Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 6

Transcription

1 Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 6 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may use calculators on this test. Use the π key on your calculator or as the approximation for pi. Write all answers on the answer sheet provided. You may not use rulers, protractors, or other measurement devices on this test.

2 Use Figure 1 for questions 1 and Use Figure 1 to find the area of the right triangle with the vertex of the right angle at the origin, O, and points A and E as the other two vertices. a) 7 sq. units c) 28 sq. units b) 8 sq. units d) 56 sq. units e) not given Y +10 A +8 B 2. What is the area of the triangle with endpoints D, E, and the origin, O? a) 10 square units b) 14 square units c) 18 square units d) 28 square units e) not given O C D E Figure 1 X 3. Chris and Kelsey want to evenly split the cost of dinner and a movie. The dinner costs $8.75 per person plus 7% tax and 15% tip based on the $8.75. Two movie tickets cost $ What is the approximate cost for each person? a) $15.00 b) $16.00 c) $17.00 d) e) not given 4. Alex arrives home from school at 3:55pm, spends ½ hour reading, 20 minutes doing math homework, then goes over to a friend s house for ¾ hour before dinner. If Alex has soccer practice at 7:00, and it is a 10 minute drive, how much time is there between when Alex returns home for dinner and the time to leave the house for soccer? a) 1 hour 10 minutes c) 1 hr. 20 minutes b) 1 hour 15 minutes d) 1 hr. 30 minutes e) not given 5. How many different outfits can you wear if you have 5 shirts, 3 jeans, 2 pair of shoes, and 4 sweatshirts? a) 14 b) 16 c) 100 d) 120 e) not given 6. What is your mean math test scores if you earned the following grades on your tests: 85%, 94%, 80%, and 91%? a) 87.5% b) 88% c) 88.5% d) 90% e) not given 7. The weather forecast predicted a 93% chance for snow. What is the probability that it will NOT snow? a) 7% b) 10% c) 12% d) 15% e) not given 8. Its pizza night at your house. One extra large pepperoni pizza is cut into 16 slices. You eat ¼ the pizza, your sister eats 1/8 of the pizza, how many slices are left? a) 8 b) 9 c) 10 d) 12 e) not given PAGE 1

3 Use the following information to answer the next 2 questions. Your 6th grade teacher s classroom has 12 girls, 14 boys, 1 rabbit, 2 snakes, 1 rat, and 1 bird. 9. What is the probability of being a girl and not a boy in the classroom? 6 7 a) b) c) 3 d) 6 e) not given What are the odds that the animal is a snake? a) 1:5 b) 1:4 c) 1:3 d) 2:3 e) not given 11. Figure 2 below shows the first 3 triangular numbers: 1, 3, 6. What would be the sum of the first 8 triangular numbers? a) 78 b) 95 c) 110 d) 120 e) not given Figure I am a palindrome number. I am greater than 500, but less than 700. My tens digit is the difference of my hundreds digit and my units digit. I am an odd number. What number am I? a) 663 b) 606 c) 515 d) 505 e) not given 13. I am the decimal number you get from taking the number of feet in a mile divided by the number of square centimeters in one square meter. What number am I? a) b) c) d) e) not given 14. Each machine can fill one gallon of orange juice every 40 seconds. How many gallons will be filled by at the end of an 8 hours from 5 machines? a) 90 b) 300 c) 720 d) 3600 e) not given 15. At Taste-Rite Café, the buffet costs $9.98 per person, which includes tax. Children 12 and under are half price. How much change does Mr. Eat Out get back if he pays for himself, his 14 year old son, and 3 daughters ages 4, 7, and 10 with 2- $20 bills? a) $5.00 b) $5.07 c) $5.31 d) $ 5.93 e) not given 16. The 10 passenger team van costs $65.25 to rent to get to your basketball tournament. The coach needs to split the cost among the 9 players. How much money will each player have to pay if each player must also pay $10 per player for the tournament fee? a) $16.53 b) $17.25 c) $18.36 d) $19.48 e) not given PAGE 2

4 17. There are 128 oz. of liquid in a gallon. How many cups are in two gallons? a) 8 b) 16 c) 24 d) 32 e) not given 18. Figure 3 shows the net of a cylinder. The volume of the cylinder is: V Find the volume. 10cm Figure 3 r = 3cm = π 2 r h a) cubic cm c) cubic cm b) cubic cm d) cubic cm e) not given 19. If 1,000,000,000,000 (one trillion) is one thousand billions, how many millions are in a trillion? a) ten c) one thousand b) one hundred d) one million e) not given 20. The movie you are going to starts at 7:35 pm. It is 105 minutes long. What time is it when the movie ends? a) 8:40 pm c) 9:20 pm b) 9:05 pm d) 9:35 pm e) not given 21. What time do you have to get up to be ready for school by 8:15 am if it takes you 10 minutes to get to school, 17 minutes to eat breakfast, and 30 minutes to get ready? a) 7:12 am c) 7:18 am b) 7:15 am d) 7:22 am e) not given 22. Add the numbers 1 to 100. Hint: = a) 1500 b) 2050 c) 4055 d) 5050 e) not given 23. If A = 1 cent, B = 2 cents, D = 3 cents, E = 4 cents, how much is the word mathematics worth? a) $1.04 c) $1.12 b) $1.10 d) $1.15 e) not given 24. Your non-stop flight from Kansas City to Florida is 2 hrs. and 40 minutes. What time do you arrive in Florida (Eastern Standard Time EST) if you leave KCI at 11:25am CST (Central Standard Time). a) 1:05 EST c) 3:05 EST b) 2:05 EST d) 4:05 EST e) not given 25. Three consecutive numbers have a sum of two times sixty-six. What is the largest of the three numbers? a) 43 b) 44 c) 45 d) 46 e) not given PAGE 3

