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AMC8 2009

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AMC8 · 2009

Q1
Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie 3 apples, keeping 4 apples for herself. How many apples did Bridget buy?
Bridget在杂货店买了一袋苹果。她把苹果的一半给了Ann。然后她给了Cassie 3个苹果，自己留了4个苹果。Bridget一共买了多少个苹果？
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Q2
On average, for every 4 sports cars sold at the local car dealership, 7 sedans are sold. The dealership predicts that it will sell 28 sports cars next month. How many sedans does it expect to sell?
当地汽车经销商平均每卖出4辆跑车，就卖出7辆轿车。经销商预测下个月将卖出28辆跑车。它预计卖出多少辆轿车？
Q3
The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of half an hour at the same speed, how many miles will she have ridden?
图表显示了Suzanna骑自行车的恒定速率。如果她以相同的速度骑总共半小时，她将骑多少英里？
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Q4
The five pieces shown at right can be arranged to form four of the five figures below. Which figure cannot be formed?
右侧显示的五个拼块可以排列成下面五个图形中的四个。哪个图形无法形成？
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Q5
A sequence of numbers starts with 1, 2 and 3. The fourth number of the sequence is the sum of the previous three numbers in the sequence: $1 + 2 + 3 = 6$. In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?
一个数字序列以1、2和3开始。序列的第四个数字是前三个数字的和：$1 + 2 + 3 = 6$。同样，第四个之后的每个数字都是前三个数字的和。序列的第八个数字是多少？
Q6
Steve's empty swimming pool will hold 24,000 gallons of water when full. It will be filled by 4 hoses, each of which supplies 2.5 gallons of water per minute. How many hours will it take to fill Steve's pool?
史蒂夫的空游泳池满水时能容纳24,000加仑水。它将由4根水管填充，每根水管每分钟供应2.5加仑水。填充史蒂夫的泳池需要多少小时？
Q7
The triangular plot of land ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD?
三角形地块ACD位于Aspen路、Brown路和一条铁路之间。Main Street呈东西走向，铁路呈南北走向。图中的数字表示英里的距离。铁路轨道的宽度可以忽略不计。地块ACD有多少平方英里？
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Q8
The length of a rectangle is increased by 10% and the width is decreased by 10%. What percent of the old area is the new area?
矩形的长度增加10%，宽度减少10%。新面积是原面积的百分之多少？
Q9
Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular pentagon, as shown. On a non-adjacent side of the pentagon, construct a regular hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?
在一个等边三角形的一条边上构造一个正方形。在正方形的一条不相邻边上构造一个正五边形，如图所示。在正五边形的一条不相邻边上构造一个正六边形。以同样的方式继续构造正多边形，直到构造出八边形。最终得到的的多边形有多少条边？
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Q10
On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?
在一个由64个单位方格组成的棋盘上，随机选择的单位方格不接触棋盘外边缘的概率是多少？
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Q11
The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pencil, paying a total of $1.43. Some of the 30 sixth graders each bought a pencil, and they paid a total of $1.95. How many more sixth graders than seventh graders bought a pencil?
Amaco 中学的书店出售铅笔，每支铅笔的价格是一个整数美分。有些七年级学生每人买了一支铅笔，总共支付了 1.43 美元。30 名六年级学生中的一些人也每人买了一支铅笔，他们总共支付了 1.95 美元。有多少名六年级学生比七年级学生多买了铅笔？
Q12
The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?
示出的两个转盘各转动一次，每个都落在编号扇形之一上。两个扇形数字之和为质数的概率是多少？
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Q13
A three-digit integer contains one of each of the digits 1, 3 and 5. What is the probability that the integer is divisible by 5?
一个三位整数包含 1、3 和 5 各一个数字。该整数能被 5 整除的概率是多少？
Q14
Austin and Temple are 50 miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging 60 miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged 40 miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?
奥斯汀和坦普沿 35 号州际公路相距 50 英里。邦妮开车从奥斯汀到坦普女儿家，平均时速 60 英里。把车留给女儿后，邦妮乘坐巴士沿同一路线返回奥斯汀，返回行程平均时速 40 英里。往返行程的平均速度是多少英里每小时？
Q15
A recipe that makes 5 servings of hot chocolate requires 2 squares of chocolate, $\frac{1}{4}$ cup sugar, 1 cup water and 4 cups milk. Jordan has 5 squares of chocolate, 2 cups of sugar, lots of water and 7 cups of milk. If she maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate she can make?
