美国数学竞赛AMC12词汇资料

19961The addition below is incorrect.What is the largest digit that can be changed to make the addition correct?641852+9732456(A)4(B)5(C)6(D)7(E)8Each day Walter gets $3for doing his chores or $5for doing them exceptionally well.After 10days of doing his chores daily,Walter has received a total of $36.On how many days did Walter do them exceptionally well?A.3B.4C.5D.6E.7(3!)!3!=(A)1(B)2(C)6(D)40(E)120Six numbers from a list of nine integers are 7,8,3,5,and 9.The largest possible value of the median of all nine numbers in this list is(A)5(B)(C)7(D)8(E)Given that 0<a <b <c <d ,which of the following is the largest?A.a +b c +d B.a +d b +c C.b +c a +d D.b +d a +c E.c +d a +bIf f (x )=x (x +1)(x +2)(x +3)then f (0)+f (−1)+f (−2)+f (−3)=A.−8/9B.0C.8/9D.1E.10/9A father takes his twins and a younger child out to dinner on the twins’birthday.The restaurant charges $4.95for the father and $0.45for each year of a child’s age,where age is defined as the age at the most recent birthday.If the bill is $9.45,which of the following could be the age of the youngest child?A.1B.2C.3D.4E.5If 3=k ·2r and 15=k ·4r ,then r =(A)−log 25(B)log 52(C)log 105(D)log 25(E)52Triangle P AB and square ABCD are in perpendicular planes.Given that P A =3,P B =4,and AB =5,what is P D ?A.5B.√34C.√41D.2√13E.8This file was downloaded from the AoPS −MathLinks Math Olympiad Resources Page Page 1http://www.mathlinks.ro/1996How many line segments have both their endpoints located at the vertices of a given cube?(A)12(B)15(C)24(D)28(E)56Given a circle of raidus 2,there are many line segments of length 2that are tangent to the circle at their midpoints.Find the area of the region consisting of all such line segments.(A)π4(B)4−π(C)π2(D)π(E)2πA function f from the integers to the integers is defined as follows:f (x )= n +3if n is odd n/2if n is evenSuppose k is odd and f (f (f (k )))=27.What is the sum of the digits of k ?(A)3(B)6(C)9(D)12(E)15Sunny runs at a steady rate,and Moonbeam runs m times as fast,where m is a number greater than 1.If Moonbeam gives Sunny a head start of h meters,how many meters must Moonbeam run to overtake Sunny?(A)hm (B)h h +m (C)h m −1(D)hm m −1(E)h +m m −1Let E (n )denote the sum of the even digits of n .For example,E (5681)=6+8=14.Find E (1)+E (2)+E (3)+···+E (100).(A)200(B)360(C)400(D)900(E)2250Two opposite sides of a rectangle are each divided into n congruent segments,and the endpoints of one segment are joined to the center to form triangle A .The other sides are each divided into m congruent segments,and the endpoints of one of these segments are joined to the center to form triangle B .[See figure for n =5,m =7.]What is the ratio of the area of triangle A to the area of triangle B ?(A)1(B)m/n (C)n/m (D)2m/n (E)2n/mA fair standard six-sided dice is tossed three times.Given that the sum of the first two tosses equal the third,what is the probability that at least one ”2”is tossed?(A)16(B)91216(C)12(D)815(E)712In rectangle ABCD ,angle C is trisected by CF and CE ,where E is on AB ,F is on AD ,BE =6,and AF =2.Which of the following is closest to the area of the rectangle ABCD ?(A)110(B)120(C)130(D)140(E)150A circle of radius 2has center at (2,0).A circle of radius 1has center at (5,0).A line is tangent to the two circles at points in the first quadrant.Which of the following is closest to the y -intercept of the line?(A)√4(B)8/3(C)1+√(D)2√(E)3The midpoints of the sides of a regular hexagon ABCDEF are joined to form a smaller hexagon.What fraction of the area of ABCDEF is enclosed by the smaller hexagon?1996(A)12(B)√33(C)23(D)34(E)√32In the xy-plane,what is the length of the shortest path from (0,0)to (12,16)that does not go inside the circle (x −6)2+(y −8)2=25?(A)10√3(B)10√5(C)10√3+5π3(D)40√33(E)10+5πTriangles ABC and ABD are isosceles with AB =AC =BD ,and BD intersects AC at E .If BD is perpendicular to AC ,then ∠C +∠D is[img]/Forum/albump ic.php ?pic i d =537[/img ](A)115◦(B)120◦(C)130◦(D)135◦(E)not uniquely determinedFour distinct points,A ,B ,C ,and D ,are to be selected from 1996points evenly spaced around a circle.All quadruples are equally likely to be chosen.What is the probability that the chord AB intersects the chord CD?(A)14(B)13(C)12(D)23(E)34The sum of the lengths of the twelve edges of a rectangular box is 140,and the distance from one corner of the box to the farthest corner is 21.The total surface area of the box is(A)776(B)784(C)798(D)800(E)812The sequence 1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,...consists of 1s separated by blocks of 2s with n 2s in the nth block.The sum of the first 1234terms of this sequence is(A)1996(B)2419(C)2429(D)2439(E)2449Given that x 2+y 2=14x +6y +6,what is the largest possible value that 3x +4y can have?(A)72(B)73(C)74(D)75(E)76An urn contains marbles of four colors:red,white,blue,and green.When four marbles are drawn without replacement,the following events are equally likely:(a)the selection of four red marbles;(b)the selection of one white and three red marbles;(c)the selection of one white,one blue,and two red marbles;and (d)the selection of one marble of each color.What is the smallest number of marbles satisfying the given condition?(A)19(B)21(C)46(D)69Consider two solid spherical balls,one centered at (0,0,212)with radius 6,and the other centeredat (0,0,1)with radius 92.How many points (x,y,z )with only integer coordinates (lattice points)are there in the intersection of the balls?(A)7(B)9(C)11(D)13(E)15On a 4×4×3rectangular parallelepiped,vertices A ,B ,and C are adjacent to vertex D .The perpendicular distance from D to the plane containing A ,B ,and C is closest to(A)1.6(B)1.9(C)2.1(D)2.7(E)2.91996If n is a positive integer such that 2n has 28positive divisors and 3n has 30positive divisors,then how many positive divisors does 6n have?(A)32(B)34(C)35(D)36(E)38A hexagon inscribed in a circle has three consecutive sides each of length 3and three consecutive sides each of length 5.The chord of the circle that divides the hexagon into two trapezoids,one with three sides each of length 3and the other with three sides each of length 5,has length equal to m n ,where m and n are relatively prime positive integers.Find m +n .(A)309(B)349(C)369(D)389(E)409。

