SAT1 MATH

现代大学英语听力1(外研版)unit1听力原文及答案Unit 1Task 5【答案】1) The student wants to have some information about the courses at Swan School.2) Each course lasts for three weeks.3) It‘s about 23 hours a week. Usually four and a half days each week.4) The first course begins on the 3rd of July and lasts until the 20th of July and the second course is from the 24th of July until the 10th of August.5) Each course costs ￡150 plus VAT, which is 15 percent, and a ￡5 registration fee.6) For each course the deposit is ￡20.7) A lady arranges the accommodation for the students with Oxford families.8) They can choose to have bed and breakfast only which is ￡20 a week, or bed, breakfast and dinner which is about ￡27 a week.【原文】Receptionist: Good morning. Can I help you?Student: Yes, please. I would want to have some information about the…erm…the courses at Swan School.Receptionist: Is that a summer course you‘re interested in?Student: Yes. Yes, please.Receptionist: Yes. Fine. OK. Well, we have…erm…short intensivefull-time courses during the summer.Student: Mm-mm. I would want to know the length of one course.Receptionist: Yes. Each course lasts for three weeks.Student: How many hours per week, please?Receptionist: Well, it‘s about 23 hours a week. Usually four and a half days each week.Student: You must have a lot of students in the class, haven‘t you?Receptionist: We have a lot of students in the school but in the classes only about between 12 and 14 students.Student: 12 and 14. Could you please give me the dates of the first and the second course?Receptionist: Yes, certainly. The first course begins on the 3rd of July and lasts until the 20th of July and the second course is from the 24th of July until the 10th of August.Student: What about the fees per course?Receptionist: Yes, each…each course costs ￡150 plus VAT, which is 15 percent, and a ￡5 registration fee.Student: And deposit, please?Receptionist: Yes. For each course we need a deposit of ￡20 and the ￡5 registration fee.Student: Oh thank you. Do we have to find our…our own accommodation?Receptionist: No, we can do that for you. We have a lady who arranges the accommodation for you with Oxford families.Student: How much does it cost?Receptionist: Well, you can choose to have bed and break fast only which is ￡20 a week, or bed,breakfast and dinner which is about ￡27 a week.Student: ￡27. Thank you very much.Receptionist: You‘re welcome.Task 6【答案】A.1) F, 2) T, 3) FB.1) Most universities will not accept students without this test. It is also used to decide how much financial aid should be given to each student.2) They must score between 1,430 and 1600.3) American universities also look at a student‘s subject grades, what they do outside of school, and their teachers‘ recommendations.4) The SAT II is the one-hour exam that can be taken in any subject, for example chemistry or French.【原文】Every year, high school juniors and seniors from across the US take the Scholastic Aptitude Test (SAT 1).The SAT 1 is a three-hour exam that tests students‘ math and verbal skills. Most universities will not accept students without this test. It is also used to help decide how much financial aid should be given to each student.Scores range from 200 to 800 for each part. There is a total of 1,600 points. The test is held every year from October to June. But seniors must take it before December in order to include their scores in their university applications. The average total score for an American high school student is around 1,000.A poor SAT score can prevent a student from going to a good university. Students who want to go to one of America‘s best universities, such as Harvard or Yale, must score between 1,430 and 1,600.The test can be taken over and over again, but all the scores will appear on the students‘ records. However, unlike Chinese universities, the score is not the only thing needed. American universities also look at a student‘s subject grades, what they do outside of school, and their teachers ‘ recommendations.In addition to the SAT 1, some universities require high school students to take at least three SAT IIs. These one-hour exams can be taken in any subject, for example chemistry or French.Task 7【答案】A.1) a, 2) c, 3) d, 4)cB.1) Many students attend special preparation schools besides their regular classes, in order to pass the exam for the best universities such as the National University of Tokyo.2) These extra schools can last for one to two years between high school and university.【原文】Japanese students need 12 years of study before entering universities.They choose the places they want to go and apply before January of their final year. The university entrance exam is a standard nationwide test held every year in January. It provides tests for 31 subjects in six subject areas: Japanese language, geography and history, civics, math, science and a foreign language. All national and public universities, as well as some private ones make use of this exam. But many places also have their own tests in February or later, before the new school year starts in April.In order to pass the exam for the best universities such as the National University of Tokyo, many students attend special preparation schools on top of their regular classes. These extra schools can last for one to two years between high school and university.Although every student has the chance of going to a Japanese university, only 50 percent of high school seniors actually choose further study.Task 8【答案】A.1) It‘s a non-profit-making educational foundation.2) No, complete beginners are not accepted.3) Other subjects available within the General English timetable include English for Business and English Literature.B.1) 200, 30-40, attractive, beautiful, with easy reach of2) dining rooms, a library, language laboratories, computers, tennis, volleyball, basketball, badminton, football.3) 214)￡1,1305) Monday, Friday6)￡670, 3, 10, 9, 3 ½【原文】The School was opened in 1955 and is part of a non-profit-making educational foundation. Its 200 students, from 30-40 countries, work in large, attractive buildings set in extensive, beautiful gardens, within easy reach of the centre of Cambridge, The School has dining rooms, a library, video filming studio, language laboratories, listening and self-access study centres, computers, as well as facilities for tennis, table tennis, volleyball, basketball, badminton and football.General English classes are for students aged 17+. Complete beginners are not accepted. Students have classes for 21 hours a week. Other subjects available within the General English timetable include English for Business and English Literature. The cost of tuition, materials and books per term is ￡1,130. Accommodation is with local families. Lunch is provided in the School Monday to Friday. All other meals are taken with the family. There is a full range of social activities including excursions, discos and theatre-visits. The total cost of all non-tuition services is ￡670 per term. There are 3 terms of 10 weeks and summer courses of 9 weeks and 3 1/2 weeks.。

美国“高考”SAT考试的数学题数学第一部分时间(25分钟）16个问题说明：这部分包含有两种类型的问题。

你将有25分钟时间来完成他们.对于1-8，在所给选项中选出一个最佳答案，然后再答题卡上填上相应的圆圈，你可以使用任何可用的草稿纸空间。

注释：1、可以使用计算器。

2、所有使用的数字均为实数。

3、在测试中，问题中所提供的数字或图表都包含一定的信息，这对于解题很有帮助。

所有图表都是比较准确的,除非在某些具体问题中，图表没有按比例绘制。

所有数字都呈现于平面上，除非另有说明。

4、除非另有规定,对于任何函数f 的值域都是所有实数x 的集合，并使得f（x) 是实数。

可能用到的公式:1、If 4（t+u）+ 3 =19，then t+u=如果4（t+u）+ 3 =19, 那么t+u=A 3B 4C 5D 6E 72、如图，三条直线相交于一点。

如果f=85，e=25，那么a 的值是多少?A 60B 65C 70D 75E 853、如果玛丽开车行驶n 英里用了t 小时，那么下列哪个可以表示她行驶的平均速度，英里/小时?A n/tB t/nC 1/ntD ntE n²t4、如果a 是一个奇数，b 是一个偶数，那么选项中哪一个是奇数?A 3bB a+3C 2（a+b）D a+2bE 2a+b5、在平面坐标内，F(—2，1),G(1,4)，H（4,1)在以P为圆心的圆上，那么点P的坐标是什么？A（0,0）B(1,1）C（1,2）D（1,—2)E(2.5,2.5）6、如图,如果-3≤x≤6，那么x 有几个值,使得f(x）=2?A 零B 一个C 两个D 三个E 三个以上7、如果t 和t+2 的算术平均值是x, t 和t-2的算术平均值是y，那么x 和y 的算术平均值是多少？A 1B 1/2C tD t+1/2E 2t8、对于任何数x 和y,假设x△y=x²+xy+y²，那么（3△1）△1等于多少？A 5B 13C 27D 170E 1839、摩根的植物在一年之内从42厘米长到57厘米。

