2023年Math League数学大联盟六年级思维探索第一阶段活动.docx

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1、 2022-2023年度美国 Math League思维探索第一阶段活动(六年级)(答题时间：75分钟，总分：175分)学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。选择题：每小题 5分，答对加 5分，答错不扣分，共 175分。1. A farmer has 36 more pigs than sheep. If he has 10 times as many pigs as sheep,how many pigs does the farmer have?A) 40B) 44

2、C) 45D) 462. If the cost of a dozen bagels increases by $1.80, the average cost of eachbagel will increase byA) 10. The integer 2 equals ? times the reciprocal of 2.A) 2 B) 4 C) 6B) 15C) 18D) 3034D) 8. Which of the following could be the perimeter of a rectangle with both odd and even whole-numbersi

3、de-lengths?A) 12. How many positive divisors of 122 are multiples of 12?A) 2 B) 6 C) 12 D) 24B) 13C) 14D) 1656. What is the difference between 23.456 rounded to the nearest tenth and 23.456 rounded to the nearesthundredth?A) 0B) 0.04C) 0.05D) 0.178. The area of a square is 36 m2. The perimeter of th

4、e square in cm isA) 900 cmB) 2400 cmC) 3600 cmD) 360 000 cm. What is the greatest odd divisor of 2 4 6 8 10 12?A) 9 B) 15 C) 45 D) 135 9. Roy painted 100 houses. If Roy painted 40% of the houses gray and 20% ofthe remaining houses yellow, how many houses did Roy paint yellow?A) 8B) 12C) 20D) 40110.

5、Which of the following expressions has the greatest value?112121 2A)B)C)D) 222222 1. The temperature of a pot of soup increases by 3 every 40 seconds. How much will the temperatureincrease in 30 minutes?A) 1352. I counted from 1 to 100 out loud, skipping every multiple of 3. How many numbers did I s

6、ay out loud?A) 66 B) 67 C) 76 D) 773. What is the difference between 2 primes whose product is 10 135?A) 2022 B) 2023 C) 2027 D) 20324. A pile of 1003 pennies can be divided equally into exactly ? equal piles worth $4 each.A) 25 B) 250 C) 2500 D) 25 000B) 450C) 750D) 180011115. In 2022 I ran on 101

7、more days than the number of days I did not run. The sumof the digits of the number of days I ran in 2022 isA) 5B) 6C) 8D) 1116. 2999 + 2999=A) 21+ 999B) 21 999C) 22 + 999D) 22 99917. If 80% of Aris savings equals 20% of Aris and Bevs savings combined, Bev must have ? times asmuch savings as Ari.A)

8、28. What is the greatest power of 2 that is a factor of the product of the 6 smallest positive 2-digit integers?A) 23 B) 24 C) 26 D) 28B) 3C) 4D) 6119. A square poster consists of an 8 cm-wide border around the perimeter of a square photo. If the area ofthe entire poster is 6400 cm2, what is the are

9、a of the photo portion of the poster?A) 4096 cm2B) 4608 cm2C) 5120 cm2D) 5184 cm220. A triangles angles have measures that are consecutive multiples of 15. What is the average measure ofthe 2 smallest angles?A) 37.5B) 52.5C) 67.5D) 82.521. I divided a multiple of 5 by a smaller multiple of 5 and got

10、 a remainder of 15. What is the smallestpossible sum of the multiples?A) 30B) 45C) 55D) 65 22. Every third gumball dispensed has cracks, but the rest do not. If I keep every 4thgumball dispensed and discard the rest, how many of the 72 gumballs I keep willhave cracks?A) 63. How many factors greater

11、than or equal to 5 does 2 5101 have?A) 101 B) 102 C) 201 D) 202B) 12C) 18D) 24224. Each of the integers from 1 through 50 was written on a separate tag, then 3 consecutively numberedtags were lost. If the sum of the integers on the 47 remaining tags is 1221, what is the sum of the digitsof the integ

12、ers on the lost tags?A) 13B) 17C) 27D) 30225. If the median of 6 consecutive integers is 4.5, what is the median of their reciprocals?294999A)B)C)D)20406. My ride to school takes from 10 to 18 minutes, depending on traffic. I cannot arrivebefore 8:10 AM or after 8:30 AM. What is the difference betwe

13、en the earliest andlatest times I could start riding to ensure that I arrive on time?A) 8 minutes7. What is the average of 2100 and 2101?A) 2100.5 B) 2 299B) 12 minutes C) 20 minutes D) 28 minutes22C) 2 2100D) 3 2998. If (0, 0) and (3, 4) are two vertices of a parallelogram in a coordinate plane, wh

14、ich of the following couldnot be another vertex of this parallelogram?A) (4, 3)B) (-1, 7)C) (-3, -4)D) (-4, 3)29. On a class test, the average score of the boys and girls combined was 88. Ifthe average score of the boys was 80, and the average score of the girls was100, which of the following number

15、s could be the total number of the boysand girls combined?A) 105 B) 63C) 48D) none of above30. A clock that uniformly loses 4 minutes every 24 hours was correctly set at 6 A.M. on January 1. What isthe correct time when the clock reads 11:39 AM on January 6 of the same year?A) 11:54 AM, January 6B)

16、12:00 PM, January 6C) 12:30 PM, January 6D) 11:00 AM, January 731. If we get a bullseye half the time that we play darts, is it most likely that weA) miss a bullseye in any single try,B) get a bullseye at least 1 time in 2 tries, orC) get a bullseye 2 or 3 times in 3 tries?32. What is the quotient o

17、f the least common multiple of the first 40 positive integers divided by the leastcommon multiple of the first 30 positive integers?A) 1209B) 1147C) 2294D) none of above 33. How many points does one have to place on a 1 inch by 3 inches rectangle to guarantee that two of themare strictly less than 1

18、 inch apart? (The rectangle here includes its complete interior.)A) 8B) 10C) 12D) none of above34. One square has twice the area of another square. Is it possible for both squares to have side lengths thatare whole numbers?A) YesB) No35. What is the radius of the circle inscribed in a triangle with side lengths 7, 24, and 25?Note: The figure below shows the circle inscribed in a triangle.A) 3B) 4.5C) 6D) none of above 2022-2023 年度美国 Math League 思维探索第一阶段活动六年级试卷答案题号答案题号答案题号答案题号答案12B3B4C5B6B7B8C9B10BA11A12B13A14C15C16A17B18B19A20B21C22D23D24C25D26B27D28C29A30B31B32C33D34B35A