AMC常用词汇一、基本图形三角形：triangle矩形：rectangle正方形：square平行四边形：parallelogram梯形：tapezoid菱形：rhombus圆：circle四边形：quadrilateral二、基本立体图形正方体：cube长方体：rectangular prism圆柱体：right circular cyclinder 圆锥体：right circular cone球体：sphere三、基本计算量长度：length面积：area体积（容积）：volume周长：perimeter表面积：surface area底面积：base area四、有关集合并集：unionproper subset 真子集：solution set 解集：五、有关数论自然数：natural number 正数：positive number负数：negative number奇数：odd integer，odd number偶数：even integer，even number整数：integer，whole number正整数：positive whole number负整数：negative whole number连续整数：consecutive number实数，有理数：real number，rational number 无理数：irrational（number）倒数：inverse合数：composite numbereg. 4,6,8,9,10,12,14,15……质数：prime numbereg.2,3,5,7,11,13,15……倒数：reciprocal公约数：common divisor倍数：multiple（最小）公约数：（last）common multiple （质）因子：（prime）factor十进制：ordinary csale，decimal scale非负的：nonnegative十位：tens个位：units众数：mode中数：median公比：common ratio六、数列等差数列：arithmetic progression（sequence）等比数列：geometric progression（sequence）七、其它近似：approximate（逆）顺时针方向：（anti）clockwise 基数：cardinal序数：ordinal正比：directproportion不同的：distinct估计，近似：estimation括号：parentheses比例：proportion组合：combination表格：table三角函数：trigonometric function单位，位：unit八、其它几何1、所有的角内错角：alternate angle同位角：corresponding angle对顶角：vertical angle圆心角：central angle内角：interior angle外角：exterior angle补角：supplement aryangles余角：complement aryangle邻角：adjacent angle锐角：acute angle钝角：obtuse angle直角：right angle周角：round angle平角：straight angle夹角：included angle2、所有的三角形等边三角形：equilateral triangle不等边三角形：scalene triangle等腰三角形：isosceles triangle直角三角形：right triangle斜三角形：oblique内接三角形：inscribed triangle3、有关收敛的平面图形，除三角形外半圆：semicircle同心圆：concentric circles四边形：quadrilateral五边形：pentagon六边形：hexagon七边形：heptagon八边形：octagon九边形：nonagon十边形：decagon多边形：polygon平行四边形：parallelogram等边形：equilateral平面：plane正方形，平方：square长方形：rectangle正多边形：regular polygon菱形：rhombus梯形：trapezoid4、其它平面图形弧：arc直线：line，straight line线段：line segment平行线：parallel lines弧形：segment of a circle5、有关立体图形立方体，立方数：cube长方体：rectangular solid正多面体：regular solid / regular polyhedron 圆柱体：circular cylinder圆锥：cone球体：sphere立体的：solid6、有关图形上的附属物高：altitude深度：depth边长：side周长：circumference，perimeter弧度：radian表面积：surface area体积：volume直角三角形的股：arm横截面：cros section圆心：center of a circle弦：chord半径：radius角平分器：angle bisector对角线：diagonal直径：diameter棱：edge立体的面：face of a solid斜边：hypotenuse夹边：included side三角形的直角边：leg三角形的中线：median of a triangle底边，底数(e.g.2的5次方,2就是底数)：base 直角三角形中的对边：opposite中点：midpoint 端点：endpoint（复数形式vertices）顶点：vertex 切线的：tangent截线：transversal截距：intercept7、有关坐标坐标系：coordinate system直角坐标系：rectangular coordinate 原点：origin横坐标：abscissa纵坐标：ordinate数轴：number line象限：quadrant斜率：slope复平面：complex plane8、其它平面几何：plane geometry三角学：trigonometry平分：bisect外切：circumscribe内切：inscribe相交：intersect垂直：perpendicular勾股定理：pythagorean theorem全等的：congruent多边的：multilateral基本数学词汇加：plus / and / positive减：minus / negative / subtract差：difference乘：multiplied by / times乘方:power积：product除：divided by可被整除的：divisible被整除：dividedevenly被除数：dividend商：quotient余数：remainder阶乘：factorial等于：equal不等于：not equal to大于：greater than小于:less than大于等于：equal or greater than小于等于：equal or less than约等于：approximate equal四舍五入：round to / to the nearest 因为：because所以：therefore开平方：square root of开立方：cube root of根号：radical sign，root sign绝对值：the absolute value函数：function图形：figure角：angle直角：right angle锐角：acute angle对折：fold 分数：fractionX-轴：X-axesY-轴：Y-axes其它次序：sequence几何的：g eometric整数：integer比例：ratio正的：positive切线（也是正切tan）：tangent半径：radius / radii不等式：inequality顶点：vertex值域：range同类项：like terms，similar terms原方程：original equation(最小)公约数：(least)common denominator 算术平均数：arithmetic mean加权平均值：weighted average指数，幂：exponent变量：variable反函数：inverse function因式分解：factorization打（12个）：dozen廿（20个）：score夸脱：quart加仑：gallon（1 gallon = 4 quart）英语数学词汇大全Aabbreviation 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Bback substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（2）基；基数base angle 底角base area 底面base line 底线base number 底数；基数base of logarithm 对数的底bearing 方位（角）；角方向（角）bell-shaped curve 钟形图bias 偏差；偏倚billion 十亿binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial expression 二项式bisect 平分；等分bisection method 分半法；分半方法bisector 等分线；平分线boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数brace 大括号bracket 括号breadth 阔度broken line graph 折线图Ccalculation 计算calculator 计算器；计算器cancel 消法；相消canellation law 消去律capacity 容量Cartesian coordinates 笛卡儿坐标Cartesian plane 笛卡儿平面category 类型；范畴central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centroid 形心；距心certain event 必然事件chance 机会change of base 基的变换change of subject 主项变换change of variable 换元；变量的换chart 图；图表checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classification 分类clnometer 测斜仪clockwise dirction 顺时针方向closed convex region 闭凸区域closed interval 闭区间coefficient 系数coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面column (1)列；纵行；(2) 柱combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common factor 公因子；公因子common logarithm 常用对数common multiple 公位数；公倍common ratio 公比common tangetn 公切commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图complement 余；补余complementary angle 余角complementary event 互补事件complementary probability 互补概率completing the square 配方complex number 复数complex root 复数根composite number 复合数；合成数compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息computation 计算computer 计算机；电子计算器concave 凹concave downward 凹向下的concave polygon 凹多边形concave upward 凹向上的concentric circles 同心圆concept 概念conclusion 结论concurrent 共点concyclic 共圆concyclic points 共圆点condition 条件conditional 条件句；条件式cone 锥；圆锥（体）congruence (1)全等；(2)同余congruent 全等congruent figures 全等图形congruent triangles 全等三角形cconjugate 共轭consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论consequent 条件；后项consistency condition 相容条件consistent 一贯的；相容的constant 常数constant speed 恒速率constant term 常项constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例contradiction 矛盾converse 逆(定理) converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形coordinate 坐标coordinate geometry 解析几何；坐标几何coordinate system 坐标系系定理；系；推论correct to 准确至；取值至correspondence 对应corresponding angles (1)同位角；(2)对应角corresponding sides 对应边cosine 余弦cosine formula 余弦公式cost price 成本counter clockwise direction逆时针方向；返时针方向counter example 反例counting 数数；计数criterion 准则critical point 临界点cross-multiplication 交叉相乘cross-section 横切面；横截面；截痕cube 正方体；立方；立方体cube root 立方根cubic 三次方；立方；三次(的)cubic equation 三次方程cuboid 长方体；矩体cumulative 累积的cumulative frequecy 累积频数；累积频率cumulative frequency curve累积频数曲cumulative frequcncydistribution 累积频数分布cumulative frequency polygon累积频数多边形；累积频率直方图curve 曲线curve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved line 曲线curved surface 曲面curved surface area 曲面面积cyclic quadrilateral 圆内接四边形cylinder 柱；圆柱体cylindrical 圆柱形的Ddata 数据decagon 十边形decay 衰变decay factor 衰变因子decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distrivutive law 分配律divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形dot 点double root 二重根due east/ south/ west /north 向东/ 南/ 西/ 北definiton 定义degree (1)度；(2)次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of precision 精确度delete 删除；删去denary number 十进数denary scale 十进法denary system 十进制denominator 分母dependence (1)相关；(2)应变dependent event(s) 相关事件；相依事件；从属事件dependent variable 应变量；应变数depreciation 折旧descending order 递降序descending powers of X X的降序detached coefficients 分离系数(法)deviation 偏差；变差deviation from the mean 离均差diagonal 对角diagram 图；图表diameter 直径difference 差digit 数字dimension 量；量网；维(数) direct proportion 正比例direct tax, direct taxation 直接税direct variation 正变（分）directed angle 有向角directed number 有向数direction 方向；方位discontinuous 间断(的)；非连续(的)；不连续(的) discount 折扣discount per cent 折扣百分率discrete 分立；离散discrete data 离散数据；间断数据discriminant 判别式dispersion 离差displacement 位移disprove 反证Eedge 棱；边elimination 消法elimination method 消去法；消元法elongation 伸张；展empirical data 实验数据empirical formula 实验公式empirical probability 实验概率；经验概率enclosure 界限end point 端点entire surd 整方根equal 相等equal ratios theorem 等比定理equal roots 等根equality 等(式)equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns(variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角(的)extreme value 极值equidistant 等距(的)equilaeral 等边(的)equilateral polygon 等边多边形equilateral triangle 等边三角形equivalent 等价(的)error 误差escribed circle 旁切圆estimate 估计；估计量Euler's formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive events 互斥事件exercise 练习expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expectedvalue 期望值；预期值experiment 实验；试验experimental 试验的experimental probability 实验概率exponent 指数express…in terms of…..以………表达expression 式；数式extension 外延；延长；扩张；扩充exterior angle 外角external angle bisector 外分角external point of division 外分点extreme point 极值点Fface 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解factorization of polynomial 多项式因式分解FALSE 假(的)feasible solution 可行解；容许解Fermat’s last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字finite 有限finite population 有限总体finite sequence 有限序列finite series 有限级数first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点flow chart 流程图foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一X form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table频数分布表frequency polygon 频数多边形；频率多边形frustum 平截头体function 函数function of function 复合函数；迭函数functional notation 函数记号Ggain 增益；赚；盈利gain per cent 赚率；增益率；盈利百分率game （1）对策；（2）博奕general form 一般式；通式general solution 通解；一般解general term 通项geoborad 几何板geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解greatest term 最大项greatest value 最大值grid lines 网网格线group 组；grouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子Hhalf closed interval 半闭区间half open interval 半开区间head 正面（钱币）height 高（度）hemisphere 半球体；半球heptagon 七边形Heron's formula 希罗公式hexagon 六边形higher order derivative 高阶导数highest common factor(H.C.F)最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图horizontal 水平的；水平horizontal line 横线；水平线hyperbola 双曲线hypotenuse 斜边Iidentical 全等；恒等identity 等（式）identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…., then 若….则；如果…..则illustration 例证；说明image 像点；像imaginary circle 虚圆imaginary number 虚数imaginary root 虚根implication 蕴涵式；蕴含式imply 蕴涵；蕴含impossible event 不可能事件improper fraction 假分数inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusive 包含的；可兼的inconsistent 不相的(的)；不一致(的)increase 递增；增加increasing function 递增函数interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角internal bisector 内分角internal division 内分割internal point of division 内分点inter-quartile range 四分位数间距intersect 相交intersection (1)交集；(2)相交；(3)交点interval 区间intuition 直观invariance 不变性invariant (1)不变的；(2)不变量；不变式inverse 反的；逆的inverse circular function 反三角函数inverse cosine function 反余弦函数inverse function 反函数；逆函数inverse problem 逆算问题inverse proportion 反比例；逆比例inverse sine function 反正弦函数inverse tangent function 反正切函数inverse variation 反变(分)；逆变(分)irrational equation 无理方程irrational number 无理数irreducibility 不可约性irregular 不规则isosceles triangle 等腰三角形increasing sequence 递增序列increasing series 递增级数increment 增量independence 独立；自变independent event 独立事件independent variable 自变量；独立变量indeterminate (1)不定的；(2)不定元；未定元indeterminate coefficient 不定系数；未定系数indeterminate form 待定型；不定型index,indices 指数；指index notation 指数记数法inequality 不等式；不等inequality sign 不等号infinite 无限；无穷infinite population 无限总体infinite sequence 无限序列；无穷序列infinite series 无限级数；无穷级数infinitely many 无穷多infinitesimal 无限小；无穷小infinity 无限(大)；无穷(大)initial point 始点；起点initial side 始边initial value 初值；始值input 输入input box 输入inscribed circle 内切圆insertion 插入insertion of brackets 加括号instantaneous 瞬时的integer 整数integral index 整数指数integral solution 整数解integral value 整数值intercept 截距；截段intercept form 截距式intercept theorem 截线定理interchange 互换interest 利息interest rate 利率interest tax 利息税interior angle 内角Jjoint variation 联变(分)；连变(分)Kknown 己知LL.H.S. 末项law 律；定律law of indices 指数律；指数定律law of trichotomy 三分律leading coefficient 首项系数least common multiple, lowestcommon multiple (L.C.M) 最小公倍数；最低公倍式least value 最小值lemma 引理length 长(度)letter 文字；字母like surd 同类根式like terms 同类项limit 极限line 线；行line of best-fit 最佳拟合line of greatest slope 最大斜率的直；最大斜率line of intersection 交线line segment 线段linear 线性；一次linear equation 线性方程；一次方程linear equation in two unknowns 二元一次方程；二元线性方程linear inequality 一次不等式；线性不等式linear programming 线性规划literal coefficient 文字系数literal equation 文字方程load 负荷loaded coin 不公正钱币loaded die 不公正骰子locus, loci 轨迹logarithm 对数logarithmic equation 对数方程logarithmic function 对数函数logic 逻辑logical deduction 逻辑推论；逻辑推理logical step 逻辑步骤long division method 长除法loss 赔本；亏蚀loss per cent 赔率；亏蚀百分率lower bound 下界lower limit 下限lower quartile 下四分位数lowest common multiple(L.C.M) 最小公倍数Mmagnitude 量；数量；长度；大小major arc 优弧；大弧major axis 长轴major sector 优扇形；大扇形major segment 优弓形；大弓形mantissa 尾数mantissa of logarithm 对数的尾数；对数的定值部many-sided figure 多边形marked price 标价mathematical induction 数学归纳法mathematical sentence 数句mathematics 数学maximize 极大maximum absolute error 最大绝对误差maximum point 极大点maximum value 极大值mean 平均(值)；平均数；中数mean deviation 中均差；平均偏差measure of dispersion 离差的量度measurement 量度median (1)中位数；(2)中线meet 相交；相遇mensuration 计量；求积法method 方法method of completing square配方法method of substitution 代换法；换元法metric unit 十进制单位mid-point 中点mid-point formula 中点公式mid-point theorem 中点定理million 百万minimize 极小minimum point 极小点minimum value 极小值minor (1)子行列式；(2)劣；较小的minor arc 劣弧；小弧minor axis 短轴minor sector 劣扇形；小扇形minor segment 劣弓形；小弓形minus 减minute 分mixed number(fraction) 带分数modal class 众数组mode 众数model 模型monomial 单项式multinomial 多项式multiple 倍数multiple root 多重根multiplicand 被乘数multiplication 乘法multiplication law (ofprobability) (概率)乘法定律multiplicative property 可乘性multiplier 乘数；乘式multiply 乘mutually exclusive events 互斥事件mutually independent 独立;互相独立mutually perpendicular lines互相垂直Nn factorial n阶乘n th root n次根；n次方根natural number 自然数negative 负negative angle 负角negative index 负指数negative integer 负整数negative number 负数neighborhood 邻域net 净(值)n-gon n边形nonagon 九边形non-collinear 不共线non-linear 非线性non-linear equation 非线性方程non-negative 非负的non-trivial 非平凡的non-zero 非零normal (1)垂直的；正交的；法线的(2)正态的(3)正常的；正规的normal curve 正态分布曲；常庇分布曲；正规曲；正庇曲normal distribution 正态分布，常态分布normal form 法线式notation 记法；记号number 数number line 数线number pair 数偶number pattern 数型number plane 数平面number system 数系numeral 数字；数码numeral system 记数系统numerator 分子numerical 数值的；数字的numerical expression 数字式numerical method 计算方法；数值法Ooblique 斜的oblique cone 斜圆锥oblique triangle 斜三角形obtuse angle 钝角obtuse-angled triangle 钝角三角形octagon 八边形octahedron 八面体odd function 奇函数odd number 奇数one-one correspondence 一一对应open interval 开区间open sentence 开句operation 运算opposite angle 对角opposite interior angle 内对角opposite side 对边optimal solution 最优解order (1)序；次序；(2)阶；级ordered pair 序偶origin 原点outcome 结果output 输出overlap 交迭；相交Pparabola 拋物线parallel 平行(的)parallel lines 平行(直线)parallelogram 平行四边形parameter 参数；参变量partial fraction 部分分数；分项分式polar coordinate system 极坐标系统polar coordinates 极坐标pole 极polygon 多边形polyhedron 多面体polynomial 多项式polynomial equation 多项式方程positive 正positive index 正指数positive integer 正整数positive number 正数power (1)幂；乘方；(2)功率；(3)检定力precise 精密precision 精确度prime 素prime factor 质因子；质因素prime number 素数；质数primitive (1)本原的；原始的；(2)原函数principal (1)主要的；(2)本金prism 梭柱(体)；角柱(体)prismoid 平截头棱锥体probability 概率problem 应用题produce 延长product 乘积；积product rule 积法则profit 盈利profit per cent 盈利百分率profits tax 利得税progression 级数proof 证(题)；证明proper fraction 真分数property 性质property tax 物业税proportion 比例proportional 成比例protractor 量角器pyramid 棱锥(体)；角锥(体)Pythagoras’Theorem 勾股定理Pythagorean triplet 毕氏三元数组partial sum 部分和partial variation 部分变(分)particular solution 特解Pascal’s triangle 帕斯卡斯三角形pattern 模型；规律pegboard 有孔版pentadecagon 十五边形pentagon 五边形per cent 百分率percentage 百分法；百分数percentage decrease 百分减少percentage error 百分误差percentage increase 百分增加percentile 百分位数perfect number 完全数perfecr square 完全平方perimeter 周长；周界period 周期periodic function 周期函数permutation 排列perpendicular 垂线；垂直(于) perpendicular bisector 垂直平分线；中垂线perpendicular line 垂直线pictogram 象形图pie chart 饼图；圆瓣图pinboard 钉板place holder 补位数字place value 位值plan (1)平面图；(2)计划plane 平面plane figure 平面图形plot 绘图plus 加point 点point circle 点圆point of contact 切点point of division 分点point of intersection 交点point-slope form 点斜式polar axis 极轴polar coordinate plane 极坐标平面polar coordinate 极坐标系统Qquadrant 象限quadratic equation 二次方程(式)quadratic formula 二次公式quardratic function 二次函数quadratic inequality 二次不等式quadratic polynomial 四边形quantity 数量quartile 四分位数quotient 商；商式RR.H.S 右radian 弧度radian measure 弧度法radical 根式；根号；根数radius, radii 半径random 随机random experiment 随机试验random number 随机数range 值域；区域；范围；极差；分布域rate 率；利率ratio 比; 比率rational expression 有理式；有理数式rational function 有理函数rational index 有理数指数rational number 有理数rationalization 有理化raw data 原始数据raw score 原始分（数）real axis 实轴real number 实数real root 实根reason 理由reciprocal 倒数rectangle 长方形；矩形rectangular block 长方体rectangular coordinate plane直角坐标平面rectangular coordinates 直角坐rectilinear figure 直线图形recurrent 循环的recurring decimal 循环小数reduce 简化reducible 可约的；可化简的reference angle 参考角reflex angle 优角；反角region 区域regular 正；规则regular polygon 正多边形reject 舍去；否定relation 关系；关系式relative error 相对误差remainder 余数；余式；剩余remainder term 余项remainder theorem 余式定理removal of brackets 撤括号；去括号repeated trials 重复试验resolve 分解revolution 旋转；周转rhombus 菱形right angle 直角right circular cone 直立圆锥（体）right circular cylinder 直立圆柱（体）right prism 直立棱柱；直立角柱(体)right pyramid 直立棱锥；直立角锥(体)right-angled triangle 直角二角形root 根rotation 旋转round angle 周角rounded number 舍数rounding(off) 舍入；四舍五入row 行；棋行rule 规则；法(则)ruler 直尺Ssalaries tax 薪俸税sample 抽样；样本sample space 样本空间satisfy 满足；适合scale 比例尺；标度；图尺scalene triangle 不等边三角形；不规则三角形scientific notation 科学记数法solution of triangle 三角形解法solve 解special angle 特殊角；特别角speed 速率sphere 球形；球面square (1)平方；(2)正方形square bracket 方括号square number 正方形数；平方数square root 平方根；二次根standard deviation 标准差；标准偏离secant 割second 秒second quartile 第二四分位数(1)截面；截线；(2)截点section (1)截面；截线；(2)截点section formula 截点公式sector 扇式segment 段；节segment of a circle 弓形selling price 售价semi-circle 半圆semi-vertical angle 半顶角sentence 句；语句sequence 序列series 级数set square 三角尺；三角板shaded portion 有阴影部分shape 形状side 边；侧sign 符号；记号signed number 有符号数significant figure 有效数字similar 相似similar figures 相似图形similar triangles 相似三角形similarity 相似(性)simple equation 简易方程simple interest 单利；单利息simplify 简化simultaneous equations 联立方程simultaneous inequalities 联立不等式simultaneous linear equationsin two unknowns 联合二次线性方程式sine 正弦sine formula 正弦公式slant edge 斜棱slant height 斜高slope 斜率；斜度；倾斜；坡度slope-intercept form 斜率截距式；斜截式solid 立体；固体soild with uniformcorss-section 有均匀横切面的立体solution 解；解法solution of equation 方程解Uuniform 一致(的)；均匀(的)uniform cross-section 均匀横切面uniform speed 匀速率uniformly distributed 均匀分布unique solution 唯一解uniqueness 唯一性unit 单位unit area 单位面积unit circle 单位圆unit volume 单位体积unknown 未知数；未知量unlike 异类项upper bound 上界upper limit 上限upper quartile 上四分位数Vvalue 值variable 变项；变量；元；变元；变数variable speed 可变速率variance 方差variation 变数；变分verify 证明；验证vertex, vertices 顶(点)；极点vertical 铅垂；垂直vertical angle 顶角vertical line 纵线；铅垂vertically opposite angles 对顶角volume 体积Wweight (1)重量；(2)权weighted average, weightedmean 加权平均数whole number 整数；完整数width 阔度without loss of generality 不失一般性Xx-axis x轴x-coordinate x坐标x-intercept x轴截距Yy-axis y轴y-coordinate y坐标y-intercept y轴截距Zzero 零zero factor 零因子zeros of a function 函数零值。