10.Geometry1.In a circle with center at O, arc ST measures 110°. What is the measure of angle STO?2.If the angles of a triangle are in the ratio of 2:3:5, what is the measure of the smallest angle?3.In the figure x.4.The diagonal of a rectangle is 26 cm and its height is 10 cm. Find the area of the rectangle in squarecentimeters.5. A ship travels 60 mi north, 90 mi west, and then 60 mi north again. How many miles is it fromits starting point?6.Find the length in inches of a tangent drawn to a circle with a 10 in. radius from a point 26 in.from the center of the circle.7.If the largest possible circular disc is cut from a rectangular piece of tin 8 in. by 12 in., what isthe area of the waste tin in square inches in terms of π?8. A circle is inscribed in a square. What is the ratio of the area of the square to that of the circle interms of π?9.At 4:20 PM., how many degrees has the hour hand of a clock moved since noon?10.Find the volume of a cube in cubic centimeters if the total surface area of its faces is 150 sq cm.11.A cylindrical can has a circular base with a diameter of 14 in. and a height of 9 in. Approxi-12.What is the volume in cubic inches of an open box made by snipping squares 2 in. by 2 in. fromthe corners of a sheet of metal 8 in. by 11 in. and then folding up the sides?13.Water 6 in. high in a fish tank 15 in. long by 8 in. wide is poured into a tank 20 in. long by 12 in.wide. What height in inches does it reach in the larger tank?14.A 6 ft pole is casting a 5 ft shadow at the same time that a flagpole is casting a 22 ft shadow. Howmany feet high is the flagpole?15.In the figure, PQRST is a regular pentagon inscribed in the circle. andthe pentagon, forming an angle of x° as shown. What does x equal?16.A treasure is buried 10 ft from tree T and 12 ft from a straight fence F. If T is 20 ft from F, in howmany places may the treasure be buried?17.If a given statement is true, which of the following statements must also be true?(A)the converse of the statement(B)the inverse of the statement(C)the contrapositive of the statement(D)the negative of the statement(E)none of these18.Given point P on a line. In a given plane containing the line, what is the total number of pointsthat are at a distance of 4 units from P and also at a distance of 3 units from the given line? 19.Point Q is 20 cm from plane P in space. What is the locus of points 8 cm from P and 12 cm frompoint Q?20.The sum of the measures of the interior angles of a convex polygon is 720°. What is the sum of themeasures of the interior angles of a second convex polygon that has two more sides than the first?10.GEOMETRY1.The correct answer is (35º).Let PT be a diameter of Circle O.2.The correct answer is (36º). Let 2x = smallest angle in degrees, 3x and 5x = other two anglesin degrees.3.The correct answer is (120º).m (alernate interior angles), and mAngle x is an exterior angle of ∆DEF and isequal to the sum of the measures of the two remote interior angles.x= 50º + 70º = 120º5.The correct answer is (150).The tangent is perpendicular to the radiusat the point of tangency.In right triangle OTP7.The correct answer is (96 - 16π).8.The correct answer isLet radius of circle be 1.Side of square is 1 + 1 =2.9.The correct answer is (130º).From noon to 4:00 PM., the hour hand has moved from 12 to 4: of360º = 120º. In the next 20 minutes it moves of the distance from 4:00 to 5:00: of30º = 10º.120º + 10º = 130º10.The correct answer is (125).11.The correct answer is (6).12.The correct answer is (56).13.The correct answer is (3).14.The correct answer isCross-multiply.15.The correct answer is (108°).16.The correct answer is (2).The locus of points 10 ft. from T is acircle of radius 10. The locus of points12 ft from F consists of two parallellines 12 ft from F on each side. Thecircle and one parallel line intersect intwo points.17.The correct answer is (C). The only statement that has the same truth value as the given statement isthe contrapositive of the original statement. This is the converse of the inverse of the original statement.18.The correct answer is (4).The locus of points 4 units from P is a circleof radius 4 with center at P. The locusof points 3 units from the given line consistsof two parallel lines 3 units from theline. The two parallel lines intersect thecircle in 4 points.19.The correct answer is (1).The locus of points 8 cm from P consistsof two planes parallel to P and 8 cm fromit. The locus of points 12 cm from Q is asphere of radius 12 and center at Q. Thesphere intersects one of the parallel planesin one point (point of tangency).20.The correct answer is (1080°). The sum of the interior angles of an n-sided polygon is (n – 2) 180°= 720°. Divide by 180.The second polygon has 6 + 2 = 8 sides.Sum of the measures of its interior angles = 180(8 – 2)= 180(6) = 1080°。

第七章单个元音字母在重读音节中的读音开音节①绝对开音节：单个元音字母后面没有辅音字母的重读音节。

例如：no blue ba-by stu-dent peo-ple 。

②相对开音节：单个元音字母后面加单个辅音字母，再加一个不发音字母e 构成的重读音节。

例如：name these bike home ex-cuse 。

闭音节单个元音字母后面有辅字组（r w y 除外）且以辅字组结尾的重读音节。

例如：bag egg fish not cup单个元音字母在开音节和闭音节中的读音元音字母读音例词编号a 在开音节中[e] name plane Jane baby cake 1-01在闭音节中[æ] bag dad hat map black back 1-02e 在开音节中[i:] he these me Chinese 1-03在闭音节中[e] bed let pen desk yes egg 1-04i 在开音节中[a] bike fly drive time nice kite 1-05在闭音节中[] fish big drink sit milk swim 1-06o 在开音节中[u] those close go hoe home no 1-07在闭音节中[] clock not box shop sock 1-08u 在开音节中[ju:] student excuse duty Tuesday 1-09在闭音节中[] bus cup jump much lunch 1-10在开音节中，元音字母u在辅音字母j l r s后面时读[u:]音，例如：June blue ruler super 1-11 1-01 规则特例：vague vogue brogue plague range change strange paste taste waste ache scythe opaque unique 这些单词中的th ng gu ch st qu 被看作一个整体，其中的元音字母按开音节规则发音。

SAT 数学知识点一Number and Operations Review 一、Properties of integers知道下列说法表示的内容：1. Integers consist of the whole numbers and their negatives (including zero).2. Integers extend infinitely in both negative and positive directions.3. Integers do not include fractions or decimals.4. Negative integers5. Positive integers6. The integer zero is neither positive nor negative.7. odd numbers（奇数）and even numbers（偶数）8. Consecutive integers9. Addition of integers(奇数偶数的加法规则)10. Multiplication of integers（奇数偶数的乘法规则）二、Arithmetic word problems（算术题）三、Number lines（数轴）四、Square and square roots（平方和平方根）五、Fractions and rational numbers（分数与有理数）六、Elementary number theory☆Factors, multiples, and remainders☆Prime numbers七、Ratios, proportions, and percents八、Sequences九、Sets(union, intersection, elements)十、Counting problems Counting problems involve figuring out how many ways you can select or arrange members of groups, such as letters of the alphabet, numbers or menu selections.☆Fundamental counting problems分步完成事件和分类完成事件发生的可能性☆Permutations and combinations （排列组合）基本排列组合理论十一、Logical reasoningThe SAT doesn’t include1.Tedious or long computations2.Matrix operations1.2.3.4.5. 6.7.8.9.10.11.12.13. 14.SAT数学知识点二Algebra and Functions Review Many math questions require knowledge of algebra. This chapter gives you some further practice. You have to manipulate and solve a simple equation for an unknown, simplify and evaluate algebraic expressions, and use algebraic expressions, and use algebraic concepts in problem-solving situations.For the math questions covering algebra and functions content, you should be familiar with all of the following basic skills and topics:一、Operations on algebraic expressions二、Factoring三、Exponents四、Evaluating expressions with exponents and roots五、Solving equations☆Working with “unsolvable” equations☆Solving for one variable in terms of another☆Solving equations involving radical expressions六、Absolute value 七、Direct translation into mathematical expressions八、Inequalities九、Systems of linear equations and inequalities十、Solving quadratic equations by factoring 十一、Rational equations and inequalities 十二、Direct and inverse variation十三、Word problems十四、Functions☆Function notation and evaluation☆Domain and range☆Using new definitions☆Functions as models☆Linear functions: their equations and graphs☆Quadratic functions: their equations and graphs☆Qualitative behavior of graphs and functions☆Translations and their effects on graphsand functionsThe SAT doesn’t include:一、Solving quadratic equations thatrequire the use of the quadraticformula二、Complex numbers三、Logarithms1.2.3.4. 5.6.7.8.9.10.SAT 数学知识点三Geometry and Measurement Review Concept you should to knowFor the mathematics questions covering geometry and measurement concepts, you should be familiar with all of the following basic skills, topics, and formulas:一、Geometric notation二、Points and lines三、Angles in the plane四、Triangles(including special triangles)☆Equilateral triangles☆Isosceles triangles☆Right triangles and the Pythagorean theorem ☆30º-60º-90ºtriangles☆45º-45º-90ºtriangles☆3-4-5 triangles☆Congruent triangles☆Similar triangles☆The triangle inequality五、Quadrilaterals☆Parallelograms☆Rectangles☆Squares六、Areas and Perimeters☆Areas of squares and rectangles☆Perimeters of squares and rectangles☆Area of triangles☆Area of Parallelograms七、Other polygons☆Angles in a polygon☆Perimeter☆Area八、Circles☆Diameter☆Radius☆Arc☆Tangent to a circle☆Circumference☆Area九、Solid geometry☆Solid figures and volumes☆Surface area十、Geometric perception十一、Coordinate geometry☆Slopes, parallel lines, and perpendicular lines☆The midpoint formula☆The distance formula十二、TransformationsThe SAT doesn’t include:一、Formal geometric proofs二、Trigonometry三、Radian measure1.2.3.4.5.6. 7.8.9.SAT 数学知识点四Data Analysis, Statistics andProbability ReviewFor the math questions covering data analysis, statistics and probability concepts, you should be familiar with all of the following basic skills and topics:一、Data interpretation二、Statistics☆Arithmetic mean☆Median☆Mode☆Weighted average☆Average of algebraic expression☆Using average to find missing numbers三、Elementary probability四、Geometric probabilityThe SAT doesn’t include:四、Computation of standard deviation 1.2.3.4.5. 6.7.8.Word Problems1.2.3.4. 5-75.6.7.1112。

