04-Divided Difference

小学上册英语全练全测英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The movement of tectonic plates can lead to ______ activity.2.I enjoy visiting the ________ (自然历史博物馆).3.I have a _____ (project) for school.4.The koala eats _________. (桉树叶)5.What is the primary color that is a mix of red and blue?A. GreenB. PurpleC. OrangeD. BrownB6.The sun is very ___ (bright) today.7.We can see many ___ in the zoo. (animals, plants, books)8.I like _____ (to cook/to eat).9.The _____ (grapevine) produces delicious fruit.10.I can ______ (让) people laugh.11. A ______ is a mammal that can fly.12.What is the name of the famous American singer known for her hit song "I Will Always Love You"?A. Mariah CareyB. Whitney HoustonC. Celine DionD. AdeleB13.I want to _______ (学会)如何制作蛋糕.14.What is the name of the famous lion in "The Lion King"?A. SimbaB. MufasaC. ScarD. NalaA15.I see a _____ on the table. (book)16.My uncle loves __________ (音乐).17.Which animal is known for its black and white stripes?A. LeopardB. ZebraC. TigerD. Panda18.What is the main ingredient in sushi?A. NoodlesB. RiceC. BreadD. PotatoesB Rice19.The ______ helps with the growth of plants.20.The first man on the moon was _______. (尼尔·阿姆斯特朗)21.The discovery of ________ has changed our understanding of the ecosystem.22.The kitten is ______ on my lap. (sitting)23.My ________ (玩具名称) is a great way to relax.24.What is the process of water turning into vapor?A. EvaporationB. CondensationC. PrecipitationD. Sublimation25.Water is made up of hydrogen and ______.26.What is the process of taking in oxygen called?A. InhalationB. ExhalationC. RespirationD. DigestionA27.What is the name of the mountain range that separates Europe and Asia?A. AndesB. HimalayasC. RockiesD. Ural MountainsD28. A starfish has five _______ (手臂).29.sustainable energy) replaces fossil fuels. The ____30. A saturated solution cannot dissolve any more _____ (solute).31.The ancient Maya built elaborate ______ (金字塔) for their ceremonies.32.What do we call the person who helps us when we are sick?A. TeacherB. NurseC. ChefD. MechanicB33.What do we call a person who examines ancient artifacts?A. ArchaeologistB. HistorianC. AnthropologistD. Sociologist34.The first man-made satellite was launched by _______.35.What is the name of the famous actress known for her role in "Breakfast at Tiffany's"?A. Audrey HepburnB. Marilyn MonroeC. Grace KellyD. Elizabeth TaylorA36.I love to watch _____ (小动物) explore their surroundings.37. A chemical reaction that requires heat to proceed is called an ________ reaction.38.What color is the sky on a clear day?A. GreenB. BlueC. RedD. Yellow39.The ______ provides a habitat for many species.40.What do you call a baby dog?A. KittenB. PuppyC. CubD. CalfB41.Which insect is known for its ability to build a hive?A. AntB. BeeC. ButterflyD. MosquitoB42.The atomic number tells us the number of ______ in an atom.43. A ____ enjoys basking in the sun and has a colorful shell.44.The stars are ___ (shining) at night.45.How many wheels does a bicycle have?A. 2B. 4C. 3D. 146. A chemical reaction can result in the formation of new ______.47.Plants absorb