2012 AMC 12B ProblemsProblem 1Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms?SolutionProblem 2A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?SolutionProblem 3For a science project, Sammy observed a chipmunk and squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide?SolutionProblem 4Suppose that the euro is worth 1.30 dollars. If Diana has 500 dollars and Etienne has 400 euros, by what percent is the value of Etienne's money greater that the value of Diana's money?SolutionProblem 5Two integers have a sum of 26. when two more integers are added to the first two, the sum is 41. Finally, when two more integers are added to the sum of the previous 4 integers, the sum is 57. What is the minimum number of even integers among the 6 integers?SolutionProblem 6In order to estimate the value of where and are real numbers with , Xiaoli rounded up by a small amount, rounded down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct?SolutionProblem 7Small lights are hung on a string 6 inches apart in the order red, red, green, green, green, red, red, green, green, green, and so on continuing this pattern of 2 red lights followed by 3 green lights. How many feet separate the 3rd red light and the 21st red light?Note: 1 foot is equal to 12 inches.SolutionProblem 8A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?SolutionProblem 9It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How seconds would it take Clea to ride the escalator down when she is not walking?SolutionProblem 10What is the area of the polygon whose vertices are the points of intersection of the curves and ?SolutionProblem 11In the equation below, and are consecutive positive integers, and , , and represent number bases: What is ?SolutionProblem 12How many sequences of zeros and ones of length 20 have all the zeros consecutive, or all the ones consecutive, or both?SolutionProblem 13Two parabolas have equations and , where , , , and are integers, eachchosen independently by rolling a fair six-sided die. What is the probability that the parabolas will have a least one point in common?SolutionProblem 14Bernardo and Silvia play the following game. An integer between 0 and 999 inclusive is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she addes 50 to it and passes the result to Bernardo. The winner is the last person who produces a number less than 1000. Let N be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of N?SolutionProblem 15Jesse cuts a circular paper disk of radius 12 along two radii to form two sectors, the smaller having a central angle of 120 degrees. He makes two circular cones, using each sector to form the lateral surface of a cone. What is the ratio of the volume of the smaller cone to that of the larger?SolutionProblem 16Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those girls but disliked by the third. In how many different ways is this possible?SolutionProblem 17Square lies in the first quadrant. Points and lie on lines and , respectively. What is the sum of the coordinates of the center of the square ?SolutionProblem 18Let be a list of the first 10 positive integers such that for each either oror both appear somewhere before in the list. How many such lists are there?SolutionProblem 19A unit cube has vertices and . Vertices , , and are adjacent to , and forvertices and are opposite to each other. A regular octahedron has one vertex in each of the segments , , , , , and . What is the octahedron's side length?SolutionProblem 20A trapezoid has side lengths 3, 5, 7, and 11. The sums of all the possible areas of the trapezoid can be written in the form of , where , , and are rational numbers and and are positive integers not divisible by the square of any prime. What is the greatest integer less than or equal to ?SolutionProblem 21Square is inscribed in equiangular hexagon with on , on , and on . Suppose that , and . What is the side-length of the square?SolutionProblem 22A bug travels from to along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?SolutionProblem 23Consider all polynomials of a complex variable, , where and are integers, , and the polynomial has a zero with What is the sum of all values over all the polynomials with these properties?SolutionProblem 24\item Define the function on the positive integers by setting and if is the prime factorization of , then For every , let. For how many in the range is the sequenceunbounded?Note: A sequence of positive numbers is unbounded if for every integer , there is a member of the sequence greater than .Problem 25\item Let . Let be the set of all right triangles whose vertices are in . For every right triangle with vertices , , and in counter-clockwise order and right angle at , let . What is。

2002 AMC 12A ProblemsProblem 1Compute the sum of all the roots ofProblem 2Cindy 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 3According to the standard convention for exponentiation,If the order in which the exponentiations are performed is changed, how many other values are possible?Problem 4Find the degree measure of an angle whose complement is 25% of its supplement.Problem 5Each 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 6For how many positive integers does there exist at least one positive integer n suchthat ?infinitely manyProblem 7A 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 8Betsy 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?Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files?Problem 10Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?Problem 11Mr. Earl E. Bird gets up every day at 8:00 AM to go to work. If he drives at an average speed of 40 miles per hour, he will be late by 3 minutes. If he drives at an average speed of 60 miles per hour, he will be early by 3 minutes. How many miles per hour does Mr. Bird need to drive to get to work exactly on time?Problem 12Both roots of the quadratic equation are prime numbers. The number ofpossible values of isProblem 13Two different positive numbers and each differ from their reciprocals by . Whatis ?For all positive integers , let .Let . Which of the following relations is true?Problem 15The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection isProblem 16Tina randomly selects two distinct numbers from the set {1, 2, 3, 4, 5}, and Sergio randomly selects a number from the set {1, 2, ..., 10}. What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina?Problem 17Several sets of prime numbers, such as use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have?Problem 18Let and be circles definedby and respectively. What is the length ofthe shortest line segment that is tangent to at and to at ?The graph of the function is shown below. How many solutions does theequation have?Problem 20Suppose that and are digits, not both nine and not both zero, and the repeatingdecimal is expressed as a fraction in lowest terms. How many different denominators are possible?Problem 21Consider the sequence of numbers: For , the -th term of thesequence is the units digit of the sum of the two previous terms. Let denote the sum of thefirst terms of this sequence. The smallest value of for which is:Problem 22Triangle is a right triangle with as its rightangle, , and . Let be randomly chosen inside ,and extend to meet at . What is the probability that ?Problem 23In triangle , side and the perpendicular bisector of meet in point ,and bisects . If and , what is the area oftriangle ?Problem 1In the year, the United States will host the International Mathematical Olympiad.Let and be distinct positive integers such that the product .What is the largest possible value of the sum ?Problem 2Problem 3Each day, Jenny ate of the jellybeans that were in her jar at the beginning of that day.At the end of the second day, remained. How many jellybeans were in the jar originally?Problem 4The Fibonacci sequence starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?Problem 5If where thenProblem 6Two different prime numbers between and are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?Problem 7How many positive integers have the property that is a positive integer?Problem 8Figures, , , and consist of , , , and non-overlapping squares. If thepattern continued, how many non-overlapping squares would there be in figure?Problem 9Mrs. Walter gave an exam in a mathematics class of five students. She entered the scores in random order into a spreadsheet, which recalculated the class average after each score was entered. Mrs. Walter noticed that after each score was entered, the average was always an integer. The scores (listed in ascending order) were 71,76,80,82, and 91. What was the last score Mrs. Walters entered?Problem 10The point is reflected in the -plane, then its image is rotatedby about the -axis to produce , and finally, is translated by 5 units in thepositive-direction to produce . What are the coordinates of ?Problem 11Two non-zero real numbers, and satisfy. Which of the following is apossible value of?Problem 12Let A, M, and C be nonnegative integers such that . What is the maximumvalue of + + + ?Problem 13One morning each member of Angela’s family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?Problem 14When the mean,median, and modeof the listare arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of?Problem 15Let be a function for which . Find the sum of all values of forwhich.Problem 16A checkerboard of rows and columns has a number written in each square, beginning inthe upper left corner, so that the first row is numbered , the secondrow , and so on down the board. If the board is renumbered so that the left column,top to bottom, is , the second column and so on across the board, some squares have the same numbers in both numbering systems. Find the sum of the numbers in these squares (under either system).Problem 17A centered at has radius and contains the point . The segment is tangent tothe circle at and . If point lieson and bisects , thenProblem 18In year , the day of the year is a Tuesday. In year , the day isalso a Tuesday. On what day of the week did th day of year occur?Problem 19triangle , , , . Let denote the midpointof and let denote the intersection of with the bisector of angle .Which of the following is closest to the area of the triangle ?Problem 20If and are positive numbers satisfyingThen what is the value of latex ?Problem 21Through a point on the hypotenuse of right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into asquare and two smaller right triangles. The area of one of the two small right triangles times the area of the square. The ratio of the area of the other small right triangle to the area of the square isProblem 22The graph below shows a portion of the curve defined by the quarticpolynomial. Which of the following is the smallest?Problem 23Professor Gamble buys a lottery ticket, which requires that he pick six different integersfrom through , inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property— the sum of the base-ten logarithms is an integer. What is the probability that Professor Gamble holds the winning ticket?Problem 24If circular arcs and centers at and , respectively, then there exists acircletangent to both and , and to . If the length of is , then the circumference of the circle isProblem 25Eight congruent Equilateral triangle each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)。

