7 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers
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1 Pellissippi State Middle School Mathematics Competition 7 th Grade Exam Scoring Format: points per correct response - each wrong response 0 for blank answers Directions: For each multiple-choice problem there are 5 possible answers listed. You are to work the problems, determine the correct answer, and indicate your choice on the separate answer sheet provided. Please use only CAPITAL letters on the answer sheet (A, B, C, D, E) and print neatly. This will enable us to correctly grade your paper. If there is any question as to what letter an answer is, it will be marked wrong. If you change your mind about your answer, be sure to erase completely. Avoid wild guessing, as wrong answers count against you. Do not make more than one answer for any problem. Make no stray marks of any kind on your answer sheet. Additional room for you to work out problems is on the back of each test page. You may take the test packet with you after you complete it. Only the answer sheet must be turned in. We will discard any test packets left in testing room so please take your packet with you if you want it. When told to do so, open your test packet and begin. There are 50 questions in all. All questions are multiple choice. The working time for the entire test is 65 minutes, so you should work quickly to finish all problems.
2 . 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 B. 6 C. 7 D. 8 E equals A. 2 B. 7 2 C. D. 4 E.. A B The length of line segment AB is approximately A. 6 mm B. 25 mm C. cm D. 8 cm E. 0.5 m 4. If these five numbers were placed in a list from smallest to largest, the middle number would be A. 0.8 B C. 7 D. 0.9 E The peel of a banana weighs /8 of the total weight of the banana. If you buy.5 kg of bananas at one kg for $.0, how much are you paying for the peels? (Round to the nearest cent.) A. $0.4 B. $0.5 C. $0.4 D. $0.48 E. $ If 2 2 inches on a map represents 00 miles, what distance does 5 4 inches represent? A. 650 miles B. 660 miles C. 670 miles D. 680 miles E. 690 miles 7. Make a correct addition problem by replacing 4 A 2 each of the variables: A, B, and C with a digit. 5 B + C The sum A+B+C equals A. 7 B. 8 C. 9 D. 0 E. 8. A $20 dollar bill is 5 cm long. If five million dollars worth of $20 bills were laid end-to-end, their length would be A..75 km B. 7.5 km C. 75 km D. 750 km E. None of these 2
3 9. A B A and B represent points on this number line. B - A equals A. 4 2 B. - C. 4 D. 2 E If x = -, -5x - 2x 2 equals A. - B. - C. - D. - E.. A painter has finished painting 2/ of a room by 2:00 PM and /4 of the same room by 2:0 PM. At this rate, when does he finish painting the room? A. :0 PM B. 4:00 PM C. 4:0 PM D. 5:00 PM E. 5:0 PM 2. Shannon and Suzanne average 68 miles per hour on a 90 mile automobile drive. If they start at 8:40 AM, when do they complete their drive? (Round to the nearest minute.) A. 2:4 PM B. 2:24 PM C. 2:40 PM D. 2:4 PM E. :4 PM. If it takes Jeremy 8 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. 2 B. 8 C. 24 D. 6 E If Kelly walks 4 of a mile in 2 minutes, what is her walking speed in miles per hour? A..75 B. 4 C. 5 D. 2 E x equals A. -66 B. -45 C. -8 D. E (The figure is not drawn to scale.) The area, in square centimeters, of the shaded region is A. 288 B. 06 C. 4 D. 20 E. 6 8 cm 6 cm 24 cm 0 cm 9cm 5 cm
4 7. 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 $.75. How much did he profit per hour for the time spent on the whole transaction? (Round to the nearest cent.) A. 8 cents/hour B. 0 cents/hour C. cents/hour D. 4 cents/hour E. 29 cents/hour 8. A city park is rectangular with a length of /4 mile and a width of 0 yards. The area of the park is what fraction of one square mile? ( mile = 760 yards) A B. 6 C. 5 6 D. 8 E For HOW MANY of these five values for x is x < x? -5 -/2 / A. One B. Two C. Three D. Four E. Five 20. 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 r A. B. 2 r C. r D. r 2 r 2 E A number x is doubled, the result is increased by 6, then that result is halved. The final answer is 6. A number y is divided by, the result is decreased by 6, then that result is tripled. The final answer is 6. The sum x + y equals A. 52 B. 57 C. 66 D. 82 E 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. 4,400 C. 25,600 D. 40,000 E. 57, is the sum of 40 consecutive odd integers. The smallest of these is A. 9 B. C. 27 D. 29 E. 5 4
