Kansas City Area Teachers of Mathematics 2005 KCATM Contest PROBLEM SOLVING TEST GRADE 5 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 3.14159 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.
1. A rectangle is 14 ft. wide. The area of the rectangle is 112 square ft. What is the perimeter of the rectangle? a) 8 ft. c) 22 ft. b) 33 ft. d) 44 ft. e) not given 2. What is the area of the rectangle with points B and E as opposite vertices of the rectangle In Figure 1? a) 24 square units b) 28 square units c) 32 square units d) 36 square units e) not given Figure 1 +10 +8 +6 +4 +2 Y A B C D E +2 +4 +6 +8 +10 X 3. John is going to have his class over for a swim party at the YMCA. The cost is $3.50 per person. John s parents will pay a maximum of $45 and John will have to pay for for the rest with his allowance. There are 19 students in his class. How much more does John have to pay to have the party for 19? a) $21.00 b) $21.50 c) $22.00 d) 22.50 e) not given 4. Alex arrives home from school at 3:45pm, spends ½ hour reading, 15 minutes doing math homework, then goes over to a friend s house for an hour before dinner. If Alex has gymnastics at 7:00, and it is a 15 minute drive, how much time is there between when Alex returns home for dinner and the time to leave the house for gymnastics? a) 45 minutes c) 1 hr. 15 minutes b) 1 hour d) 1 hr. 30 minutes e) not given 5. How many different ways can the letters M, A, T, H be rearranged? a) 4 b) 8 c) 12 d) 24 e) not given 6. What is your average (mean) math test score if you earned the following grades on your tests: 75%, 84%, 78%, and 91%? a) 82% b) 83% c) 84% d) 85% e) not given 7. The weather forecast predicted a 75% chance for snow. What is the probability that it will NOT snow? a) 15% b) 25% c) 35% d) 75% e) not given 8. Its pizza night at your house. One large pepperoni pizza is cut into 12 slices. You eat ½ the pizza, your sister eats ¼ of the pizza, how many slices are left? a) 1 b) 2 c) 3 d) 4 e) not given PAGE 1
9.-10. Use the following information to answer the next 2 questions. Your 5th grade teacher s classroom has 12 girls, 14 boys, 2 rabbits, 3 hamsters, 1 snake, and 1 bird. 9. What is the probability of being a boy and not a girl in the classroom? 6 7 a) b) c) 3 d) 6 e) not given 13 13 8 7 10. What are the odds that the animal is a snake? a) 1:6 b) 1:5 c) 1:3 d) 1:2 e) not given 11. Figure 2 below shows the first 3 triangular numbers: 1, 3, 6. What would be the 10 th triangular number? 1 3 6 a) 45 b) 55 c) 66 d) 78 e) not given Figure 2 12. I am a palindrome number. I am greater than 200, but less than 400. My tens digit is the quotient of my hundreds digit and my units digit. I am an odd number. What number am I? a) 263 b) 393 c) 313 d) 303 e) not given 13. I am the number you get from taking the number of inches in a yard times the number of pints in quart plus the number of centimeters in meter. What number am I? a) 106 b) 172 c) 244 d) 1024 e) not given 14. A machine can fill one small jar of pickles every 5 seconds. How many jars will be filled at the end of two hours? a) 24 b) 300 c) 600 d) 1440 e) not given 15. At Taste-Rite Café, the buffet costs $7.98 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 a $20 bill and a $10 bill? a) $2.00 b) $2.07 c) $2.31 d) $ 2.53 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
17. There are 128 oz. of liquid in a gallon. How many cups are in one gallon? a) 8 b) 16 c) 24 d) 32 e) not given 18. Figure 3 shows the net of a polyhedron. If one of the sides of the square is 2 cm, what would be the volume of the polyhedron? Figure 3 a) 4 cubic cm c) 12 cubic cm b) 8 cubic cm d) 24 cubic cm e) not given 19. If 1,000,000,000 (one billion) is one thousand millions, how many 100,000 s are in a billion? a) ten c) one thousand b) one hundred d) one hundred thousand e) not given 20. The movie you are going to starts at 4:45 pm. It is 115 minutes long. What time is it when the movie ends? a) 6:40 pm c) 6:50 pm b) 6:45 pm d) 6:55 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 12 minutes to get to school, 25 minutes to eat breakfast, and 15 minutes to get ready? a) 7:17 am c) 7:30 am b) 7:23 am d) 7:37 am e) not given 22. Add the numbers 1 to 50. Hint: 1 + 2 + 3 + 4 +.. + 50 = a) 895 b) 965 c) 1055 d) 1275 e) not given 23. If A = 1 cent, B = 2 cents, C = 3 cents, D = 4 cents, how much is the word Kansas worth? a) $.65 c) $.84 b) $.73 d) $.91 e) not given 24. Your non-stop flight from Kansas City to Florida is 2 hrs. and 15 minutes. What time do you arrive in Florida (Eastern Standard Time EST) if you leave KCI at 11:35am CST (Central Standard Time). a) 11:50 EST c) 1:50 EST b) 12:50 EST d) 2:50 EST e) not given 25. Three consecutive numbers have a sum of two times fifty-four. What is the largest of the three numbers? a) 34 b) 35 c) 36 d) 37 e) not given PAGE 3
26. Figure 4 is a net of one of the five Platonic solids. It is an octahedron. 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 octahedron? a) 27.8 sq. cm c) 35.4 sq. cm b) 31.2 sq. cm d) 39.6 sq. cm e) not given Figure 4 27. The odometer in your parent s car reads 42,123.5 miles. You gas tank is full when you begin a trip to your grandparents. When you arrive the odometer reads 42,418.3 miles and you fill the tank again. It takes 12.55 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) 23.5 miles e) not given 28. How many of the cubes in Figure 5 have exactly 3 faces showing? Figure 5 a) 6 b) 7 c) 8 d) 9 e) not given 29. Using two regular 6 sided dice, what is the probability of getting a sum of 7? 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: 2, 3, 5, 8, 13, 21, What is the 12 th term? a) 89 b) 144 c) 233 d) 377 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 feet does it travel in 10 rotations? a) 62.80 feet c) 376.8 feet b) 75.36 feet d) 753.6 feet e) not given PAGE 4
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 ½ mile from school? a) ¼ mile b) 3/8 mile c) 5/8 mile d) ¾ mile e) not given 34. Solve: 2 3 3(2) + 5 a) 5 b) 6 c) 7 d) 8 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 $6.35? a) 3 nickels, 4 dimes, 3 dollars c) 1 nickel, 1 dime, 2 quarters, 3 dollars b) 1 nickel, 6 dimes, 4 dollars d) 3 nickels, 3 dimes, 3 dollars e) not given 36. Cara is 12 years old, Alexis is 3 years older than Cara, and Sara is 2 years older than Alexis. If Sara s mom is 3 times as old as Sara, how much older is Sara s mom than Cara? a) 37 years b) 39 years c) 43 years d) 51 years e) not given 37. You averaged 87% on three tests. If you had 2 tests of 83 and 91, what was your 3rd test score? a) 85 b) 86 c) 87 d) 88 e) not given 38. Solve: 2x 2 + 8 = 26 a) 1 b) 2 c) 3 d) 4 e) not given 39. Stormy eats 3 treats and Windy eats 6 treats during Gary Lezak s program at the KCATM Awards Banquet in April. If your bag has 150 treats in it, how many programs can Gary, Stormy, and Windy perform using the same bag without having to purchase another one? a) 12 b) 14 c) 15 d) 16 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
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
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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