.AMC常用词汇一、基本图形三角形：triangle矩形：rectangle正方形：square平行四边形：parallelogram梯形：tapezoid菱形：rhombus圆：circle四边形：quadrilateral二、基本立体图形正方体：cube长方体：rectangular prism圆柱体：right circular cyclinder 圆锥体：right circular cone球体：sphere三、基本计算量长度：length面积：area体积（容积）：volume周长：perimeter表面积：surface area底面积：base area四、有关集合并集：unionproper subset 真子集：solution set 解集：五、有关数论自然数：natural number 正数：positive number负数：negative number奇数：odd integer，odd number偶数：even integer，even number整数：integer，whole number正整数：positive whole number负整数：negative whole number连续整数：consecutive number实数，有理数：real number，rational number 无理数：irrational（number）倒数：inverse合数：composite numbereg. 4,6,8,9,10,12,14,15……质数：prime numbereg.2,3,5,7,11,13,15……倒数：reciprocal公约数：common divisor倍数：multiple（最小）公约数：（last）common multiple （质）因子：（prime）factor十进制：ordinary csale，decimal scale非负的：nonnegative十位：tens个位：units众数：mode中数：median公比：common ratio六、数列等差数列：arithmetic progression（sequence）等比数列：geometric progression（sequence）.七、其它近似：approximate（逆）顺时针方向：（anti）clockwise 基数：cardinal序数：ordinal正比：directproportion不同的：distinct估计，近似：estimation括号：parentheses比例：proportion组合：combination表格：table三角函数：trigonometric function单位，位：unit八、其它几何1、所有的角内错角：alternate angle同位角：corresponding angle对顶角：vertical angle圆心角：central angle内角：interior angle外角：exterior angle补角：supplement aryangles余角：complement aryangle邻角：adjacent angle锐角：acute angle钝角：obtuse angle直角：right angle周角：round angle平角：straight angle夹角：included angle2、所有的三角形等边三角形：equilateral triangle不等边三角形：scalene triangle等腰三角形：isosceles triangle直角三角形：right triangle斜三角形：oblique内接三角形：inscribed triangle3、有关收敛的平面图形，除三角形外半圆：semicircle同心圆：concentric circles四边形：quadrilateral五边形：pentagon六边形：hexagon七边形：heptagon八边形：octagon九边形：nonagon十边形：decagon多边形：polygon平行四边形：parallelogram等边形：equilateral平面：plane正方形，平方：square长方形：rectangle正多边形：regular polygon菱形：rhombus梯形：trapezoid4、其它平面图形弧：arc直线：line，straight line线段：line segment平行线：parallel lines弧形：segment of a circle.5、有关立体图形立方体，立方数：cube长方体：rectangular solid正多面体：regular solid / regular polyhedron 圆柱体：circular cylinder圆锥：cone球体：sphere立体的：solid6、有关图形上的附属物高：altitude深度：depth边长：side周长：circumference，perimeter弧度：radian表面积：surface area体积：volume直角三角形的股：arm横截面：cros section圆心：center of a circle弦：chord半径：radius角平分器：angle bisector对角线：diagonal直径：diameter棱：edge立体的面：face of a solid斜边：hypotenuse夹边：included side三角形的直角边：leg三角形的中线：median of a triangle底边，底数(e.g.2的5次方,2就是底数)：base 直角三角形中的对边：opposite中点：midpoint 端点：endpoint（复数形式vertices）顶点：vertex 切线的：tangent截线：transversal截距：intercept7、有关坐标坐标系：coordinate system直角坐标系：rectangular coordinate 原点：origin横坐标：abscissa纵坐标：ordinate数轴：number line象限：quadrant斜率：slope复平面：complex plane8、其它平面几何：plane geometry三角学：trigonometry平分：bisect外切：circumscribe内切：inscribe相交：intersect垂直：perpendicular勾股定理：pythagorean theorem全等的：congruent多边的：multilateral基本数学词汇加：plus / and / positive减：minus / negative / subtract差：difference乘：multiplied by / times.乘方:power积：product除：divided by可被整除的：divisible被整除：dividedevenly被除数：dividend商：quotient余数：remainder阶乘：factorial等于：equal不等于：not equal to大于：greater than小于:less than大于等于：equal or greater than小于等于：equal or less than约等于：approximate equal四舍五入：round to / to the nearest 因为：because所以：therefore开平方：square root of开立方：cube root of根号：radical sign，root sign绝对值：the absolute value函数：function图形：figure角：angle直角：right angle锐角：acute angle对折：fold 分数：fractionX-轴：X-axesY-轴：Y-axes其它次序：sequence几何的：g eometric整数：integer比例：ratio正的：positive切线（也是正切tan）：tangent半径：radius / radii不等式：inequality顶点：vertex值域：range同类项：like terms，similar terms原方程：original equation(最小)公约数：(least)common denominator 算术平均数：arithmetic mean加权平均值：weighted average指数，幂：exponent变量：variable反函数：inverse function因式分解：factorization打（12个）：dozen廿（20个）：score夸脱：quart加仑：gallon（1 gallon = 4 quart）英语数学词汇大全Aabbreviation 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 aplane angle between two planes 两平面的交角angle bisection 角平分 anglebisectorangle 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Bback substitution 回代bar chart 棒形图；条线图；条形图；线条图 base （1）底；（2）基；基数 base angle 底角 base area 底面base linebase number 底数；基数 base of logarithm 对数的底 bearing 方位（角）；角方向（角） bell-shaped curve 钟形图 bias 偏差；偏倚 billion 十亿binary number 二进数binary operation 二元运算 binary scale 二进法 binary system 二进制 binomial 二项式 binomial expression 二项式 bisect 平分；等分 bisection method 分半法；分半方法bisector boundary condition 边界条件 boundary line 界（线）；边界 bounded 有界的 bounded above 有上界的；上有界的 bounded below 有下界的；下有界的 bounded function 有界函数 brace 大括号 bracket 括号 breadth 阔度 broken line graph 折线图 C calculation 计算 calculator 计算器；计算器 cancel 消法；相消 canellation law 消去律 capacity 容量 Cartesian coordinates 笛卡儿坐标 Cartesian plane 笛卡儿平面 category 类型；范畴central line central tendency 集中趋 centre 中心；心 centre of a circle 圆心 centroid 形心；距心 certain event 必然事件 chance 机会 change of base 基的变换 change of subject 主项变换 change of variable 换元；变量的换 chart 图；图表 checking 验算 chord 弦 chord of contact 切点弦 circle 圆 circular 圆形；圆的 circular function 圆函数；三角函数 circular measure 弧度法 circumcentre 外心；外接圆心 circumcircle 外接圆 circumference 圆周 circumradius 外接圆半径 circumscribed circle 外接圆 class 区；组；类 class boundary 组界 class interval 组区间；组距 class limit 组限；区限 class mark 组中点；区中点 classification 分类 clnometer 测斜仪 clockwise dirction 顺时针方向 closed convex region 闭凸区域 closed interval 闭区间 coefficient 系数 coincide 迭合；重合 collection of terms 并项collinear collinear planes 共线面 column (1)列；纵行；(2) 柱 combination 组合 common chord 公弦 common denominator 同分母；公分母 common difference 公差 common divisor 公约数；公约 common factor 公因子；公因子 common logarithm 常用对数 common multiple 公位数；公倍 common ratio 公比common tangetn commutative law 交换律 comparable 可比较的 compass 罗盘 compass bearing 罗盘方位角 compasses 圆规 compasses construction 圆规作图 complement 余；补余 complementary angle 余角 complementary event 互补事件 complementary probability 互补概率 completing the square 配方 complex number 复数 complex root 复数根 composite number 复合数；合成数 compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息 computation 计算 computer 计算机；电子计算器 concave 凹 concave downward 凹向下的 concave polygon 凹多边形 concave upward 凹向上的 concentric circles 同心圆 concept 概念 conclusion 结论 concurrent 共点 concyclic 共圆 concyclic points 共圆点 condition 条件 conditional 条件句；条件式 cone 锥；圆锥（体）congruence (1)全等；(2)同余 congruent 全等 congruent figures 全等图形congruent triangles 全等三角形cconjugate 共轭consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论consequent 条件；后项consistency condition 相容条件consistent 一贯的；相容的constant 常数constant speed 恒速率constant term 常项constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例contradiction 矛盾converse 逆(定理)converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形coordinate 坐标coordinate geometry 解析几何；坐标几何coordinate system 坐标系系定理；系；推论correct to 准确至；取值至correspondence 对应corresponding angles (1)同位角；(2)对应角corresponding sides 对应边cosine 余弦cosine formula 余弦公式cost price 成本counter clockwise direction逆时针方向；返时针方向counter example 反例counting 数数；计数criterion 准则critical point 临界点cross-multiplication 交叉相乘cross-section 横切面；横截面；截痕cube 正方体；立方；立方体cube root 立方根cubic 三次方；立方；三次(的)cubic equation 三次方程cuboid 长方体；矩体cumulative 累积的cumulative frequecy 累积频数；累积频率cumulative frequencycurvecumulative frequcncydistribution 累积频数分布cumulative frequency polygon累积频数多边形；累积频率直方图curvecurve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved linecurved surface 曲面curved surface area 曲面面积cyclic quadrilateral 圆内接四边形cylinder 柱；圆柱体cylindrical 圆柱形的Ddata 数据decagon 十边形decay 衰变decay factor 衰变因子decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distrivutive law 分配律divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形dot 点double root 二重根due east/ south/ west /north 向东/ 南/ 西/ 北definiton 定义degree (1)度；(2)次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of precision 精确度delete 删除；删去denary number 十进数denary scale 十进法denary system 十进制denominator 分母 dependence (1)相关；(2)应变 dependent event(s) 相关事件；相依事件；从属事件 dependent variable 应变量；应变数 depreciation 折旧 descending order 递降序 descending powers of X X 的降序 detached coefficients 分离系数(法) deviation 偏差；变差 deviation from the mean 离均差 diagonaldiagram 图；图表 diameter 直径 difference 差 digit 数字dimension 量；量网；维(数) direct proportion 正比例 direct tax, direct taxation 直接税 direct variation 正变（分） directed angle 有向角 directed number 有向数 direction 方向；方位 discontinuous 间断(的)；非连续(的)；不连续(的) discount 折扣 discount per cent 折扣百分率 discrete 分立；离散 discrete data 离散数据；间断数据 discriminant 判别式 dispersion 离差 displacement 位移 disprove 反证 E edge 棱；边 elimination 消法 elimination method 消去法；消元法elongation 伸张；展 empirical data 实验数据 empirical formula 实验公式 empirical probability 实验概率；经验概率 enclosure 界限 end point 端点 entire surd 整方根 equal 相等 equal ratios theorem 等比定理equal roots 等根 equality 等(式) equality sign 等号 equation 方程 equation in one unknown 一元方程equation in two unknowns (variables) 二元方程 equation of a straight line 直线方程 equation of locus 轨迹方程 equiangular 等角(的) extreme value 极值 equidistant 等距(的) equilaeral 等边(的) equilateral polygon 等边多边形 equilateral triangle 等边三角形 equivalent 等价(的) error 误差 escribed circle 旁切圆 estimate 估计；估计量 Euler's formula 尤拉公式；欧拉公式 evaluate 计值 even function 偶函数even number 偶数evenly distributed 均匀分布的 event 事件exact 真确exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解 example 例 excentre 外心 exception 例外 excess 起exclusive 不包含exclusive events 互斥事件 exercise 练习 expand 展开expand form 展开式 expansion 展式 expectation 期望expectation value, expected value 期望值；预期值 experiment 实验；试验 experimental 试验的experimental probability 实验概率exponent 指数express …in terms of ….. 以………表达expression 式；数式 extension 外延；延长；扩张；扩充exterior angle 外角external angle bisector外分external point of division 外分点extreme point 极值点Fface 面factor 因子；因式；商 factor method 因式分解法 factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式.