Ninth 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 B. $82 C. $124 D. $130 E. $146
2. 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. B. C. D. E.
3. 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. $12,820 B. $15,550 C. $18,760 D. $22,140 E. $24,860
4. “The Scholar’s Arithmetic”, written in 1815 by
Daniel Adams, included this conversion table. 8 gallons make one Firkin of Ale
How many more gallons are in one Puncheon 9 gallons make one Firkin of Beer
of Beer than in one Puncheon of Ale? 2 Firkins make one Kilderkin
2 Kilderkins make one Barrel
A. 0 B. 2 C. 4 D. 6 E. 8 2 Barrels make one Puncheon
5. 3982 = 158404; 39982 = 15984004; 399982 = 1599840004; and 3999982 = 159998400004.
What is the sum of the digits of 3,999,999,9982 ?
A. 75 B. 76 C. 84 D. 85 E. 94
6. Among the 42,500 men playing college baseball, about will eventually play Major League baseball. What is of 42,500?
A. 85 B. 110 C. 142 D. 2125 E. 8500
7. [(x – y) – (y – 2x)] – [(y – x) – (2y – x)] equals
A. 3x – y B. 3x – 3y C. x – y D. x – 3y E. 5x - 5y
8. 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% B. 5.6% C. 5.9% D. 6.2% E. 36.9%
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 B. 70 C. 90 D. 110 E. 130
10. Suppose 800 soldiers were placed in a garrison, and their provisions were computed sufficient for two months. How many soldiers must depart so that the provisions may serve the garrison for 5 months? (The Scholar’s Arithmetic, Daniel Adams, 1815)
A. 300 B. 360 C. 420 D. 480 E. 540
11. For a clock with an hour hand and a minute hand, how fast is the hour hand rotating in degrees per minute?
A. 0.5 B. 1 C. 2 D. 3 E. 6
12. In 1973, the horse Secretariat won the Belmont Stakes in 2 minutes, 24 seconds, by running the 1.5 miles in the fastest time ever. What was his average speed in miles per hour?
A. 22.4 B. 28.6 C. 31.4 D. 37.5 E. 40.2
13. The only two digit number that is both a perfect square and a perfect cube is 64. What is the sum of the digits of the only 3-digit number that is both a perfect square and a perfect cube?
A. 7 B. 12 C. 13 D. 18 E. 23
14. In an arithmetic sequence, the third term is 1227 and the ninth term is 2001.
What is the fifth term of this sequence?
A. 1356 B. 1399 C. 1427 D. 1485 E. 1614
15. Each side of this square is trisected.
What fraction of the square is shaded?
A. B. C. D. E.
16. Example: When 22 is divided by 5, the "whole number remainder" is 2 .
Which of the following five division problems has the SMALLEST whole number remainder?
A. B. C.
D. E.
17. Marge played varsity basketball all four years of high school. Each year she increased her average points per game by 20% over the preceding year. If she scored 18 points per game as a junior, what was the difference in points per game between her senior year average and her freshman year average?
A. 9 B. 9.1 C. 9.6 D. 10.08 E. 10.92
18. If M is a whole number, which one of these five numbers could equal 6M + 1 ?
A. 512 B. 513 C. 514 D. 515 E. 517
19. GIVEN: 0.5 x 2 and -8 y -4
What is the smallest possible value of: ?
A. -17 B. -15 C. -8 D. -7 E. 0
20. ABC is an isosceles triangle with AB = AC.
BD is the bisector of angle ABC.
AE is perpendicular to BD.
If ÐC=40o, what is the measure of ÐEAD?
A. 20o B. 25o C. 30o D. 35o E. 40o
21. If 6 men build a wall 20 feet long, 6 feet high, and 4 feet wide in 16 days, in what time will 24 men build one 200 feet long, 8 feet high, and 6 feet wide? (The Scholar’s Arithmetic, Daniel Adams, 1815.)