小学英语三年级上册单词表Unit 1ruler ['ru:ləə] n.直尺pencil [ˈpensl] n. 铅笔eraser [ i'reisə] n. 橡皮擦crayon ['kreiən] n. 蜡笔bag [bæg] n.包pen [pen] n. 钢笔pencil box n. 铅笔盒book [buk] n. 书no [nəu] 不your [jɔ:ə] 你（们）的Unit 2Red [red] n. 红色adj. 红色的green [ɡriːn] adj. 绿色的n.绿色yellow 黄色的n. 黄色blue [bluː] n. 蓝色adj. 蓝色的black [blæk] n. 黑色adj. 黑色的brown [braun] n.棕色adj.棕色的white [(h)wait] adj.白色的n. 白色orange n.橙色adj.橙色的OK 好；行Unit 3Face [feis] n. 脸Ear [iə] n. 耳朵eye [ai] n. 眼睛nose [nəuz] n. 鼻子mouth [mauθ] n. 嘴arm [ɑ:m] n. 胳膊hand [hænd] n. 手head [hed] n. 头body ['bɔdi] n. 身体leg [leg] n. 腿foot [fut] n. 脚school [sku:l] n. 学校Unit 4 duck [dʌk] n. 鸭子pig [piɡ] n. 猪cat [kæt] n. 猫bear [beəə] n. 熊dog [dɔg] n. 狗elephant ['elifənt] n. 大象monkey ['mʌŋki] n. 猴子bird [bə:əd] n. 鸟tiger ['taigə] n. 老虎panda ['pændə] n. 熊猫zoo [zuː] n. 动物园funny [‘fʌni] adj. 滑稽的Unit 5bread [bred] n. 面包juice [dʒu:s] n. 果汁、液egg [eg] n. 蛋milk [milk] n. 牛奶water ['wɔ:tə] n. 水cake [keik] n. 蛋糕fish [fiʃ] n. 鱼rice [rais] n. 米饭Unit 6one 一two 二three 三four 四five 五six六seven ['sevn]七eight [eit]八nine [nain]九ten [ten]十brother [ ‘brʌðə] n.兄；弟plate [pleit] n. 盘子三年级英语下册词汇表Unit 1UK 英国USA 美国China ['tʃaɪnə] 中国she [ʃiː]她student ['stjuːd(ə)nt] 学生he [hiː]他teacher ['tiːtʃə] 教师boy [bɔɪ] 男孩and [ənd] 和；与girl [gɜːl]女孩new [njuː]新的friend [frend] 朋友today [tə'deɪ] 今天Unit 2Father ['fɑːðə]父亲；爸爸dad [dæd] （口语）爸爸；爹爹man [mæn] 男人woman ['wʊmən] 女人mother ['mʌðə] 母亲；妈妈sister ['sɪstɚ] 姐；妹brother ['brʌðə] 兄；弟grandmother（外）祖母grandma （口语）（外）祖母grandfather （外）祖父grandpa （口语）（外）祖父family ['fæməli] 家；家庭Unit 3thin [θin] 瘦的fat [fæt] 胖的；肥的tall 高的short 矮的；短的long 长的small 小的big 大的so [səʊ] 这么；那么children ['tʃildrən] (child的复数)儿童Unit 4on [ɒn] 在…之上in [ɪn] 在…里under ['ʌndə] 在…下面chair [tʃeə] 椅子desk [desk] 书桌cap [kæp] 帽子ball [bɔːl]球car [kɑː]小汽车boat [bəʊt] 小船map [mæp] 地图toy [tɔɪ] 玩具box [bɒks] 盒；箱Unit 5pear [peə] 梨apple 苹果orange 橙子banana [bə'nɑːnə]香蕉grape [greɪp] 葡萄buy [baɪ] 买fruit [fruːt]水果Unit 6eleven 十一twelve [twelv] 十二thirteen ['θɜːtiːn]十三fourteen ['fɔːtiːn]十四fifteen ['fɪftiːn]十五sixteen ['sɪkstiːn]十六seventeen ['sevntiːn]十七eighteen ['eɪtiːn]十八nineteen ['naɪntiːn]十九twenty ['twentɪ] 二十kite [kaɪt] 风筝四年级上册单词表Unit 1classroom [klɑ:sru:m] 教室window [windəu] 窗户blackboard [bɔ:d] 黑板light [lait] 电灯picture [ˊpiktʃə] 图画door [dɔ:] 门teacher’s desk 讲台computer [kəmˊpju:tə] 电脑fan [fæn] 风扇wall [wɔ:l] 墙floor [flɔ:] 地板near [niə] 在…的旁边TV 电视clean [kli:n] 打扫；清洁；擦干净的help [help] 帮助；帮忙Unit 2schoolbag 书包math [mæθ] book 数学书English book 英语书Chinese book 语文书story—book [ˊstɔ:ri buk] 故事书candy [kændi] 糖果notebook [ˊnəutbuk] 笔记本toy [tɔi] 玩具key [ki ] 钥匙cute [kju:t] 可爱的Unit 3strong [strɔŋ] 强壮的friendly [frendli] 朋友(们)quiet [ˊkwaiət] 安静的hair [hɛə] 头发shoe [ʃu: ] 鞋glasses [gla:siz] 眼镜his [hiz] 他的or [ɔ:r] 或者right [rait] 正确的hat [hæt] 帽子her [hə:] 她的Unit 4bedroom 卧室living room [ˈliviŋ ru:m] 起居室study [ˊstʌdi] 书房kitchen [ˊkitʃin] 厨房bathroom [ˊbɑ:θrum] 卫生间bed [bed] 床phone [fəun] 电话table [ˊteibl] 桌子sofa [ˊsəufə] 沙发fridge [fridʒ] 冰箱find [faid] 找到them 他(她；它)们（宾格）Unit 5beef [bi:f] 牛肉chicken [ˊtʃikin] 鸡肉noodle(s) [ˊnu:dl(s)] 面条soup [su:p] 汤vegetable [ˊvedʒitəbl] 蔬菜chopsticks [ˈtʃɔpˌstɪk] 筷子bowl [bəul ] 碗fork [fɔ:k] 叉子knife [naif] 小刀spoon [spu:n] 勺子dinner [ˊdinə] 晚餐；正餐pass [pɑ:s] 给；递try [trai] 尝试；试Unit 6Parents [ˊpɛərənts] 父母cousin 同辈表亲或堂亲uncle [ʌŋkl] 叔叔；舅舅aunt [ɑ:nt] 姑姑；婶；姨baby [beibi] 婴儿doctor [ˊdɔktə] 医生cook [ˊkuk] 厨师driver [ˊdraivə] 司机farmer [ˊfɑ:mə] 农民nurse [nə:s] 护士but 但是little 小的puppy [ˊpʌpi] 小狗job [dʒɔb] 工作basketball [baskit bɔ:l] 篮球四年级英语下册单词表Unit 1first floor 一楼second floor 二楼teacher’s office 教师办公室library 图书馆playground 操场computer room 计算机房art room 美术教室music room 音乐教室next to 紧邻；在……近旁homework 作业class 班；班级forty 四十way 方向Unit 2breakfast 早餐；早饭English class 英语课lunch 午餐；午饭music class 音乐课PE class 体育课dinner （中午或晚上吃的）正餐get up 起床go to school 去上学go home 回家go to bed 上床睡觉over 结束now 现在；目前o’clock （表示整点）……点钟kid 小孩thirty 三十hurry 快点come on 快；加油Unit 3cold 寒冷的；冷的cool 凉的；凉爽的warm 温暖的；暖和的hot 热的；烫的sunny 阳光充足的windy 多风的；风大的cloudy 阴天的；多云的snowy 下雪（多）的rainy 阴雨的；多雨的outside 在户外weather 天气fly 放（风筝等）love 爱Unit 4tomato 西红柿potato 马铃薯；土豆carrot 胡萝卜horse 马cow 母牛；奶牛sheep 羊；绵羊hen 母鸡these （this的复数形式）animal 兽；动物those （that的复数形式）那些garden 花园；菜园farm 农场goat 山羊eat 吃Unit 5clothes 衣服；服装pants 裤子hat （常指带檐的）帽子dress 连衣裙skirt 女裙coat 外衣；大衣sweater 毛衣sock 短袜shorts 短裤jacket 夹克衫shirt （尤指男士）衬衫yours 你的；你们的whose 谁的mine 我的Unit 6Glove （分手指的）手套umbrella 伞；雨伞sunglasses 太阳镜pretty 美观的；精致的expensive 昂贵的；花钱多的cheap 花钱少的；便宜的nice 好的try on 试穿size 尺码；号too 太；过于just 正好；恰好how much 多少钱eighty 八十dollar 美元more 更多的us 我们(宾格)五年级上册单词表Unit1old [əuld] 年老的young [jʌŋ]年轻的funny ['fʌni] 滑稽可笑的. kind [kaind] 和蔼的strict [strikt] 严格的.polite [pəˈlaɪt] 有礼貌的hard-working 努力工作的,勤奋的helpful [’helpfl]有帮助的clever [’klevə(r)] 聪明的shy [ʃaɪ] 害羞的know [n əʊ] 知道. 了解our [aʊə] 我们的sometimes 有时候robot [ˈrəʊbɒt] 机器人him (he的宾格) 他speak [spi:k] 会说，会讲finish [ˈfɪnɪʃ] 完成；做完Unit2Monday (Mon.)星期一['mʌndei] Tuesday (Tue.)星期二['tju:zdei] Wednesday(Wed.)星期三['wenzdei] Thursday (Thu.)星期四['θə:zdei] Friday (Fri.)星期五['fraidei] Saturday (Sat.)['sætədei]星期六Sunday (Sun.) ['sʌndei]星期天. weekend [ˌwi:kˈend] 周末wash [wɒʃ] 洗watch [wɒtʃ] 看do 做；干do homework ['həumwə:k] 做作业read [ri:d] 看，读play [pleɪ] 踢、玩、参加(体育运动) play football 踢足球cooking [ˈkʊkɪŋ] 烹饪；烹调often [ˈɒfn] 常常；时常park [pɑ:k] 公园sport [spɔ:t] 体育运动every [ˈevri] 每个；每一个day [deɪ] 一天；一日Unit3sandwich [ˈsænwɪtʃ] 三明治salad [ˈsæləd] 蔬菜沙拉；混合沙拉hamburger 汉堡包ice cream [aɪs kri:m] 冰淇淋tea [ti:] 茶水；茶fresh [freʃ] 新鲜的health y['helθi]健康的;有益健康的delicious 美味的hot [hɒt] 辣的；辛辣的sweet [swi:t] 甜的drink [drɪŋk] 喝；饮thirsty [ˈθɜ:sti] 渴的口渴的favourite ['feivərit] 最喜爱的food [fu:d] 食物onion [ˈʌnjən] 洋葱；葱头Unit4Sing [sɪŋ] 唱；歌唱Song [sɒŋ] 歌曲play the pipa 弹琵琶Kung fu [kʌŋ fu] 功夫武术do kung fu 练武术dance [dɑ:ns] 跳舞draw [drɔ:] 画cartoon [kɑ:ˈtu:n] 漫画cook [kʊk] 烹调swim [swɪm] 游泳play basketball 打篮球play ping-pong 打乒乓球speak English 说英语party [ˈpɑ:ti]聚会；派对next [nekst] 下一个的；紧接着的wonderful [ˈwʌndəfl] 了不起的learn [lɜ:n] 学；学习；学会any [ˈeni]任何的；任一的problem [ˈprɒbləm] 问题want [wɒnt] 想要send [send] 发送；邮寄Unit5Clock [klɒk] 钟，时钟plant [plɑ:nt] 植物bottle [ˈbɒtl] 瓶子water bottle 水瓶bike [baɪk] 自行车photo [ˈfəʊtəʊ] 照片；相片in front of 在……前面between [bɪˈtwi:n] 在…之间；above [əˈbʌv] 在……上面beside [bɪˈsaɪd] 在…旁边（附近) behind [bɪˈhaɪnd] 在…的后面there [ðeə(r)] （表示存在或发生）their [ðeə] 他（她，它）们的house [haʊs] 房屋；房子；住宅lots of 大量，许多flower [ˈflaʊə] 花；花朵move [mu:v] 搬家dirty [ˈdɜ:ti] 肮脏的everywhere [ˈevriweə] 到处，处处mouse [maʊs] 老鼠live [lɪv] 居住nature [neitʃə(r)] 自然界；大自然Unit6forest ['fɔrist] 森林river ['rivə] 河流lake [leik] 湖泊mountain ['mauntin] 高山；山脉hill [hil] 小山tree [tri:] 树；树木bridge [bridʒ] 桥building ['bildiŋ]建筑物village ['vilidʒ] 乡村；村庄house [haus] 房子；住宅boating [’bəʊtɪŋ] 划船go boating 去划船rabbit [ˈræbɪt] 兔子，野兔high [haɪ] 高的单词表六年级上册。