分解factorization of polynomial 多项式因式分解FALSE 假(的)feasible solution 可行解；容许解Fermat’s last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字finite 有限finite population 有限总体finite sequence 有限序列finite series 有限级数first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点flow chart 流程图foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一X form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table频数分布表frequency polygon 频数多边形；频率多边形frustum 平截头体function 函数function of function 复合函数；迭函数functional notation 函数记号Ggain 增益；赚；盈利gain per cent 赚率；增益率；盈利百分率game （1）对策；（2）博奕general form 一般式；通式general solution 通解；一般解general term 通项geoborad 几何板geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解greatest term 最大项greatest value 最大值grid lines 网网格线groupgrouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子Hhalf closed interval 半闭区间half open interval 半开区间head 正面（钱币）height 高（度）hemisphere 半球体；半球heptagon 七边形Heron's formula 希罗公式hexagon 六边形higher order derivative 高阶导数highest common factor(H.C.F)最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图horizontal 水平的；水平horizontallinehyperbolahypotenuse 斜边Iidentical 全等；恒等identity 等（式）identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…., then 若….则；如果…..则illustration 例证；说明image 像点；像imaginary circle 虚圆imaginary number 虚数imaginary root 虚根.implication 蕴涵式；蕴含式 imply 蕴涵；蕴含 impossible event 不可能事件 improper fraction 假分数 inclination 倾角；斜角 inclined plane 斜面 included angle 夹角 included side 夹边 inclusive 包含的；可兼的 inconsistent 不相的(的)；不一致(的) increase 递增；增加 increasing function 递增函数 interior angles on the same side of the transversal 同旁内角 interior opposite angle 内对角internal bisector internal division 内分割 internal point of division 内分点 inter-quartile range 四分位数间距 intersect 相交 intersection (1)交集；(2)相交；(3)交点 interval 区间 intuition 直观 invariance 不变性 invariant (1)不变的；(2)不变量；不变式 inverse 反的；逆的 inverse circular function 反三角函数 inverse cosine function 反余弦函数 inverse function 反函数；逆函数 inverse problem 逆算问题 inverse proportion 反比例；逆比例 inverse sine function 反正弦函数 inverse tangent function 反正切函数 inverse variation 反变(分)；逆变(分) irrational equation 无理方程 irrational number 无理数 irreducibility 不可约性 irregular 不规则 isosceles triangle 等腰三角形 increasing sequence 递增序列 increasing series 递增级数 increment 增量 independence 独立；自变independent event 独立事件independent variable 自变量；独立变量 indeterminate (1)不定的；(2)不定元；未定元indeterminate coefficient 不定系数；未定系数indeterminate form 待定型；不定型index,indices 指数；指index notation 指数记数法inequality 不等式；不等 inequality sign 不等号 infinite 无限；无穷 infinite population 无限总体 infinite sequence 无限序列；无穷序列 infinite series 无限级数；无穷级数 infinitely many 无穷多 infinitesimal 无限小；无穷小 infinity 无限(大)；无穷(大) initial point 始点；起点 initial side 始边 initial value 初值；始值 input 输入 input box 输入 inscribed circle 内切圆 insertion 插入 insertion of brackets 加括号 instantaneous 瞬时的 integer 整数 integral index 整数指数 integral solution 整数解 integral value 整数值 intercept 截距；截段 intercept form 截距式 intercept theorem 截线定理 interchange 互换 interest 利息 interest rate 利率 interest tax 利息税 interior angle 内角J joint variation 联变(分)；连变(分)K known 己知L L.H.S. 末项 law 律；定律 law of indices 指数律；指数定律 law of trichotomy 三分律 leading coefficient 首项系数 least common multiple, lowest common multiple (L.C.M) 最小公倍数；最低公倍式 least value 最小值 lemma 引理 length 长(度) letter 文字；字母 like surd 同类根式 like terms 同类项 limit 极限 line 线；行line of best-fit line of greatest slope最大斜line of intersection line segment 线段 linear 线性；一次 linear equation 线性方程；一次方程 linear equation in two unknowns 二元一次方程；二元线性方程 linear inequality 一次不等式；线性不等式 linear programming 线性规划 literal coefficient 文字系数 literal equation 文字方程 load 负荷 loaded coin 不公正钱币 loaded die 不公正骰子 locus, loci 轨迹 logarithm 对数 logarithmic equation 对数方程 logarithmic function 对数函数 logic 逻辑 logical deduction 逻辑推论；逻辑推理 logical step 逻辑步骤 long division method 长除法 loss 赔本；亏蚀 loss per cent 赔率；亏蚀百分率 lower bound 下界 lower limit 下限 lower quartile 下四分位数 lowest common multiple(L.C.M) 最小公倍数 M magnitude 量；数量；长度；大小 major arc 优弧；大弧 major axis 长轴 major sector 优扇形；大扇形 major segment 优弓形；大弓形 mantissa 尾数 mantissa of logarithm 对数的尾数；对数的定值部 many-sided figure 多边形 marked price 标价 mathematical induction 数学归纳法 mathematical sentence 数句 mathematics 数学 maximize 极大 maximum absolute error 最大绝对误差 maximum point 极大点 maximum value 极大值mean 平均(值)；平均数；中数 mean deviation 中均差；平均偏差 measure of dispersion 离差的量度 measurement 量度 median (1)中位数；(2) meet 相交；相遇 mensuration 计量；求积法 method 方法 method of completing square 配方法method of substitution 代换法；换元法 metric unit 十进制单位 mid-point 中点 mid-point formula 中点公式 mid-point theorem 中点定理 million 百万 minimize 极小 minimum point 极小点 minimum value 极小值 minor (1)子行列式；(2)劣；较小的 minor arc 劣弧；小弧 minor axis 短轴 minor sector 劣扇形；小扇形 minor segment 劣弓形；小弓形 minus 减 minute 分 mixed number(fraction) 带分数 modal class 众数组 mode 众数 model 模型monomial 单项式 multinomial 多项式 multiple 倍数multiple root 多重根 multiplicand 被乘数 multiplication 乘法multiplication law (of probability) (概率)乘法定律 multiplicative property 可乘性 multiplier 乘数；乘式 multiply 乘 mutually exclusive events 互斥事件 mutually independent 独立; 互相独立 mutually perpendicularlines N n factorial n 阶乘 n th root n 次根；n 次方根 natural number 自然数 negative 负 negative angle 负角 negative index 负指数 negative integer 负整数negative number 负数neighborhood 邻域net 净(值) n-gon n 边形 nonagon 九边形non-collinear non-linear 非线性non-linear equation 非线性方程 non-negative 非负的 non-trivial 非平凡的 non-zero 非零 normal (1)垂直的；正交的；法线的 (2)正态的 (3)正常的；正规的 normalcurve正 normal distribution 正态分布，常态分布 normal form 法线式 notation 记法；记号 number 数number line number pair 数偶 number pattern 数型 number plane 数平面 number system 数系 numeral 数字；数码 numeral system 记数系统 numerator 分子 numerical 数值的；数字的 numerical expression 数字式 numerical method 计算方法；数值法 O oblique 斜的 oblique cone 斜圆锥 oblique triangle 斜三角形 obtuse angle 钝角 obtuse-angled triangle 钝角三角形 octagon 八边形 octahedron 八面体 odd function 奇函数 odd number 奇数 one-one correspondence 一一对应 open interval 开区间 open sentence 开句 operation 运算 opposite angle 对角 opposite interior angle 内对角 opposite side 对边 optimal solution 最优解 order (1)序；次序；(2)阶；级 ordered pair 序偶 origin 原点 outcome 结果 output 输出 overlap 交迭；相交 Pparabola parallel 平行(的) parallel lines 平行(直线) parallelogram 平行四边形 parameter 参数；参变量 partial fraction 部分分数；分项分式 polar coordinate system 极坐标系统 polar coordinates 极坐标 pole 极 polygon 多边形 polyhedron 多面体 polynomial 多项式 polynomial equation 多项式方程 positive 正 positive index 正指数 positive integer 正整数 positive number 正数 power (1)幂；乘方；(2)功率；(3)检定力 precise 精密 precision 精确度 prime 素 prime factor 质因子；质因素 prime number 素数；质数 primitive (1)本原的；原始的；(2)原函数 principal (1)主要的；(2)本金 prism 梭柱(体)；角柱(体) prismoid 平截头棱锥体 probability 概率 problem 应用题 produce 延长 product 乘积；积 product rule 积法则 profit 盈利profit per cent 盈利百分率profits tax 利得税 progression 级数proof 证(题)；证明proper fraction 真分数property 性质property tax 物业税 proportion 比例 proportional 成比例 protractor 量角器 pyramid 棱锥(体)；角锥(体) Pythagoras ’ Theorem 勾股定理 Pythagorean triplet 毕氏三元数组 partial sum 部分和 partial variation 部分变(分) particular solution 特解 Pascal ’s triangle 帕斯卡斯三角形pattern 模型；规律pegboard 有孔版pentadecagon 十五边形 pentagon 五边形 per cent 百分率 percentage 百分法；百分数 percentage decrease 百分减少 percentage error 百分误差 percentage increase 百分增加 percentile 百分位数 perfect number 完全数 perfecr square 完全平方 perimeter 周长；周界 period 周期 periodic function 周期函数permutation 排列 perpendicular 垂线；垂直(于) perpendicular bisector垂直平perpendicular line pictogram 象形图 pie chart 饼图；圆瓣图 pinboard 钉板 place holder 补位数字 place value 位值 plan (1)平面图；(2)计划 plane 平面 plane figure 平面图形 plot 绘图 plus 加 point 点 point circle 点圆 point of contact 切点 point of division 分点 point of intersection 交点 point-slope form 点斜式 polar axis 极轴 polar coordinate plane 极坐标平面 polar coordinate 极坐标系统 Q quadrant 象限 quadratic equation 二次方程(式) quadratic formula 二次公式 quardratic function 二次函数 quadratic inequality 二次不等式 quadratic polynomial 四边形 quantity 数量 quartile 四分位数 quotient 商；商式 R R.H.S 右 radian 弧度 radian measure 弧度法 radical 根式；根号；根数 radius, radii 半径 random 随机 random experiment 随机试验 random number 随机数 range 值域；区域；范围；极差；分布域 rate 率；利率 ratio 比 ; 比率 rational expression 有理式；有理数式 rational function 有理函数 rational index 有理数指数 rational number 有理数 rationalization 有理化 raw data 原始数据 raw score 原始分（数） real axis 实轴 real number 实数 real root 实根 reason 理由 reciprocal 倒数 rectangle 长方形；矩形 rectangular block 长方体 rectangular coordinate plane 直角坐标平面rectangular coordinates 直角坐rectilinear figure 直线图形 recurrent 循环的 recurring decimal 循环小数 reduce 简化 reducible 可约的；可化简的 reference angle 参考角 reflex angle 优角；反角 region 区域 regular 正；规则 regular polygon 正多边形 reject 舍去；否定 relation 关系；关系式 relative error 相对误差 remainder 余数；余式；剩余 remainder term 余项 remainder theorem 余式定理 removal of brackets 撤括号；去括号 repeated trials 重复试验resolve 分解revolution 旋转；周转 rhombus 菱形 right angle 直角 right circular cone 直立圆锥（体） right circular cylinder 直立圆柱（体） right prism 直立棱柱；直立角柱(体) right pyramid 直立棱锥；直立角锥(体) right-angled triangle 直角二角形 root 根 rotation 旋转 round angle 周角 rounded number 舍数 rounding(off) 舍入；四舍五入 row 行；棋行 rule 规则；法(则) ruler 直尺 S salaries tax 薪俸税 sample 抽样；样本 sample space 样本空间 satisfy 满足；适合scale 比例尺；标度；图尺 scalene triangle 不等边三角形；不规则三角形 scientific notation 科学记数法 solution of triangle 三角形解法 solve 解 special angle 特殊角；特别角 speed 速率 sphere 球形；球面 square (1)平方；(2)正方形square bracket 方括号square number 正方形数；平方数square root 平方根；二次根 standard deviation 标准差；标准偏离secant second 秒second quartile 第二四分位数(1)截面；截线；(2)截点 section (1)(2)截点section formula 截点公式 sector 扇式 segment 段；节segment of a circle 弓形 selling price 售价 semi-circle 半圆semi-vertical angle 半顶角 sentence 句；语句 sequence 序列 series 级数set square 三角尺；三角板 shaded portion 有阴影部分 shape 形状 side 边；侧sign 符号；记号signed number 有符号数 significant figure 有效数字 similar 相似similar figures 相似图形 similar triangles 相似三角形 similarity 相似(性)simple equation 简易方程 simple interest 单利；单利息 simplify 简化simultaneous equations 联立方程simultaneous inequalities 联立不等式simultaneous linear equations in two unknowns 联合二次线性方程式 sine 正弦sine formula 正弦公式 slant edge 斜棱 slant height 斜高slope 斜率；斜度；倾斜；坡度slope-intercept form 斜率截距式；斜截式 solid 立体；固体 soild with uniform corss-section 有均匀横切面的立体solution 解；解法solution of equation 方程解U uniform 一致(的)；均匀(的) uniform cross-section 均匀横切面 uniform speed 匀速率uniformly distributed 均匀分布unique solution 唯一解 uniqueness 唯一性 unit 单位 unit area 单位面积unit circle 单位圆unit volume 单位体积unknown 未知数；未知量 unlike 异类项 upper bound 上界 upper limit 上限upper quartile 上四分位数V value 值 variable 变项；变量；元；变元；变数variable speed 可变速率 variance 方差variation 变数；变分 verify 证明；验证vertex, vertices 顶(点)；极点 vertical 铅垂；垂直 vertical angle 顶角vertical line vertically opposite angles 对顶角volume 体积Wweight (1)重量；(2)权weighted average, weighted mean 加权平均数whole number 整数；完整数width 阔度without loss of generality 不失一般性X x-axis x 轴 x-coordinate x 坐标 x-intercept x 轴截距Y y-axis y 轴 y-coordinate y 坐标 y-intercept y 轴截距Z zero 零zero factor 零因子zeros of a function 函数零值。

