AMC考题和答案解析
amc试题及答案
amc试题及答案1. 问题：已知函数 \( f(x) = 3x^2 - 2x + 5 \)，求 \( f(2) \) 的值。
答案：将 \( x = 2 \) 代入函数 \( f(x) \) 中，得到 \( f(2) = 3(2)^2 - 2(2) + 5 = 12 - 4 + 5 = 13 \)。
2. 问题：解方程 \( 2x - 5 = 9 \)。
答案：首先将方程两边同时加5，得到 \( 2x = 14 \)，然后除以2，得到 \( x = 7 \)。
3. 问题：如果一个圆的直径是10厘米，那么它的半径是多少？答案：圆的半径是直径的一半，所以半径 \( r = \frac{10}{2} = 5 \) 厘米。
4. 问题：计算 \( \sqrt{49} \)。
答案：\( \sqrt{49} = 7 \)。
5. 问题：一个班级有30名学生，其中20名是男生。
这个班级的男生比例是多少？答案：男生比例是 \( \frac{20}{30} = \frac{2}{3} \)。
6. 问题：如果一个三角形的两个内角分别是 \( 45^\circ \) 和\( 60^\circ \)，那么第三个角是多少度？答案：三角形的内角和为 \( 180^\circ \)，所以第三个角是\( 180^\circ - 45^\circ - 60^\circ = 75^\circ \)。
7. 问题：计算 \( 2^3 \)。
答案：\( 2^3 = 2 \times 2 \times 2 = 8 \)。
8. 问题：一个数的平方根是4，这个数是多少？答案：这个数是 \( 4^2 = 16 \)。
9. 问题：如果一个数的两倍加上3等于15，求这个数。
答案：设这个数为 \( x \)，那么 \( 2x + 3 = 15 \)。
解这个方程，得到 \( 2x = 12 \)，所以 \( x = 6 \)。
10. 问题：一个长方形的长是10厘米，宽是5厘米，求它的周长。
美国数学竞赛AMC8 -- 2005年真题解析(英文解析+中文解析)
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=$2.5.中文解析：Karl按原价买了5个文件夹，支付的费用是：2.5*5=12.5. 折扣价是：1.25*0.8=10。
如果Karl 等一天，可以省2.5元。
答案是C.Problem 3Answer: DSolution:Rotating square ABCD counterclockwise 45° so that the line of symmetry BD is a vertical line makes it easier to see that 4 squares need to be colored to match its corresponding square.中文解析：如上图所示，以BD为对称轴，标蓝色的方块需要涂黑。
共4块，答案是D。
Problem 4Answer: CSolution:The perimeter of the triangle is 6.1+8.2+9.7=24cm. A square's perimeter is four times its side length, since all its side lengths are equal. If the square's perimeter is 24, the side length is24/4=6, and the area is 6*6=36.中文解析：三角形的周长是：6.1+8.2+9.7=24. 正方形的周长和三角形相等，也是24，则其边长是24/4=6. 其面积是：6*6=36. 答案是C。
amc10真题与答案解析
amc10真题与答案解析AMC10真题与答案解析美国数学竞赛（AMC）是一项极具挑战性的数学竞赛，旨在推动学生的数学学习和解决问题的能力。
其中AMC10是为中学生设计的竞赛，是很多学生展现才华并锻炼数学素养的重要机会。
本文将对一道AMC10真题进行解析，帮助读者理解和掌握解题技巧。
以下是一道来自AMC10的真题："In the xy-plane, the graph of$\log_{16}x+\log_{16}y=\tfrac{3}{2}$ is drawn. The line$y=x$ intersects the graph at points $A$ and $B$. What is the length of segment $AB$?"这道题目涉及了对数的性质和直线与曲线的交点问题。
首先，我们先来理解题目所给出的等式。
$\log_{16}x$表示以16为底的对数，可以简化为$\log_2x^4$。
同样地，$\log_{16}y$可以简化为$\log_2y^4$。
所以等式可以写为$\log_2x^4 + \log_2y^4 =\frac{3}{2}$。
我们可以将等式进一步简化为$\log_2 (x^4y^4) =\frac{3}{2}$。
根据对数的性质，我们可以将等式转化为指数形式，得到$x^4y^4 = 2^{\frac{3}{2}}$。
然后我们来解决直线$y=x$与曲线$y=x^4$的交点问题。
我们可以将$x$代入曲线方程中，得到$y=x^4$。
因此，我们可以将交点问题转化为求解以下方程组：$x^4 =x$和$x^4y^4 = 2^{\frac{3}{2}}$。
首先，我们来解原方程$x^4 = x$。
很明显，$x=0$和$x=1$是方程的两个根。
我们可以进一步分析，当$x>1$时，$x^4$的增长速度比$x$快，所以方程没有其他解。
然后，我们来解方程$x^4y^4 = 2^{\frac{3}{2}}$。
美国数学竞赛AMC8 -- 2008年真题解析(英文解析+中文解析)
美国数学竞赛AMC8 – 2008年真题解析(英文解析+中文解析)Problem 1Answer: BSolution:50-12-24=14中文解析：总共花的钱是：12+12*2=36元。
剩余50-36=14元。
答案是BProblem 2Answer: ASolution:We can derive that c=8,L=6, U=7,and E=1. Therefore, the answer is 8671.中文解析：这10个字母的对应关系是： B -0；E-1; S-2; ......K -9. 按照这个对应关系：C-8，L-6，U-7，E-1. 即8671. 答案是A。
Problem 3Answer: ASolution:We can go backwards by days, but we can also backwards by weeks. If we go backwards by weeks, we see that February 6 is a Friday. If we now go backwards by days, February 1 is a Sunday.中文解析：13日是周五，则13-7=6，即6日也是周五，则倒推2月1日是周日。
答案是A。
Problem 4Answer: CSolution:The area outside the small triangle but inside the large triangle is 16-1=15. This is equally distributed between the three trapezoids. Each trapezoid has an area of 15/3=5.中文解析：大三角形的面积等于小的等边三角形的面积加上3个梯形的面积。
据此，三个梯形的面积是16-1=15. 每个梯形的面积是15/3=5. 答案是C。
AMC考题和答案解析
