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AMC8每日一题(2001年真题#05)

2018-06-01
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　　多年来，AMC还扮演为美国培育世界数学奥林匹克(IMO)选手的重责大任。AMC的研究人员透过AMC 8、AMC 10、AMC 12、AIME一系列测验，找出绩优生参加美国数学奥林匹克(USAMO)，再从全美数十州筛选出24至30位精英，成立数学奥林匹克夏令营 (MOSP)。经过AMC的密集训练，事实证明，以1990年到2000年这十年为例，有九年由AMC集训的美国队赢得奖牌。AMC不但是美国顶尖数学人才的人才库，更为学校提供了解申请入学者在数学科目上的学习成就与表现评估。AMC成功地为许多学生因测验成绩优良而进入理想学校。藉由设计严谨的试题，达到激发应试者解决问题的能力，培养对数学的兴趣。试题由简至难兼具，使任何程度的学生都能感受到挑战，还可以筛选出特有天赋者。为了方便同学们的AMC备考，课窝考试网小编为大家收集整理了AMC课程历年真题练习，供大家学习参考，希望能为同学们的考试提供帮助。

2001 AMC 8 竞赛试题/第05题

Problem

On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning.

$\text{(A)}\ 1 \qquad \text{(B)}\ 1\frac{1}{2} \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 2\frac{1}{2} \qquad \text{(E)}\ 3$

Solution

During those $10$ seconds, the sound traveled $1088\times10=10880$ feet from the lightning to Snoopy. This is equivalent to $\frac{10880}{5280}\approx2$ miles, $\boxed{\text{C}}$ .

2001 AMC 8 竞赛试题/第06题

Problem

Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?

$\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 105 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 140$

Solution

There are $3$ spaces between the 1st and 4th trees, so each of these spaces has $\frac{60}{3}=20$ feet. Between the first and last trees there are $5$ spaces, so the distance between them is $20\times5=100$ feet, $\boxed{\text{B}}$ .