2011AMC10美国数学竞赛A卷附中文翻译和答案
美国数学竞赛AMC题目及答案
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?
2011年-AMC10数学竞赛A卷-附中文翻译和答案
2011年A M C1 0美国数学竞赛A 卷
1. A cell phone plan costs $20 each month, plus 5¢per text message sent, plus 10¢for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
(A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00
2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}?
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 =
2011AMC10美国数学竞赛A卷 中文翻译及答案
2011AMC10美国数学竞赛A卷
1. 某通讯公司手机每个月基本费为20美元, 每传送一则简讯收 5美分(一美
元=100 美分)。若通话超过30小时,超过的时间每分钟加收10美分。已知小美一月份共传送了100条简讯及通话30.5小时,则她需要付多少美元?
(A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00
2.小瓶装有35毫升的洗发液,大瓶可装500毫升的洗发液。小华至少要买多少瓶小瓶的洗发液才能装满一个大瓶的洗发液?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
3. 若以 [a b]表示 a , b两数的平均数, 以 {a b c} 表示a, b, c三数的平均数,则{{1 1 0} [0 1] 0}之值为何?
(A) 2
9(B)5
18
(C)1
3
(D) 7
18
(E) 2
3
4. 设 X 和 Y 为下列等差级数之和:
X= 10 + 12 + 14 + …+ 100.
Y= 12 + 14 + 16 + …+ 102.
则Y X
之值为何?
(A) 92 (B) 98 (C) 100 (D) 102 (E) 112
5. 在某小学三年级,四年级及五年级的学生,每天分别平均跑12, 15, 及10 分钟, 已知三年级的学生人数是四年级人数的两倍,四年级的学生人数是五年级学生人数
的两倍。试问所有这些学生每天平均跑几分钟?
(A) 12 (B) 373 (C) 887 (D) 13 (E) 14
6. 已知集合A 中有20个元素, 集合B 中有 15 个元素. A ∪B 是集合A 和集合B 的联集,它是由集合A 与集合B 中所有元素所形成的集合,则集合A ∪B 中至少有多少个元素?
2023年AMC10美国数学竞赛A卷附中文翻译和答案
2023AMC10美国数学竞赛A卷
1. A cell phone plan costs $20 each month, plus 5¢ per text message sent, plus 10¢ for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
(A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00
2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}?
美国AMC10中文版试题及答案
2000到20XX年AMC10美国数学竞赛
0 0
P 0 A 0 B 0 C 0
D 0 全美中学数学分级能力测验(AMC 10)
2000年 第01届 美国AMC10 (2000年2月 日 时间75分钟)
1. 国际数学奥林匹亚将于 在美国举办,假设I 、M 、O 分别表示不同的正整数,且满足I ⨯M ⨯O =2001,则试问I +M +O 之最大值为 。
(A) 23 (B) 55 (C) 99 (D) 111 (E) 671
2. 2000(20002000)为 。
(A) 20002001 (B) 40002000 (C) 20004000 (D) 40000002000 (E) 20004000000
3. Jenny 每天早上都会吃掉她所剩下的聪明豆的20%,今知在第二天结束时,有32颗剩下,试问一开始聪明豆有 颗。
(A) 40 (B) 50 (C) 55 (D) 60 (E) 75
4. Candra 每月要付给网络公司固定的月租费及上网的拨接费,已知她12月的账单为12.48元,而她1月的账单为17.54元,若她1月的上网时间是12月的两倍,试问月租费是 元。
(A) 2.53 (B) 5.06 (C) 6.24 (D) 7.42 (E) 8.77
5. 如图M ,N 分别为PA 与PB 之中点,试问当P 在一条平行AB 的直 在线移动时,下列
各数值有 项会变动。
(a) MN 长 (b) △P AB 之周长 (c) △P AB 之面积 (d) ABNM 之面积
(A) 0项 (B) 1项 (C) 2项 (D) 3项 (E) 4项 6. 费氏数列是以两个1开始,接下来各项均为前两项之和,试问在费氏数列各项的个位数字中, 最后出现的阿拉伯数字为 。
AMC10美国数学竞赛讲义
AMC 中的数论问题
1:Remember the prime between 1 to 100:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 91 2:Perfect number: Let
is the prime number.if
21p - is also the prime number. then
1(21)2p p --is the perfect number. For example:6,28,496.