2017 AMC 8 考题及答案Problem 1Which of the following values is largest?Problem 2Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?Problem 3What is the value of the expression ?Problem 4When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following?Problem 5What is the value of the expression ? Problem 6If the degree measures of the angles of a triangle are in the ratio , what is the degree measure of the largest angle of the triangle?Problem 7Let be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of ?Problem 8Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."(1) It is prime.(2) It is even.(3) It is divisible by 7.(4) One of its digits is 9.This information allows Malcolm to determine Isabella's house number. What is its units digit?Problem 9All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?Problem 10A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?Problem 11A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?Problem 12The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?Problem 13Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?Problem 14Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only of the problems she solved alone, but overall of her answers were correct. Zoe had correct answers to of the problems she solved alone. What was Zoe's overall percentage of correct answers?Problem 15In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.Problem 16In the figure below, choose point on so that and have equal perimeters. What is the area of ?Problem 17Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?Problem 18In the non-convex quadrilateral shown below, is a right angle, , , , and .What is the area of quadrilateral ?Problem 19For any positive integer , the notation denotes the product of the integers through . What is the largest integer for which is a factor of the sum?Problem 20An integer between and , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?Problem 21Suppose , , and are nonzero real numbers, and . What are the possible value(s) for ?Problem 22In the right triangle , , , and angle is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?Problem 23Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?Problem 24Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren?Problem 25In the figure shown, and are line segments each of length 2, and. Arcs and are each one-sixth of a circle with radius 2. What is the area of the region shown?2017 AMC 8 Answer Key1. A2. E3. C5. B6. D7. A8. D9. D10.C11.C12.D13.B14.C15.D16.D17.C18.B19.D20.B21.A22.D23.C24.D。
AMC美国数学竞赛AMC.B 试题及答案解析
2003A M C10 B 1、Which of the following is the same asSolution2、Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs more than a pink pill, and Al’s pills cost a total of for the two weeks. How much does one green pill costSolution3、The sum of 5 consecutive even integers is less than the sum of the rst consecutive odd counting numbers. What is the smallest of the even integersSolution4、Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the gure. She plants one flower per square foot in each region. Asters cost 1 each, begonias 1.50 each, cannas 2 each, dahlias 2.50 each, and Easter lilies 3 each. What is the least possible cost, in dollars, for her gardenSolution5、Moe uses a mower to cut his rectangular -foot by -foot lawn. The swath he cuts is inches wide, but he overlaps each cut by inches tomake sure that no grass is missed. He walks at the rate of feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawnSolution.6、Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is . The horizontal length of a “-inch” television screen is closest, in inches, to which of the followingSolution7、The symbolism denotes the largest integer not exceeding . For example. , and . ComputeSolution.8、The second and fourth terms of a geometric sequence are and . Which of the following is a possible first termSolution9、Find the value of that satisfies the equationSolution10、Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of three letters followed by three digits. By how many times is the number of possible license plates increasedSolution11、A line with slope intersects a line with slope at the point . What is the distance between the -intercepts of these two linesSolution12、Al, Betty, and Clare split among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of . Betty and Clare have both doubled their money, whereas Al has managed to lose . What was Al’s original portionSolution.13、Let