2017年美国数学竞赛8年级(AMC8)真题(附答案)(电脑版)

Middle Primary DivisionQuestions 1 to 10 are worth 3 marks each.1-10题，每题3分1.What is the total number of petals on all 5 flowers?图中5朵花总计有多少片花瓣?(A)10 (B)15 (C)20 (D)25 (E)502.2+3+7+8=(A)10 (B)20 (C)30 (D)40 (E)503.Which one of these shapes is a rectangle?哪个选项是长方形?(A) (B)(C)(D) (E)4.Which digital clock time matches the time shown on the clock face?哪个选项中的数字时钟显示的时间与钟面相同?(A)3:09 (B)[ 9:03 (C) 9:15(D)10:03 (E)10:155.Emma has a bag containing 5 red,4 yellow,1 black and 2 blue buttons.When she chooses 1 button at random,what colour is it most likely to be?艾玛有一袋纽扣，里面有5个红色纽扣，4个黄色纽扣，1个黑色纽扣和2个蓝色纽扣。

从中随机选出一个纽扣，这个纽扣最有可能是什么颜色?(A)green 绿色(B)blue 蓝色(C)black 黑色(D)yellow 黄色(E)red 红色6.What fraction of the circle is part A?A 部分占整个圆的几分之几?(A) one-half 二分之一(B) one-third 三分之一(C) two-thirds 三分之二(D) one-quarter 四分之一(E) three-quarters 四分之三7.In a board game,Nik rolls three standard dice,one at a time.He needs his three rolls to add to 12.His first two dice rolls are 5 and 3.What does he need his third roll to be?棋盘游戏中，尼克投掷三枚标准的骰子，每次掷出一枚。

美国数学竞赛AMC8 -- 2010年真题解析(英文解析+中文解析)Problem 1Answer: CSolution:Given that these are the only math teachers at Euclid Middle School and we are told how many from each class are taking the AMC 8, we simply add the three numbers to find the total.11+8+9=28.中文解析:参加竞赛的学生总人数是：11+8+9=28. 答案是C。

Problem 2Answer: DSolution:Substitute a=5, b=10 into the expression for a@b to get: 5@10=(5*10)/(5+10)=50/15=10/3.中文解析：（5*10）/（5+10）=50/15=10/3. 答案是D。

Problem 3Answer: CSolution:The highest price was in Month 1, which was $17. The lowest price was in Month 3, which was $10. 17 is 17/10 =170% of 10, and is 170-100=70% more than 10. Therefore, the answer is 70. 中文解析：最高价是1月，17美元。

最低价格是3月10美元。

最高价比最低价多：（17-10）/10=70%。

答案是C。

Problem 4Answer: CSolution:Putting the numbers in numerical order we get the list 0,0,1,2,3,3,3,4 The mode is 3, The median is (2+3)/2=2.5. The average is 2. is The sum of all three is 3+2.5+2=7.5.中文解析：这组数按照从小到大的顺序排列是：0，0，1，2，3，3，3，4. 中位数Median是2.5；mode 是3，mean是16/8=2. 因此mean,median,mode的和是: 2.5+3+2=7.5. 答案是C。

美国数学竞赛AMC8 – 2005年真题解析(英文解析+中文解析)Problem 1Answer: BSolution:If x is the number, then 2x=60 and x=30. Dividing the number by 2 yields 15.中文解析：按照Connie的计算，这个数乘以2是60，可知这个数是30. 应该做的计算是30除以2，因而正确答案应该是15. 答案是B。

Problem 2Answer: CSolution:Karl paid 5*2.5=$12.5. 20% of this cost that he saved is 12.5*0.2=$2.5.中文解析：Karl按原价买了5个文件夹，支付的费用是：2.5*5=12.5. 折扣价是：1.25*0.8=10。

如果Karl 等一天，可以省2.5元。

答案是C.Problem 3Answer: DSolution:Rotating square ABCD counterclockwise 45° so that the line of symmetry BD is a vertical line makes it easier to see that 4 squares need to be colored to match its corresponding square.中文解析：如上图所示，以BD为对称轴，标蓝色的方块需要涂黑。