3: Let ,
0n abc a =≠ is three digital integer .if 333n a b c =++
Then the number n is called Daffodils number . There are only four numbers: 153 370 371 407 Let ,
0n abcd a =≠ is four digital integer .if 4444d n a b c +=++
Then the number n is called Roses number . There are only three numbers: 1634 8208 9474
4:The Fundamental Theorem of Arithmetic
Every natural number can be written as a product of primes uniquely up to order.
amc10美国数学竞赛真题
amc10美国数学竞赛真题amc10(美国数学竞赛)真题:
1. 微积分方面:
(1)求一元二次微分方程的有限解;
(2)求曲线y = f(x)在a点的切线斜率;
(3)求曲面z = f(x,y)在a点的切面方向;(4)决定泰勒展开式中n次项的系数;
(5)判断函数f(x)的极值;
(6)研究极限函数的存在性及无穷性;
(7)解决解析函数的定义域;
2. 数论方面:
(1)计算包含一定系数的多项式的余数;
(2)判断两个多项式的最大公因数;
(3)判断一个数的完全平方数;
(4)证明或否定一个数在某数域中的存在性;
3. 统计学:
(1)奇数和偶数的含义;
(2)样本容量的定义;
(3)求一组数据中最小值、最大值和中位数;(4)决定随机变量的条件概率;
(5)求一组数据的散布图;
4. 几何学:
(1)求平面两点间的距离;
(2)求直线的斜率;
(3)分析不相交平面的法向量;
(4)解决三角形的各个角度;
(5)计算圆的周长;
(6)两个圆的位置关系;
(7)求圆环的面积;
(8)求立体图形的体积。
5. 其它方面:
(1)分析逻辑表达式;
(2)求图论问题的最小生成树;
(3)计算算法问题的复杂度;
(4)计算概率论问题中的概率;
(5)规划组合优化问题的最优解;
(6)根据资料采纳正确的统计预测方法。
美国数学竞赛AMC10A、10B试题及答案
答案:1. C
2. E
3. E
4. B
5. A
6. C
7. A
8. E
9. A
10. C
11. C
12. C
13. B
14. D
15. A
16. B
17. D
18. E
19. D
20. C
21. B
22. B
23. E
24. B
25. C
答案:1.C 2.D 3.D 4.B 5.E 6.B 7.B 8.B 9.D 10.C 11.C 12.C 13.C 14.C 15.B 16.B 17.D 18.E 19.D 20.B
21.C 22.A 23.C 24.B 25.A【下载本文档,可以自由复制内容或自由编辑修改内容,更多精彩文章,期待你的好评和关注,我将一如既往为您服务】
2011AMC10美国数学竞赛A卷附中文翻译和答案
2011AMC10美国数学竞赛A卷
1. A cell phone plan costs $20 each month, plus 5¢ per text message sent, plus 10¢ for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
(A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00
2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}?
美国数学竞赛AMC10A、10B试题及答案精编版
答案:1. C
2. E
3. E
4. B
5. A
6. C
7. A
8. E
9. A
10. C
11. C
12. C
13. B
14. D
15. A
16. B
17. D
18. E
19. D
20. C
21. B
22. B
23. E
24. B
25. C
答案:1.C 2.D 3.D 4.B 5.E 6.B 7.B 8.B 9.D 10.C 11.C 12.C 13.C 14.C 15.B 16.B 17.D 18.E 19.D 20.B 21.C 22.A 23.C 24.B 25.A
AMC10美国数学竞赛讲义全
AMC 中的数论问题
1:Remember the prime between 1 to 100:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 91 2:Perfect number:
Let is the prime number.if 21p - is also the prime number. then 1
(21)2
p
p --is the perfect
number. For example:6,28,496。
3: Let ,0n abc a =≠ is three digital integer 。if 333n a b c =++
Then the number n is called Daffodils number. There are only four numbers : 153 370 371 407
Let ,0n abcd a =≠ is four digital integer 。if 4444d n a b c +=++ Then the number n is called Roses number. There are only three numbers: 1634 8208 9474
4:The Fundamental Theorem of Arithmetic
Every natural number can be written as a product of primes uniquely up to order.
美国AMC10中文版试题及答案
2000到20XX年AMC10美国数学竞赛
0 0
P 0 A 0 B 0 C 0
D 0 全美中学数学分级能力测验(AMC 10)
2000年 第01届 美国AMC10 (2000年2月 日 时间75分钟)
1. 国际数学奥林匹亚将于 在美国举办,假设I 、M 、O 分别表示不同的正整数,且满足I ⨯M ⨯O =2001,则试问I +M +O 之最大值为 。
(A) 23 (B) 55 (C) 99 (D) 111 (E) 671
2. 2000(20002000)为 。
(A) 20002001 (B) 40002000 (C) 20004000 (D) 40000002000 (E) 20004000000
3. Jenny 每天早上都会吃掉她所剩下的聪明豆的20%,今知在第二天结束时,有32颗剩下,试问一开始聪明豆有 颗。
(A) 40 (B) 50 (C) 55 (D) 60 (E) 75
4. Candra 每月要付给网络公司固定的月租费及上网的拨接费,已知她12月的账单为12.48元,而她1月的账单为17.54元,若她1月的上网时间是12月的两倍,试问月租费是 元。
(A) 2.53 (B) 5.06 (C) 6.24 (D) 7.42 (E) 8.77
5. 如图M ,N 分别为PA 与PB 之中点,试问当P 在一条平行AB 的直 在线移动时,下列
各数值有 项会变动。
(a) MN 长 (b) △P AB 之周长 (c) △P AB 之面积 (d) ABNM 之面积
(A) 0项 (B) 1项 (C) 2项 (D) 3项 (E) 4项 6. 费氏数列是以两个1开始,接下来各项均为前两项之和,试问在费氏数列各项的个位数字中, 最后出现的阿拉伯数字为 。
AMC10的真题答案及中文翻译
AMC10的真题答案及中文翻译
1、一张展览票原价为20美元。Susan使用优惠券购买4张票,享受75折优惠。Pam使用优惠券购买5张票,享受7折优惠。Pam比Susan多花了多少美元?
