AMC美国数学单词

number n. 数，数字

natural number 自然数

prime number 质数

composite number 合数

positive number 正数

mean 平均数

odd adj. 奇数

even n. 偶数

even integer, even number 偶数

integer（whole number) n. 整数

value 值

minimum 最小值

maximum n. 最大的，最大值minimum n. 最小的，最小值least possible value 最小可能值divisor n. 约数，除数

least common multiple 最小公倍数positive integer 正整数

fraction n. 分数

proper fraction 真分数

vulgar fraction 普通分数denominator 分母

least common denominator 最小公分母numerator 分子

mixed number 带分数remainder 余数

simple(common)fraction 简分数

decimal n. 小数

circulating decimal 循环小数

decimal point 小数点

decimal faction 纯小数

mixed decimal 混合小数percentage 百分比proportion 比例

quarter 四分之一

more than 大于

less than 小于

not more than 不大于

digit n. 数字，阿拉伯数字unit’s digit 个位数字

tens digit 十位数字

units 个位

tens 十位

tenths 十分位

sum n. 和，总数subtract 减minus(take away) 减，负，负数subtrahend 减数minuend 被减数multiply（times) 乘multiplicand 被乘数multiplication 乘法

multiple 乘数difference 差

subtract 减subtrahend 被减数

divide 除

equal 相等，等于divided evenly 被整除dividend 被整除，红利average n. 平均数power 乘方quotient 商

product 积

round off(round to) 四舍五入equation n. 方程

satisfy v. 满足increase n. 增加

reduce v. 减少

line segment 线段

length 长

parallel lines 平行线regular triangle 正三角形isosceles triangle 等腰三角形parallelogram n. 平行四边形trapezia n. 梯形rhombus 菱形