美国数学竞赛AMC8常用数学英语单词1.数学mathematics [ˌmæθə'mætɪks],maths（BrE）, math（AmE）2.被除数dividend ['dɪvɪdend]3.除数divisor [dɪ'vaɪzə]4.商quotient ['kwəʊʃnt]5.等于equals ['iːkwəl],is equal to, is equivalent to [ɪ'kwɪvələnt]6.大于is greater than [ɡreɪtə]7.小于is lesser than ['lesə(r)]8.大于等于is equal or greater than9.小于等于is equal or lesser than10.运算符operator ['ɒpəreɪtə]11.数字digit ['dɪdʒɪt]12.数number13.自然数natural number ['nætʃrəl]14.公理axiom ['æksiəm]15.定理theorem ['æksiəm]16.计算calculation [ˌkælkju'leɪʃn]17.运算operation [ˌɒpə'reɪʃn]18.证明prove [pruːv]19.假设hypothesis [haɪ'pɒθəsɪs]20.命题proposition [ˌprɒpə'zɪʃn] 21.算术arithmetic [ə'rɪθmətɪk]22.加plus（prep.）[plʌs],add（v.）, addition（n.）[ə'dɪʃn]23.被加数augend ['ɔːdʒend],summand ['sʌmænd]24.加数addend [ə'dend]25.和sum26.减minus（prep.）['maɪnəs],Subtract(v.) subtraction(n.) [səb'trækt], [səb'trækʃn]27.被减数minuend ['mɪnjʊend]28.减数subtrahend ['sʌbtrəhend]29.差remainder [rɪ'meɪndə]30.乘times（prep.）, multiply（v.）['mʌltɪplaɪ],multiplication（n.）[ˌmʌltɪplɪ'keɪʃn]31.被乘数multiplicand , faciend [ˌmʌltɪplɪ'kænd], ['feɪʃɪend]32.乘数multiplicator ['mʌltɪplɪkeɪtə]33.积product ['prɒdʌkt]34.除divided by（prep.）[dɪ'vaɪdɪd],divide（v.）division（n.）[dɪ'vaɪd], [dɪ'vɪʒn]35.整数integer ['ɪntɪdʒə]36.小数decimal ['desɪml]37.小数点decimal point ['desɪml pɔɪnt]38.分数fraction ['frækʃn]39.分子numerator ['njuːməreɪtə]40.分母denominator [dɪ'nɒmɪneɪtə]41.比ratio ['reɪʃiəʊ]42.正positive ['pɒzətɪv]43.负negative ['neɡətɪv]44.零null, nil [nʌl], [nɪl]Zero, nought ['zɪərəʊ], [nɔːt]45.十进制decimal system ['desɪml] ['sɪstəm]46.二进制binary system ['baɪnəri]47.十六进制hexadecimal system [ˌheksə'desɪml]48.截尾truncation49.四舍五入round [raʊnd]50.下舍入round down51.上舍入round up52.有效数字significant digit [sɪɡ'nɪfɪkənt] ['dɪdʒɪt]53.无效数字insignificant digit [ˌɪnsɪɡ'nɪfɪkənt] ['dɪdʒɪt]54.代数algebra ['ældʒɪbrə]55.几何geometry [dʒi'ɒmətri]56.公式formula ['fɔːmjələ]57.未知数unknown,x-factor, y-factor, z-factor ['fæktə] 58.等式/方程式e quation [ɪ'kweɪʒn]59.一次方程simple equation ['sɪmpl]60.二次方程quadratic equation [kwɒ'drætɪk]61.三次方程cubic equation ['kjuːbɪk]62.四次方程quartic equation ['kwɔːtɪk]63.不等式inequation [ɪnɪ'kweɪʃən]64.二次方/平方s quare [skweə]65.三次方/立方c ube [kjuːb]66.四次方the power of four,the fourth power ['paʊə]67.n次方the power of n, the nth power68.开方evolution, extraction [ˌiːvə'luːʃn], [ɪk'strækʃn]69.二次方根/平方根square root [skweə] [ruːt]70.三次方根，立方根cube root [kjuːb]71.四次方根the root of four, the fourth root72.n次方根the root of n, the nth root73.集合aggregate ['æɡrɪɡət]74.元素element ['elɪmənt]75.函数function ['fʌŋkʃn]76.常量constant ['kɒnstənt]77.变量variable ['veəriəbl]78.奇偶性parity ['pærəti]79.有理数rational number ['ræʃnəl]80.点point [pɔɪnt]81.线line [laɪn]82.面plane [pleɪn]83.体solid ['sɒlɪd]84.线段segment ['seɡmənt]85.射线radial ['reɪdiəl]86.平行parallel ['pærəlel]87.相交intersect [ˌɪntə'sekt]88.角angle ['æŋɡl]89.角度degree [dɪ'ɡriː]90.弧度radian ['reɪdiən]91.锐角acute angle [ə'kjuːt]['æŋɡl]92.直角right angle93.钝角obtuse angle [əb'tjuːs]94.平角straight angle [streɪt]95.周角perigon ['perɪgɒn]96.底base [beɪs]97.边side [saɪd]98.高height [haɪt]99.三角形triangle ['traɪæŋɡl] 100.锐角三角形acute triangle [ə'kjuːt]101.直角三角形right triangle102.钝角三角形obtuse triangle [əb'tjuːs]103.不等边三角形scalene triangle ['skeɪliːn]104.等腰三角形isosceles triangle [aɪ'sɒsɪliːz]105.等边三角形equilateral triangle [ˌiːkwɪ'lætərəl]106.直角边right-angle side107.斜边hypotenuse [haɪ'pɒtənjuːz]108.勾股定理Pythagorean theorem [piθægə'ri:ən] ['θɪərəm] 109.四边形quadrilateral [ˌkwɒdrɪ'lætərəl] 110.平行四边形parallelogram [ˌpærə'leləɡræm] 111.矩形rectangle ['rektæŋɡl]112.长length [leŋθ]113.宽width [wɪdθ]114.菱形rhomb, rhombus [rɒm], ['rɒmbəs]rhombi, diamond ['rɒmbaɪ], ['daɪəmənd] 115.正方形square [skweə]116.梯形trapezoid ['træpəzɔɪd]117.直角梯形right trapezoid118.等腰梯形isosceles trapezoid [aɪ'sɒsɪliːz]119.五边形pentagon ['pentəɡən]120.六边形hexagon ['heksəɡən]121.七边形heptagon ['heptəɡən]122.八边形octagon ['ɒktəɡən] 123.九边形enneagon ['enɪəˌgɒn] 124.十边形decagon ['dekəɡən] 125.十一边形hendecagon [hen'dekəɡən] 126.十二边形dodecagon [dəʊ'dekəɡən] 127.多边形polygon ['pɒlɪɡən] 128.正多边形equilateral polygon [ˌiːkwɪ'lætərəl] 129.圆circle ['sɜːkl]130.圆心centre（BrE）['sentə]center（AmE）['sentə] 131.半径radius ['reɪdiəs] 132.直径diameter [daɪ'æmɪtə] 133.圆周率pi [paɪ]134.弧arc [ɑːk]135.半圆semicircle ['semisɜːkl] 136.扇形sector ['sektə] 137.环ring [rɪŋ]138.椭圆ellipse [ɪ'lɪps] 139.圆周circumference [sə'kʌmfərəns] 140.周长perimeter [pə'rɪmɪtə] 141.面积area ['eəriə] 142.表面积surface area ['sɜːfɪs] 143.体积volume ['vɒljuːm]144.轨迹locus , loca（pl.）['ləʊkəs], ['ləʊkə] 145.相似similar ['sɪmələ]146.全等congruent ['kɒŋgrʊənt]147.四面体tetrahedron [ˌtetrə'hiːdrən] 148.五面体pentahedron [ˌpentə'hiːdrən] 149.六面体hexahedron [ˌheksə'hiːdrən] 150.平行六面体parallelepiped [ˌpærəle'lepɪped] 151.立方体cube [kjuːb]152.七面体heptahedron [ˌheptə'hiːdrən] 153.八面体octahedron [ˌɒktə'hiːdrən] 154.九面体enneahedron [ˌenɪə'hiːdrən] 155.十面体decahedron [ˌdekə'hiːdrən] 156.十一面体hendecahedron [henˌdekə'hiːdrən] 157.十二面体dodecahedron [ˌdəʊdekə'hiːdrən] 158.二十面体icosahedron ['aɪkəsə'hedrən] 159.多面体polyhedron [ˌpɒli'hiːdrən] 160.棱锥pyramid ['pɪrəmɪd]161.棱柱prism ['prɪzəm]162.棱台frustum of a prism ['frʌstəm] ['prɪzəm] 163.旋转rotation [rəʊ'teɪʃn]164.轴axis ['æksɪs]165.圆锥cone [kəʊn] 166.圆柱cylinder ['sɪlɪndə] 167.圆台frustum of a cone ['frʌstəm] 168.球sphere [sfɪə(r)] 169.半球hemisphere ['hemɪsfɪə] 170.底面undersurface ['ʌndəˌsɜːfɪs] 171.空间space [speɪs] 172.坐标系coordinates [kə'ʊɔːdənəts] 173.坐标轴x-axis, y-axis, z-axis ['æksɪs] 174.横坐标x-coordinate[kəʊ'ɔːdɪneɪt] 175.纵坐标y-coordinate176.统计statistics [stə'tɪstɪks] 177.平均数average ['ævərɪdʒ] 178.比例proportion [prə'pɔːʃn] 179.百分比percent [pə'sent] 180.百分点percentage [pə'sentɪdʒ] 181.百分位数percentile [pə'sentaɪl] 182.排列permutation [ˌpɜːmju'teɪʃn] 183.组合combination [ˌkɒmbɪ'neɪʃn] 184.概率probability [ˌprɒbə'bɪləti] 185.图表graph [ɡræf]186.条形统计图bar graph [bɑː] [ɡræf]187.柱形统计图histogram ['hɪstəɡræm] 188.折线统计图broken line graph ['brəʊkən]189.曲线统计图curve diagram [kɜːv] ['daɪəɡræm] 190.扇形统计图pie diagram [paɪ] ['daɪəɡræm]。

