2014年美国“数学大联盟杯赛”(中国赛区)初赛七年级(初一)详解.pdf

20132013 20142014 年度美国年度美国 数学大联盟杯赛数学大联盟杯赛 中国赛区中国赛区 初赛答案初赛答案 七年级七年级 一 一 选择题选择题 1 B No even number can be written as the product of two odd integers Since 11 is the product of 1 and 11 Skip may have run 11 kilometers A 10 B 11 C 12 D 14 2 B 250 450 650 850 450 650 850 250 A 50 B 250 C 550 D 1050 3 C The reciprocal of 2 the reciprocal of 8 1 2 1 8 4 8 1 8 5 8 5 1 8 5 times the reciprocal of 8 A 2 B 6 C 8 D 10 4 A Since 0 0449 is closer to 0 04 than 0 05 it rounds to 0 04 A 0 04 B 0 045 C 0 05 D 0 055 5 D The sum of the angle measures of a triangle is 180 so the two largest angles must each be less than 90 A isosceles B equilateral C acute D right 6 A 639 10515 A 9 B 11 C 12 D 18 7 B I have equal numbers of nickels dimes and quarters One coin of each value is worth 0 40 10 0 40 25 so I can have 24 of each A 20 B 24 C 25 D 29 8 D Twelve hours after 10 A M is 10 P M two hours earlier is 8 P M A 8 A M B 10 A M C 6 P M D 8 P M 9 D The product of the three smallest prime numbers divided by the sum of these three prime numbers is 2 3 5 2 3 5 30 10 3 A 6 5 B 1 C 5 3 D 3 10 D Keep doubling until you exceed 1000 2 4 8 16 32 64 128 256 512 1024 It is 10 days after Sunday when the bell first rang more than 1000 times 10 days after Sunday is a Wednesday A Friday B Sunday C Tuesday D Wednesday 11 A The ratio of boys to girls is 4 5 The number of boys is 4 5 60 48 and 60 48 12 A 12 B 15 C 18 D 21 12 D A square with a perimeter of 64 has a side length of 16 Its area is 256 A 32 B 64 C 144 D 256 13 B Since 1 6 of 60 10 and this is 5 less than 1 4 of 60 Sue and Lou do 60 stretches A 120 B 60 C 29 D 24 14 B Rewrite as 25 1000 34 1000 43 1000 and 52 1000 We have 34 43 25 52 A 25000 B 34000 C 43000 D 52000 15 B 5 5 5 5 5 21 5 5 5 5 5 29 Finally 29 21 8 A 0 B 8 C 15 D 24 16 A 0 25 of 50 of 1600 0 0025 0 5 1600 2 A 2 B 40 C 100 D 200 17 A All primes greater than 2 are odd Since the sum is odd one addend is 2 A 2 B 3 C 5 D 7 18 B If 2 sides of an isosceles triangle are 10 and 25 its perimeter is 10 25 25 A 45 B 60 C 70 D 75 19 C Out of 7 acotrs I choose one as Hamlet and another as Othello These two roles may be chosen in 7 6 42 different ways A 13 B 21 C 42 D 49 20 D As shown each of the two remaining angles measures 120 since each linear pair equals 180 A 40 B 60 C 90 D 120 21 B Since 1 m 100 cm the big bottle is 200 cm tall Since 2 cm on the big bottle equal 1 mm on the model the model is 100 mm tall Finally 100 mm 0 1 m A 50 B 60 C 100 D 110 22 D The probability of an event cannot be more than 1 A 0 02 B 3 C 3 5 D 7 6 23 A 64 55 6 4 1 5 150 A 150 B 80 C 66 D 40 24 D Since 36 24 3 2 54 36 36 splikes 54 splorks A 12 B 24 C 48 D 54 25 D The sum of these integers is at least 32 34 36 38 40 42 44 46 312 A 240 B 256 C 276 D 312 26 C The ones digits of powers of 8 repeat in a cycle of 8 4 2 6 8 4 2 6 The ones digit of the weight in kg could be 6 A 0 B 3 C 6 D 9 27 D As shown only choice D is not a product of a divisor of 24 and a divisor of 35 A 1 1 B 6 7 C 8 7 D 6 11 28 B The sum of the dimensions is 40 2 20 Its dimensions are 16 4 and its area is 64 A 100 B 64 C 40 D 24 29 A Her average score for 6 tests was 82 So her total was 6 82 492 Adding 2 98 her total for 8 tests was 688 Her average score was 86 A 86 B 88 C 90 D 94 30 D F