2017 Pinal County Middle School Math Competition. Team Round

Transcription

1 2017 Pinal County Middle School Math Competition Team Round

2 Provide an appropriate response. The three-part inequality a < x b means "a is less than x and x is less than or equal to b". Which of these inequalities is not satisfied by any real number x? a.) 8 < x 7 b.) 5 < x 11 d.) 2 < x 6 c.) 0 < x 4 Question 1

3 Find the smallest angle between the hands of a clock when it is 4 o clock. a.) 120 b.) 20 c.) 240 d.) 95 Question 2

4 Which of the following statements regarding number systems is true? a.) Whole numbers are a subset of the Counting numbers. b.) Real numbers are a subset of the Rational numbers. c.) All Whole numbers are included in the set of Integers. d.) All Integers are included in the set of Whole numbers. Question 3

5 In a group of 50 students, 23 take math, 11 take psychology, and 7 take both math and psychology. If one student is selected at random, find the probability that the student takes math or psychology. a.) 11/50 b.) 23/50 c.) 27/50 d.) 34/50 Question 4

6 Hanif, Horace, Hilary and Hannah are students. Hanif and Horace speak Chinese, whereas the others speak Arabic. Horace and Hannah speak Albanian. Everyone except Hanif speaks Esperanto. Who only speaks Arabic and Esperanto? a.) Hanif b.) Horace d.) Hannah c.) Hilary Question 5

7 If the radius of the circle is 5 units and AC = 13 units, find AD. a.) 14 b.) 16 c.) 12 d.) 8 Question 6

8 Which of the following choices shows equivalent values? a.) 1 1 4, 1.14, 114% d.) 2 3, 0.66, 66% b.) 2 1 2, 2.2, 220% c.) 1 1 5, 1.2, 120% Question 7

9 The winner of a raffle will receive a new sports utility vehicle. If 500 raffle tickets were sold and you purchased ten tickets, what are the odds against your winning the car? a.) 1 to 49 b.) 49 to 1 c.) 1 to 50 d.) 50 to 1 Question 8

10 A ride service charges a $5 pickup fee plus $0.50 for each mile of the trip. If a customer gives the driver $20 and asks for $4 change. Which of the following statements would allow us to calculate the size of the tip given to the driver? a.) The trip was 14 miles long. b.) The tip was 1/3 the total trip charge. c.) The distance charge was 140% of the pickup charge. d.) Choices a.), b.), and c.) Question 9

11 The instructions on a bottle of liquid plant insecticide call for mixing two parts of the insecticide with three parts of water. To mix the entire 16- ounce bottle of insecticide, how much water is needed, in cups? a.) 24 b.) 16 c.) 8 d.) 3 Question 10

12 A student has 6 black marbles and 2 red marble in his pocket. He selects one marble at random, looks at it and puts it back. Then he will select another marble at random. What is the probability that the student selects black marbles both times? a.) 1 b.) 5/8 d.) 9/16 c.) 1/2 Question 11

13 Consider the statement Not all pets are animals. Which of the following statements has exactly the same meaning? a.) Any animal can be a pet. b.) All pets are not animals. c.) Some pets are not animals. d.) Some animals are not pets. Question 12

14 Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them. a.) Carla:5 years, Jim: 6 years, Peter: 19 years b.) Carla:5 years, Jim: 7 years, Peter: 20 years c.) Carla:5 years, Jim: 3 years, Peter: 16 years d.) Carla:5 years, Jim: 5 years, Peter: 18 years Question 13

15 If E and F are midpoints and EF = 9, and DC = 15, find AB. a.) 5 b.) 3 c.) 2 d.) 4 Question 14

16 The average of 1, 2, 5, 9, and x is 4. The average of 2, 3 and y is 6. What is the value of x + y? a.) 5 b.) 10 c.) 16 d.) 17 Question 15

17 Draw a valid conclusion from the given premises. if a student misses a test, then they can make it up. if a student makes up a test, then they won t be penalized. Therefore, a.) if a student is penalized, then they missed a test. b.) If a student misses a test, then they won t be penalized. c.) If a student doesn t miss a test, then they will be penalized. d.) if a student is penalized, then they didn t miss a test. Question 16

18 If three times the smaller of two consecutive integers is added to four times the larger, the result is 123. Find the smaller integer. a.) 16 b.) 17 c.) 18 d.) 51 Question 17

19 Find the length of XZ. a.) 30 b.) 54 c.) 40 d.) 58 Question 18

20 The chart shows the results of a survey asking the current age of students in the freshman class. What percent of the students surveyed were 14 years old? a.) 50% b.) 60% c.) 66% d.) 70% Age Students 13 years years years 19 Question 19

21 Study the pattern in the examples to the right. Then select the equation that describes the pattern. a.) a x # a y = a x+y+4 b.) a x # a y = a x+2y a 4 # a 6 = a 14 a 2 # a 3 = a 9 a 7 # a 5 = a 16 c.) a x # a y = a 2x+y d.) a x # a y = a x y+2 Question 20