共4块，答案是D。

Problem 4Answer: CSolution:The perimeter of the triangle is 6.1+8.2+9.7=24cm. A square's perimeter is four times its side length, since all its side lengths are equal. If the square's perimeter is 24, the side length is24/4=6, and the area is 6*6=36.中文解析：三角形的周长是：6.1+8.2+9.7=24. 正方形的周长和三角形相等，也是24，则其边长是24/4=6. 其面积是：6*6=36. 答案是C。

2001年AMC8（全美中學數學分級能力測驗8年級）試題及答案1. 凱西的商店正在製作一個高爾夫球獎品。

他必須給一顆高爾夫球面上的300個小凹洞著色，如果他每著色一個小凹洞需要2秒鐘，試問共需多少分鐘才能完成他的工作？(A) 4 (B) 6 (C) 8 (D) 10 (E) 122. 我正在思考兩個正整數，它們的乘積是24且它們的和是11，試問這兩個數中較大的數是什麼？(A) 3 (B) 4 (C) 6 (D) 8 (E) 123. 史密斯有63元，艾伯特比安加多2元，而安加所有的錢是史密斯的三分之一，試問艾伯特有多少元？(A) 17 (B) 18 (C) 19 (D) 21 (E) 234. 在每個數字只能使用一次的情形下，將1 ，2，3 ，4及9作成最小的五位數，且此五位數為偶數，則其十位數字為？(A) 1 (B) 2 (C) 3 (D) 4 (E) 95. 在一個暴風雨的黑夜裡，史努比突然看見一道閃光。

10秒鐘後，他聽到打雷聲音。

聲音的速率是每秒1088呎，但1哩是5280呎。

若以哩為單位的條件下，估計史努比離閃電處的距離最接近下列何者？(A) 1 (B) 1 1/2 (C) 2 (D) 2 1/2 (E) 36. 在一筆直道路的一旁有等間隔的6棵樹。

第1棵樹與第4棵樹之間的距離是60呎。

試問第1棵樹到最後一棵樹之間的距離是多少呎？(A) 90 (B) 100 (C) 105 (D) 120 (E) 140※競賽場所上的風箏展覽問題7、8以及9是有關這些風箏的問題葛妮芙為提升她的學校年度風箏奧林匹亞競賽的品質，製作了一個小風箏與一個大風箏，並陳列在公告欄展覽，這兩個風箏都如同圖中的形狀，葛妮芙將小風箏張貼在單位長為一吋（即每兩點距離一吋）的格子板上，並將大風箏張貼在單位長三吋（即每兩點距離三吋）的格子板上。

7. 試問小風箏的面積是多少平方吋？(A) 21 (B) 22 (C) 23 (D) 24 (E) 258. 葛妮芙在大風箏內裝設一個連接對角頂點之十字交叉型的支撐架子，她必須使用多少吋的架子材料？(A) 30 (B) 32 (C) 35 (D) 38 (E) 399. 大風箏要用金箔覆蓋。

美国数学竞赛AMC8 -- 2019年真题解析（英文解析+中文解析）Problem 1Answer: DSolution:We maximize the number of sandwiches Mike and Ike can buy by finding the lowest multiple of 4.5 that is less than 30 This number is 6.Therefore, they can buy 6 sandwiches for 4.5*6=27. They spend the remaining money on soft drinks, so they buy30-27=3 soft drinks. Combining the items, Mike and Ike buy 6+3=9 items.中文解析：4.5*6=27. 因此买6个Sandwiches，剩下的3元钱买3个Drinks.Problem 2Answer: ESolution:Using the diagram we find that the larger side of the small rectangle is 2 times the length of the smaller side. Therefore the longer side is 5*2=10. So the area of the identical rectangles is5*10=50. We have 3 identical rectangles that form the large rectangle. Therefore the area of the large rectangle is 50*3=150.中文解析：长方形的短边的长度是5，则AD=5+5=10. CD=AD=10. 即长方形的长边是10. ABCD的面积是: AB *BC =(10+5)*10=150.答案是E。