denote the sum of the digits of the positive integer . For example, and . For how many two-digit values of isSolution14、Given that , where both and are positive integers, find the smallest possible value for .Solution15、There are players in a singles tennis tournament. The tournament is single elimination, meaning that a player who loses a match is eliminated. In the first round, the strongest players are given a bye, and the remaining players are paired off to play. After each round, the remaining players play in the next round. The match continues until only one player remains unbeaten. The total number of matches played isSolution16、A restaurant offers three desserts, and exactly twice as many appetizers as main courses. A dinner consists of an appetizer, a main course, and a dessert. What is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the yearSolution.17、An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly ll the cone. Assume that the melted ice cream occupies of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radiusSolution18、What is the largest integer that is a divisor offor all positive even integersSolution19、Three semicircles of radius are constructed on diameter of a semicircle of radius . The centers of the small semicircles divide into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicirclesSolution20、In rectangle , and . Points and are on so that and . Lines and intersect at . Find the area of .Solution21、A bag contains two red beads and two green beads. You reach into the bag and pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are red after three such replacementsSolution22、A clock chimes once at minutes past each hour and chimes on the hour according to the hour. For example, at 1 PM there is one chime and at noon and midnight there are twelve chimes. Starting at 11:15 AM on February , , on what date will the chime occurSolution23、A regular octagon has an area of one square unit. What is the area of the rectangleSolution24、The rst four terms in an arithmetic sequence are , , , and, in that order. What is the fth termSolution25、How many distinct four-digit numbers are divisible by and have as their last two digitsSolution。
AMC8(美国数学竞赛)历年真题、答案及中英文解析
AMC8（美国数学竞赛）历年真题、答案及中英文解析艾蕾特教育的AMC8 美国数学竞赛考试历年真题、答案及中英文解析：AMC8-2020年：真题 --- 答案---解析（英文解析+中文解析）AMC8 - 2019年：真题----答案----解析（英文解析+中文解析）AMC8 - 2018年：真题----答案----解析（英文解析+中文解析）AMC8 - 2017年：真题----答案----解析（英文解析+中文解析）AMC8 - 2016年：真题----答案----解析（英文解析+中文解析）AMC8 - 2015年：真题----答案----解析（英文解析+中文解析）AMC8 - 2014年：真题----答案----解析（英文解析+中文解析）AMC8 - 2013年：真题----答案----解析（英文解析+中文解析）AMC8 - 2012年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 2010年：真题----答案----解析（英文解析+中文解析）AMC8 - 2009年：真题----答案----解析（英文解析+中文解析）AMC8 - 2008年：真题----答案----解析（英文解析+中文解析）AMC8 - 2007年：真题----答案----解析（英文解析+中文解析）AMC8 - 2006年：真题----答案----解析（英文解析+中文解析）AMC8 - 2005年：真题----答案----解析（英文解析+中文解析）AMC8 - 2004年：真题----答案----解析（英文解析+中文解析）AMC8 - 2003年：真题----答案----解析（英文解析+中文解析）AMC8 - 2002年：真题----答案----解析（英文解析+中文解析）AMC8 - 2001年：真题----答案----解析（英文解析+中文解析）AMC8 - 2000年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 1998年：真题----答案----解析（英文解析+中文解析）AMC8 - 1997年：真题----答案----解析（英文解析+中文解析）AMC8 - 1996年：真题----答案----解析（英文解析+中文解析）AMC8 - 1995年：真题----答案----解析（英文解析+中文解析）AMC8 - 1994年：真题----答案----解析（英文解析+中文解析）AMC8 - 1993年：真题----答案----解析（英文解析+中文解析）AMC8 - 1992年：真题----答案----解析（英文解析+中文解析）AMC8 - 1991年：真题----答案----解析（英文解析+中文解析）AMC8 - 1990年：真题----答案----解析（英文解析+中文解析）AMC8 - 1989年：真题----答案----解析（英文解析+中文解析）AMC8 - 1988年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 1986年：真题----答案----解析（英文解析+中文解析）AMC8 - 1985年：真题----答案----解析（英文解析+中文解析）◆AMC介绍◆AMC（American Mathematics Competitions) 由美国数学协会（MAA）组织的数学竞赛，分为 AMC8 、 AMC10、 AMC12 。
amc数学竞赛试题
amc数学竞赛试题 AMC数学竞赛试题是一种具有挑战性的数学竞赛，旨在激励学生对数学的兴趣和才华，并培养他们解决实际问题的能力。
AMC数学竞赛涵盖广泛的数学领域，是学生们展示数学知识和解题能力的重要场所。
AMC数学竞赛试题一般包括代数、几何、数据分析和概率等多个知识领域。
这些试题通常设计得非常巧妙，要求学生具备深入理解和分析问题的能力。
接下来，我们将通过一些典型的AMC数学竞赛试题，来了解一下其中的难点和解题思路。