2003 AMC 12A ProblemsProblem 1What is the difference between the sum of the first even counting numbers and the sum of the first odd counting numbers?SolutionProblem 2Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League?SolutionProblem 3A solid box is cm by cm by cm. A new solid is formed by removing a cube cm on a side from each corner of this box. What percent of the original volume is removed?SolutionProblem 4It takes Mary minutes to walk uphill km from her home to school, but it takes her only minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?SolutionProblem 5The sum of the two 5-digit numbers and is . Whatis ?SolutionProblem 6Define to be for all real numbers and . Which of the following statements is not true?for all andfor all andfor allfor allifSolutionProblem 7How many non-congruent triangles with perimeter have integer side lengths?SolutionProblem 8What is the probability that a randomly drawn positive factor of is less than ?SolutionProblem 9A set of points in the -plane is symmetric about the orgin, both coordinate axes, and the line . If is in , what is the smallest number of points in ?SolutionProblem 10Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio of , respectively. Due to some confusion they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be the correct share of candy, what fraction of the candy goes unclaimed?SolutionProblem 11A square and an equilateral triangle have the same perimeter. Let be the area of the circle circumscribed about the square and the area of the circle circumscribed around the triangle. Find .SolutionProblem 12Sally has five red cards numbered through and four blue cardsnumbered through . She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?SolutionProblem 13The polygon enclosed by the solid lines in the figure consists of 4 congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?SolutionProblem 14Points and lie in the plane of the square suchthat , , , and are equilateral triangles. If has an area of 16, find the area of .SolutionProblem 15A semicircle of diameter sits at the top of a semicircle of diameter , as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is calleda lune. Determine the area of this lune.SolutionProblem 16A point P is chosen at random in the interior of equilateral triangle . What is the probability that has a greater area than each of and ?SolutionProblem 17Square has sides of length , and is the midpoint of . A circle with radius and center intersects a circle with radius and center at points and . What is the distance from to ?SolutionProblem 18Let be a -digit number, and let and be the quotient and the remainder, respectively, when is divided by . For how many values of is divisibleby ?SolutionProblem 19A parabola with equation is reflected about the -axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of and , respectively. Which of the following describes the graph of ?SolutionProblem 20How many -letter arrangements of A's, B's, and C's have no A's in thefirst letters, no B's in the next letters, and no C's in the last letters?SolutionProblem 21The graph of the polynomialhas five distinct -intercepts, one of which is at . Which of the following coefficients cannot be zero?SolutionProblem 22Objects and move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object starts at and each of its steps is either right or up, both equally likely. Object starts at and each of its steps is either to the left or down, both equally likely. Which of the following is closest to the probability that the objects meet?SolutionProblem 23How many perfect squares are divisors of the product ?SolutionProblem 24If what is the largest possible value ofSolutionProblem 25Let . For how many real values of is there at least one positive value of for which the domain of and the range are the same set?Solution答案：SolutionSolution 1The first even counting numbers are .The first odd counting numbers are .Thus, the problem is asking for the valueof .Solution 2Using the sum of an arithmetic progression formula, we can write thisas .Solution 3The formula for the sum of the first even numbers, is , (E standing for even).Sum of first odd numbers, is , (O standing for odd).Knowing this, plug for ,.Problem 2SolutionSince T-shirts cost dollars more than a pair of socks, T-shirts cost dollars. Since each member needs pairs of socks and T-shirts, the total cost for member is dollars.Since dollars was the cost for the club, and was the cost per member, the number of members in the League isProblem 3SolutionThe volume of the original box isThe volume of each cube that is removed isSince there are corners on the box, cubes are removed.So the total volume removed is .Therefore, the desired percentage isProblem 4SolutionSolution 1Since she walked km to school and km back home, her total distanceis km.Since she spent minutes walking to school and minutes walking back home, her total time is minutes = hours.Therefore her average speed in km/hr is .Solution 2The average speed of two speeds that travel the same distance is the harmonic mean ofthe speeds, or (for speeds and ). Mary's speed going to schoolis , and her speed coming back is . Plugging the numbers in, we getthat the average speed is .Problem 5SolutionSince , , and are digits, , , .Therefore, .Problem 6SolutionExamining statement C:when , but statement C says that it does for all .Therefore the statement that is not true isProblem 7SolutionBy the triangle inequality, no side may have a length greater than the semiperimeter, which is .Since all sides must be integers, the largest possible length of a side is . Therefore, all such triangles must have all sides of length , , or . Since , at least one side must have a length of . Thus, the remaining two sides have a combined length of . So, the remaining sides must be either and or and . Therefore, the number of triangles is .Problem 8SolutionSolution 1For a positive number which is not a perfect square, exactly half of the positive factors will be less than .Since is not a perfect square, half of the positive factors of will be lessthan .Clearly, there are no positive factors of between and .Therefore half of the positive factors will be less than .So the answer is .Solution 2Testing all numbers less than , numbers , and divide . The prime factorization of is . Using the formula for the number of divisors, the total number of divisors of is . Therefore, our desired probabilityisProblem 9SolutionIf is in , then is also, and quickly we see that every point of theform or must be in . Now note that these points satisfy all of the symmetry conditions. Thus the answer is .Problem 10SolutionBecause the ratios are , Al, Bert, and Carl believe that they need to take , , and of the pile when they each arrive, respectively. After each personcomes, , , and of the pile's size (just before each came) remains. The pile starts at , and at the end of the original pile goes unclaimed. (Notethat because of the properties of multiplication, it does not matter what order the threecome in.) Hence the answer is.Problem 11SolutionSuppose that the common perimeter is Then, the side lengths of the square and triangle, respectively, are and The circle circumscribed about the square has a diameter equal to the diagonal of the square, which is Therefore, the radiusis and the area of the circle isNow consider the circle circumscribed around the equilateral triangle. Due to symmetry, the circle must share a center with the equilateral triangle. The radius of the circle is simply the distance from the center of the triangle to a vertex. This distance is of an altitude. By right triangle properties, the altitude is where s is the side. So, the radius is The area of the circleis So,Problem 12Let and designate the red card numbered and the blue card numbered , respectively.is the only blue card that evenly divides, so must be at one end of the stack and must be the card next to it.is the only other red card that evenly divides , so must be the other card next to .is the only blue card that evenly divides, so must be at one end of the stack and must be the card next to it.is the only other red card that evenly divides , so must be the other card next to .doesn't evenly divide , so must be next to , must be next to ,and must be in the middle.This yields the following arrangement from top tobottom:Therefore, the sum of the numbers on the middle three cards isProblem 13Solution 1Let the squares be labeled , , , and .When the polygon is folded, the "right" edge of square becomes adjacent to the "bottom edge" of square , and the "bottom" edge of square becomes adjacent to the "bottom" edge of square .So, any "new" square that is attatched to those edges will prevent the polygon from becoming a cube with one face missing.Therefore, squares , , and will prevent the polygon from becoming a cube with one face missing.Squares , , , , , and will allow the polygon to become a cube with one face missing when folded.Thus the answer is .Solution 2Another way to think of it is that a cube missing one face has of its faces. Since the shape has faces already, we need another face. The only way to add another face is ifthe added square does not overlap any of the others. ,, and overlap, while squares to do not. The answer isProblem 14SolutionSolution 1Since the area of square ABCD is 16, the side length must be 4. Thus, the side length of triangle AKB is 4, and the height of AKB, and thus DMC, is .The diagonal of the square KNMC will then be . From here there are 2 ways to proceed:First: Since the diagonal is , the side length is , and the area isthus .Solution 2Since a square is a rhombus, the area of the square is , where and are the diagonals of the rhombus. Since the diagonal is , the areais .Problem 15SolutionLet denote the area of region in the figure above.The shaded area is equal to the area of the smaller semicircle minus the area of a sector of the larger circle plus the area of a triangle formed by two radii of the larger semicircle and the diameter of the smaller semicircle .The area of the smaller semicircle is .Since the radius of the larger semicircle is equal to the diameter of the smaller semicircle, the triangle is an equilateral triangle and the sector measures .The area of the sector of the larger semicircle is . The area of the triangle is .So the shaded areaisProblem 16SolutionSolution 1After we pick point , we realize that is symmetric for this purpose, and so the probability that is the greatest area, or or , are all the same. Sincethey add to , the probability that has the greatest area isSolution 2We will use an approach of geometric probability to solve this problem. Let us take point P, and draw the perpendiculars to AB, BC, and AC, and call the feet of these perpendiculars D, E, and F respectively. The area of triangle ACP is simply 1/2 * AC * PF. Similarly we can find the area of triangles BCP and ABP. If we add these up and realize that it equals the area of the entire triangle, we see that no matter where we choose P, PD + PE + PF = the height of the triangle. Setting the area of triangle ACP greater than ABP and BCP, we want PF to be the largest of PF, PD, and PE. We then realize that PF = PD = PE when P is the orthocenter of ABC. Let us call the orthocenter of the triangle Q. If we want PF to be the largest of the three, by testing points we realize that P must be in the interior of quadrilateral QFCE. So our probability (using geometric probability) is the area of QFCE divided by the area of ABC. We will now show that the three quadrilaterals, QFCE, QEBD, and QDAF are congruent. As the definition of point Q yields, QF = QD = QE. Since ABC is equilateral, Q is also the circumcenter of ABC, so QA = QB = QC. Using the Pythagorean theorem, BD = DA = AF = FC = CE = EB. Also, angles BDQ, BEQ, CEQ, CFQ, AFQ, and ADQ are all equal to 90 degrees by the definition of analtitude. Also, angles DBE, FCE, DAF are all equal to 60 degrees as equilateral triangles are also equiangular. It is now clear that QFCE, QFAD, QEBD are all congruent. Summing up these areas gives us the area of ABC. QFCE contributes to a third of that area, as they are all congruent, so the ratio of the areas of QFCE to ABC is 1/3 (C). Problem 17Solution 1Let be the origin. is the point and is the point . We are given the radius of the quarter circle and semicircle as and , respectively, so their equations, respectively, are:Algebraically manipulating the second equation gives:Substituting this back into the first equation:Solving each factor for 0 yields . The first value of is obviously referring to the x-coordinate of the point where the circles intersect at the origin, , so the second value must be referring to the x coordinate of . Since is the y-axis, the distance to it from is the same as the x-value of the coordinate of , so the distancefrom to isSolution 2Note that is merely a reflection of over . Call the intersectionof and . Drop perpendiculars from and to , and denote their respective points of intersection by and . We then have , with a scale factor of 2. Thus, we can find and double it to get our answer. With some analytical geometry, we find that , implying that .Solution 3As in Solution 2, draw in and and denote their intersection point . Next, drop a perpendicular from to and denote the foot as . as they areboth radii and similarly so is a kite and by awell-known theorem.Pythagorean theorem gives us .Clearly by angle-angleand by Hypotenuse Leg. Manipulating similar triangles gives usProblem 18SolutionWhen a -digit number is divided by , the first digits become the quotient, , and the last digits become the remainder, .Therefore, can be any integer from to inclusive, and can be any integer from to inclusive.For each of the possible values of , there are atleast possible values of such that .Since there is "extra" possible value of that is congruent to , each of the values of that are congruent to have more possible value of such that .Therefore, the number of possible values of suchthat isProblem 19SolutionIf we take the parabola and reflect it over the x - axis, we have the parabola . Without loss of generality, let us say that the parabola is translated 5 units to the left, and the reflection to the right. Then:Adding them upproduces:This is a line with slope . Since cannot be (because would be a line) we end up withProblem 20SolutionThe answer is .Note that the first five letters must be B's or C's, the next five letters must be C's or A's, and the last five letters must be A's or B's. If there are B's in the first five letters, then there must be C's in the first five letters, so there must be C's and A's in the next five letters, and A's and B's in the last five letters. Therefore the number of each letter in each group of five is determined completely by the number of B's in the first 5 letters, and the number of ways to arrange these 15 letters with thisrestriction is (since there are ways to arrange B's and C's).Therefore the answer is .Problem 21SolutionSolution 1Let the roots be . According to Vieta's formulas, wehave . The first four terms contain and are therefore zero, thus . This is a product of four non-zero numbers, therefore must be non-zero .Solution 2Clearly, since is an intercept, must be . But if was , would divide the polynomial, which means it would have a double root at , which is impossible, since all five roots are distinct.Problem 22SolutionIf and meet, their paths connect and There are such paths, so the probability isProblem 23SolutionWe want to find the number of perfect square factors in the product of all the factorials of numbers from . We can write this out and take out the factorials, and then find a prime factorization of the entire product. We can also find this prime factorization by finding the number of times each factor is repeated in each factorial. This comes out to be equal to . To find the amount of perfect square factors, we realize that each exponent in the prime factorization must be even: . To find the total number of possibilities, we add to each exponent and multiply them all together. This gives us .Problem 24SolutionUsing logarithmic rules, we see thatSince and are both positive, using AM-GM gives that the term in parentheses must be at least , so the largest possible values isProblem 25SolutionThe function has a codomain of all non-negative numbers,or . Since the domain and the range of are the same, it follows that the domain of also satisfies .The function has two zeroes at , which must be part of the domain. Since the domain and the range are the same set, it follows that is in the codomain of ,or . This implies that one (but not both) of is non-positive. If is positive, then , which implies that a negative number falls in the domain of , contradiction. Thus must be non-positive, is non-negative, and the domain of the function occurs when, orCompleting the square, by the Trivial Inequality (remember that ). Since is continuous and assumes this maximal value at , it follows that the range of isAs the domain and the range are the same, we havethat (we can divide through by since it is given that is positive). Hence , which both we can verify work, and the answer is .。