A. 32 days B. 48 days C. 60 days D. 80 days E. 96 days
22. In trapezoid ABCD, AB = 88 cm and BC = CD = DA. If the perimeter of the trapezoid is 208 cm, what is the area, in square centimeters, of the trapezoid?
A. 1280 B. 1600 C. 2048 D. 2816 E. 3520
23. The sum of five consecutive odd numbers is 5x + 20. If x represents the smallest of the five numbers, what is the largest of the five numbers?
A. x + 4 B. x + 7 C. x + 8 D. x + 9 E. x + 10
24. Astronomers detect a large planet circling a star 7 x 1013 miles from Earth. If the astronomer on Earth sends a signal that travels at 186,000 miles per second to that planet, how many years will it take the signal to reach the planet? Round to the nearest year.
A. 4 B. 12 C. 26 D. 286 E. 716
25. In quadrilateral ABCD, angle A is 32o larger than angle B; angle C is twice the measure of angle A; and angle D is 22o larger than angle A. What is the sum of the measures of angles B and C?
A. 177.2o B. 180.6o C. 188o D. 190o E. 196.4o
26. A veterinarian buys 40 meters of fence to
build four pens along the back of a kennel building.
The 40 meters of fence are used for the three
exterior fences as well as the three interior
dividers. If the vet lets D = 10 m, what is the
total area in square meters enclosed by the four pens?
A. 60 B. 75 C. 80 D. 100 E. 150
27. 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 D. 1/4 E. 3/8
28. The line: 2x + 5y = 20 is reflected over the x-axis. The equation of the new line is
A. 2x - 5y = 20 B. 2x + 5y = -20 C. 5x - 2y = 20
D. -5x + 2y = 20 E. 5x + 2y = 20
29. 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
30. Marissa tosses her spare pennies, nickels, and dimes into a jar. When she counts her coins, she finds that she has ten more nickels than pennies and three times as many dimes as nickels. If she has p pennies, which expression represents the total value, in dollars, of her collection?
A. 3.50 + 0.36p B. 0.50 + 0.36p C. 2.00 + 0.16p
D. 2.50 + 0.16p E. 1.00 + 0.26p
31.
By inserting exactly one pair of parentheses into this expression, HOW MANY of the following five numbers can be produced?
2 3.75 12 21 36
A. One B. Two C. Three D. Four E. Five
32. To construct a pyramid from a 24 cm by 24 cm square
piece of construction paper, Valerie cuts along the eight
bold segments to form an 8 cm by 8 cm square PQRS as
the base of the pyramid. She then folds points A, B, C,
and D up to meet at the vertex of the pyramid.
What is the height, in cm, of Valerie’s pyramid?
A. B. C.
D. E. 8
Use the same spinner for problems #33 and #34.
33. 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. B. C. D. E.
34. If the fair spinner from Problem #33 is spun three times, what is the probability that the sum of the three numbers is odd?
A. B. C. D. E.
35. When (1020 – 5)2 is calculated, the sum of its digits is:
A. 1 B. 26 C. 115 D. 178 E. 187
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 that month could be:
A. III only B. I or III, only C. II or III, only D. I or II, only E. I, II, or III
37. Triangle ABC is a right isosceles triangle,
with right angle at B.
AB = 2 cm .
M is the midpoint of BC .
C is the midpoint of AD.
What is the area, in square cm, of triangle CDM?
A. 1 B. C. D. E. 2
38. 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 C. Between 1 yard and 1 mile
D. Between 1 mile and 10 miles E. More than 10 miles
39. The sides of the smaller regular hexagon lie on the
diagonals of the larger regular hexagon. What is the
ratio of the area of the larger hexagon to the area of the
smaller hexagon?
A. B. C. D. 2 E. 3
40. A teacher asked Garfield to calculate five 10-digit perfect square numbers. After a lot of arithmetic, Garfield turned in 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. 3150352384
B. 2384271241
C. 4878184372
D. 5184864036
E. 8983248400
- 2 -