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AMC8 2016

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AMC8 · 2016

Q1
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes. How many minutes was this?
历史上最长的职业网球比赛总共持续了11小时5分钟。这是多少分钟？
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Q2
In rectangle ABCD, AB = 6 and AD = 8. Point M is the midpoint of AD. What is the area of $\triangle AMC$?
在矩形ABCD中，AB = 6，AD = 8。点M是AD的中点。$ riangle AMC$的面积是多少？
Q3
Four students take an exam. Three of their scores are 70, 80, and 90. If the average of their four scores is 70, then what is the remaining score?
四个学生参加考试。其中三个分数是70、80和90。如果四个分数的平均分是70，那么剩下的分数是多少？
Q4
When Cheenu was a boy he could run 15 miles in 3 hours and 30 minutes. As an old man he can now walk 10 miles in 4 hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?
Cheenu小时候能在3小时30分钟内跑15英里。现在作为老人，他能在4小时内走10英里。现在走一英里比小时候多花多少分钟？
Q5
The number $N$ is a two-digit number. -- When $N$ is divided by 9, the remainder is 1. -- When $N$ is divided by 10, the remainder is 3. What is the remainder when $N$ is divided by 11?
数$N$是一个两位数。 -- 当$N$除以9时，余数是1。 -- 当$N$除以10时，余数是3。 $N$除以11的余数是多少？
Q6
The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names? *(Bar graph with horizontal axis labeled name length: 3,4,5,6,7 and vertical axis frequency; frequencies: 7 at 3, 3 at 4, 1 at 5, 4 at 6, 4 at 7)*
下图柱状图表示19个人的名字长度（以字母数计）。这些名字的长度中位数是多少？*(柱状图横轴标签为名字长度：3,4,5,6,7，纵轴为频数；频数：3处为7，4处为3，5处为1，6处为4，7处为4)*
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Q7
Which of the following numbers is not a perfect square?
下列哪个数不是完全平方数？
Q8
Find the value of the expression $100 - 98 + 96 - 94 + 92 - 90 + \cdots + 8 - 6 + 4 - 2$.
求表达式的值：$100 - 98 + 96 - 94 + 92 - 90 + \cdots + 8 - 6 + 4 - 2$。
Q9
What is the sum of the distinct prime integer divisors of 2016?
2016的互异素整数因数的和是多少？
Q10
Suppose that $a * b$ means $3a - b$. What is the value of $x$ if $2*(5*x) = 1$?
假设$a * b$表示$3a - b$。若$2*(5*x) = 1$，则$x$的值是多少？
Q11
Determine how many two-digit numbers satisfy the following property: When the number is added to the number obtained by reversing its digits, the sum is 132.
确定有多少个两位数满足以下性质：将该数与其数字反转后得到的数相加，和为132。
Q12
Jefferson Middle School has the same number of boys and girls. Three-fourths of the girls and two-thirds of the boys went on a field trip. What fraction of the students on the field trip were girls?
杰斐逊中学男孩和女孩数量相同。\frac{3}{4}的女孩和\frac{2}{3}的男孩参加了实地考察旅行。实地考察旅行中的学生有女孩占几分之几？
Q13
Two different numbers are randomly selected from the set $\{-2, -1, 0, 3, 4, 5\}$ and multiplied together. What is the probability that the product is 0?
从集合$\{-2, -1, 0, 3, 4, 5\}$中随机选取两个不同的数相乘。乘积为0的概率是多少？
Q14
Karl's car uses a gallon of gas every 35 miles, and his gas tank holds 14 gallons when it is full. One day Karl started with a full tank of gas, drove 350 miles, bought 8 gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?
Karl的小汽车每35英里耗油1加仑，其油箱满时可装14加仑。有一天Karl从满油箱开始，开车350英里，买了8加仑油，继续开车到目的地。到达时油箱半满。那天Karl总共开了多少英里？
Q15
What is the largest power of 2 that is a divisor of $13^4 - 11^4$?
$13^4 - 11^4$的最大2的幂次除数是多少？
Q16
Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead, because she runs 25% faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
Annie 和 Bonnie 在一个 400 米椭圆跑道上跑圈。她们一起起跑，但 Annie 已经领先，因为她的速度比 Bonnie 快 25%。当她第一次超过 Bonnie 时，Annie 会跑完多少圈？
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Q17
An ATM password at Fred's Bank is composed of four digits from 0 to 9, with repeated digits allowable. If no password may begin with the sequence 9, 1, 1, then how many passwords are possible?
Fred 银行的 ATM 密码由 0 到 9 的四位数字组成，允许重复数字。如果密码不得以序列 9,1,1 开头，则可能有多少个密码？
Q18
In an All-Area track meet, 216 sprinters enter a 100-meter dash competition. The track has 6 lanes, so only 6 sprinters can compete at a time. At the end of each race the five non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine the champion sprinter?
在全区田径比赛中，有 216 名短跑运动员参加 100 米短跑比赛。跑道有 6 条道，因此每次只能有 6 名运动员比赛。每场比赛结束后，五名非获胜者被淘汰，获胜者将在稍后的比赛中再次参赛。需要多少场比赛才能确定冠军短跑运动员？
Q19
The sum of 25 consecutive even integers is 10,000. What is the largest of these 25 consecutive even integers?
25 个连续偶数的和是 10,000。这些 25 个连续偶数中最大的是多少？
Q20
The least common multiple of $a$ and $b$ is 12, and the least common multiple of $b$ and $c$ is 15. What is the least possible value of the least common multiple of $a$ and $c$?
$a$ 和 $b$ 的最小公倍数是 12，$b$ 和 $c$ 的最小公倍数是 15。$a$ 和 $c$ 的最小公倍数的最小可能值是多少？
Q21
A box contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?
一个盒子里有3个红筹码和2个绿筹码。从盒子里随机抽取筹码，一次抽一个，不放回，直到抽到所有3个红筹码或抽到两个绿筹码为止。抽到3个红筹码的概率是多少？
Q22
Rectangle DEFA below is a 3×4 rectangle with DC = CB = BA = 1. The area of the “bat wings” (the shaded area) is
下面的矩形DEFA是一个3×4的矩形，且DC = CB = BA = 1。“蝙蝠翅膀”（阴影区域）的面积是
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Q23
Two congruent circles centered at points A and B each pass through the other’s center. The line containing both A and B is extended to intersect the circles at points C and D. The two circles intersect at two points, one of which is E. What is the degree measure of $\angle CED$?
两个全等的圆分别以点A和B为中心，每个圆都经过对方的中心。包含A和B的直线延长，与圆相交于点C和D。两个圆相交于两点，其中之一是E。$\angle CED$ 的度量是多少度？
Q24
The digits 1, 2, 3, 4, and 5 are each used once to write a five-digit number PQRST. The three-digit number PQR is divisible by 4, the three-digit number QRS is divisible by 5, and the three-digit number RST is divisible by 3. What is P?
数字1、2、3、4和5各使用一次，写成五位数PQRST。三位数PQR能被4整除，三位数QRS能被5整除，三位数RST能被3整除。P是多少？
Q25
A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?
一个半圆内接于一个底边长16、高15的等腰三角形中，使得半圆的直径包含在三角形的底边上，如图所示。求半圆的半径。
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Time Left 40:00