carbon dioxide through their ______.48.The ______ (生态) impacts plant diversity.49.y of Versailles ended _______. (第一次世界大战) The Trea50.The sun _____ (rises/sets) in the east.51.Sedimentary rocks can be formed from ______ materials.52.We have a ______ (丰富的) range of activities at school.53.The playground is ___ (fun/boring).54.The __________ (历史的前景) invites potential.55.The doctor gives _____ (建议) on health.56.He plays _____ (足球) on weekends.57.Which animal is known for its ability to change colors?A. ChameleonB. ElephantC. LionD. DogA58.The chemical formula for potassium chloride is _______.59.I hope to make a difference in the world using my ________ (玩具名) creativity.60.The ____ is a tiny creature that flutters from flower to flower.61.The ________ (小岛) is a great vacation spot.62.We have a ______ (丰富的) curriculum that includes arts.63.What do we call the journey of a bird to a warmer place during winter?A. MigrationB. HibernationC. NestingD. ForagingA64.I love to listen to the __________ when it rains. (雨)65.What is the capital of Canada?A. TorontoB. OttawaC. VancouverD. Montreal66.The cake is ______ and tasty. (sweet)67. A _______ (小骆驼) can go long without water.68.What color is a school bus?A. BlueB. YellowC. GreenD. Red69.The boy is _____ (playing/sleeping) in the grass.70.Botanical gardens often have ______ (教育) programs.71. A mixture that has a variable composition is called a _______ mixture.72.My sister enjoys making ____ (videos) for fun.73.What is 7 + 3?A. 8B. 9C. 10D. 1174.Plants can be used for decoration and ______ (美化).75.What is the opposite of "full"?A. EmptyB. HeavyC. LightD. RichA76.What is 10 divided by 2?A. 3B. 4C. 5D. 6C77.Certain plants can ______ (产生) natural fibers.78.What is the color of an orange?A. GreenB. BlueC. OrangeD. PurpleC79.They are __________ to the store.80. A compound made of carbon, hydrogen, and oxygen is a ______.81.What is the name of the largest land animal?A. ElephantB. GiraffeC. HippopotamusD. RhinoA82.What is the color of grass?A. BlueB. GreenC. YellowD. BrownB83.Which month comes after January?A. DecemberB. FebruaryC. MarchD. AprilB84.What do we call the person who repairs shoes?A. TailorB. CobblerC. BakerD. Mechanic85.The ________ (向日葵) turns towards the sun and is very bright.86.The density of water is _______ grams per cubic centimeter.87.The ____ has a long body and is often seen slithering on the ground.88.Which holiday is celebrated on December 25th?A. ThanksgivingB. HalloweenC. ChristmasD. EasterC89.What do you call the person who repairs shoes?A. BakerB. TailorC. CobblerD. ButcherC90.My uncle is a _______ (职业). 他在 _______ (地点)工作.91.The playground is ________ (适合孩子们).92.I enjoy spending time at ______ with my friends.93.The ancient Egyptians built their pyramids as _____ for their pharaohs.94. A mixture is made of two or more ______.95.Burning wood produces __________.96.The pH of pure water is ______.97.This girl, ______ (这个女孩), is passionate about wildlife conservation.98.The _____ (图书馆) has many books.99.The ice cream is _____ melting. (slowly)100.Which season comes after winter?A. SpringB. SummerC. FallD. AutumnA。