Trinity College三一学院全美文理学院排名第三十六三一学院(哈特福德)是美国最古老的院校之一，建于1823年，三一学院是康乃狄克州的第二所大学，也是经过新英格兰大学协会鉴定的一所无宗教派别、不受文理科限制的高等教育文理学院。

三一学院经过185年的发展，目前的三一学院(哈特福德)不但吸引了美国国内43个州的学生来此就读，还使得30多个国家的海外学子慕名而来。

学校基本信息校训：For the Church and For the Nation创校：1823 年类型：私立大学排名：全美文理学院排名第36位校长：James F. Jones, Jr.所在地：Hartford, CT康涅狄格州，哈特福德校园：市区(100英亩)教员：约略187学生：2，388学校地址：Trinity College Admissions Office, 300 Summit Street, Hartford, CT, 06106, USA联系方式：(860) 297-2180颜色：蓝色、金色代号：Bantams吉祥物：Bantam 矮脚鸡学校特色和荣誉美国三一学院是美国最古老的院校之一，建于1823年,是康乃狄克州Connecticut的第二所大学，也是经过新英格兰大学协会鉴定的一所无宗教派别、不受文理科限制的高等教育文理学院。

经过185 年的发展，目前的三一学院不仅吸引了美国国内43个州的学生来此就读，还使得30多个国家的海外学子慕名而来，在校全日制本科生多达2，240名。

此外，三一学院还是少数工程学专业通过工程和技术认证委员会权威认证的学院之一，美国第8所荣获Phi Beta Kappa颁发荣誉的高校，在国内外享有极高的荣誉。

三一学院也是学子求学深造的理想选择。

学院设有38个专业，最有名气的是政治学、经济学、历史、英语和心理学，各个专业都拥有自己雄厚的师资力量，92%的教师都取得所在专业的最高学位，无论是基础课程还是高级课程都有丰富的经验；他们还得到国家科学基金会、文艺基金会、国际研究与交流组织、美国航空航天局等社会各界的大力资助，从而顺利进行最前沿的教学与研究。