amc历年试题AMC历年试题是指美国数学竞赛（AMC）的历年考题，这个竞赛是一个旨在鼓励和发展学生对数学的兴趣和才能的国际竞赛。

以下是一些与AMC历年试题相关的参考内容。

一、AMC概述：AMC由美国数学协会（MAA）举办，分为AMC 8、AMC 10、AMC 12和AIME四个阶段。

AMC 8是中学生竞赛，面向8年级以下学生，时限40分钟，50道选择题。

AMC 10和AMC12是中学生竞赛，时限75分钟，25道选择题。

AIME是AMC的补充考试，面向表现优异的学生，共有15道题目。

二、AMC参考内容：1. 历年试题：可以通过搜索AMC历年试题来找到以往考试的试题以及答案和解析。

通过做历年试题，可以了解AMC的考点和难度分布。

2. 数学竞赛教材：准备AMC考试的学生可以使用一些数学竞赛教材进行复习。

一些经典的数学竞赛教材，如《资深数学竞赛历届试题详解》、《美国数学竞赛AMC8高分秘笈》等，都是非常不错的参考资料。

3. 解题技巧：AMC考试的题目通常涉及多个数学领域，对于学生来说，掌握一些解题技巧是非常重要的。

例如，要熟悉常见的数学定理和公式，灵活运用数学知识进行计算和推理，注意阅读题目中的信息，从而找到解题的思路。

4. 知识点总结：AMC历年试题中涉及的数学知识点非常广泛，但是有一些重点领域需要重点掌握。

例如，代数、几何、概率与统计等方面的知识常常是出题的焦点。

学生可以通过制作知识点总结表格、归纳题目中常见的模式和解题方法等方式进行备考。

5. 模拟考试：进行模拟考试是备考阶段的重要环节。

可以使用AMC历年试题组成的模拟试卷进行练习和考核。

模拟考试有助于熟悉考试时间和解题节奏，提高解题效率和应试能力。

以上是与AMC历年试题相关的一些参考内容。

通过研究历年试题、提高解题技巧、总结知识点、进行模拟考试等方式，学生可以提高自己的数学水平，并在AMC考试中取得不错的成绩。

2000年AMC8（全美中学数学分级能力测验8年级）试题及答案1. 安妮今年42岁，凯琳比柏娜小五岁，而柏娜的年龄是安妮的一半。

试问凯琳今年几岁？(A) 15 (B) 16 (C) 17 (D) 21 (E) 372. 下列那一个数小于它的倒数？(A) -2 (B) -1 (C) 0 (D) 1 (E) 23. 有多少个整数介于5/3和2π之间？(A) 2 (B) 3 (C) 4 (D) 5 (E) 无限多4. 在卡林市，1960年只有5%的成年工作者在家工作，至1970年在家工作人数增加到8%，1960年大约有15%的人在家工作，而在1990年则有30%。

试问下面那一个图是这种情形的最佳说明。

5. 林肯中学每一位校长都洽服务一次三年任期，则在8年期间林肯中学最多有几位校长？(A) 2 (B) 3 (C) 4 (D) 5 (E) 86. 右图ABCD是正方形。

此正方形内有3个较小的正方形，它们的边长如图中所标示，则L行黑影区域的面积为多少？(A) 7 (B) 10 (C) 12.5 (D) 14 (E) 157. 从-8，-6，-4，0，3，5，7中任取三个不同数做乘积，则最小的乘积是(A) -336 (B) -280 (C) -210 (D) -192 (E) 08. 每面标有1至6点的三颗骰子推成一串，如右图所示，其中可见七个面，而十一个面是看不到的(背面、底面，之间的面)，试问看不见的面其点数总和是(A) 21 (B) 22 (C) 31 (D) 41 (E) 539. 填数游戏：右方格子中横的三个格子内(自左至右)填入三位数，此三位数可表为2m(m为正整数)，纵的三个格子内(自上至下)填入三位数，此三位数可表为5n(n为正整数)；试问，粗黑的格子内只能出现那一个数字？(A) 0 (B) 2 (C) 4 (D) 6 (E) 810. 杰克和珍妮佛两人的身高本来相同。