cube n. 正方体，立方体，立方cuboid adj. 长方体column n. 圆柱

taper n. 圆锥measure n.尺寸，v. 度量semicircle 半圆

radius n. 半径diameter n. 直径

surface area 表面积polygon 多边形convex polygon 凸多边形regular polygon 正多边形right-angle 直角

right-triangle 直角三角形acute-angle 锐角

obtuse angle 钝角

side 边长

perimeter n. 周长

circumference 周长，圆周

width 宽

area n. 面积

volume 体积

apiece 每人

arithmetic progression(sequence) 等差数列

altitude 高

bisect 平分

divisor 因子

factor 因子

prime factor 质因子

common factor 公因子

common multiple 公倍数

common divisor 公因数

common fraction 普通分数

complex fraction 繁分数

consecutive number 连续整数

consecutive even integer 连续偶数

consecutive odd integer 连续奇数

direct proportion 正比

inverse proportion 反比

distinct 不同的

factorial 阶乘

inverse 倒数

reciprocal 倒数

progression 数列

the extremes of a proportion 比例外项

the means of a proportion 比例内med

median 中位数，中值

mode 众数，一组数据中出现最多的数arranged 安排的

统计statistics

平均数average

加权平均数weighted average

方差variance

标准差root-mean-square deviation，standard deviation

比例proportion

百分比percent

百分点percentage

百分位数percentile

排列permutation

组合combination

概率，或然率probability

分布distribution

正态分布normaldistribution

非正态分布abnormaldistribution

图表graph

条形统计图bargraph

柱形统计图histogram

折线统计图brokenlinegraph

曲线统计图curvediagram

扇形统计图piediagram

空间space

坐标系coordinates

坐标轴x-axis，y-axis，z-axis

横坐标x-coordinate

纵坐标y-coordinate

原点origin

双曲线hyperbola

抛物线parabola

三角trigonometry

正弦sine

余弦cosine

正切tangent

余切cotangent

正割secant

余割cosecant

反正弦arcsine

反余弦arccosine

反正切arctangent

反余切arccotangent

反正割arcsecant

反余割arccosecant

相位phase

周期period

振幅amplitude

内心incentre（BrE）

外心excentre（BrE）

旁心escentre（BrE）

垂心orthocentre（BrE）

重心barycentre（BrE）

内切圆inscribedcircle

外切圆circumcircle

四面体tetrahedron

五面体pentahedron

六面体hexahedron

平行六面体parallelepiped

立方体cube

七面体heptahedron

八面体octahedron

九面体enneahedron

十面体decahedron

十一面体hendecahedron

十二面体dodecahedron

二十面体icosahedron

多面体polyhedron

棱锥pyramid

棱柱prism

棱台frustumofaprism

旋转rotation

轴axis

圆锥cone

圆柱cylinder

圆台frustumofacone

球sphere

半球hemisphere

底面undersurface

表面积surfacearea

体积volume

圆circle

圆心centre（BrE），center（AmE）

半径radius

直径diameter

圆周率pi

弧arc

半圆semicircle

扇形sector

环ring

椭圆ellipse

圆周circumference

周长perimeter

面积area

轨迹locus，loca（pl.）

相似similar

全等congruent

三角形triangle

锐角三角形acutetriangle

直角三角形righttriangle

直角边leg

斜边hypotenuse

勾股定理Pythagoreantheorem

钝角三角形obtusetriangle

不等边三角形scalenetriangle

等腰三角形isoscelestriangle

等边三角形equilateral triangle

四边形quadrilateral

平行四边形parallelogram

矩形rectangle

长length

宽width

菱形rhomb，rhombus，rhombi（pl.），diamond 正方形square

梯形trapezoid

直角梯形righttrapezoid

等腰梯形isoscelestrapezoid

正多边形equilateralpolygon

几何geometry

点point

线line

面plane

体solid

线段segment

射线radial

平行parallel

相交intersect

角angle

角度degree

弧度radian

锐角acuteangle

直角right angle

钝角obtuseangle

平角straightangle

周角perigon

底base

边side

高height

集合aggregate

元素element

空集void

子集subset

交集intersection

并集union

补集complement

映射mapping

函数function

定义域domain，fieldof definition

值域range

常量constant

变量variable

单调性monotonicity

奇偶性parity

周期性periodicity

图象image

数列，级数series

微积分calculus

微分differential

导数derivative

极限limit

无穷大infinite（a.）infinity（n.）

无穷小infinitesimal

积分integral

定积分definiteintegral

不定积分indefiniteintegral

有理数rationalnumber

无理数irrationalnumber

实数realnumber

虚数imaginarynumber

复数complexnumber

矩阵matrix

行列式determinant

未知数unknown，x-factor，y-factor，z-factor 等式，方程式equation

一次方程simpleequation

二次方程quadraticequation

三次方程cubicequation

四次方程quarticequation

不等式inequation

阶乘factorial

对数logarithm

指数，幂exponent

乘方power

二次方，平方square

三次方，立方cube

n次方thepowerofn，thenthpower

开方evolution，extraction

二次方根，平方根squareroot

三次方根，立方根cuberoot

n次方根therootofn，thenthroot

整数integer

小数decimal

小数点decimalpoint

分数fraction

分子numerator

分母denominator

比ratio

正positive

负negative

零null，zero，，nil

十进制decimalsystem

二进制binarysystem

十六进制hexadecimalsystem

权weight，significance

进位carry

截尾truncation

四舍五入round

下舍入rounddown

上舍入roundup

有效数字significantdigit

无效数字insignificantdigit

代数algebra

公式formula，formulae（pl.）

单项式monomial

多项式polynomial，multinomial

系数coefficient

数学mathematics，maths（BrE），math（AmE）

被除数dividend

除数divisor

商quotient

等于equals，isequalto

大于isgreaterthan

小于islesserthan

大于等于isequalorgreaterthan

小于等于isequalorlesserthan

运算符operator

数字digit

数number

自然数naturalnumber

公理axiom

定理theorem

计算calculation

运算operation

证明prove

假设hypothesis，hypotheses（pl.）

命题proposition

算术arithmetic

加plus（prep.），add（v.），addition（n.）

被加数augend，summand

加数addend

和sum

减minus（prep.），subtract（v.），subtraction（n.）被减数minuend

减数subtrahend

差remainder

乘times（prep.），multiply（v.），multiplication（n.）被乘数multiplicand，faciend

乘数multiplication

积product

除dividedby（prep.），divide（v.），division（n.）

AMC10美国数学竞赛A卷附中文翻译和答案之欧阳学创编

2011AMC10美国数学竞赛A卷时间：2021.03.03 创作：欧阳学 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)(B)(C)(D)(E) 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 ?

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}? (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 ?