amc数学竞赛知识点AMC数学竞赛知识点AMC数学竞赛（American Mathematics Competitions）是美国最具影响力的数学竞赛之一，旨在培养和激发学生对数学的兴趣和才能。

参与AMC竞赛的学生需要掌握一定的数学知识点和解题技巧。

下面将介绍一些常见的AMC数学竞赛知识点。

1. 数论：数论是AMC竞赛中常见的一个考点，它研究整数的性质和关系。

在数论中，学生需要掌握质数、因数分解、最大公因数、最小公倍数等基本概念，以及一些数论定理和性质，如费马小定理、欧拉定理等。

2. 代数：代数是AMC竞赛中的另一个重要知识点。

学生需要熟悉代数运算、多项式的基本性质、方程与不等式的解法等。

此外，还需要掌握一些常见的代数函数，如线性函数、二次函数、指数函数等，以及它们的图像和性质。

3. 几何：几何是AMC竞赛中的必考内容之一。

学生需要了解点、线、面等基本概念，以及几何图形的性质和判定方法。

此外，还需要掌握一些几何定理和公式，如勾股定理、相似三角形的性质、平行线与角的关系等。

4. 概率与统计：概率与统计是AMC竞赛中的另一个考点。

学生需要了解概率的基本概念和性质，如事件、样本空间、概率的计算方法等。

此外，还需要熟悉一些统计学的基本知识，如均值、中位数、标准差等。

5. 组合数学：组合数学是AMC竞赛中的一项重要内容。

学生需要了解排列组合的基本概念和计算方法，如阶乘、二项式系数等。

此外，还需要掌握一些组合数学的定理和性质，如鸽巢原理、容斥原理等。

6. 数列与数列求和：数列与数列求和是AMC竞赛中常见的一个考点。

学生需要了解等差数列和等比数列的性质和计算方法，以及一些常见的数列求和公式，如等差数列求和公式、等比数列求和公式等。

7. 不等式：不等式是AMC竞赛中常见的一个知识点。

学生需要掌握不等式的基本性质和解法，如一元一次不等式、二元一次不等式等。

此外，还需要了解一些常见的不等式定理和性质，如柯西不等式、均值不等式等。

USA AMC 12/AHSME 20121 A bug crawls along a number line, starting at. It crawls to, then turns around and crawls to . How many units does thebug crawl altogether?2 Cagney can frost a cupcake every seconds and Lacey can frost a cupcake everyseconds. Working together, how manycupcakes can they frost in minutes?3 A box centimeters high, centimeters wide, and centimeters long can hold grams of clay. A second box with twice theheight, three times the width, and the same length as the first box can hold grams of clay. What is ?4 In a bag of marbles, of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number ofblue marbles stays the same, what fraction of the marbles will be red?5 A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total ofpieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?6 The sums of three whole numbers taken in pairs are ,, and. What is the middle number?7 Mary divides a circle into sectors. The central angles of these sectors, measured in degrees, are all integers and they form anarithmetic sequence. What is the degree measure of the smallest possible sector angle?8 An iterative average of the numbers , , , , and is computed in the following way. Arrange the five numbers in some order.Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure?9 A year is a leap year if and only if the year number is divisible by(such as ) or is divisible by but not by (such as ). The anniversary of the birth of novelist Charles Dickens was celebrated on February , , a Tuesday. On what day of the week was Dickens born?10 A triangle has area , one side of length, and the median to that side of length . Let be the acute angle formed by thatside and the median. What is ?11 Alex, Mel, and Chelsea play a game that has rounds. In each round there is a single winner, and the outcomes of the roundsare independent. For each round the probability that Alex wins is , and Mel is twice as likely to win as Chelsea. What is the probability that Alex wins three rounds, Mel wins two rounds, and Chelsea wins one round?12 A square region is externally tangent to the circle with equation at the point on the side.Vertices and are on the circle with equation . What is the side length of this square?13 Paula the painter and her two helpers each paint at constant, but different, rates. They always start at, and all three always take the same amount of time to eat lunch. On Monday the three of them painted of a house, quitting at . On Tuesday, when Paula wasn't there, the two helpers painted only of the house and quit at . On Wednesday Paula worked by herself and finished the house by working until . How long, in minutes, was each day's lunch break?14The closed curve in the figure is made up of congruent circular arcs each of length, where each of the centers of thecorresponding circles is among the vertices of a regular hexagon of side . What is the area enclosed by the curve?15 Asquare is partitioned into unit squares. Each unit square is painted either white or black with each color being equally likely, chosen independently and at random. The square is the rotated clockwise about its center, and every white square in a position formerly occupied by a black square is painted black. The colors of all other squares are left unchanged. What is the probability that the grid is now entirely black?16 Circlehas its center lying on circle . The two circles meet at and. Point in the exterior oflies on circleand, , and . What is the radius of circle ?17 Let be a subset ofwith the property that no pair of distinct elements in has a sum divisible by . What isthe largest possible size of ?18 Trianglehas ,, and. Let denote the intersection of the internal angle bisectors of. What is ?19 Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends witheach other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?20 Consider the polynomialThe coefficient of is equal to. What is ?21 Letand be positive integers withsuch thatWhat is ?22Distinct planes intersect the interior of a cube. Let be the union of the faces of and let. Theintersection ofandconsists of the union of all segments joining the midpoints of every pair of edges belonging to the same© Copyright 2012 AoPS Incorporated. All Rights Reserved.Contact Us • Privacy • Terms & Conditionsface of . What is the difference between the maximum and minimum possible values of ?23 Let be the square one of whose diagonals has endpoints and. A point is chosen uniformly atrandom over all pairs of real numbers and such that and . Let be a translated copy ofcentered at . What is the probability that the square region determined by contains exactly two points with integercoordinates in its interior?24 Letbe the sequence of real numbers defined by,and more generallydigits for the number in parentheses, and the top number if is odd and the bottom number if is even.Rearranging the numbers in the sequence in decreasing order produces a new sequence . What is the sum of all the integers , , such that ?25 Letwheredenotes the fractional part of . The number is the smallest positive integer such that theequationhas at least real solutions . What is ?Note: the fractional part of is a real number , such thatand is an integer.。

美国数学大联盟常用英文词汇一、基础数学词汇1. Arithmetic 算术2. Algebra 代数3. Geometry 几何4. Trigonometry 三角学5. Calculus 微积分6. Statistics 统计学7. Probability 概率论8. Combinatorics 组合数学9. Number theory 数论10. Set theory 集合论二、代数词汇1. Variable 变量2. Equation 方程3. Inequality 不等式4. Function 函数5. Graph 图像6. Polynomial 多项式7. Factorization 因式分解8. Exponent 指数9. Logarithm 对数10. Matrix 矩阵三、几何词汇1. Point 点2. Line 线3. Plane 平面4. Angle 角度5. Triangle 三角形6. Quadrilateral 四边形7. Circle 圆8. Perimeter 周长9. Area 面积10. Volume 体积四、三角学词汇1. Sine 正弦2. Cosine 余弦3. Tangent 正切4. Cosecant 余割5. Secant 正割6. Cotangent 余切7. Arcsine 反正弦8. Arccosine 反余弦9. Arctangent 反正切10. Radian 弧度五、微积分词汇1. Derivative 导数2. Integral 积分3. Limit 极限4. Series 级数5. Sequence 数列6. Differentiation 微分7. Integration 积分8. Differential equation 微分方程9. Taylor series 泰勒级数10. Fourier series 傅里叶级数六、统计学词汇1. Data 数据2. Sample 样本3. Population 总体4. Mean 平均值5. Median 中位数6. Mode 众数7. Standard deviation 标准差8. Variance 方差9. Probability distribution 概率分布10. Hypothesis testing 假设检验七、概率论词汇1. Event 事件2. Probability 概率3. Random variable 随机变量4. Probability space 概率空间5. Conditional probability 条件概率6. Bayes' theorem 贝叶斯定理7. Independence 独立性8. Law of large numbers 大数定律9. Central limit theorem 中心极限定理10. Random walk 随机游走八、组合数学词汇1. Permutation 排列2. Combination 组合3. Binomial coefficient 二项式系数4. Pascal's triangle 帕斯卡三角形5. Catalan number 卡塔兰数6. Fibonacci sequence 斐波那契数列7. Partition 分割8. Graph theory 图论9. Ramsey theory 拉姆齐理论10. Combinatorial design 组合设计九、数论词汇1. Prime number 质数2. Composite number 合数3. Divisor 因数4. GCD 最大公约数5. LCM 最小公倍数6. Modular arithmetic 模运算7. Fermat's little theorem 费马小定理8. Euler's theorem 欧拉定理9. Chinese remainder theorem 中国剩余定理10. RSA encryption RSA加密十、集合论词汇1. Set 集合2. Element 元素3. Union 并集4. Intersection 交集5. Complement 补集6. Power set 幂集7. Cartesian product 笛卡尔积8. Function 函数9. Relation 关系10. Equivalence relation 等价关系美国数学大联盟常用英文词汇一、基础数学词汇1. Arithmetic 算术2. Algebra 代数3. Geometry 几何4. Trigonometry 三角学5. Calculus 微积分6. Statistics 统计学7. Probability 概率论8. Combinatorics 组合数学9. Number theory 数论10. Set theory 集合论二、代数词汇1. Variable 变量2. Equation 方程3. Inequality 不等式4. Function 函数5. Graph 图像6. Polynomial 多项式7. Factorization 因式分解8. Exponent 指数9. Logarithm 对数10. Matrix 矩阵三、几何词汇1. Point 点2. Line 线3. Plane 平面4. Angle 角度5. Triangle 三角形6. Quadrilateral 四边形7. Circle 圆8. Perimeter 周长9. Area 面积10. Volume 体积四、三角学词汇1. Sine 正弦2. Cosine 余弦3. Tangent 正切4. Cosecant 余割5. Secant 正割6. Cotangent 余切7. Arcsine 反正弦8. Arccosine 反余弦9. Arctangent 反正切10. Radian 弧度五、微积分词汇1. Derivative 导数2. Integral 积分3. Limit 极限4. Series 级数5. Sequence 数列6. Differentiation 微分7. Integration 积分8. Differential equation 微分方程9. Taylor series 泰勒级数10. Fourier series 傅里叶级数六、统计学词汇1. Data 数据2. Sample 样本3. Population 总体4. Mean 平均值5. Median 中位数6. Mode 众数7. Standard deviation 标准差8. Variance 方差9. Probability distribution 概率分布10. Hypothesis testing 假设检验七、概率论词汇1. Event 事件2. Probability 概率3. Random variable 随机变量4. Probability space 概率空间5. Conditional probability 条件概率6. Bayes' theorem 贝叶斯定理7. Independence 独立性8. Law of large numbers 大数定律9. Central limit theorem 中心极限定理10. Random walk 随机游走八、组合数学词汇1. Permutation 排列2. Combination 组合3. Binomial coefficient 二项式系数4. Pascal's triangle 帕斯卡三角形5. Catalan number 卡塔兰数6. Fibonacci sequence 斐波那契数列7. Partition 分割8. Graph theory 图论9. Ramsey theory 拉姆齐理论10. Combinatorial design 组合设计九、数论词汇1. Prime number 质数2. Composite number 合数3. Divisor 因数4. GCD 最大公约数5. LCM 最小公倍数6. Modular arithmetic 模运算7. Fermat's little theorem 费马小定理8. Euler's theorem 欧拉定理9. Chinese remainder theorem 中国剩余定理10. RSA encryption RSA加密十、集合论词汇1. Set 集合2. Element 元素3. Union 并集4. Intersection 交集5. Complement 补集6. Power set 幂集7. Cartesian product 笛卡尔积8. Function 函数9. Relation 关系10. Equivalence relation 等价关系十一、数学竞赛相关词汇1. Contest 竞赛2. Problem 问题3. Solution 解答4. Strategy 策略5. Practice 练习6. Challenge 挑战7. Competition 比赛8. Award 奖项9. Medal 奖牌10. Rank 排名十二、数学教育相关词汇1. Curriculum 课程2. Lesson 课3. Exercise 练习4. Homework 作业5. Test 测试6. Assessment 评估7. Instruction 指导8. Resource 资源9. Tool 工具10. Technique 技巧十三、数学研究相关词汇1. Research 研究2. Theory 理论3. Hypothesis 假设4. Proof 证明5. Result 结果6. Experiment 实验7. Observation 观察8. Analysis 分析9. Conclusion 结论10. Publication 发表十四、数学应用相关词汇1. Application 应用2. Model 模型3. Algorithm 算法4. Simulation 模拟5. Optimization 优化6. Data 数据7. Analysis 分析8. Solution 解答9. Design 设计10. Evaluation 评估十五、数学文化相关词汇1. History 历史2. Development 发展3. Influence 影响4. Mathematician 数学家5. Theory 理论6. Concept 概念7. Idea 思想8. Innovation 创新9. Tradition 传统10. Legacy 遗产通过掌握这些常用英文词汇，你将能够更好地理解和参与美国数学大联盟的数学竞赛、教育、研究以及应用等领域的讨论和交流。