如今珍妮佛又长高20%，而杰克只长高珍妮佛所长高的一半。

2000年AMC8（全美中学数学分级能力测验8年级）试题及答案1. 安妮今年42岁，凯琳比柏娜小五岁，而柏娜的年龄是安妮的一半。

试问凯琳今年几岁？(A) 15 (B) 16 (C) 17 (D) 21 (E) 372. 下列那一个数小于它的倒数？(A) -2 (B) -1 (C) 0 (D) 1 (E) 23. 有多少个整数介于5/3和2π之间？(A) 2 (B) 3 (C) 4 (D) 5 (E) 无限多4. 在卡林市，1960年只有5%的成年工作者在家工作，至1970年在家工作人数增加到8%，1960年大约有15%的人在家工作，而在1990年则有30%。

试问下面那一个图是这种情形的最佳说明。

5. 林肯中学每一位校长都洽服务一次三年任期，则在8年期间林肯中学最多有几位校长？(A) 2 (B) 3 (C) 4 (D) 5 (E) 86. 右图ABCD是正方形。

此正方形内有3个较小的正方形，它们的边长如图中所标示，则L行黑影区域的面积为多少？(A) 7 (B) 10 (C) 12.5 (D) 14(E) 157. 从-8，-6，-4，0，3，5，7中任取三个不同数做乘积，则最小的乘积是(A) -336 (B) -280 (C) -210 (D) -192 (E) 08. 每面标有1至6点的三颗骰子推成一串，如右图所示，其中可见七个面，而十一个面是看不到的(背面、底面，之间的面)，试问看不见的面其点数总和是(A) 21 (B) 22 (C) 31 (D) 41(E) 539. 填数游戏：右方格子中横的三个格子内(自左至右)填入三位数，此三位数可表为2m(m为正整数)，纵的三个格子内(自上至下)填入三位数，此三位数可表为5n(n为正整数)；试问，粗黑的格子内只能出现那一个数字？(A) 0 (B) 2 (C) 4 (D) 6 (E) 810. 杰克和珍妮佛两人的身高本来相同。

