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2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段四年级

2024年1月1日发(作者：马鞍山)

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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

(四年级)

(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. 本试卷是四年级试卷，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. (123 + 456) + 678 = (123 + 678) + ?

A) 123 B) 456 C) 579 D) 678

2. Bea sharpened 1200 pencils. Half the pencils had erasers, and

half of all the erasers were pink. How many pencils with pink

erasers did Bea sharpen?

A) 200 B) 300

C) 400 D) 600

3. I have a prime number of pairs of socks. The total number of socks I have could not be

A) 26 B) 38 C) 46 D) 54

4. The product of 500 000 and 200 000 has exactly ? zeros.

A) 5 B) 6 C) 10 D) 11

5. Divide 100 by 10, then multiply the result by 10. The final answer is

A) 0 B) 1 C) 10 D) 100

6. At most how many complete 8-minute songs can I sing in 3 hours?

A) 22 B) 23 C) 24 D) 180

7. 2 × (44 + 44 + 44) = 88 + 88 + ?

A) 0 B) 44 C) 66 D) 88

8. A rectangle has sides of even lengths and perimeter 12. Its area is

A) 6 B) 8 C) 9 D) 16

第1页，共4页

9. 16 × (17 + 1) – ? × (15 + 1) = 0

A) 15 B) 16 C) 17 D) 18

10. The crowd clapped for 840 seconds, stopping at 8:15 P.M. They

started clapping at ? P.M.

A) 7:59 B) 8:01

C) 8:08 D) 8:14

11. If each digit of my 5-digit ID code is different, the sum of its digits

is at most

A) 15 B) 25 C) 35 D) 45

12. At the museum, adult tickets cost $4 each and child tickets cost $3 each. With $50, I can

buy ? more child tickets than adult tickets.

A) 1 B) 4 C) 12 D) 16

13. Each day last week I read for a whole number of hours. I read for

the same number of hours each day except Sunday. If I read for 12

hours last week, I read for ? hours on Sunday.

A) 7 B) 6 C) 5 D) 4

14. The product 2 × 3 × 4 × 5 × 6 has the same value as the product ? × 3 × 5.

A) 12 B) 36 C) 48 D) 63

15. The average test grade in my class is a whole number, and the sum of the test grades is

2400. Of the following, which could be the total number of test grades?

A) 18 B) 21 C) 27 D) 32

16. If twice a whole number is 120 less than five times the same whole number, then half the

whole number is

A) 10 B) 20 C) 40 D) 60

17. The number of bees I have doubles each day. If I had 1024 bees last Friday, the first day

the number of bees was more than 100 was a

A) Tuesday B) Wednesday

C) Thursday D) Friday

18. Each of 6 dogs ate 3 treats from each of 4 bags. If each bag started with 30 treats, the 4

bags together ended with ? treats.

A) 36 B) 48 C) 72 D) 96

19. What is the greatest possible product of two different even whole numbers whose sum is

100?

A) 196 B) 625 C) 2496 D) 2500

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20. Ed built 3 times as many houses as Bob, who built half as many houses as

Ally. If the 3 of them built 96 houses in all, Ed and Ally built a combined

total of ? houses.

A) 16 B) 32

C) 48 D) 80

21. How many factors of 2 × 4 × 8 × 16 are multiples of 4?

A) 3 B) 4 C) 8 D) 9

22. When I divide a certain number by 3 or 5, I get a remainder of 2. The sum of the digits of

the least number for which this is true is

A) 1 B) 3 C) 7 D) 8

23. My 144 fish are split between 2 tanks so that 1 tank has twice as many

fish as the other. How many fish must I move from one tank to

the other so that both tanks have the same number of fish?

A) 24 B) 48

C) 60 D) 72

24. A 3-digit number is the product of at most ? whole numbers greater than 1.

A) 2 B) 3 C) 9 D) 10

25. Abby earns $2 for every clam she finds and $3 for every oyster. If Abby finds 5 times as

many oysters as clams, which of the following could be her total earnings?

A) $150 B) $160 C) $170 D) $180

26. (The average value of the 10 smallest even whole numbers greater than 0) – (the average

value of the 10 smallest odd whole numbers) =

A) 0 B) 1 C) 10 D) 11

27. Ana planted seeds in rows. If the total number of rows

equaled the number of seeds in each row, the number

of seeds planted could have been

A) 194 B) 216 C) 250 D) 289

28. What is the greatest possible sum of five 2-digit whole numbers if all 10 digits of the five

numbers are different?

A) 270 B) 315 C) 360 D) 485

29. I thought I wrote every whole number between 1 and 500 in order from least to greatest,

but actually I skipped 3 numbers in a row. If I left out a total of 8 digits, what is the sum of

the numbers I skipped?

A) 100 B) 150 C) 300 D) 390

第3页，共4页

30. Written backwards, 123 becomes 321. How many whole numbers between 100 and 200

have a larger value when written backwards?

A) 70 B) 80 C) 90 D) 98

31. The average of four different numbers is 18. And the least of the four numbers is 3. What

is the least possible value of the biggest of the four numbers?

A) 21 B) 23 C) 24 D) 60

32. 3 tigers can eat 36 Big Macs in 6 minutes. How many Big Macs can 12 tigers eat in 3

minutes?

A) 18 B) 36 C) 72 D) 288

33. In the following sequence, 2, 0, 1, 8, 2, 0, 1, 8, … (repeating), what is its 2018th term?

A) 2 B) 0 C) 1 D) 8

34.

2a0b1c8 is a multiple of 9. What is the least possible value of

abc? (Note:

abc

is a

three-digit number, which means a is not 0.)

A) 7 B) 100 C) 106 D) 997

35. What is the least common multiple of 84 and 112?

A) 28 B) 196 C) 336 D) 9408

36. In triangle ABC, C = 90°, A = 15°, AB = 20. What is the area of this triangle?

A) 20 B) 50 C) 100 D) 200

37. ABCD is a rectangle and its perimeter is 22, as shown at the right.

EFGH is a square. AH = 6. CF = ?

A) 4 B) 5

C) 6 D) 8

38. How many leap years are there between 2018 and 2081?

A) 16 B) 17 C) 18 D) 19

39. My class was lined up on the gym floor in 8 rows, with 2 students in each row. If our

coach rearranged us so that the number of rows was the same as the number of students in

each row, how many rows were there after we were rearranged?

A) 4 B) 6 C) 10 D) 16

40. Of the 100 numbers from 1 to 100, how many of them don’t contain 7 as its digit?

A) 65 B) 75

C) 80 D) none of the above

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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

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