首先，我们先来看一道代数题： 1. 给定实数x，如果满足方程|2x+1| + 3x = 5x，则x的值是？ 解析：首先我们将绝对值分成两种情况：当2x+1≥0时，|2x+1|=2x+1；当2x+1<0时，|2x+1|=-(2x+1)。
然后，我们依次将这两种情况带入原方程，进行化简，最后得到x=1/7。
接下来，我们来看一道几何题： 2. 如图，一个等边三角形内切在一个圆内，然后又在等边三角形内切一个圆，重复这样的操作无穷次。
求最后等边三角形的边长与最初等边三角形的边长的比值。
解析：设最初等边三角形的边长为a，我们可以发现不断嵌套下来，趋近于一个极限值。
假设极限值为L，那么根据相似三角形的性质，我们可以得到L=2L+a，解方程得到L=a/3。
因此，最后等边三角形的边长与最初等边三角形的边长的比值为1/3。
再来看一道数据分析题： 3. 有一组数据集{(1, 2), (2, 4), (3, 6), (4, 8), (5, 10)}，其中横坐标表示时间，纵坐标表示速度。
根据这组数据集，我们能否得到一个准确的速度-时间图像？如果能，请画出图像；如果不能，请说明原因。
解析：我们可以计算出每个点的斜率，也就是速度，发现每个点的速度都是2。
因此，这组数据集得到的速度-时间图像是一个速度恒定的水平直线。
以上只是AMC数学竞赛试题的一小部分示例，它们展示了竞赛中可能遇到的不同类型的问题。
参加AMC数学竞赛不仅可以提高学生的数学水平，还可以锻炼他们的思维能力和解决问题的能力。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
A M C考题和答案解析Document serial number【NL89WT-NY98YT-NC8CB-NNUUT-NUT108】2017 AMC 8 考题及答案Problem 1Which of the following values is largestProblem 2Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all togetherProblem 3What is the value of the expressionProblem 4When is multiplied by 7,928,564 the product is closest to which of the followingProblem 5What is the value of the expressionProblem 6If the degree measures of the angles of a triangle are in the ratio , what is the degree measure of the largest angle of the triangleProblem 7Let be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor ofProblem 8Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tellshim, "My house number has two digits, and exactly three of the following four statements about it are true."(1) It is prime.(2) It is even.(3) It is divisible by 7.(4) One of its digits is 9.This information allows Malcolm to determine Isabella's house number. What is its units digitProblem 9All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could haveProblem 10A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selectedProblem 11A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floorProblem 12The smallest positive integer greater than 1 that leaves a remainderof 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbersProblem 13Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he winProblem 14Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only of the problems she solved alone, but overall of her answers were correct. Zoe had correct answers to of the problems she solved alone. What was Zoe's overall percentage of correct answersProblem 15In the arrangement of letters and numerals below, by how manydifferent paths can one spell AMC8 Beginning at the A in the middle,a path allows only moves from one letter to an adjacent (above, below,left, or right, but not diagonal) letter. One example of such a path is traced in the picture.Problem 16In the figure below, choose point on so that and have equal perimeters. What is the area ofProblem 17Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasurechests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I haveProblem 18In the non-convex quadrilateral shown below, is a right angle, , , , and .What is the area of quadrilateralProblem 19For any positive integer , the notation denotes the product of the integers through . What is the largest integer for whichis a factor of the sumProblem 20An integer between and , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinctProblem 21Suppose , , and are nonzero real numbers, and . What are the possible value(s) forProblem 22In the right triangle , , , and angle is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircleProblem 23Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the fourtripsProblem 24Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phonecall from any of her grandchildrenProblem 25In the figure shown, and are line segments each of length 2, and . Arcs and are each one-sixth of a circle with radius 2. What is the area of the region shown2017 AMC 8 Answer Key1.A2.E3.C4.D5.B6.D7.A8.D9.D10.C11.C12.D13.B14.C15.D16.D17.C18.B19.D20.B21.A22.D23.C24.D25.B。