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2018-2019年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)
(初赛时间：2018年11月14日,考试时间90分钟,总分200分)
学生诚信协议：考试期间,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,
我确定以下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。
如果您同意遵守以上协议请在装订线内签名
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. A 6 by 6 square has the same area as a 4 by ? rectangle.
2. Every prime has exactly ? positive divisors.
3. If I answered 34 out of 40 questions on my math test correctly, I answered ? % of the questions correctly.
4. 120 ÷ 3 ÷ 4 × 12 =
5. 10 × 20 × 30 × 40 = 24 × ?
A) 1000 | B) 10 000 | C) 100 000 | D) 1000 000 |
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6. One of my boxes contains 1 pencil and the others each contain 5 pencils. If there are 101 pencils in my boxes, how many boxes do I have?
7. An electrical company imports 2016 light bulbs. Unfortunately, 25%
of tho are damaged. How many light bulbs are not damaged?
A) 25 | B) 504 | C) 1512 | D) 2016 |
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8. 50 × (16 + 24) is the square of
9. Which of the following numbers has exactly 3 positive divisors?
10. Ten people stand in a line. Counting from the left, Jerry stands at the 5th position. Counting from the right, which position is he at?
11. On a teamwork project, Jack contributed 2/7 of the total amount of work, Jill contributed 1/4 of the work, Pat contributed 1/5 of the work, and Matt contributed the rest. Who contributed the most toward this project?
A) Jack | B) Jill | C) Pat | D) Matt |
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12. Which of the following numbers is a factor of 2016?
13. 2 × 4 × 8 × 16 × 32 × 64 =
A) 210 | B) 215 | C) 221 | D) 2120 |
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14. On a game show, Al won four times as much as Bob, and Bob won four times as much as Cy. If Al won $1536, how much did Al, Bob, and Cy win together?
A) $96 | B) $384 | C) $1920 | D) $2016 |
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15. The sum of two composites cannot be
16. If a and b are positive integers such that a/b = 5/7, then a + b is
A) 12 | B) 24 | C) 36 | D) not able to be determined |
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17. What is the greatest odd factor of the number of hours in all the days of the year 2015?
18. If the current month is February, what month will it be 1 199 999 months from now?
A) January | B) February | C) March | D) April |
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19. Two angles are complementary. One of the angles is 36° less than the other. What is the measure of the larger angle?
20. (The square root of 16) + (the cube root of 64) + (the 4th root of 256) =
21. In ∆ABC, m∠A – m∠B = m∠B – m∠C. What is the degree measure of ∠B?
22. For every 3 math books I bought, I bought 2 biology books. I bought 55 books in all. How many of tho are math books?
23. John wrote a number who digits consists entirely of 1s. This number was a composite number. His number could contain exactly ? 1s.
24. Weird Town us three types of currencies: Cons, Flegs, and Sels. If 3 Sels = 9 Cons and 2 Cons = 4 Flegs, then 5 Sels = ? Flegs.
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If the length of a rectangular prism with volume V is doubled while the width and the height are halved, the volume of the new prism will be 26. Rick and Roy each stands at different ends of a straight road that is 64 m long. They run toward each other. Rick’s speed is 3 m/s and Roy’s speed is 5 m/s. They will meet in
?
conds.
27. If the area of a certain circle is 2016, its radius is
A) sqrt(2016/π) | B) sqrt(4032/π) |
C) 2016/π | D) 1008/π |
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28. In a toy shop, the cost of a Teddy Bear is 200% as much as that of a toy train. The cost of a toy train is 6/5 the cost of a pack of the wooden blocks. The cost of a pack of wooden blocks is $50. What is the cost, in dollars, of the Teddy Bear?
29. In the quence 2016, 225, 141, 66, 432, 99, 1458 …, each term after the first term is the sum of the cubes of the digits of the previous term. What is the 100th term of this quence?
30. What is the sum of all the positive divisors of 210?
