Pellissippi State Middle School Mathematics Competition

Transcription

1 Pellissippi State Middle School Mathematics Competition 8 th Grade Eam Scoring Format: 3 points per correct response - each wrong response 0 for blank answers Directions: For each multiple-choice problem there are possible answers listed. You are to work the problems, determine the correct answer, and indicate our choice on the separate answer sheet provided. Please use onl capital letters on the answer sheet (A, B, C, D, E) and print neatl. This will enable us to correctl grade our paper. If there is an question as to what letter an answer is, it will be marked wrong. If ou change our mind about our answer, be sure to erase completel. Avoid wild guessing, as wrong answers count against ou. Do not mark more than one answer for an problem. Make no stra marks of an kind on our answer sheet. Additional room for ou to work out problems is on the back of each test page. You ma take the test packet with ou after ou complete it. Onl the answer sheet must be turned in. When told to do so, open our test packet and begin. When ou have finished one page, go on to the net. There are 3 questions in all. Questions -30 are multiple choice. The final five questions are short response. Enter the correct number (or short phrase as in #3) answer in the answer blank for those five questions. The working time for the entire test is 6 minutes, so ou should work quickl.

2 . Which number is a rational number? A) 6 B) 9 C) π D) 6 E) 8π 2. What is the solution for in the equation f() = g(), where f() = and g() = 4 7? A) 2 B) 4 C) 24 D) 26 E) Jennifer received the four cards shown below. She was asked to put the cards in order from least to greatest value. Which list shows the correct order of the cards? A) Q, R, S, T B) S, R, Q, T C) R, S, T, Q D) R, T, S, Q E) R, S, Q, T 4. Matthew compared the price of windows at four different stores. Which store sells the windows at the lowest price per window? A) Store V sells for $260. B) Store W sells 0 for $00. C) Store X sells for $67. D) Store Y sells 24 for $720. E) Store Z sells 30 for $, Q R S T. What is the slope of a line that is perpendicular to the line that passes through the points (4, 2) and (0, 36)? A) 4 B) 6 C) 4 D) 4 E) -4

3 f() = Given { g() = What is the solution to f() = g()? A) -40 B) -30 C) 0 D) 30 E) The table below shows the masses of some of the planets in our solar sstem. Mass of Planets Mass Planet (in kilograms) Earth Saturn Venus Neptune Which list of planets is in order from the least mass to the greatest mass? A) Earth, Venus, Saturn, Neptune B) Earth, Venus, Neptune, Saturn C) Venus, Earth, Saturn, Neptune D) Venus, Earth, Neptune, Saturn E) Saturn, Neptune, Venus, Earth 8. The distance from the planet Mars to the sun is about kilometers. Light travels at a rate of 3 0 kilometers per second. How much time, in seconds, does it take for light to travel from the sun to Mars? A) B) C) 89 D) E) John measured a right triangle with a hpotenuse 3 centimeters long and one leg centimeters long. What is the length of the other leg of the triangle in centimeters? A) 6 B) 8 C) 0 D) 2 E) 44

4 0. In the diagram below, three right triangles are shown. The following lengths are given: AC = 3 units and AB = 2 units. Find the length of AD. (You should not assume that the diagram is drawn to scale). B A A) 2 units B) 3 units C) 4 units D) 4. units E) There is not enough information to find that length. D C. If a 8 = b 4 = c 2 where a, b, and c are positive real numbers, then ab c = 4 3 A) B) 4 3 a C) a D) a a 2 E) An of the above could be correct, depending on the value of a. 2. The first digit of a number written in a base other than 0 is and the last digit is and there are several 0 s in between with a 3 in the middle. We know there are at least 4 zeros, mabe more. What is the smallest the number could be in base 0? A) 4,289 B) 4,292 C) 8 D) 80 E) The math club designs a t-shirt as a wa to publicize the club. The local t-shirt store charges a one-time $ set up fee and $0 for each shirt the math club orders. Ta is not charged since the math club is associated with a ta-eempt school. Consider the graph of the math club s amount owed to the t-shirt store in dollars for purchasing n shirts as a function of n. Which of the following is true? A) The slope is constant and is 2. B) The slope is constant and is. C) The slope is constant and is 0. D) The slope is 0. E) The slope is not constant.