SAT数学难题汇总及答案x^2 表示x 的平方，=！表示不等于。

pi 表示圆周率类型 1：20. The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set(A) 25(B) 26(C) 50(D) 51(E) 5214. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible16. Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z(A) x + y + k(B) x + y - k(C) x + y + 2k(D) x + y - 2k(E) 2x + 2y - 2k20. There are 75 more women than men enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men17. A merchant sells three types of clocks that chime as indicated by the check marks in the table above. What is the total number of chimes of the inventory of clocks in the 90-minute period from 7:15 to8:4518. If the 5 cards shown above are placed in a row so is never at eithe end, how many different arrangements are possible20. When 15 is divided by the positive integer k, the remainder is 3. For how many different values of k is this true(A) One(B) Two(C) Three(D) Four(E) Five17. On the number line above, there are 9 equal intervals between 0 and 1. What is the value of x19. If a, b. c, and f are four nonzero numbers, then all of the following proportions are equivalentEXCEPT (A)a/f=b/c(B)f/c=b/a(C) c/a=f/b(D)a/c=b/f(E)af/bc=1/18. If a and b are positive integers and what is the value of ab(A) 6(B) 12(C) 18(D) 24(E) 3616. After the first term, each term in a sequence is3 greater than 1/3 of the preceding term. If t is the first term of the sequence and t=!0. what is the ratio of the second term to the first term15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possiblep. r. and s are three different prime numbers greater than 2, and n = p * r * s, how many positive factors, including 1 and n. does n have18. If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x (A) 23(B) 25(C) 50(D) 75(E) 9417. For all positive integers j and k. let j \R\ k be defined as the whole number remainder when j is divided by k. If 13 \R\k = 2, what is the value of k19, In a set of eleven different numbers, which of the following CANNOT affect the value of the median(A) Doubling eachnumber(B) Increasing each number by10(C) Increasing the smallest numberonly (D) Decreasing the largestnumber only (E) Increasing thelargest number only15. A store charges $28 for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store employees can purchase any remaining sweaters at 30 percent off the store's cost How much would it cost an employee topurchase a sweater of this type atthis sale (A) $(B)$ (C)$ (D)$ (E) $and Corinne stand back-to-back. They each take 10 steps in opposite directions away from each other and stop. Alice then turns around, walks toward Corinne. and reaches her in 17 steps. The length of one of Alice's steps is how many times the length of one of Corinne's steps (All of Alice's steps are the same length and all of Corinne's steps are the same length.)14. If n and p are integers greater than 1 and if p is a factor of both n +3 and n + 10. what is the value of p(A) 3(B) 7(C)10(D) 13(E) 3016. In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture14. How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime(A) Zero(B) One(C) Two(D) Three(E) Four20. If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer(A) 2k(B) 2k + 3(C) 2k+ 4(D) 4k+1(E) 4k+ 2类型 2：18. The shaded region in the figure above is bounded by the x ‐axis, the line x = 4, and the graph of y = f(x).If the point (a, b) lies in the shaded region, which of the following must be trueI. a < 4II. b < aIII. b < f(a) (A) I only(B) III only(C) I and IIonly (D) I andIII only (E)I. II, and III19. At a bottling company, machine A fills, a bottle with spring water and machine B accepts the bottleonly if the number of fluid ounces is between11 7 8 and 12 1 8 If machine B accepts a bottle containing n fluid ounces, which of the following describes all possiblevalues of n7. Dwayne has a newspaper route for which he collects k dollars each day. From this amount he pays out k/3 dollars per day for the cost of the papers, and he saves the rest of the money. In terms of k, how many days will it take Dwayne to save $1,00017. In the xy-coordinate plane, the graph of x = y*y -4 intersects line l at (0, p) and (5, t). What is the greatest possible value of the slope of l18. Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning14. If (a + b)^ = (a - b) ^, which of the following must betrue (A) b = 0(B) a + b = 1(C) a - b = 1(D) a^2 + b^2 = 1(E) a^2 - b^2 = 115. The figure above shows the graphs of y = x*x and y = a - x*x for some constanta. If the length ofPQ is equal to 6, what is the valueof a (A) 6(B) 9(C) 12(D) 1518. During a sale, a customer can buy one shirt for x dollars. Each additional shirt the customer buys costs z dollars less than the first shirt. For example, the cost of the second shirt is x - z dollars. Which of the following represents the customer's cost, in dollars, for n shirts bought during this sale16. Let the function h be defined by h(x) = 14 + x^2/4. If h(2m) = 9m, what is one possible value of m16. If x is an integer greater than 1 and if y = x + 1/x, which of the followingmust be true I. y =! x II. y is an integer. III. xy > x^2(A) I only(B) III only(C) I and IIonly (D) I andIII only (E) I,II, and III6. If m and k are positive and 10(m^2)*k^-1= 100m, what is m^-1! interms of k (A) k/10(B) k/90(C) k^10 (D)1/10k(E) 1/90k8. The figure above shows the graph of a quadratic function f that has a minimum at the point (1,1). If f(b) = f(3), which of the following could be the value of b(A) -3(B) -2(C) -1(D) 1(E) 516. If a + 2b is equal to 125 percent of 4b, what is the value of a/b's biology experiment involved timing 12 hamsters in a maze. Each hamster received at least one practice before being timed. The scatter plot above shows the time each hamster took to complete the maze and the corresponding number of practices that each hamster received. Based on the data, which of the following functions best models the relationship between t, the number of seconds to complete the maze, and p, the number of practices(A) t(p) = 44(B) t(p) = p(C) t(p) =44p(D) t(p) =p/44 (E)t(p)= p+ 4420. For all numbers .t and v. let the operation □ be defined by x □ v = xy - y If a and b re positive integers, which of the following can be equal to zeroI. a□bII. (a + b)□b IIl. a□(a + b) (A)I only(B) II only(C) IIlonly (D) Iand ll (E)I and IIl18. In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y =p*x^3, where p is a constant. If the area of ABCD is 4, what is the value of p19. If k, n, x, and y are positive numbers satisfying x ^(-4/3)= k^-2 and y^(4/3) = n^2, what is(xy)^(-2/3 in terms of n and k(A) 1(B)1/2 (C)3/2(D) 6/5(E) 38. The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d. what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee15. Ifx^2-y^2 = 10 and x +y = 5. what is the valueof x - y18. The average (arithmetic mean) of the test scores of a class of p students is 70. and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86.What is the value ofp/n14. Which of the following is equivalent to h(m+ 1) (A) g(m)(B) g(m) +l (C)g(m)-1 (D)h(m)+1 (E)h(m)-1has containers of two different sizes. The total capacity of 16 containers of-one size is x gallons, and the total capacity of 8 containers of the other size is also x gallons, and x > 0. In terms of x, what is the capacity, in gallons, of each of the larger containers(A) 4x(B) 2x(C)x/2(D)x/8(E)x/1618. Let the function f be defined by f(x) = x^2+ 18. If m is a positive number such that f(2m) = 2f(m), what is the value of m19. The cost of maintenance on an automobile increases each year by 10 percent, and Andrew paid S300 this year for maintenance on his automobile. If the cost c for maintenance on Andrew's automobile n years from now is given by the function c(n) = 300x^n, what is the value of x(A)(B)(C)(D)(E) 30xy = 7 and x- y = 5. then x^2*y-xy^2=(A) 2(B) 12(C) 24(D) 35(E) 7017. Line m (not shown) passes through O and intersects AB between A and B. What isone possible value of the slope of line m17. If k and h are constants and x^2+kx+7is equivalent to(x + 1)(x + h). what isthe value of k (A) 0(B) 1(C) 7(D) 8(E) It cannot be determined from the informationgiven.(A) 1(B) 5(C) 24(D) 25(E) 2616. To celebrate a colleague's graduation, the m coworkers in an office agreed to contribute equally to a catered lunch that costs a total of y dollars. If p of the coworkers fail to contribute, which of the following represents the additional amount, in dollars, that each of the remaining coworkers must contribute to pay for the lunch类型 318. In the xy-coordinate plane, the distance between point B(10, 18) and point A(x,3) is 17. What is one possible value of x16. The pattern shown above is composed of rectangles. This pattern is used repeatedlyto completely cover a rectangular region 12L units long and 10L units wide. How manyrectangles of dimension L by W are needed(A) 30(B) 36(C) 100(D) 150(E) 18018. In the figure above, AB = BC and DE = EF = DF If the measure of /.ABC is 30° and the measure of/.BDE is 50°, what is the measure of/DFA (A) 30°(B)35° (C)40° (D)45° (E)50°17. The three-dimensional figure above has two parallel bases and 18 edges. Line segments are to be drawn connecting vertex V with each of the other 11 vertices in the figure. How many of these segments will not lie on an edge of the figure15. In the figure above, what is the sum. in terms of n, of the degree measures of the four angles marked with arrows(A) n(B) 2n(O 180 - n(D) 360 - n(E) 360 -2n16. The figure above consists of two circles that have the same center. If the shaded area is 64pi square inches and the smaller circle has a radius of 6 inches, what is the radius, in inches, of the larger circle20. The figures above show the graphs of the functions f and g. The function f is defined by f(x) = x^3 - 4x. The function g is defined by g(x) = f(x + h) + k, where h and k it are constants. What is the value of hk(A) -6(B) -3(C) -2(D) 3(E) 615. The cube shown above has edges of length 2, and A and 8 are midpoints of two of the edges. What is the length of AB (not shown)the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8. then the perimeter of the shaded region is(A) 8 - 3pi(B) 10+3pi(C) 14+3pi(D) 1 + 6pi(E) 12+6pi16. In rectangle ABCD, point E is the midpoint of BC. If the area of quadrilateral ABED is 2/3, what is the area of rectangle ABCD(A)1/2(B)3/4 (C)8/9 (D)1(E)8/3ABCD lies in the xy -coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD(A) -2(B) -1(C)0(D) 1(E) 216. In the figure above,y+z= (A)180(B)195(C)215(D)230(E)24518. The figure above shows part of a circle whose circumference is 45. If arcs of length 2 and length b continue to alternate around the ensure circle so that there are 18 arcs of each length, what is the degree measure of each of the arcs of length b(A) 4°(B) 6°(C)10° (D)16° (E)20°20. If the five line segments in the figure above are all congruent, what is the ratio of the length of AC (not shown) to the length of BD(A) 2^ to 1(B) 3^ to 1(C) 2^ to 2(D) 3^ to 2(E)3^ to 2^0..515. In the figure above, EBCD is a square and AE =8 What is the area of EBCD18. In the figure above, if the legs of triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC(A) 2. 29^ (B)2. 5, and 7(C)3,3,and3*2^ (D)3, 4, and 5(E) 4, 5, and 41^类型 4：18. If the average (arithmetic mean) of x and y is k, which of the following is the average of x, y, and z(A)(2k+z)/3 (B)(2k+z)/2(C)(k+z)/3(D)(k+z)/2(E) 2(k+z)/3IN A PRESCHOOL CLASSNumberof Siblings Numberof Students03162231table above shows how many students in a class of 12 preschoolers had 0,1, 2, or 3 siblings. Later, a new student joined the class, and the average (arithmetic mean) number of siblings per student became equal to the median number of siblings per student. How many siblings did the new student have(A)(B)1(C)2(D)3(E)418. The table above shows student enrollment at Weston High School from 1992 through 1996. If the median enrollment for the five years was 1351, and no two years had the same enrollment what is the greatest possible value for x【答案】。