2018年美国数学竞赛 AMC 试题

2018 AIME I Problems Problem 1 Let be the number of ordered pairs of integers with and such that the polynomial can be factored into the product of two (not necessarily distinct) linear factors with integer coefficients. Find the remainder when is divided by . Problem 2 The number can be written in base as , can be written in base as , and can be written in base as , where . Find the base- representation of . Problem 3 Kathy has red cards and green cards. She shuffles the cards and lays out of the cards in a row in a random order. She will be happy if and only if all the red cards laid out are adjacent and all the green cards laid out are adjacent. For example, card orders RRGGG, GGGGR, or RRRRR will make Kathy happy, but RRRGR will not. The probability that Kathy will be happy is , where and are relatively prime positive integers. Find . Problem 4 In and . Point lies strictly between and on and point lies strictly between and on so that . Then can be expressed in the form , where and are relatively prime positive integers. Find . Problem 5 For each ordered pair of real numbers satisfying there is a real number such that

2019AMC 8(美国数学竞赛)题目

2019 AMC 8 Problems Problem 1 Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy? Problem 2 Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is feet, what is the area in square feet of rectangle ?

Problem 3 Which of the following is the correct order of the fractions , , and , from least to greatest? Problem 4 Quadrilateral is a rhombus with perimeter meters. The length of diagonal is meters. What is the area in square meters of rhombus ? Problem 5 A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance traveled by the two animals over time from start to finish?

AMC美国数学竞赛AMCB试题及答案解析

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AMC2020 A Problem 1 Carlos took of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left? Problem 2 The acronym AMC is shown in the rectangular grid below with grid lines spaced unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMC Problem 3 A driver travels for hours at miles per hour, during which her car gets miles per gallon of gasoline. She is paid per mile, and her only expense is gasoline at per gallon. What is her net rate of pay, in dollars per hour, after this expense?

Problem 4 How many -digit positive integers (that is, integers between and , inclusive) having only even digits are divisible by Problem 5 The integers from to inclusive, can be arranged to form a -by- square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum? Problem 6 In the plane figure shown below, of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry

美国数学竞赛AMC题目及答案

2. is the value of 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 $ to cover her portion of the total bill. What was the total bill 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 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

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 fair coin is tossed 3 times. What is the probability of at least two consecutive heads 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 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

美国数学竞赛amc12

2002 AMC 12A Problems Problem 1 Compute the sum of all the roots of Problem 2 Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly? Problem 3 According to the standard convention for exponentiation, If the order in which the exponentiations are performed is changed, how many other values are possible? Problem 4 Find the degree measure of an angle whose complement is 25% of its supplement. Problem 5

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region. Problem 6 For how many positive integers does there exist at least one positive integer n such that ? infinitely many Problem 7 A arc of circle A is equal in length to a arc of circle B. What is the ratio of circle A's area and circle B's area? Problem 8 Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let be the total area of the blue triangles, the total area of the white squares, and the area of the red square. Which of the following is correct?

AMC 美国数学竞赛 2001 AMC 10 试题及答案解析

USA AMC 10 2001 1 The median of the list is . What is the mean? 2 A number is more than the product of its reciprocal and its additive inverse. In which interval does the number lie? 3 The sum of two numbers is . Suppose 3 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers? 4 What is the maximum number of possible points of intersection of a circle and a triangle? 5 How many of the twelve pentominoes pictured below have at least one line of symettry?

6 Let and denote the product and the sum, respectively, of the digits of the integer . For example, and . Suppose is a two-digit number such that . What is the units digit of ? 7 When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number? 8 Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will

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美国数学竞赛amc8的常用数学英语单词 数学 mathematics, maths（BrE）, math（AmE）被除数 dividend 除数 divisor 商 quotient 等于 equals, is equal to, is equivalent to 大于 is greater than 小于 is lesser than 大于等于 is equal or greater than 小于等于 is equal or lesser than 运算符 operator 数字 digit 数 number 自然数 natural number 公理 axiom 定理 theorem 计算 calculation 运算 operation 证明 prove 假设 hypothesis, hypotheses（pl.） 命题 proposition 算术 arithmetic 加 plus（prep.）, add（v.）, addition（n.）

被加数 augend, summand 加数 addend 和 sum 减 minus（prep.）, subtract（v.）, subtraction（n.） 被减数 minuend 减数 subtrahend 差 remainder 乘 times（prep.）, multiply（v.）, multiplication（n.）被乘数 multiplicand, faciend 乘数 multiplicator 积 product 除 divided by（prep.）, divide（v.）, division（n.） 整数 integer 小数 decimal 小数点 decimal point 分数 fraction 分子 numerator 分母 denominator 比 ratio 正 positive

