Kansas City Area Teachers of Mathematics 2013 KCATM Math Contest MATHLETICS GRADE 6
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1 Kansas City Area Teachers of Mathematics 2013 KCATM Math Contest MATHLETICS GRADE 6 INSTRUCTIONS WRITE YOUR TEAM NUMBER AND SCHOOL NAME ON THE LINE PROVIDED ON EACH SHEET EACH TIME YOU BEGIN A NEW PROBLEM. Do NOT turn this page until instructed to do so. 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 key on your calculator or as the approximation for pi. You may not use rulers, protractors, or other measurement devices on this test. Many problems came from or adapted from: Problem Solving Strategies for Efficient and Elegant Solutions, Alfred Posamentier & Stephen Krulik, Corwin Press, 2008 Team Number: School: Team Members:
2 Problem 1 3 points 3 minutes A local pet store owner just bought her holiday supply of baby chickens and baby rabbits. She doesn t really remember how many of each she bought, but she has a system. She knows that she bought a total of 22 animals, a number exactly equal to her age. Furthermore, she also recalls that the animals had a total of 56 legs, her mother s age. How many chickens and how many rabbits did she buy? Answers: Chickens = Rabbits = School TEAM # PAGE # 1
3 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 2 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 2
4 Problem 2 2 points 2 minutes A sledding hill is 160 feet long. You start at the top at a rate of 3mph. Every 20 feet, your speed increases by 10%. What is your speed at the bottom of the hill? Round your answer to the nearest hundredth mph. Answer: PAGE # 3
5 School TEAM # Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 3 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 4
6 Problem 3 1 point 1 minute If the interior of the rectangular planter shown measures 48" x 24" and 18" tall. Dirt is sold by the cubic yard. Garden soil is priced at $34 per cu. yard delivered from Acme Soil Company. What is the cost of the dirt that would fill fourteen planters for a park? Round your answer to the nearest whole dollar. Answer: School TEAM # PAGE # 5
7 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 4 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 6
8 Problem 4 2 points 2 minutes The letters A, B, C, D, and E have whole number values 1 through 5. Find the value of each letter using the equations and table below. 1. B D = E 2. C + D = A + E 3. B + 1 = C A B C D E Answers: A = B = C = D = E = School TEAM # PAGE # 7
9 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 5 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 8
10 Problem 5 - Hoop Stars 3 points 3 minutes Answers: Daniel: Player Kirk: Player Josh: Player Michael: Player Roger: Player School TEAM # PAGE # 9
11 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 6 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 10
12 Problem 6 1 point 1 minute Find the smallest integer value for x 12 for which x 1 yields an integer. Answer: School TEAM # PAGE # 11
13 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 7 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 12
14 Problem 7 2 points 2 minutes What is the sum of the values in the 25 th row of the following array? (Hint: Look for a pattern in your table of values.) Row 1 1 Row Row Row Row Row Row Total n Answer: School TEAM # PAGE # 13
15 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 8 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 14
16 Problem 8 3 points 3 minutes The diameter of the small circle is 2 in. and the medium-sized circle has a diameter of 3 in. Find the ratio of the area of the shaded region to the area of the largest circle. A = π r 2 (You may use π on calculator or ) Answer: School TEAM # PAGE # 15
17 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 9 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 16
18 Problem 9 3 points 3 minutes What is the length of the diagonal of a cube-shaped room with walls, floor and ceiling measuring 8 feet (length, width, and height)? Round your answer to the nearest tenth of a foot. A 8 B 8 8 Answer: ft. School TEAM # PAGE # 17
19 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 10 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 18
20 Problem 10 2 points 2 minutes There are three integer solutions for the value of x in the following equation. Find at least two of them. (3x 7) ( x 2 9) 1 Answer: and School TEAM # PAGE # 19
21 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 11 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 20
22 Problem 11 1 point 1 minute Simplify: 5!(3!) 6! Answer: School TEAM # PAGE # 21
23 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 12 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 22
24 Problem 12 3 points 3 minutes A cat chases a mouse, which has a 160 meter head start. For every 7m the mouse runs, the cat runs 9m. How far must the cat run to catch the mouse? Answer: meters School TEAM # PAGE # 23
25 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 13 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 24
26 Problem 13 2 points 2 minutes Given a regular pentagram, find the angle measure at each of the congruent vertices A, B, C, D, and E. Answer: o School TEAM # PAGE # 25
27 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 14 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 26
28 Problem 14 3 points 3 minutes You leave school Olathe East HS and travel 1 mile east to Pflumm Road, then north 2 miles on Plfumm to College Blvd. You then turn east 1 mile until reaching Quivira, at which time you turn north 1 mile to Interstate I-435. You head east on I-435 for 4 miles. If you had a futuristic vehicle that could have taken you on a direct route to your location, how much distance would have saved? Round your answer to the nearest tenth of a mile. Start Answer: miles School TEAM # PAGE # 27
29 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 15 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 28
30 Problem 15 2 points 2 minutes 1 Given that 8 1 of a number is 5 5, what is 8 of that number? Answer: School TEAM # PAGE # 29
31 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 16 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 30
32 Problem 16 2 points 2 minutes Four married couples belong to a theater club. The wives names are Alice, Barbara, Christa, and Edith. The husband s names are Al, Frank, Fred, and Ernest. Who is married to whom? 1. Al is Edith s brother. 2. Edith and Fred were once engaged, but broke up when Edith met her present husband. 3. Christa has a sister, but her husband is an only child. 4. Alice is married to Ernest. Al Frank Fred Ernest Alice Barbara Christa Edith Answers: Al is married to: Frank is married to: Fred is married to: Ernest is married to: School TEAM # PAGE # 31
33 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 Problem # 17 Do NOT turn the page until you are told to do so. Team Number: School: PAGE # 32
34 Problem 17 3 points 3 minutes What is the sum of the consecutive integers from 23 to 227? Answer: School TEAM # PAGE # 33
35 Kansas City Area Teachers of Mathematics 2013 KCATM Contest Mathletics Grade 6 ANSWER KEY PAGE # 34
36 Answers: chickens and 6 rabbits mph 3. $ A=5; B=3; C=4; D=2; E=1 5. See figure on right = 8. 12/25 or 12:25; other options: 9.425:19.625, or 48: , -3, and meters The cat gains 2 meters for every 9 meter intervals. To catch up with the mouse, the cat must run 160/2 or 80 intervals. 80 x 9 = 720 meters o (5-2)180 = 540; 540/5 = 108 o ; Supp = 72 o as base angles of an isosceles triangle. 180 (2 x 72) = = 36 o = Al is married to Barbara Frank is married to Edith Fred is married to Christa Ernest is married to Alice (given) , pairs of (24+227) = (25+226) (251) = 25,625 PAGE # 35
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