Mathematica函数大全--运算符及特殊符号一、运算符及特殊符号Line1;执行Line，不显示结果Line1,line2顺次执行Line1，2，并显示结果name关于系统变量name的信息name关于系统变量name的全部信息!command执行Dos命令n! N的阶乘!!filename显示文件内容<Expr>> filename打开文件写Expr>>>filename打开文件从文件末写() 结合率[]函数{}一个表<*Math Fun*> 在c语言中使用math的函数(*Note*)程序的注释#n第n个参数##所有参数rule& 把rule作用于后面的式子%前一次的输出%%倒数第二次的输出%n第n个输出var::note变量var的注释"Astring "字符串Context ` 上下文a+b 加a-b减a*b或a b 乘a/b除a^b 乘方base^^num以base为进位的数lhs&&rhs且lhs||rhs或!lha非++,-- 自加1，自减1+=,-=,*=,/= 同C语言>,<,>=,<=,==,!=逻辑判断（同c）lhs=rhs立即赋值lhs:=rhs建立动态赋值lhs:>rhs建立替换规则expr//funname相当于filename[expr]expr/.rule将规则rule应用于exprexpr//.rule 将规则rule不断应用于expr知道不变为止param_ 名为param的一个任意表达式（形式变量）param__名为param的任意多个任意表达式（形式变量）二、系统常数Pi 3.1415....的无限精度数值E 2.17828...的无限精度数值Catalan 0.915966..卡塔兰常数EulerGamma 0.5772....高斯常数GoldenRatio 1.61803...黄金分割数Degree Pi/180角度弧度换算I复数单位Infinity无穷大-Infinity负无穷大ComplexInfinity复无穷大Indeterminate不定式三、代数计算Expand[expr]展开表达式Factor[expr]表达式因式分解Factor[poly,Modulus->p] Z p域分解Factor[poly,Extension->{a1, a2,… }] 代数数域分解Factor[poly,GaussianIntegers->True] 复整数域分解Factor[poly,Extension->Automatic]poly的系数所在数域分解（以下函数都可在各数域内进行）Simplify[expr]化简表达式FullSimplify[expr]将特殊函数等也进行化简PowerExpand[expr]展开所有的幂次形式ComplexExpand[expr,{x1,x2...}]按复数实部虚部展开FunctionExpand[expr]化简expr中的特殊函数Collect[expr, x]合并同次项Collect[expr, {x1,x2,...}]合并x1,x2,...的同次项Together[expr]通分Apart[expr]部分分式展开Apart[expr, var] 对var的部分分式展开Cancel[expr]约分ExpandAll[expr]展开表达式ExpandAll[expr, patt] 展开表达式FactorTerms[poly]提出共有的数字因子FactorTerms[poly, x] 提出与x无关的数字因子FactorTerms[poly, {x1,x2...}]提出与xi无关的数字因子Coefficient[expr, form]多项式expr中form的系数Coefficient[expr, form, n]多项式expr中form^n的系数Exponent[expr, form]表达式expr中form的最高指数Numerator[expr] 表达式expr的分子Denominator[expr]表达式expr的分母ExpandNumerator[expr]展开expr的分子部分ExpandDenominator[expr]展开expr的分母部分ExpandDenominator[expr]展开expr的分母部分TrigExpand[expr]展开表达式中的三角函数TrigFactor[expr]给出表达式中的三角函数因子TrigFactorList[expr]给出表达式中的三角函数因子的表TrigReduce[expr]对表达式中的三角函数化简TrigToExp[expr] 三角到指数的转化ExpToTrig[expr]指数到三角的转化RootReduce[expr]ToRadicals[expr]四、解方程Solve[eqns, vars]从方程组eqns中解出varsSolve[eqns, vars, elims] 从方程组eqns中削去变量elims,解出vars DSolve[eqn, y, x]解微分方程，其中y是x的函数DSolve[{eqn1,eqn2,...},{y1,y2...},x]解微分方程组，其中yi是x的函数DSolve[eqn, y, {x1,x2...}]解偏微分方程RSolve[eqn, a[n], n] 解函数方程例1、RSolve u x2x1u x1zu x2,u x,x{{u[x] BesselJ[x,z] C[1]+BesselY[x,z] C[2]}} 2、RSolve[{y[x+2]==ay[x+1]+y[x],y[0]==0,y[1]==1},y,x]RSolve[{eqn1, eqn2, … }, {a1[n], a2[n], …}, n]RSolve[eqn, a[n1, n2, …], {n1, n2, …}]Resolve[expr]Resolve[expr, dom]FindInstance[expr, vars]求不定方程的特解FindInstance[expr, vars, dom]求不定方程的特解（在dom数域内）FindInstance[expr, vars, dom, n]求不定方程的n个特解Eliminate[eqns, vars] 把方程组eqns中变量vars约去SolveAlways[eqns, vars] 给出等式成立的所有参数满足的条件Reduce[eqns, vars] 化简并给出所有可能解的条件Reduce x22y21&&x0&&y0&&x y Integers,x,y LogicalExpand[expr] 用&&和||将逻辑表达式展开InverseFunction[f] 求函数f的逆函数Root[f, k] 求多项式函数的第k个根Roots[lhs==rhs, var] 得到多项式方程的所有根五、微积分函数D[f, x]求f[x]的微分∂f/∂xD[f, {x, n}]求f[x]的n阶微分n f x nD[f,x1,x2..] 求f[x]对x1,x2...偏微分x1x2...fDt[f, x]求f[x]的全微分df/dxDt[f]求f[x]的全微分dfDt[f, {x, n}] n阶全微分df^n/dx^nDt[f,x1,x2..]对x1,x2..的偏微分d d x1d d x2...fIntegrate[f, x] f[x]对x在的不定积分Integrate[f, {x, xmin, xmax}] f[x]对x在区间(xmin,xmax)的定积分Integrate[f, {x, xmin, xmax}, {y, ymin, ymax}] f[x,y]的二重积分Limit[expr, x->x0] x趋近于x0时expr的极限Limit[expr, x->x0, Direction -> 1] x趋近于x0+时expr的极限Limit[expr, x->x0, Direction ->-1] x趋近于x0-时expr的极限Residue[expr, {x,x0}] expr在x0处的留数Series[f, {x, x0, n}] 给出f[x]在x0处的幂级数展开Series[f, {x, x0,nx}, {y, y0, ny}]先对y幂级数展开，再对xNormal[expr]化简并给出最常见的表达式（可截断Series的误差O[x]）SeriesCoefficient[series, n]给出级数中第n次项的系数SeriesCoefficient[series, {n1,n2...}]' 或Derivative[n1,n2...][f]一阶导数InverseSeries[s, x] 给出逆函数的级数ComposeSeries[serie1,serie2...] 给出两个基数的组合SeriesData[x,x0,{a0,a1,..},nmin,nmax,den]表示一个在x0处x的幂级数，其中aii 为系数O[x]^n n阶小量x^nO[x, x0]^n n阶小量(x-x0)^n六、多项式函数Variables[poly]给出多项式poly中独立变量的列表CoefficientList[poly, var]给出多项式poly中变量var的系数CoefficientList[poly, {var1,var2...}]给出多项式poly中变量var(i)的系数列? PolynomialMod[poly, m] poly中各系数mod m同余后得到的多项式，m可为整式PolynomialQuotient[p, q, x]以x为自变量的两个多项式之商式p/q PolynomialRemainder[p, q, x] 以x为自变量的两个多项式之余式PolynomialGCD[poly1,poly2,...] poly(i)的最大公因式PolynomialLCM[poly1,poly2,...] poly(i)的最小公倍式PolynomialReduce[poly, {poly1,poly2,...},{x1,x2...}]得到一个表{{a1,a2,...},b}其中Sum[ai*polyi]+b=polyResultant[poly1,poly2,var] 约去poly1,poly2中的varFactor[poly] 因式分解（在整式范围内）FactorTerms[poly] 提出poly 中的数字公因子FactorTerms[poly, {x1,x2...