5 4. What approimate percentage of the circular region lies outside the square? A) 2% B) 36% C) 4% D) 0% E) %. The following are graphs of five functions = f(). Which graph is the graph of a function that is increasing but at a decreasing rate? A) B) C) D) E)

6 6. If the coordinates in the tables below were graphed, which graph would have a quadratic shape? A) B) C) ¼ 2 /8 3 /6 4 /32 /64 D) E) Find the area of the rhombus below. EG = 22 units and FH = units. A) 220 square units B) 0 square units C) 00 square units D) 0 square units E) square units E F H J G

7 8. The data in the table below has the propert that is directl proportional to When is 2.2, what is the value of? A) B) C) D) E) Which of the following is not equivalent to a b? A) a b ab B) C) D) ( ab) 2 ( ab) E) All of the above are equivalent to a b

8 20. Figure Figure 2 Figure 3 As illustrated above there are tiles in Figure. How man tiles are in figure 00? A) 704 B) 9,406 C) 9,604 D) 0,406 E) 0, Solve: 3 = 2 A) B) 2 C) - D) A, B, and C E) A and C onl 22. The population of Haiti is approimatel The population of Greenland is approimatel 6 0. About how man times as large as the population of Greenland is the population of Haiti? A) 3, 000, 000 times as large B). times as large C) 00 times as large D) times as large E) 2 times as large 23. Which of the following equations has eactl one solution? A) + 3 = - 2 B) = C) + 6 = - 6 D) 7 - = 7 - E) 3 + = - 2

9 24. Ma rows a kaak on a river. An 8 mile trip upstream, against the current, takes four hours. Ma stops, has lunch, and then rows back to his starting point. The return trip, with the current now, takes one hour. If Ma rows at a constant rate, what is the speed of the river current? A) mile per hour B) 2 miles per hour C) 3 miles per hour D) 4 miles per hour E) miles per hour 2. Find the altitude of a triangular face of a right pramid whose base is a square with edge length 8 centimeters and whose height is 2 centimeters. A) 2 centimeters B) 4 3 centimeters C) 4 centimeters D) 4 0 centimeters E) 0 centimeters 26. Let f be the function defined b the graph shown. Find f(2). A) 0 B) C) 2 D) 3 E) 4

10 27. Five cars travel for 4 minutes on straight flat roads without interruption. Information about their speeds and time at each speed follows. Car A travels at km/min for 30 min then travels at.2 km/min for min. Car B travels at mi/min for 20 min then.8 mi/min for 2 min. Car C travels at 0 mi/hr for 2 min then 70 mi/hr for 20 min. Car D travels at 60 km/hr for min then 80 km/hr for 30 min. Car E travels at 60 mi per hour for 4 minutes. Which car has the highest average speed for the entire trip? A) Car A B) Car B C) Car C D) Car D E) Car E 28. As illustrated below: The first triangular number is. The second triangular number is 3. The third triangular number is 6. The fourth triangular number is 0. What is the 00 th triangular number? A),000 B),00 C),00 D) 0,000 E) 0, Mr. Smith asked his students whether the prefer to go to a museum or the zoo for a field trip. He found that 4% of the students prefer to go to a museum, 2% prefer to go to the zoo, and the rest have no preference. What is the ratio of students who have no preference to the students who prefer to go to the museum? A) 2:3 B) :2 C) 4:9 D) 9:6 E) 3:6

11 30. Which is more likel to happen when flipping a fair coin? A) Getting eactl 4 heads in 0 coin tosses B) Getting eactl 40 heads in 00 coin tosses C) Getting eactl 400 heads in,000 coin tosses D) Each is equall likel E) A) and B) are equall likel, and more likel than C). SHORT ANSWER PORTION: Write the answer to the following on the answer blank on the test form. 3. In the English Premier Soccer League, a team earns three points for a win and one point for a tie. Teams pla 38 games per season. Suppose a team finishes the season with 3 points. Let m be the minimum number of games the could possibl have won and let M be the maimum number of games the could possibl have won. What is m + M? 32. If a clock runs 3 minutes fast per da, how fast is the angle of its second hand changing? Your answer should be eact and be stated in degrees per second. 33. An English class requires 4 papers. The grade on each paper counts twice as much as toward the final average as did the previous paper, in order to reward students for progress in their writing skills. The grades for Jill s first 3 papers out of 00 were, in order, 60, 0, and 60. What is the minimum grade she can make on the fourth paper in order to have an 80 average? 34. In how man was can we pick three different numbers from the set {8, 9, 0,, 2, 3, 4} such that the sum of the three numbers is divisible b 3? 3. In a game of tug-of-war, 3 bos pull with the same force as 4 girls. One adult pulls with the same force of 2 bos and girl. Team A is made up of one adult and 3 girls. Team B is made up of 4 bos. These teams are uneven. Which tpe of person needs to be added to which team to make the teams even? You must state BOTH the tpe of person and the team.