_2010 KCATM MATHLETICS GRADE 6. Kansas City Area Teachers of Mathematics 2010 KCATM Contest MATHLETICS GRADE 6
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1 Kansas City Area Teachers of Mathematics 2010 KCATM Contest MATHLETICS GRADE 6 INSTRUCTIONS Do NOT turn this page until instructed to do so. WRITE YOUR TEAM NUMBER AND SCHOOL NAME ON THE LINE PROVIDED ON THE FRONT OF EACH SHEET EACH TIME YOU BEGIN A NEW PROBLEM. Write your TEAM NUMBER and the ANSWER on each back page. This will be checked and recorded for each problem. You may use calculators on this test. Scratch paper can be used. Do NOT write on the team number card! Use the π key on your calculator as the approximation for pi. You may not use rulers, protractors, or other measurement devices on this test. Team Number: School:
2 Problem 1 1 point 1 minute S, H, and E are different digits. Replace the letters with numbers to make the statement true. (HE)² = SHE Answer: S = ; H = ; E = TEAM #
3 Problem 2 1 point 1 minute The areas of 3 faces of a rectangular solid are 54, 72, and 108 square units. Find the lengths of the edges. Answer: Team #
4 Problem 3 3 points 3 minutes You have only dimes, nickels, and pennies in your pocket. Seven of the coins are dimes, 25% of the coins are nickels, and 5/9 of them are pennies. How many coins do you have? Answer: Team #
5 Problem 4 2 points 2 minutes What are all the possible ages of three children in a family if: The product of their ages is 96 One person is a teenager Answer: Team #
6 Problem 5 1 point 1minute A square piece of paper is folded in half vertically. If the resulting figure has a perimeter of 12 cm, what was the area of the original square? Answer: TEAM #
7 Problem 6 1 point 1 minute If a ɣ b is defined as 2a b 4b - a² what is the value of a ɣ b when a = 2 and b = -3? Answer: TEAM #
8 Problem 7 3 points 3 minutes In a tug of war, the first two rounds were ties. Who will win the third round? How do you know? Round 1: On one side were four acrobats, each of equal strength. On the other side were 5 grandmas, each of equal strength. The round was a tie. Round 2: One side was Ivan the dog. On the other side were two of the grandmas and one acrobat. This round was also a tie. Round 3: On one side is Ivan and three of the grandmas. On the other side are four acrobats. Who will win? Answer: TEAM #
9 Problem 8 3 points 3 minutes The mean (average) age of the first seven people to arrive at Grandpa Jones birthday party was 21. Arriving next was Jerry, who is 29 and his twin sister Mary. The last person to arrive was Grandpa, and the mean age jumped up to Mary s age. How old is Grandpa? Answer: years old TEAM #
10 Problem 9 1 point 1 minute Find a number such that: It has two digits The sum of its digits is 10 The difference of its digits is 2 It s less than 50 Answer: TEAM #
11 Problem 10 2 points 2 minutes The 6 th grade collected $5 for the Red Cross on Friday. They had exactly 100 coins. They had one half dollar, no quarters, and no nickels. How many dimes and how many pennies did they have? Answer: dimes; pennies TEAM #
12 Problem 11 3 points 3 minutes John has 3 more brothers than sisters. How many more brothers than sisters does Mary, his sister have? Answer: TEAM #
13 Problem 12 2 points 2 minutes A store buys a TV for $350, and sells it for 225% of the cost. A store coupon has been issued in the paper for 20% off. You also have a coupon for an additional 15% off. How much did you pay for the TV? Answer: TEAM #
14 Problem 13 1 point 1 minute Find the sum of the numbers Answer: TEAM #
15 Problem 14 2 points 2 minutes A ball is dropped from a height of 88 feet. On each bounce, it rises ¾ the height of the previous height. How many times will it bounce before it rises to a height less than 10 feet? Answer: TEAM #
16 Problem 15 2 points 2 minutes How many different ways are there to make 17? Answer: TEAM #
17 Problem 16 3 points 3 minutes The inhabitants of a Canadian town speak either French or English or both. Seventy-three percent speak French, and eighty-seven percent speak English. What percentage speak both languages? Answer: % TEAM #
18 Problem 17 3 points 3 minutes Chad and Blossom (brother and sister) come from a large family. Chad has as many brothers as he has sisters, but Blossom has only half as many sisters as she has brothers. How many children (total) are in the family? Answer: TEAM #
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