}] 提出poly 中与xi 无关项的数字公因子FactorList[poly] 给出poly 各个因子及其指数{{poly1,exp1},{...}...}FactorSquareFreeList[poly] 同上FactorTermsList[poly,{x1,x2...}] 给出各个因式列表，第一项是数字公因子，第二项是与xi 无关的因式，其后是与xi 有关的因式按升幂的排排?Cyclotomic[n, x] C n x k x e 2i k n （割圆多项式，即单位根的极小多项式）Decompose[poly, x] 迭代分解，给出{p1,p2,...},其中p1(p2(...))=polyInterpolatingPolynomial[data, var] 在数据data 上的插值多项式 data 可以写为{f1,f2..}相当于{{x1=1,y1=f1}..} data 可以写为{{x1,f1,df11,df12,..},{x2,f2,df21..} 可以指定数据点上的n 阶导数值RootSum[f, form] 得到f[x]=0的所有根，并求得Sum[form[xi]]七、随机函数Random[type,range] 产生type 类型且在range 范围内的均匀分布随机数,type 可以为Integer,Real,Complex,不写默认为Real ,range 为{min,max}，不写默认为{0,1} Random[] 0～1上的随机实数SeedRandom[n] 以n 为seed 产生伪随机数 如果采用了 <在 2.0版本为 <<"D:\\Math\\PACKAGES\\STATISTI\\Continuo.m"Random[distribution]可以产生各种分布如Random[BetaDistribution[alpha, beta]]stribution[alpha, beta]}Random[NormalDistribution[miu,sigma]]等常用的分布如BetaDistribution,CauchyDistribution,ChiDistribution, NoncentralChiSquareDistribution,ExponentialDistribution, ExtremeValueDistribution,NoncentralFRatioDistribution,GammaDistribution,HalfNormalDistribution, LaplaceDistribution, LogNormalDistribution,LogisticDistribution,RayleighDistribution,NoncentralStudentTDistribution,UniformDistribution, WeibullDistribution八、数值函数N[expr] 表达式的机器精度近似值N[expr, n]表达式的n位近似值，n为任意正整数NSolve[lhs==rhs, var]求方程数值解NSolve[eqn, var, n] 求方程数值解，结果精度到n位NDSolve[eqns, y, {x, xmin, xmax}]微分方程数值解NDSolve[eqns, {y1,y2,...}, {x, xmin, xmax}]FindRoot[lhs==rhs, {x,x0}]以x0为初值，寻找方程数值解FindRoot x52,x,1,WorkingPrecision100精确到100位有效数字FindRoot[lhs==rhs, {x, xstart, xmin, xmax}]NSum[f, {i,imin,imax,di}] 数值求和，di为步长NSum[f, {i,imin,imax,di}, {j,..},..] 多维函数求和NProduct[f, {i, imin, imax, di}]函数求积NIntegrate[f, {x, xmin, xmax}] 函数数值积分优化函数：FindMinimum[f, {x,x0}]以x0为初值，寻找函数最小值FindMinimum[f, {x, xstart, xmin, xmax}]LinearProgramming[c,m,b]解线性组合c.x在m.x>=b&&x>=0约束下的最小值，x,b,c为向量,m为矩阵LatticeReduce[{v1,v2...}]向量组vi的极小无关组数据处理：Fit[data,funs,vars]用指定函数组对数据进行最小二乘拟和data可以为{{x1,y1,..f1},{x2,y2,..f2}..}多维的情况emp: Fit[{10.22,12,3.2,9.9}, {1, x, x^2,Sin[x]}, x]Interpolation[data]对数据进行差值,data同上，另外还可以为{{x1,{f1,df11,df12}},{x2,{f2,.}..}指定各阶导数InterpolationOrder默认为3次，可修改ListInterpolation[array]对离散数据插值，array可为n维ListInterpolation[array,{{xmin,xmax},{ymin,ymax},..}] FunctionInterpolation[expr,{x,xmin,xmax}, {y,ymin,ymax},..]以对应expr[xi,yi]的为数据进行插值Fourier[list] 对复数数据进行付氏变换InverseFourier[list]对复数数据进行付氏逆变换Min[{x1,x2...},{y1,y2,...}]得到每个表中的最小值Max[{x1,x2...},{y1,y2,...}]得到每个表中的最大值Select[list, crit] 将表中使得crit为True的元素选择出来Count[list, pattern] 将表中匹配模式pattern的元素的个数Sort[list] 将表中元素按升序排列Sort[list,p]将表中元素按p[e1,e2]为True的顺序比较list 的任两个元素e1,e2,实际上Sort[list]中默认p=Greater集合论：Union[list1,list2..] 表listi的并集并排序Intersection[list1,list2..]表listi的交集并排序Complement[listall,list1,list2...]从全集listall中对listi的差集九、虚数函数Re[expr]复数表达式的实部Im[expr] 复数表达式的虚部Abs[expr] 复数表达式的模Arg[expr]复数表达式的辐角Conjugate[expr] 复数表达式的共轭十、数的头及模式及其他操作Integer _Integer整数Real _Real实数Complex _Complex复数Rational_Rational 有理数(*注：模式用在函数参数传递中，如MyFun[Para1_Integer,Para2_Real]规定传入参数的类型，另外也可用来判断If[Head[a]==Real,...]*) IntegerDigits[n,b,len]数字n以b近制的前len个码元RealDigits[x,b,len]类上FromDigits[list] IntegerDigits的反函数Rationalize[x,dx] 把实数x有理化成有理数，误差小于dxChop[expr, delta]将expr中小于delta的部分去掉,dx默认为10^-10 Accuracy[x]给出x小数部分位数,对于Pi,E等为无限大Precision[x]给出x有效数字位数,对于Pi,E等为无限大SetAccuracy[expr, n] 设置expr显示时的小数部分位数SetPrecision[expr, n] 设置expr显示时的有效数字位数十一、区间函数Interval[{min, max}] 区间[min, max](* Solve[3 x+2==Interval[{-2,5}],xx]*) IntervalMemberQ[interval, x] x在区间内吗？IntervalMemberQ[interval1,interval2]区间2在区间1内吗？IntervalUnion[intv1,intv2...] 区间的并IntervalIntersection[intv1,intv2...]区间的交十二、矩阵操作a.b.c或Dot[a, b, c]矩阵、向量、张量的点积Inverse[m] 矩阵的逆Transpose[list]矩阵的转置Transpose[list,{n1,n2..}]将矩阵list 第k行与第nk列交换Det[m]矩阵的行列式Eigenvalues[m]特征值Eigenvectors[m]特征向量Eigensystem[m]特征系统，返回{eigvalues,eigvectors}LinearSolve[m, b] 解线性方程组m.x==bNullSpace[m] 矩阵m的零空间，即m.NullSpace[m]==零向量RowReduce[m] m化简为阶梯矩阵Minors[m, k] m的所有k*k阶子矩阵的行列式的值(伴随阵，好像是) MatrixPower[mat, n] 阵mat自乘n次MatrixExp[mat]e matOuter[f,list1,list2..] listi中各个元之间相互组合，并作为f的参数的到的矩矩? Outer[Times,list1,list2]给出矩阵的外积SingularValues[m] m的奇异值，结果为{u,w,v},m=Conjugate[Transpose[u]].DiagonalMatrix[w].vPseudoInverse[m] m的广义逆QRDecomposition[m] QR分解SchurDecomposition[m] Schur分解LUDecomposition[m] LU分解Norm[z]＝Abs[z]；Norm[v]＝Sqrt[v.Conjugate[v]]；向量的模（内积开平方）Norm[v, p]＝Total[Abs[v^p]]^(1/p)。