2、一个养鱼缸的底部为矩形,长100cm,宽40cm,高50cm。水位高度为40cm。将一个底部为矩形,长40cm,宽20cm,高10cm的砖块放入缸中。水位上升了多少厘米?
3、两个连续的奇数中,较大的数是较小的数的3倍。它们的和是多少?
4、一个学校商店售卖7支铅笔和8个笔记本需要4.15美元,售卖5支铅笔和3个笔记本需要1.77美元。那么16支铅笔和10个笔记本需要多少钱?
5、Euclid高中在2002年有60名学生参加AMC10,在2003年有66名,2004年有70名,2005年有76名,2006年有78名,2007年有85名。在相邻的哪两年中人数增长的百分率最大?
6、去年,John Q. Public先生继承了一笔遗产。他需要支付20%的联邦税和剩下的部分中10%的州税。他需要支付美元的总税费。这笔遗产有多少美元?
答案:(C) 美元
有多少个正整数对(m, n),满足m > n且它们的平方差是96?
美国数学竞赛AMC题目及答案
2.
3.Whatisthevalueof
4.
5.Hammieisinthe
gradeandweighs106pounds.Hisquadrupletsistersaretinybabiesandweigh5,5,6,and8pounds.W hichisgreater,theaverage(mean)weightofthesefivechildrenorthemedianweight,andbyhowman ypounds
6.Thenumberineachboxbelowistheproductofthenumbersinthetwoboxesthattouchitintherowab ove.Forexample,.Whatisthemissingnumberinthetoprow
7.
8.Afaircoinistossed3times.Whatistheprobabilityofatleasttwoconsecutiveheads
9.TheIncredibleHulkcandoublethedistancehejumpswitheachsucceedingjump.Ifhisfirstjumpis1 meter,thesecondjumpis2meters,thethirdjumpis4meters,andsoon,thenonwhichjumpwillhefirst beabletojumpmorethan1kilometer
10.Whatistheratiooftheleastcommonmultipleof180and594tothegreatestcommonfactorof180a nd594
2011AMC10美国数学竞赛A卷附中文翻译和答案
2011AMC10美国数学竞赛A卷
1. A cell phone plan costs $20 each month, plus 5¢ per text message sent, plus 10¢ for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
(A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00
2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}?
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2011AMC10美国数学竞赛A卷
1. A cell phone plan costs $20 each month, plus 5¢ per text message sent, plus 10¢ for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
(A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00
2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}?
(A) 2
9(B)5
18
(C)1
3
(D) 7
18
(E) 2
3
4. Let X and Y be the following sums of arithmetic sequences: X= 10 + 12 + 14 + …+ 100.
Y= 12 + 14 + 16 + …+ 102.
What is the value of Y X
?
(A) 92 (B) 98 (C) 100 (D) 102
(E) 112
5. At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?
(A) 12 (B) 373 (C) 887 (D) 13 (E) 14
6. Set A has 20 elements, and set B has 15 elements. What is the smallest possible number of elements in A ∪B, the union of A and B?
(A) 5 (B) 15 (C) 20 (D) 35 (E) 300
7. Which of the following equations does NOT have a solution?
(A) 2(7)0x += (B) -350x += (C) 20=
(D) 80= (E) -340x -=
8. Last summer 30% of the birds living on Town Lake were geese, 25% were swans, 10% were herons, and 35% were ducks. What percent of the birds that were not swans were geese?
(A) 20 (B) 30 (C) 40 (D) 50 (E) 60
9. A rectangular region is bounded by the graphs of the equations y=a, y=-b, x=-c, and x=d, where a, b, c, and d are all positive numbers. Which of the following represents the area of this region?
(A) ac + ad + bc + bd
(B) ac – ad + bc – bd (C) ac + ad – bc – bd
(D) –ac –ad + bc + bd (E) ac – ad – bc + bd
10. A majority of the 20 students in Ms. Deameanor’s class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than 1. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $17.71. What was the cost of a pencil in cents?
(A) 7 (B) 11 (C) 17 (D) 23 (E) 77
11. Square EFGH has one vertex on each side of square ABCD. Point E is on AB with AE=7·EB. What is the ratio of the area of EFGH to the area of ABCD?
(A) 4964 (B) 2532 (C) 78 (D) 8 (E)
12. The players on a basketball team made some three-point shots, some two-point shots, some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team’s total score was 61 points. How many free