如今珍妮佛又长高20%，而杰克只长高珍妮佛所长高的一半。

2.3.What is the value of ?4.Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?5.Hammie is in the grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?6.The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, . What is the missing number in the top row?7.Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?8.A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?9.The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer?10.What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?11. Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour, he would have spent less time on the treadmill. How many minutes less?12. At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save?13. When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?14. Let the two digits be and .The correct score was . Clara misinterpreted it as . The difference between the two iswhich factors into . Therefore, since the difference is a multiple of 9, the only answerchoice that is a multiple of 9 is .15. If , , and , what is the product of , , and ?16. A number of students from Fibonacci Middle School are taking part in a community service project.The ratio of -graders to -graders is , and the the ratio of -graders to -graders is .What is the smallest number of students that could be participating in the project?17. The sum of six consecutive positive integers is 2013. What is the largest of these six integers?18. Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?--Arpanliku 16:22, 27 November 2013 (EST) Courtesy of Lord.of.AMC19. Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show theirs to anyone. Cassie says, 'I didn't get the lowest score in our class,' and Bridget adds, 'I didn't get the highest score.' What is the ranking of the three girls from highest to lowest?20.A rectangle is inscribed in a semicircle with longer side on the diameter. What is the area of the semicircle?21. Samantha lives 2 blocks west and 1 block south of the southwest corner of City Park. Her school is 2 blocks east and 2 blocks north of the northeast corner of City Park. On school days she bikes on streets to the southwest corner of City Park, then takes a diagonal path through the park to the northeast corner, and then bikes on streets to school. If her route is as short as possible, how many different routes can she take?22. Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?23.Angle of is a right angle. The sides of are the diameters of semicircles asshown. The area of the semicircle on equals , and the arc of the semicircle on has length .What is the radius of the semicircle on ?24.Squares , , and are equal in area. Points and are the midpoints of sidesand , respectively. What is the ratio of the area of the shaded pentagon to the sum of theareas of the three squares?25. A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of3 semicircular arcs whose radii are inches, inches, and inches, respectively.The ball always remains in contact with the track and does not slip. What is the distance the center of theball travels over the course from A to B?1.2.The 50% off price of half a pound of fish is $3, so the 100%, or the regular price, of a half pound of fishis $6. Consequently, if half a pound of fish costs $6, then a whole pound of fish is dollars.3.Notice that we can pair up every two numbers to make a sum of 1:Therefore, the answer is .4.Each of her seven friends paid to cover Judi's portion. Therefore, Judi's portion must be .Since Judi was supposed to pay of the total bill, the total bill must be .5.The median here is obviously less than the mean, so option (A) and (B) are out.Lining up the numbers (5, 5, 6, 8, 106), we see that the median weight is 6 pounds.The average weight of the five kids is .Therefore, the average weight is bigger, by pounds, making the answer.6.Solution 1: Working BackwardsLet the value in the empty box in the middle row be , and the value in the empty box in the top row be . is the answer we're looking for.We see that , making .It follows that , so .Solution 2: Jumping Back to the StartAnother way to do this problem is to realize what makes up the bottommost number. This method doesn't work quite as well for this problem, but in a larger tree, it might be faster. (In this case, Solution 1 would be faster since there's only two missing numbers.)Again, let the value in the empty box in the middle row be , and the value in the empty box in the top row be . is the answer we're looking for.We can write some equations:Now we can substitute into the first equation using the two others:7.If Trey saw , then he saw .2 minutes and 45 seconds can also be expressed as seconds.Trey's rate of seeing cars, , can be multiplied by on the top and bottom (and preserve the same rate):. It follows that the most likely number of cars is .Solution 2minutes and seconds is equal to .Since Trey probably counts around cars every seconds, there are groups of cars thatTrey most likely counts. Since , the closest answer choice is .8.First, there are ways to flip the coins, in order.The ways to get two consecutive heads are HHT and THH.The way to get three consecutive heads is HHH.Therefore, the probability of flipping at least two consecutive heads is .9.This is a geometric sequence in which the common ratio is 2. To find the jump that would be over a 1000meters, we note that .However, because the first term is and not , the solution to the problem is10. To find either the LCM or the GCF of two numbers, always prime factorize first.The prime factorization of .The prime factorization of .Then, find the greatest power of all the numbers there are; if one number is one but not the other, use it(this is ). Multiply all of these to get 5940.For the GCF of 180 and 594, use the least power of all of the numbers that are in both factorizations andmultiply. = 18.Thus the answer = = .We start off with a similar approach as the original solution. From the prime factorizations, the GCF is .It