5 24. A package of 20 plastic forks costs $0.9. 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. $.6 B. $4.20 C. $4.59 D. $5.4 E. $ 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. One B. Two C. Three D. Four E. More than four 26. 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.) 24 cm A. 4.2 B C D. 6.6 E. Cannot be determined 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: The score of a student who answers 6 questions with 2 correct and 4 wrong answers is A. 74 B. 80 C. 84 D. 90 E A student has N correct answers and receives a score of 02. The number of possible values of N is A. One B. Three C. Four D. Five E. More than five ********************************************** D 29. MATH is a rectangle. DH = HT. The area of triangle DHT is 8. The area of triangle AHT is. The area of triangle MAD is A. 4.5 B. 5 C. 5.5 D. 6.5 E. M H T A 5
6 0. -0, -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. 60 B. 85 C. 90 D. 05 E. 20. Example: The "sum of digits" of 656 is = 8. HOW MANY whole numbers from to 2000 have their "sum of digits" equal to 25? A. 0 B. 2 C. D. 5 E Last year Suzanne's father, Rick, was three times as old as Suzanne. Today, Rick is 2 years older than Suzanne. (In this problem, all "ages" are whole numbers.) What will be the sum of their ages next year? A. 64 years B. 65 years C. 66 years D. 67 years E. 68 years. The radius of circle C is 20 cm. A 20 o sector is removed from circle C. Segments AC and BC are taped to form a cone with Vertex C. What is the area of the base of the cone? (Round to the nearest square centimeter.) B 20 o 20 C A C 20 A. 559 B. 628 C. 656 D. 88 E. Cannot be determined A, B 4. 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. E A F B The length of BF, in centimeters, is (Round to the nearest tenth.) A..4 cm B..6 cm C..8 cm D G C D. 2.0 cm E. 2.2 cm 6
7 5. Triangle ABC is an isosceles right triangle with A 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.) The area, in square centimeters (rounded to the nearest hundredth), of the shaded region BPQ is B P Q D C A B..00 C..4 D..2 E of 9 20 equals N. What does N equal? A. 40 B. 80 C. 9 D. 29 E In this multiplication problem, replace each letter MEGSL with a digit chosen from 0 through 9, inclusive. M 0. x 4 Replace identical letters with the same number Different letters represent different numbers. LSGEM The sum M+E+G+S+L equals A. 20 B. 22 C. 2 D. 26 E. 27 Problems #8 and #9 each use the following diagram Always following the direction of the arrows, the number of distinct paths from to 9 is A. 2 B. 4 C. 6 D. 8 E If the above pattern were continued up to 5, the number of distinct paths from to 5 would be A. 600 B. 60 C. 620 D. 60 E
8 40. The prime factorization of 2000 can be written 2000 = 2 x 5 y. The sum x + y equals A. 6 B. 7 C. 8 D. 9 E Suzanne buys bagels for $6.60 per dozen. She spends $6.50 for the bagels and then sells all of them for $2.70. What is her average profit per bagel? A. $0.24 B. $0.0 C. $0.6 D. $0.40 E. $ A circle with radius 6 cm is inscribed in a square. Rounded to the nearest square centimeter, the area of the shaded region is A. B. 55 C. 74 D. 7 E 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. 5 E. None of these 44. For what value of x does: + x + x x + x + 8 = 998? A. B. 5 C. 7 D. 8 E Among the 500 spectators at a basketball game, 0% were not students. Among the students, 0% were sophomores. Among the sophomores, 60% were boys. How many female sophomores were spectators at the game? A. 8 B. 27 C. 42 D. 54 E 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 $0.0 on Day, $0.02 on Day 2, $0.04 on Day, $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. $0.24 C. $,024 D. $5, E. $0, 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. Tuesday C. Wednesday D. Thursday E. Friday 8
9 48. A small hose fills a swimming pool in 6 hours. A large hose fills the same pool in 2 hours. With the pool empty, the owner turns on the smaller hose at 8:00 AM. He turns on the larger hose at 0:00 AM. Both hoses are used from 0:00 AM to :00 PM. Rounded to the nearest percent, how full is the pool at :00 PM? A. 27% B. 48% C. 7% D. 85% E. 02% 49. A clock chimes on the hour once at o'clock, twice at 2 o'clock, three times at o'clock, and so on, up to a maximum of twelve times at 2 o'clock. How many total times does this clock chime between 0:5 AM one day and 6:50 AM the next day? A. 00 B. C. 2 D. 22 E Two standard six-sided dice are rolled. The probability that the sum of the two dice is 9 or larger is A. B. 4 C. 6 D. 9 E
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