hose fills a swimming pool in 16 hours. A large hose fills the same pool in 12 hours. With the pool empty, the owner turns on the smaller hose at 8:00 AM. He turns on the larger hose at 10:00 AM. Both hoses are used from 10:00 AM to 3:00 PM. Rounded to the nearest percent, how full is the pool at 3:00 PM?
A. 27%B. 48%C. 73%D. 85% E.102%
18.A clock chimes on the hour once at 1 o'clock, twice at 2 o'clock, three times at 3 o'clock, and so on, up to a maximum of twelve times at 12 o'clock. How many total times does this clock chime between 10:15 AM one day and 6:50 AM the next day?
A.100 B. 111 C. 112 D. 122E. 130
19.Two standard six-sided dice are rolled.
The probability that the sum of the two dice is 9 or larger is
A. B. C. D. E.
20.If the lengths of two sides of a right triangle are 8 cm and 15 cm, the length of the third side can be x cm or y cm. Rounded to the nearest tenth cm, the sum x + y equals
A. 24 B. 25.4 C. 29.7 D. 30E.35.7
21.Randomly select two different numbers from this set: -5 , -2 , 4 , 8 .
The probability that the product of the two selected number is positive is
A. B. C. D. E.
22.In baseball, home plate is a pentagon with AB = BC , DE = 2 AE = 2 CD, B
and with right angles at vertices B, D, and E . DE = 20 cm.
The area, rounded to the nearest square centimeter, of home plate is A C
A. 240 B. 264 C. 284 D. 292 E. 300
E D
23.A train traveling a constant 75 miles per hour departs from St. Louis to New Orleans at 2:00 PM. At 5:30 PM, a plane that flies a constant 350 miles per hour departs from St. Louis to New Orleans. When the plane arrives at New Orleans at 7:00 PM, how far is the train from New Orleans? (Assume that the distance from St. Louis to New Orleans by plane equals the distance by train.)
A.150 miles B. 175 miles C. 262.5 miles D. 375 miles E. 525 miles
24.A Leap Year has 366 days and the year 2000 will be a Leap Year. Rick's 49th birthday on
April 1, 1999, will be on a Thursday. Rick's 50th birthday will be on a
A.Tuesday B. Wednesday C.Friday D. Saturday E. Sunday
25.A circular spinner is divided into six equal sectors.
The spinner arrow, initially pointing straight right,
is spun counter-clockwise through 1999o .B
In which sector does the arrow stop?CA
A.AB.BC.C
DF
D.DE.EE
26.The straight line distance from Fairfield to Pleasantville is 35 miles. The straight line distance from Pleasantville to Happytown is 12 miles. Let D represent the straight line distance from Fairfield to Happytown .
I.D could be 40 miles II. D could be 25 milesIII. D could be 19 miles
Which of these three statements are TRUE?
A. I only B.I and II onlyC. II and III only D. All of them E. None of them
27.x and y are digits in the eight-digit number 59x219y4 which is a perfect square number. The sum x + y equals
A.8 B. 10 C. 11 D. 13 E. 15
28.The Earth takes approximately 365.25 days to orbit the Sun. The Earth's orbit is nearly circular with a radius of 92 million miles. Using these approximations, calculate the speed in feet per second of the Earth as it orbits the sun. Round to the nearest 1000 feet per second.
(1 mile = 5280 feet)
A.15,000B. 48,000C. 97,000D. 536,000E. 5,803,000
29.In the ninth-grade class, each of 130 students attends exactly one of the five English classes. Each class has fewer than 30 students. What is the least possible number of students in any one of these five classes?
A. 10B. 14C. 20D. 23 E. 26
L
30.A farmer intends to use 240 meters of fence to construct
rectangular pens with length L and width W. He plans
to build the boundary fences plus one internal dividing
fence (see the diagram). W
If he lets the width be 40 meters, the total area enclosed
will be A square meters. If he lets the width be 48 meters,
the total area enclosed will be B square meters.
The difference A - B (in square meters) equals
A.96 B. -96 C. 256 D. -256E. 0
31.M and N are Whole Numbers. 75M is a perfect square. 75N is a perfect cube.
The smallest possible value of M + N is
A. 12B.48C.120D.5628E. 5700
32.
The product of these 49 factors is:
A. 1 B. C. D.E.None of these
33.ABC is an equilateral triangle. ACDE is a rectangle. B
Arcs APF and CQF are arcs of circles
with centers E and D, respectively.
A C
If AB = 6 cm, the area, rounded to the nearest
square centimeter, of the entire region isF
E D
A.69B.76C.82
P Q
D.90E.93
Questions #34 and #35 refer to the following horse race.
In a 6-horse race with no ties, Family finished fifth, 14 meters behind Doggie and 20 meters behind Boya. Alpha finished 8 meters ahead of Eppa and 10 meters behind Captain.
34.Which horse finished fourth?
A.AlphaB. Boya C. Captain D. Doggie E. Cannot be determined
35.The distance, in meters, between the first place horse and the second place horse is
A.2 B. 5C.6 D. 12 E. Cannot be determined
36.When 1020 - 1999 is written as a single whole number, the sum of its digits is
A. 144B. 153C. 156D. 162 E. 171
37.A farm consists of a right triangle and the three squares
on the sides of the right triangle. The length of the three
sides of the right triangle are a, b, and c .c b
The farmer decides to keep the triangular piece of land
for himself. He shares the rest of the farm equally, in terms of
area, between his two children. a
What area of land does each child receive?
A . B. C.
D. E.
38.Six posts in a row are 10 meters apart. A painter selects a post as a starting point. She paints that post, walks to an unpainted post and paints it. She walks to another unpainted post and paints it. She continues until all six posts are painted, stopping at the last post she paints. Determine the LEAST EFFICIENT way for her to paint the posts. That is, from the first post she paints to the last post she paints, what is the MAXIMUM distance, in meters, that she could walk?
A.140B.150C.160D.170E.180
Questions #39 and #40 refer to Figures 1, 2, and 3, which depict Stages I, II, and III, respectively, of a figure called "Koch's Snowflake". At each stage, the middle third of each edge is removed and replaced by the 'other' two sides of an equilateral triangle.
In Figure 1, AB = BC = CA .
In Figure 2, AB = BC = CD = DE = BD, and the construction on all other edges is identical.
In Figure 3, AB = BC = CD = DE = BD, and the construction on all other edges is identical.
FIGURE 1 FIGURE 2FIGURE 3
Assume that Stage IV of Koch's Snowflake is constructed by continuing the pattern described above.
39.If the perimeter of the equilateral triangle ABC in Figure 1 equals 3S,
what is the perimeter of the region in Stage IV of Koch's Snowflake?
A. B.C.D.E.
40.If the area of the equilateral triangle ABC in Figure 1 equals A,
what is the area of the region in Stage IV of Koch's Snowflake?
A. B. C. D. E.
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