is a well known fact that . So we have,.Dividing by yields .Therefore, .11. We use that fact that . Let d= distance, r= rate or speed, and t=time. In this case, letrepresent the time.On Monday, he was at a rate of . So, .For Wednesday, he walked at a rate of . Therefore, .On Friday, he walked at a rate of . So, .Adding up the hours yields + + = .We now find the amount of time Grandfather would have taken if he walked at per day. Set upthe equation, .To find the amount of time saved, subtract the two amounts: - = . To convert this to minutes, we multiply by .Thus, the solution to this problem is12. First, find the amount of money one will pay for three sandals without the discount. We have.Then, find the amount of money using the discount: .Finding the percentage yields .To find the percent saved, we have13. Let the two digits be and .The correct score was . Clara misinterpreted it as . The difference between the two iswhich factors into . Therefore, since the difference is a multiple of 9, the only answerchoice that is a multiple of 9 is .14. The probability that both show a green bean is . The probability that both show a red beanis . Therefore the probability is15.Therefore, .Therefore, .To most people, it would not be immediately evident that , so we can multiply 6's until we get the desired number:, so .Therefore the answer is .16. Solution 1: AlgebraWe multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8th graders, in order that we can put the two ratios together:Therefore, the ratio of 8th graders to 7th graders to 6th graders is . Since the ratio is in lowestterms, the smallest number of students participating in the project is .Solution 2: FakesolvingThe number of 8th graders has to be a multiple of 8 and 5, so assume it is 40 (the smallest possibility).Then there are 6th graders and 7th graders. The numbers of students is17. Solution 1The mean of these numbers is . Therefore the numbers are, so the answer isSolution 2Let the number be . Then our desired number is .Our integers are , so we have that.Solution 3Let the first term be . Our integers are . We have,18. Solution 1There are cubes on the base of the box. Then, for each of the 4 layers above the bottom (assince each cube is 1 foot by 1 foot by 1 foot and the box is 5 feet tall, there are 4 feet left), there arecubes. Hence, the answer is .Solution 2We can just calculate the volume of the prism that was cut out of the original box. Each interior side of the fort will be feet shorter than each side of the outside. Since the floor is foot, theheight will be feet. So the volume of the interior box is .The volume of the original box is . Therefore, the number of blocks contained inthe fort is .19. If Hannah did better than Cassie, there would be no way she could know for sure that she didn't get the lowest score in the class. Therefore, Hannah did worse than Cassie. Similarly, if Hannah did worse than Bridget, there is no way Bridget could have known that she didn't get the highest in the class.Therefore, Hannah did better than Bridget, so our order is .20.A semicircle has symmetry, so the center is exactly at the midpoint of the 2 side on the rectangle, makingthe radius, by the Pythagorean Theorem, . The area is .21.The number of ways to get from Samantha's house to City Park is , and the number of ways toget from City Park to school is . Since there's one way to go through City Park (just walking straight through), the number of different ways to go from Samantha's house to City Park to school.22.There are vertical columns with a length of toothpicks, and there are horizontal rows with a length of toothpicks. An effective way to verify this is to try a small case, i.e. a grid of toothpicks.Thus, our answer is .23. Solution 1If the semicircle on AB were a full circle, the area would be 16pi. Therefore the diameter of the first circle is 8. The arc of the largest semicircle would normally have a complete diameter of 17. The Pythagoreantheorem says that the other side has length 15, so the radius is .Solution 2We go as in Solution 1, finding the diameter of the circle on AC and AB. Then, an extended version of the theorem says that the sum of the semicircles on the left is equal to the biggest one, so the area of thelargest is , and the middle one is , so the radius is .24.First let (where is the side length of the squares) for simplicity. We can extend until it hits theextension of . Call this point . The area of triangle then is The area of rectangleis . Thus, our desired area is . Now, the ratio of the shaded area to thecombined area of the three squares is .Solution 2Let the side length of each square be .Let the intersection of and be .Since , . Since and are vertical angles, they arecongruent. We also have by definition.So we have by congruence. Therefore, .Since and are midpoints of sides, . This combined with yields.The area of trapezoid is .The area of triangle is .So the area of the pentagon is .The area of the squares is .Therefore, .Solution 3Let the intersection of and be .Now we have and .Because both triangles has a side on congruent squares therefore .Because and are vertical angles .Also both and are right angles so .Therefore by AAS(Angle, Angle, Side) .Then translating/rotating the shaded into the position ofSo the shaded area now completely covers the squareSet the area of a square asTherefore, .25. Solution 1The radius of the ball is 2 inches. If you think about the ball rolling or draw a path for the ball (see figurebelow), you see that in A and C it loses inches, and it gains inches on B.So, the departure from the length of the trackmeans that the answer is . Solution 2The total length of all of the arcs is . Since we want the path from the center,the actual distance will be shorter. Therefore, the only answer choice less than is . Thissolution may be invalid because the actual distance can be longer if the path the center travels is on the outside of the curve, as it is in the middle bump.。