一份制作 5 份热巧克力的配方需要 2 块巧克力、$\frac{1}{4}$ 杯糖、1 杯水和 4 杯牛奶。乔丹有 5 块巧克力、2 杯糖、充足的水和 7 杯牛奶。如果她保持相同的配方比例，她最多能做多少份热巧克力？
Q16
How many 3-digit positive integers have digits whose product equals 24?
有多少个3位正整数，其各位数字的乘积等于24？
Q17
The positive integers $x$ and $y$ are the two smallest positive integers for which the product of 360 and $x$ is a square and the product of 360 and $y$ is a cube. What is the sum of $x$ and $y$?
正整数$x$和$y$是满足360与$x$的乘积为完全平方数且360与$y$的乘积为完全立方数的最小的两个正整数。求$x$和$y$的和。
Q18
The diagram represents a 7-foot-by-7-foot floor that is tiled with 1-square-foot black tiles and white tiles. Notice that the corners have white tiles. If a 15-foot-by-15-foot floor is to be tiled in the same manner, how many white tiles will be needed?
图示是一个7英尺×7英尺的地板，用1平方英尺的黑白瓷砖铺成。注意角落处是白瓷砖。如果要以相同方式铺一个15英尺×15英尺的地板，需要多少白瓷砖？
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Q19
Two angles of an isosceles triangle measure 70° and $x$°. What is the sum of the three possible values of $x$?
一个等腰三角形的两个角分别是70°和$x$°。三个可能$x$值的和是多少？
Q20
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
如下所示的8个点阵中，有多少个顶点在三个点的非全等的三角形？
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Q21
Andy and Bethany have a rectangular array of numbers with 40 rows and 75 columns. Andy adds the numbers in each row. The average of his 40 sums is $A$. Bethany adds the numbers in each column. The average of her 75 sums is $B$. What is the value of $\frac{A}{B}$?
Andy 和 Bethany 有一个有 40 行和 75 列的矩形数字阵列。Andy 计算每行的数字之和。他的 40 个和的平均值为 $A$。Bethany 计算每列的数字之和。她的 75 个和的平均值为 $B$。$ rac{A}{B}$ 的值为多少？
Q22
How many whole numbers between 1 and 1000 do not contain the digit 1?
1 到 1000 之间有多少个不含数字 1 的整数？
Q23
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?
在放学的最后一天，Wonderful 夫人给她的班级分发果冻豆。她给每个男孩的果冻豆数量等于班上男孩的数量。她给每个女孩的果冻豆数量等于班上女孩的数量。她带来了 400 颗果冻豆，分发完毕后还剩 6 颗。班上有比女孩多 2 个男孩。她的班级有多少学生？
Q24
The letters A, B, C and D all represent different digits. If $\begin{array}{cc} & A & B \\ + & C & A \\ \hline & D & A \end{array}$ and $\begin{array}{cc} & A & B \\ - & C & A \\ \hline & & A \end{array}$, what digit does D represent?
字母 A、B、C 和 D 分别代表不同的数字。如果 $ \begin{array}{cc} & A & B \\ + & C & A \\ \hline & D & A \end{array}$ 和 $ \begin{array}{cc} & A & B \\ - & C & A \\ \hline & & A \end{array}$，D 代表什么数字？
Q25
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is $\frac{1}{2}$ foot from the top face. The second cut is $\frac{1}{3}$ foot below the first cut, and the third cut is $\frac{1}{17}$ foot below the second cut. From the top to the bottom the pieces are labeled A, B, C and D. The pieces are then glued together end to end in the order C, B, A, D to make a long solid as shown below. What is the total surface area of this solid in square feet?
一个 1 立方英尺的立方体被三刀平行于立方体顶面切割成四块。第一刀距顶面 $ rac{1}{2}$ 英尺。第二刀在第一刀下方 $ rac{1}{3}$ 英尺，第三刀在第二刀下方 $ rac{1}{17}$ 英尺。从上到下，块依次标记为 A、B、C 和 D。然后将这些块按 C、B、A、D 的顺序端对端粘合，形成一个长固体，如下图所示。这个固体的总表面积是多少平方英尺？
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