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2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段六年级

2024年1月1日发(作者：stranger是什么意思英语)

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2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段

(六年级)

(活动日期：2018年11月25日，答题时间：90分钟，总分：200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。

请在装订线内签名表示你同意遵守以上规定。

考前注意事项：

1. 本试卷是六年级试卷，请确保和你的参赛年级一致；

2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；

3. 请确保你已经拿到以下材料：

本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、

草稿纸。试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。

4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一

半题目的学生就应该受到表扬和鼓励。

选择题：每小题

5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。

1. (2 × 4 × 8) ÷ 2 = 4 × ?

A) 2 B) 4 C) 8 D) 16

2. Al sleeps daily for 3 times as many hours as he is awake. For how

many hours does Al sleep daily?

A) 6 B) 9 C) 12 D) 18

3. The number 36 is the product of -6 and

A) -6 B) 6 C) -30 D) 42

4. 20 × 18 = 20 × 19 + 20 × ?

A) -1 B) 0 C) 1 D) 20

5. Angel arrived

310 of an hour early for her noon appointment. At what time did Angel

arrive?

A) 11: B) 11: C) 11: D) 11:

6. The product of the least and greatest positive odd factors of 2019 is

A) 673 B) 2019 C) 2020 D) 6057

7. The average value of the ten whole numbers from 0 through 9 is

A) 5.5 B) 5 C) 4.5 D) 4

8. 2019 × 3 + 2019 ÷ 3 = 2019 × (3 + ? )

A) 0

C) 1 D) 3

第1页，共4页

9. The product of four 4s equals the sum of ? 4s.

A) 4 B) 3 × 4 C) 43 D) 44

10. What is the area of a square if one-third its side-length is 4?

A) 12 B) 16 C) 48 D) 144

11. On a Monday my surf club had 20 members. If the number of members

doubled each day, on what day did my club first have over 2018 members?

A) Sunday B) Monday

C) Tuesday D) Friday

12. Rounding a decimal to the nearest whole number yields a number that is at most ?

greater than the original decimal.

A) 0.05 B) 0.1 C) 0.5 D) 0.9

13. The perimeter of a rectangle with area 2019 and integral side-lengths is greatest when its

length and width differ by

A) 0 B) 1 C) 670 D) 2018

14. If half of my pals have at least 1 pet, and 1/3 of my pals with a pet

have more than 1 pet, what fraction of my pals have exactly 1 pet?

16 B)

13 C)

23 D)

15. The average of 0.5, 1.5, and 2.5 equals the average of 1 and

A) 1 B) 1.5 C) 2 D) 2.5

16. 9 × 90 × 900 × 9000 = 9 × ?

A) 1003 B) 9003 C) 90003 D) 9 000 0003

17. What is one less than the product -18 × 19?

A) -341 B) -342 C) -343 D) -344

18. When I divide the number of digits in the decimal form of 102018 by 4, the remainder is

A) 3 B) 2 C) 1 D) 0

19. My first name has 60% as many letters as my last name. My first name could be

A) Al B) Ali C) Alex D) Alexa

20. What is the least possible sum of two integers whose product is 12?

A) -13 B) -11 C) 7 D) 8

21. Of the first 100 positive integers, ? are not multiples of both 2 and 3.

A) 16 B) 32 C) 64 D) 84

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22. If one-third of the eggs in each carton of 1-dozen eggs are cracked, I must buy ?

cartons to get 16-dozen eggs that are not cracked.

A) 48 B) 36 C) 24 D) 20

23. Which of the following is nearest in value to 8.25?

82105 B)

82510 C)

810 D)

825

24. I bowled on 2 days every week, on a different pair of days each week

that I bowled. For at most how many weeks did I bowl?

A) 14 B) 21

C) 28 D) 35

25. Which of the following has the least value?

A) 0.1 B) 0.01 C) 0.0011 D) (0.01)2

26. A rectangular prism is 5 m long, 4 m wide, and 6 m high. What is the sum of the lengths

of its edges?

A) 15 m B) 60 m C) 80 m D) 120 m

27. What is the ratio of

113 to its reciprocal?

A) 1

3 C)

4 D)

16439

28. Pens come in packs of 3, 6, 8, and 12. I bought 12 packs and got a total of

121 pens. If I bought at least one of each size pack, how many packs of

8 pens did I buy?

A) 1 B) 2

C) 3 D) 4

29. 32 × 82 × 52 = 62 × ? × 102

B) 2 C) 22 D) 23

30. I wrote the first 100 positive integers in order, and then erased every “1” I had written.

How many digits did I erase?

A) 18 B) 19 C) 20 D) 21

31. What is the difference between the product and the sum of the nonzero digits of 2010

when

it is written in decimal form?

A) 1 B) 2 C) 102 D) 2 × 10

第3页，共4页

32. In the sequence 20,

1918172,

4, … , each term after the first term is gotten by

subtracting 1 from the previous term’s numerator and adding 1 to the previous term’s

denominator. How many terms in this sequence are positive integers?

A) 1 B) 2 C) 3 D) 4

33. Two congruent rectangular cards partially overlap. The area of overlap is

a square with area 4, and the total area of the regions of the faces of the

two cards that do not overlap is 12. What is the area of one card?

A) 4 B) 6

C) 8 D) 10

34. If the mean of three positive integers is 5, then the product of all 3 integers is at most

A) 105 B) 120 C) 125 D) 150

35. What is the sum of the digits of the least 3-digit integer whose square is a 6-digit integer?

A) 5 B) 7 C) 9 D) 11

36. If the sum of two consecutive even integers is 2018, what is their average?

A) less than 1009 B) 1009

C) bigger than 1009 and less than 2018 D) 2018

37. What is the area of a rectangle whose shorter sides have length 3 if a

line segment drawn from a vertex of the rectangle to the midpoint

of the rectangle's longer side (as shown) has length 5?

A) 18 B) 21 C) 24 D) 36

38. At 12:30, what is the degree-measure of the smaller angle formed by the minute and hour

hands of a circular 12-hour clock?

A) 160 B) 165 C) 170 D) 175

39. If N is a 3-digit integer, and the result of reversing the digits of N is the number M, what is

the maximum value of N – M?

A) 809 B) 890

C) 908 D) none of the above

40. What is the digit sum of the smallest integer greater than 237 for which each digit of the

integer is a prime number?

A) 11 B) 12

C) 14 D) none of the above

第4页，共4页

2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段

六年级试卷答案

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