AMC12美国数学竞赛 2012-2014

AMC12 2014A Problem 1 What is Solution At the theater children get in for half price. The price for adult tickets and child tickets is . How much would adult tickets and child tickets cost? Solution Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible? Solution Suppose that cows give gallons of milk in days. At this rate, how many gallons of milk will cows give in days? Solution

On an algebra quiz, of the students scored points, scored points, scored points, and the rest scored points. What is the difference between the mean and median score of the students' scores on this quiz? Solution The difference between a two-digit number and the number obtained by reversing its digits is times the sum of the digits of either number. What is the sum of the two digit number and its reverse? Solution The first three terms of a geometric progression are , , and . What is the fourth term? Solution A customer who intends to purchase an appliance has three coupons, only one of which may be used: Coupon 1: off the listed price if the listed price is at least Coupon 2: dollars off the listed price if the listed price is at least Coupon 3: off the amount by which the listed price exceeds For which of the following listed prices will coupon offer a greater price reduction than either coupon or coupon ?

美国数学竞赛AMC12词汇

A abbreviation 简写符号；简写 absolute error 绝对误差 absolute value 绝对值 accuracy 准确度 acute angle 锐角 acute-angled triangle 锐角三角形 add 加 addition 加法 addition formula 加法公式 addition law 加法定律 addition law(of probability)（概率）加法定律additive property 可加性 adjacent angle 邻角 adjacent side 邻边 algebra 代数 algebraic 代数的 algebraic equation 代数方程 algebraic expression 代数式 algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式 algebraic operation 代数运算 alternate angle （交）错角 alternate segment 交错弓形 altitude 高；高度；顶垂线；高线 ambiguous case 两义情况；二义情况 amount 本利和；总数 analysis 分析；解析 analytic geometry 解析几何 angle 角 angle at the centre 圆心角 angle at the circumference 圆周角 angle between a line and a plane 直与平面的交角 angle between two planes 两平面的交角 angle bisection 角平分 angle bisector 角平分线 ；分角线 angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角 angle of elevation 仰角 angle of greatest slope 最大斜率的角 angle of inclination 倾斜角angle of intersection 相交角；交角 angle of rotation 旋转角 angle of the sector 扇形角 angle sum of a triangle 三角形内角和 angles at a point 同顶角 annum(X% per annum) 年（年利率X%） anti-clockwise direction 逆时针方向；返时针方向anti-logarithm 逆对数；反对数 anti-symmetric 反对称 apex 顶点 approach 接近；趋近 approximate value 近似值 approximation 近似；略计；逼近 Arabic system 阿刺伯数字系统 arbitrary 任意 arbitrary constant 任意常数 arc 弧 arc length 弧长 arc-cosine function 反余弦函数 arc-sin function 反正弦函数 arc-tangent function 反正切函数 area 面积 arithmetic 算术 arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列 arithmetic series 等差级数 arm 边 arrow 前号 ascending order 递升序 ascending powers of X X 的升幂 associative law 结合律 assumed mean 假定平均数 assumption 假定；假设 average 平均；平均数；平均值 average speed 平均速率 axiom 公理 axis 轴 axis of parabola 拋物线的轴 axis of symmetry 对称轴

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2013 AMC8 Problems 1. Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way? 2. A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars? What is the value of ? 3. 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?

AMC美国数学竞赛AMCB试题及答案解析

A M C美国数学竞赛 A M C B试题及答案解析 The latest revision on November 22, 2020

2003 AMC 10B 1、Which of the following is the same as 2、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 cost 3、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 integers 4、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 each, cannas 2 each, dahlias each, and Easter lilies 3 each. What is the least possible cost, in dollars, for her garden 5、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 to make 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 lawn

2004 AMC12A(美国数学竞赛)

Alicia earns dollars per hour, of which is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes? Solution On the AMC 12, each correct answer is worth points, each incorrect answer is worth points, and each problem left unanswered is worth points. If Charlyn leaves of the problems unanswered, how many of the remaining problems must she answer correctly in order to score at least ? Solution For how many ordered pairs of positive integers is ? Solution Bertha has daughters and no sons. Some of her daughters have daughters, and the rest have none. Bertha has a total of daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children? Solution