5 26. Figure 4 is a net of one of the five Platonic solids. It is an icosahedron. If the base of one of the triangles is 3cm and the height of the triangle is 2.6, what would be the surface area of the icosahedron? a) 39 sq. cm c) 117 sq. cm Figure 4 b) 78 sq. cm d) 156 sq. cm e) not given 27. The odometer in your parent s car reads 52,123.5 miles. You gas tank is full when you begin a trip to your grandparents. When you arrive the odometer reads 52,418.3 miles and you fill the tank again. It takes 18.9 gallons of gas to fill your car. How many miles per gallon does the car get? a) 15.6 miles c) 16.8 miles b) 17.2 miles d) 34.4 miles e) not given 28. How many of the cubes in Figure 5 have exactly 2 faces showing? Figure 5 a) 4 b) 5 c) 6 d) 7 e) not given 29. Using two regular 6 sided dice, what is the probability of getting a sum of 12? a) 1/36 b) 5/36 c) 1/6 d) 7/36 e) not given 30. The following shapes in Figure 6 are pentominoes. A pentomino shape is made from 5 squares in all the different ways the squares can be placed. How many more figures would there be in a set of pentominoes? Figure 6 a) 3 c) 9 b) 7 d) 12 e) not given 31. One Fibonacci sequence is: 3, 5, 8, 13, 21, What is the 12 th term? a) 144 b) 233 c) 377 d) 610 d) not given 32. The formula for circumference of a circle is C = π d. If a bicycle tire has a diameter of 24 inches, how many miles does it travel in 1000 rotations? (1 mile = 5280 ft.) a) 1.19 miles c) 4.55 miles b) 2.38 miles d) 7.26 feet e) not given PAGE 4

6 33. You live half way between your school and the park. Your friend lives half way between you and the park. How far away does your friend live from school if you live 1/4 mile from school? a) ¼ mile b) 1/8 mile c) 3/8 mile d) ½ mile e) not given 34. Solve: (-2) 3 3(-2) + 5 a) -9 b) 3 c) 9 d) 19 e) not given 35. Which is the correct change given back to a customer if the customer gives a clerk $10 bill to pay a bill of $7.15? a) 2 nickels, 3 quarters, 3 dollars c) 1 nickel, 7 dimes, 2 dollars b) 1 dime, 3 quarters, 3 dollars d) 1 dime, 3 quarters, 2 dollars e) not given 36. Alpha is 12 years old, Beta is 3 years older than Alpha, and Gamma is 2 years younger than Beta. If Beta s dad is 3 times as old as Beta, how much older is Beta s dad than Gamma? a) 32 years b) 33 years c) 34 years d) 45 years e) not given 37. You averaged 91% on three tests. If you had 2 tests of 85 and 94, what was your 3 rd test score? a) 91 b) 92 c) 93 d) 94 e) not given 38. Solve: 2x 2-5 = 67 a) 5 b) 6 c) 7 d) 8 e) not given 39. Stormy eats 3 treats and Windy eats 4 treats during Gary Lezak s program at the KCATM Awards Banquet in April. If your bag has 120 treats in it, how many programs can Gary, Stormy, and Windy perform using the same bag without having to purchase another one? a) 15 b) 16 c) 17 e) 18 e) not given 40. Eenie, Meenie, Minie, and Mo are trying to do their best on this test. Eenie says I don t leave anything blank, because guessing at least gives me a chance. Meenie says I start at the back and move to the front because the easiest problems are always first. Minie says I write on the test and mark my answers when there are 2 minutes left. Mo says: The more I get to, the better chance I have to get some right. Which one or ones are strategies for this multiple choice test? a) Eenie b) Eenie & Meenie c) Eenie, Meenie, and Minie d) Eenie, Meenie, Minie, and Mo e) none of them are strategies (not given) PAGE 5

7 Shade the correct answer! Example: a b c d e Name School 1. a b c d e 21. a b c d e 2. a b c d e 22. a b c d e 3. a b c d e 23. a b c d e 4. a b c d e 24. a b c d e 5. a b c d e 25. a b c d e 6. a b c d e 26. a b c d e 7. a b c d e 27. a b c d e 8. a b c d e 28. a b c d e 9. a b c d e 29. a b c d e 10. a b c d e 30. a b c d e 11. a b c d e 31. a b c d e 12. a b c d e 32. a b c d e 13. a b c d e 33. a b c d e 14. a b c d e 34. a b c d e 15. a b c d e 35. a b c d e 16. a b c d e 36. a b c d e 17. a b c d e 37. a b c d e 18. a b c d e 38. a b c d e 19. a b c d e 39. a b c d e 20. a b c d e 40. a b c d e PAGE 6

8 Shade the correct answer! Example: a b c d e Name School 1. a b c d e 21. a b c d e 2. a b c d e 22. a b c d e 3. a b c d e 23. a b c d e 4. a b c d e 24. a b c d e 5. a b c d e 25. a b c d e 6. a b c d e 26. a b c d e 7. a b c d e 27. a b c d e 8. a b c d e 28. a b c d e 9. a b c d e 29. a b c d e 10. a b c d e 30. a b c d e 11. a b c d e 31. a b c d e 12. a b c d e 32. a b c d e 13. a b c d e 33. a b c d e 14. a b c d e 34. a b c d e 15. a b c d e 35. a b c d e 16. a b c d e 36. a b c d e 17. a b c d e 37. a b c d e 18. a b c d e 38. a b c d e 19. a b c d e 39. a b c d e 20. a b c d e 40. a b c d e PAGE 7

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