AMC常用词汇一、基本图形正数： positive number三角形： triangle 负数： negative number矩形： rectangle 奇数： odd integer，odd number正方形： square 偶数： even integer， even number平行四边形： parallelogram 整数： integer，whole number梯形： tapezoid 正整数： positive whole number菱形： rhombus 负整数： negative whole number圆： circle 连续整数： consecutive number四边形： quadrilateral 实数，有理数： real number，rational number无理数： irrational （number）二、基本立体图形倒数： inverse正方体： cube 合数： composite number长方体： rectangular prism eg. 4,6,8,9,10,12,14,15⋯⋯圆柱体： right circular cyclinder 质数： prime number圆锥体： right circular cone ⋯⋯eg.2,3,5,7,11,13,15球体： sphere 倒数： reciprocal公约数： common divisor三、基本计算量倍数： multiple长度： length （最小）公约数：（last）common multiple面积： area （质）因子：（ prime）factor体积（容积）：volume 十进制： ordinary csale，decimal scale周长： perimeter 非负的： nonnegative表面积： surface area 十位： tens底面积： base area 个位： units众数： mode四、有关集合中数： median并集： union 公比： common ratioproper subset 真子集：solution set 解集：六、数列等差数列： arithmetic progression（ sequence）五、有关数论等比数列： geometric progression（ sequence）自然数： natural number七、其它近似： approximate（逆）顺时针方向：（anti） clockwise 基数： cardinal序数： ordinal正比： directproportion不同的： distinct估计，近似： estimation括号： parentheses比例： proportion组合： combination表格： table三角函数： trigonometric function单位，位： unit八、其它几何1、所有的角内错角： alternate angle同位角： corresponding angle对顶角： vertical angle圆心角： central angle内角： interior angle外角： exterior angle补角： supplement aryangles余角： complement aryangle邻角： adjacent angle 等边三角形： equilateral triangle 不等边三角形： scalene triangle 等腰三角形： isosceles triangle 直角三角形： right triangle斜三角形： oblique内接三角形： inscribed triangle3、有关收敛的平面图形，除三角形外半圆： semicircle同心圆： concentric circles四边形： quadrilateral五边形： pentagon六边形： hexagon七边形： heptagon八边形： octagon九边形： nonagon十边形： decagon多边形： polygon平行四边形： parallelogram等边形： equilateral平面： plane正方形，平方： square长方形： rectangle正多边形： regular polygon菱形： rhombus梯形： trapezoid锐角： acute angle钝角： obtuse angle 4、其它平面图形直角： right angle 弧： arc周角： round angle 直线： line，straight line 平角： straight angle 线段： line segment夹角： included angle 平行线： parallellines弧形： segment of a circle 2、所有的三角形5、有关立体图形立方体，立方数： cube长方体： rectangular solid正多面体： regular solid / regular polyhedron圆柱体： circular cylinder圆锥： cone球体： sphere立体的： solid6、有关图形上的附属物高： altitude深度： depth边长： side周长： circumference，perimeter弧度： radian表面积： surface area体积： volume直角三角形的股： arm横截面： cros section圆心： center of a circle弦： chord半径： radius角平分器： angle bisector对角线： diagonal直径： diameter棱： edge立体的面： face of a solid斜边： hypotenuse夹边： included side三角形的直角边： leg三角形的中线： median of a triangle底边，底数 (e.g.2 的 5 次方 ,2 就是底数 )：base直角三角形中的对边： opposite中点： midpoint 端点： endpoint（复数形式vertices）顶点： vertex 切线的： tangent截线： transversal截距： intercept7、有关坐标坐标系： coordinate system直角坐标系： rectangular coordinate 原点： origin横坐标： abscissa纵坐标： ordinate数轴： number line象限： quadrant斜率： slope复平面： complex plane8、其它平面几何： plane geometry三角学： trigonometry平分： bisect外切： circumscribe内切： inscribe相交： intersect垂直： perpendicular勾股定理： pythagorean theorem全等的： congruent多边的： multilateral基本数学词汇加： plus / and / positive减： minus / negative / subtract 差： difference乘： multiplied by / times乘方 :power积： product除： divided by可被整除的： divisible被整除： dividedevenly被除数： dividend商： quotient余数： remainder阶乘： factorial等于： equal不等于： not equal to大于： greater than小于 :less than大于等于： equal or greater than小于等于： equal or less than约等于： approximate equal四舍五入： round to / to the nearest 因为： because所以： therefore开平方： square root of开立方： cube root of根号： radical sign，root sign绝对值： the absolute value函数： function图形： figure角： angle直角： right angle锐角： acute angle对折： fold 分数： fractionX- 轴： X-axesY-轴： Y-axes其它次序： sequence几何的： g eometric整数： integer比例： ratio正的： positive切线（也是正切tan）：tangent半径： radius / radii不等式： inequality顶点： vertex值域： range同类项： like terms，similar terms原方程： original equation(最小 )公约数： (least)common denominator 算术平均数： arithmetic mean加权平均值： weighted average指数，幂： exponent变量： variable反函数： inverse function因式分解： factorization打（ 12 个）： dozen廿（ 20 个）： score夸脱： quart加仑： gallon（ 1 gallon = 4 quart）英语数学词汇大全Aabbreviation 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 algebraicexpression 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 thecentre 圆心角angle at thecircumference 圆周角angle between aline and a planeangle between two planes 两平面的交角angle bisection 角平分 anglebisectorangle 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 angleof intersection 相交角；交角angle of rotation 旋转角 angle ofthe sector 扇形角 angle sum of atriangle 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 approximatevalue 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Bback substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（ 2）基；基数 base angle 底角 base area 底面base linebase number 底数；基数 base of logarithm 对数的底bearing 方位（角）；角方向（角） bell-shaped curve 钟形图bias 偏差；偏倚billion 十亿binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial expression 二项式bisect 平分；等分bisection method 分半法；分半方法bisectorboundary condition 边界条件 boundary line 界（线）；边界 bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数brace 大括号bracket 括号breadth 阔度broken line graph 折线图chart 图；图表checking 验算chord 弦chord of contact 切点弦 circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circumcentre 外心；外接圆心 circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classification 分类clnometer 测斜仪clockwise dirction 顺时针方common ratio 公比common tangetncommutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图complement 余；补余complementary angle 余角complementary event 互补事件complementary probability 互补概率completing the square 配方complex number 复数complex root 复数根composite number 复合数；合成数compound bar chart 综合棒形图Ccalculation 计算calculator 计算器；计算器cancel 消法；相消canellation law 消去律 capacity 容量Cartesian coordinates 笛卡儿坐标Cartesian plane 笛卡儿平面 category 类型；范畴 central linecentral tendency 集中趋 centre 中心；心centre of a circle圆心 centroid 形心；距心 certain event必然事件 chance 机会change of base 基的变换 change of subject 主项变换change of variable 换元；变量的换向compounddiscount 复折扣closed convexregion 闭凸区compoundinterest复利；复利域息closed interval 闭区间computation 计算coefficient 系数computer 计算机；电子计算coincide 迭合；重合器collection ofterms 并项concave 凹collinear concave downward 凹向下的collinear planes 共线面concavepolygon 凹多边形column (1) 列；纵行；(2)柱concave upward 凹向上的combination 组合concentriccircles 同心圆common chord 公弦concept 概念common denominator 同分母；conclusion 结论公分母concurrent 共点common difference 公差concyclic 共圆common divisor 公约数；公concyclicpoints 共圆点约condition 条件common factor 公因子；公因conditional条件句；条件式子cone 锥；圆锥（体）commonlogarithm 常用对数congruence (1) 全等； (2)同余common multiple 公位数；公congruent 全等倍congruentfigures 全等图形congruent triangles 全等三角形cconjugate 共轭consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论cosine formula 余弦公式cost price 成本counter clockwisedirection逆时针方向；返时针方向 counter example反例counting 数数；计数 criterion 准则critical point 临界点decimal place 小数位decimal point 小数点decimal system 十进制decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列consequent 条件；后项consistency condition 相容条cross-multiplication 交叉相乘 decreasing series 递减级数； cross-section 横切面；横截面；下降级数件consistent 一贯的；相容的constant 常数constant speed 恒速率constant term 常项constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例 continued ratio 连比continuous 连续的continuous data 连续数据continuous function 连续函数 continuousproportion 连续比例contradiction 矛盾converse 逆 (定理 ) converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形coordinate 坐标coordinate g eometry 解析几何；坐标几何coordinate s ystem 坐标系系定理；系；推论correct to 准确至；取值至 correspondence 对应correspondingangles (1) 同位角； (2) 对应角correspondingsides 对应边cosine 余弦截痕cube 正方体；立方；立方体 cuberoot 立方根cubic 三次方；立方；三次 (的) cubicequation 三次方程cuboid 长方体；矩体cumulative 累积的cumulative frequecy 累积频数；累积频率cumulative frequency curvecumulative frequcncydistribution 累积频数分布cumulative frequency polygon累积频数多边形；累积频率直方图curvecurve sketching 曲线描绘 (法 )curve tracing 曲线描迹 (法 )curved linecurved surface 曲面curved surface area 曲面面积cyclic quadrilateral 圆内接四边形cylinder 柱；圆柱体cylindrical 圆柱形的Ddata 数据decagon 十边形decay 衰变decay factor 衰变因子decimal 小数decrement 减量deduce 演绎deduction 推论deductivereasoning 演绎推理definite 确定的；定的distance 距离distance formula 距离公式distinctroots 相异根 distincrsolution 相异解distribution 公布distrivutive law 分配律divide 除dividend (1) 被除数； (2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor ofzero 零因子dodecagon 十二边形dot 点double root 二重根due east/ south/ west/north向东/南/西/北definiton 定义degree (1)度； (2) 次degree of apolynomial 多项式的次数degree ofaccuracy 准确度 degree ofprecision 精确度 delete删除；删去denary number 十进数denary scale 十进法denary system 十进制denominator 分母 dependence (1)相关； (2)应变 dependent event(s) 相关事件；相依事件；从属事件dependent variable 应变量；应变数depreciation 折旧descending order 递降序descending powers of X X的降序detached coefficients 分离系数( 法)deviation 偏差；变差deviation from the mean离均差diagonaldiagram 图；图表diameter 直径difference 差digit 数字dimension 量；量网；维(数 ) direct proportion 正比例 direct tax, direct taxation 直接税direct variation 正变（分）directed angle 有向角directed number 有向数direction 方向；方位discontinuous 间断(的 )；非连续( 的)；不连续 (的 ) discount 折扣discount per cent 折扣百分率discrete 分立；离散discrete data 离散数据；间断数据discriminant 判别式dispersion 离差displacement 位移disprove 反证Eedge 棱；边elimination 消法elimination method 消去法；消元法elongation 伸张；展empirical data 实验数据 empiricalformula 实验公式 empiricalprobability 实验概率；经验概率enclosure 界限 end point端点 entire surd 整方根equal 相等equal ratios theorem 等比定理equal roots 等根equality 等 (式 )equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns(variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角 (的 ) extremevalue 极值 equidistant 等距 (的 )equilaeral 等边 (的 ) equilateralpolygon 等边多边形equilateral triangle 等边三角形equivalent 等价 (的 )error 误差escribed circle 旁切圆estimate 估计；估计量Euler's formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive events 互斥事件exercise 练习expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expectedvalue 期望值；预期值experiment 实验；试验 experimental 试验的experimental probability 实验概率exponent 指数express ⋯ in terms of ⋯ ..以⋯⋯⋯表达expression 式；数式extension 外延；延长；扩张；扩充exterior angle 外角external a ngle bisector 外分external point of division外分点extreme point 极值点Fface 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解frequency distribution table 数据factorization of polynomial 多频数分布表grouping terms 并项；集项项式因式分解FALSE 假 (的 )feasible solution 可行解；容许解Fermat’s last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数 figure (1) 图(形) ；(2) 数字 finite有限finite population 有限总体finite sequence 有限序列finite series 有限级数first quartile 第一四分位数first term 首项fixed deposit 定期存款 fixed point 定点 flow chart 流程图foot of perpendicular垂足 for all X 对所有Xfor each /every X 对每一 X form 形式；型frequency polygon 频数多边形；频率多边形frustum 平截头体function 函数function of function 复合函数；迭函数functional notation 函数记号Ggain 增益；赚；盈利gain per cent 赚率；增益率；盈利百分率game （ 1）对策；（ 2）博奕 general form 一般式；通式 general solution 通解；一般解 general term通项 geoborad 几何板geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列 geometric series 等比级数 geometry 几何；几何学growth 增长growth factor 增长因子Hhalf closed interval 半闭区间 half openinterval 半开区间head 正面（钱币）height 高（度）hemisphere 半球体；半球 heptagon 七边形Heron's formula 希罗公式 hexagon 六边形higher order derivative高阶导数highest common factor(H.C.F)最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图horizontal 水平的；水平 horizontal lineformal proof 形式化的证明 format 格式；规格formula(formulae) 公式four rules 四则 four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程 fractional index 分数指数 fractional inequality 分式不等式free fall 自由下坠frequency 频数；频率frequency distribution 频数分布；频率分布given 给定；已知hyperbolagolden section 黄金分割hypotenuse 斜边grade 等级gradient (1)斜率；倾斜率；(2)I 梯度grand total 总计identical 全等；恒等graph 图像；图形；图表identity 等（式）graph paper 图表纸identityrelation 恒等关系式graphical method 图解法if and onlyif/iff当且仅当；若graphical representation 图示；且仅若以图样表达if ⋯ ., then 若⋯ .则；如果⋯ ..graphical solution 图解则greatest term 最大项illustration 例证；说明greatest value 最大值image 像点；像grid lines 网网格线imaginarycircle 虚圆group imaginary number 虚数grouped data 分组数据；分类imaginaryroot 虚根implication 蕴涵式；蕴含式 imply 蕴涵；蕴含impossible event 不可能事件 improper fraction 假分数 inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusive 包含的；可兼的inconsistent 不相的 (的 )；不一致( 的)increase 递增；增加increasing function 递增函数interior angles on the sameside of the transversal同旁内角interior opposite angle内对角internal bisector 切函数inverse variation 反变( 分 )；逆变(分)irrational equation 无理方程 irrational number无理数 irreducibility 不可约性irregular 不规则isosceles triangle 等腰三角形 increasing sequence递增序列increasing series 递增级数increment 增量independence 独立；自变independent event 独立事件independent variable 自变量；独立变量indeterminate (1) 不定的；(2)不定元；未定元integer 整数integral index 整数指数 integralsolution 整数解integral value 整数值intercept 截距；截段intercept form 截距式intercept theorem 截线定理interchange 互换interest 利息interest rate 利率interest tax 利息税interior angle 内角Jjoint variation 联变 (分 )；连变( 分 )internal division 内分割internal point of division 内分点inter-quartile range 四分位数indeterminate coefficient 不定系数；未定系数K indeterminate form 待定型； known 己知不定型间距intersect 相交intersection (1) 交集； (2) 相交；(3)交点interval 区间intuition 直观invariance 不变性invariant (1) 不变的； (2) 不变量；不变式inverse 反的；逆的inverse circular function反三角函数inverse cosine function反余弦函数inverse function 反函数；逆函数inverse problem逆算问题 inverseproportion 反比例；逆比例inverse sinefunction 反正弦函数inverse tangentfunction 反正index,indices 指数；指 indexnotation 指数记数法inequality 不等式；不等inequality sign 不等号infinite 无限；无穷infinite population 无限总体infinite sequence 无限序列；无穷序列infinite series 无限级数；无穷级数infinitely many 无穷多infinitesimal 无限小；无穷小infinity 无限 (大 )；无穷 (大 )initial point 始点；起点 initialside 始边initial value 初值；始值 input输入input box 输入 inscribed circle 内切圆 insertion 插入insertion of brackets 加括号instantaneous 瞬时的LL.H.S. 末项law 律；定律law of indices 指数律；指数定律law of trichotomy 三分律leading coefficient 首项系数least common multiple, lowestcommon multiple (L.C.M)最小公倍数；最低公倍式least value 最小值lemma 引理length 长 (度 )letter 文字；字母like surd 同类根式like terms 同类项limit 极限line 线；行line of best-fitline of greatest slope 最大斜line of intersectionline segment 线段linear 线性；一次linear equation 线性方程；一次方程linear equation in two unknowns 二元一次方程；二元线性方程linear inequality 一次不等式；线性不等式linear programming 线性规划形形mantissa 尾数minus 减mantissa of logarithm 对数的minute 分尾数；对数的定值部mixednumber(fraction)带分many-sided figure 多边形数marked price 标价modalclass 众数组mathematicalinduction 数学mode 众数归纳法model 模型mathematical sentence 数句monomial 单项式mathematics 数学multinomial 多项式maximize 极大multiple倍数literal coefficient 文字系数 literal equation文字方程 load 负荷loaded coin 不公正钱币loaded die 不公正骰子locus, loci 轨迹logarithm 对数logarithmicequation 对数方程logarithmicfunction 对数函数logic 逻辑logical deduction逻辑推论；逻辑推理logical step 逻辑步骤long division method 长除法 loss 赔本；亏蚀loss per cent 赔率；亏蚀百分maximum absolute error 最大绝对误差maximum point 极大点maximum value 极大值mean 平均 (值 )；平均数；中数mean deviation 中均差；平均偏差measure of dispersion 离差的量度measurement 量度median (1)中位数； (2)meet 相交；相遇mensuration 计量；求积法method 方法method of completingsquare配方法method of substitution 代换法；multiple root 多重根multiplicand 被乘数multiplication 乘法multiplication law (ofprobability) ( 概率 )乘法定律 multiplicativeproperty 可乘性multiplier 乘数；乘式multiply 乘mutuallyexclusive events互斥事件mutually independent独立 ;互相独立mutuallyperpendicular linesN率lower bound 下界lower limit 下限lower quartile 下四分位数lowest commonmultiple(L.C.M) 最小公倍数Mmagnitude 量；数量；长度；大小major arc 优弧；大弧major axis 长轴major sector 优扇形；大扇形 major segment 优弓形；大弓换元法n factorial n 阶乘metricunit 十进制单位n th root n 次根； n 次方根mid-point 中点natural number 自然数mid-pointformula 中点公式negative 负mid-pointtheorem 中点定理negative angle 负角million 百万negative index 负指数minimize 极小negativeinteger 负整数minimum point 极小点negativenumber 负数minimum value 极小值neighborhood 邻域minor (1) 子行列式； (2)劣；较net 净 (值 )小的n-gon n 边形minorarc 劣弧；小弧nonagon 九边形minor axis 短轴non-collinearminor sector 劣扇形；小扇形non-linear非线性minor segment 劣弓形；小弓non-linearequation 非线性方程non-negative 非负的non-trivial 非平凡的non-zero 非零normal (1)垂直的；正交的；法线的 (2) 正态的 (3) 正常的；正规的operation 运算opposite angle 对角opposite interior angle内对角opposite side 对边optimal solution 最优解order (1)序；次序； (2)阶；级ordered pair 序偶prism 梭柱 (体 )；角柱( 体) prismoid 平截头棱锥体 probability 概率problem 应用题produce 延长product 乘积；积product rule 积法则normal curve origin 原点outcome 结果output 输出normal distribution 正态分布， overlap 交迭；相交常态分布normal form 法线式Pnotation 记法；记号number 数parabolanumber line parallel 平行 (的 )number pair 数偶parallellines平行 (直线 )number pattern 数型parallelogram 平行四边形number plane 数平面parameter 参数；参变量number system 数系partial fraction 部分分数；分numeral 数字；数码项分式numeral system 记数系统polarcoordinate system 极坐numerator 分子标系统numerical 数值的；数字的polarcoordinates 极坐标numericalexpression 数字式pole 极numerical method 计算方法；polygon 多边形数值法polyhedron 多面体polynomial 多项式O polynomialequation 多项式方程oblique 斜的positive 正obliquecone 斜圆锥positiveindex正指数oblique triangle 斜三角形positive integer 正整数obtuseangle 钝角positivenumber 正数obtuse-angled 钝角三power (1) 幂；乘方；(2) 功率；triangle角形(3)检定octagon 八边形precise密octahedron八面体precisi确度oddfunction 奇函数primeodd number 奇数primefactorone-one correspondence 一一prime n对应primiti的；openinterval 开区间(2)原函open sentence 开句princip本金profit 盈利profit per cent 盈利百分率profits tax 利得税 progression 级数 proof 证(题 )；证明 proper fraction 真分数property 性质property tax 物业税proportion 比例proportional 成比例protractor 量角器pyramid 棱锥 (体 )；角锥 (体 ) Pythagoras ’ Theorem 勾股定理Pythagorean triplet 毕氏三元数组partial sum 部分和partial variation 部分变 (分 ) particular solution 特解 Pascal’s triangle 帕斯卡斯三角形pattern 模型；规律 pegboard 有孔版 pentadecagon十五边形pentagon 五边形 per cent 百分率 percentage 百分法；百分数 percentage decrease 百分减少percentage error 百分误差 percentage increase 百分增加percentile 百分位数 perfect number 完全数perfecr square 完全平方perimeter 周长；周界period 周期periodic function 周期函数permutation 排列perpendicular 垂线；垂直(于) perpendicular bisector 垂直平perpendicular line pictogram 象形图pie chart 饼图；圆瓣图 pinboard 钉板place holder 补位数字 place value 位值plan (1) 平面图； (2) 计划plane 平面plane figure 平面图形plot 绘图plus 加point 点point circle 点圆point of contact 切点point of division 分点 point ofintersection 交点point-slope form 点斜式 polar axis 极轴polar coordinate plane 极坐标平面polar coordinate 极坐标系统Qquadrant 象限quadratic equation 二次方程(式 )quadratic formula 二次公式 quardratic function 二次函数 quadratic inequality 二次不等式quadratic polynomial 四边形quantity 数量quartile 四分位数quotient 商；商式RR.H.S 右radian 弧度radian measure 弧度法radical 根式；根号；根数radius, radii 半径 random 随机random experiment 随机试验random number 随机数 range 值域；区域；范围；极差；分布域rate 率；利率ratio 比 ; 比率rational expression 有理式；有理数式rational function 有理函数rational index 有理数指数rational number 有理数rationalization 有理化raw data 原始数据raw score 原始分（数）real axis 实轴real number 实数real root 实根reason 理由reciprocal 倒数rectangle 长方形；矩形rectangular block 长方体rectangular coordinateplane直角坐标平面rectangular coordinates 直角坐rectilinear figure 直线图形recurrent 循环的recurring decimal 循环小数reduce 简化reducible 可约的；可化简的reference angle 参考角reflex angle 优角；反角region 区域regular 正；规则regular polygon 正多边形reject 舍去；否定 relation关系；关系式 relative error相对误差remainder 余数；余式；剩余remainder term 余项 remaindertheorem 余式定理removal of brackets 撤括号；去括号repeated trials 重复试验 resolve 分解revolution 旋转；周转 rhombus 菱形right angle 直角right c ircular cone 直立圆锥（体）right circular cylinder直立圆柱（体）right prism 直立棱柱；直立角柱(体)right pyramid 直立棱锥；直立角锥 (体)right-angled triangle 直角二角形root 根rotation 旋转round angle 周角 roundednumber 舍数 rounding(off)舍入；四舍五入 row 行；棋行rule 规则；法 (则 )ruler 直尺Ssalaries tax 薪俸税sample 抽样；样本sample space 样本空间satisfy 满足；适合scale 比例尺；标度；图尺scalene triangle 不等边三角形；不规则三角形scientific notation 科学记数法solution of triangle 三角形解法solve 解special angle 特殊角；特别角speed 速率sphere 球形；球面square (1)平方； (2) 正方形square bracket 方括号in two unknowns 联合二次线square number 正方形数；平性方程式方数sine 正弦square root 平方根；二次根sine formula 正弦公式standard deviation 标准差；标slant edge 斜棱准偏离slant height 斜高secant slope 斜率；斜度；倾斜；坡second 秒度secondquartile 第二四分位slope-interceptform斜率截数(1) 截面；截线；(2) 截点距式；斜截式section (1) (2) solid 立体；固体截点soild with unifor msectionformula 截点公式corss-section 有均匀横切面sector 扇式的立体segment 段；节solution 解；解法segment of acircle 弓形solution of equation 方程解sellingprice 售价semi-circle 半圆U semi-verticalangle 半顶角sentence 句；语句uniform 一致 (的 )；均匀(的 )sequence 序列uniform cross-section 均匀横series 级数切面set square 三角尺；三角板uniform speed 匀速率shadedportion 有阴影部分uniformlydistributed 均匀分shape 形状布side 边；侧unique solution 唯一解sign 符号；记号uniqueness 唯一性signed number 有符号数unit 单位significant figure 有效数字unitarea 单位面积similar 相似unit circle 单位圆similarfigures 相似图形unit volume 单位体积similartriangles 相似三角形unknown 未知数；未知量similarity 相似(性 ) unlike 异类项simple 简易方程upper bound 上界equationsimpleinterest 单利；单利息upper l simplify 简化upper q simultaneous equations 联立方程simultaneousinequalities联立不等式value值simultaneouslinear equationsvariable元；变数variable speed 可变速率variance 方差variation 变数；变分verify 证明；验证vertex, vertices 顶(点 )；极点vertical 铅垂；垂直vertical angle 顶角vertical linevertically opposite angles 对顶角volume 体积Wweight (1) 重量； (2) 权weighted average, weightedmean 加权平均数whole number 整数；完整数width 阔度without loss of generality 不失一般性Xx-axis x 轴x-coordinate x 坐标x-intercept x 轴截距Yy-axis y 轴y-coordinate y 坐标y-intercept y 轴截距Zzero 零zero factor 零因子zeros of a function 函数零值。