汉英翻译篇章练习Practice 1近读报纸，对国内名片和请柬的议论颇多，于是想起客居巴黎时经常见到的法国人手中的名片和请柬，随笔记下来，似乎不无借鉴之处。

在巴黎，名目繁多的酒会、冷餐会是广交朋友的好机会。

在这种场合陌生人相识，如果是亚洲人，他们往往开口之前先毕恭毕敬地用双手把自己的名片呈递给对方，这好像是不可缺少的礼节。

然而，法国人一般却都不大主动递送名片，双方见面寒喧几句甚至海阔天空地聊一番也就各自走开。

只有当双方谈话投机，希望继续交往时，才会主动掏出名片。

二话不说先递名片反倒有些勉强。

法国人的名片讲究朴素大方，印制精美，但很少有镶金边儿的，闪光多色的或带香味儿的，名片上的字体纤细秀丽，本人的名字也不过分突出，整张纸片上空白很大，毫无拥挤不堪的感觉。

Practice 2我想,教师要给学生的,是一把开启知识宝库的钥匙,而不是把学生的脑子变成一个容器。

教师的工作是启发学生,通过自己的思考、实践、试验去求得知识,鼓励他们大胆提出问题和不同意见。

经过研讨,得出自己的结论,而不是由教师包办代替。

我喜欢那些爱提“怪”问题的学生。

提不出问题的,不能算是好学生。

其实,学习就是一个不断出错误和改正错误的过程。

年轻人要学,我们自己也要学。

一句话,教育是要使人从无知变成有知,从愚昧变成聪明,从野蛮变成文明,而不是相反。

就说这流行音乐吧,我就不如年轻人懂得多。

我有个习惯,自己不懂得东西，绝不轻易反对,而是努力去学懂它。

你看吧,大街上姑娘们大声谈笑,我行我素；小伙子也穿红戴绿。

中国人胆子大起来了，不那么缩头缩脑了。

你还能拿年轻人头发长短、裤脚大小来衡量谁是好学生谁是坏学生吗？Practice 3我所追求的幸福在西方流传着一句据说是来自古老中国的谚语，只是我在中国从未听说过：“如果你想要几小时的幸福，就去喝醉酒；如果你想要三年的幸福，就去结婚；如果你想要一辈子的幸福，就去做个园丁。

”他们对园丁能一辈子幸福的解释是：“做有用的事，与自然融合，对身体的锻炼和每天都会有新的喜悦。

中英文数学对照代数Algebra正数positive负数negative零zero数字digit/number整数integer分数fractions假分数proper fraction带分数mixture fractions/improper fraction 分子numerator分母denominator小数decimal百分数percentage/percent数字1one2two3three4four5five6six7seven8eight9nine10ten11eleven12twelve13thirteen14fourteen15fifteen16sixteen17seventeen18eighteen19nineteen20twenty100hundred1000thousand10000million1000000000billion奇数odd偶数even质数prime合数composite最大公约数maximum common factor 最小公倍数least common multiples加法addition减法subtraction乘法multiple除法division被除数dividend除数divisor商quotient和sum乘积product因数factor结合律association交换律communication分配律distribution因式分解factoring因子factors简化simplify等式/方程equation不等式inequation倒数receiption符号symbol约等于/近似approximately估算estimation实数real numbers有理数rational numbers无理数irrational numbers一元二次方程linear equations二元一次方程quadratic equations绝对值方程absolute equations方程的根root方程组system of equations变量variable常量constant多项式polynomial单项式monomial反比例函数inverse proportional function 正比例函数proportional function指数函数exponential function对数函数logarithmic function三角函数trigonometric function消元法elimination代入法substitute集合set并集union set交集intersection set空集empty set坐标轴axis横轴x-axis纵轴y-axis截距x,y-intercepts象限quadrant抛物线parabola顶点vertex准线directrix对称轴symmetric axis主轴Major axis副轴Minor axis水平对称轴horizontal symmetric axis垂直对称轴vertical symmetric axis数列sequence/series等差数列arithmetic sequence等比数列geometric sequence几何geometric点point线line面plane曲线curve多边形polygon平行四边形parallelogram菱形rhombus长方形rectangular正方形square梯形trapezoid三角形triangle斜三角形skew triangle正三角形right triangle等腰三角形isosceles triangle锐角三角形acute triangle直角三角形right triangle钝角三角形obtuse triangle凹多边形concave polygon凸多边形convex polygon对边opposite site邻边adjacent side斜边hypotenuse side对角线diagonal髙height底面base中线midline垂直平分线perpendicular bisector 垂直perpendicular平分bisector重心gravity垂心orthocenter角angle锐角acute angle直角right angle钝角obtuse angle圆circle半径radius直径diameter弦chord弧arc优弧major arc劣弧minor arc切线tangent line割线secant line长方形rectangle正方形square边side椭圆ellipse抛物线parabola双曲线hyperbola相交intersection相切tangent正交orthogonal立体图形solid立方体cube三棱柱triangular prism棱柱prism棱锥pyramid圆锥cone圆柱cylinder球sphere规则多边体不规则多边体勾股定理Pythagorean theorem 边长side length面积area周长perimeter/circumference 体积volume表面积surface area侧面积lateral area底面积base area斜边slant立方体的高altitude位似变化transformation位移translation水平平移horizontal shift垂直平移vertical shift对称reflection放大/缩小dilation strectch/compress 旋转rotation公式formula定理theorem矩阵matrix行列式determinant行row列column排列permutation组合combination概率probability极限limit导数derivative微分differential积分integral平均数average/mean方差variance标准差standard variance中位数median众数mode。

absolute error绝对误差,relative error and significant digits 相对误差和有效数字(n-digit)accurate to 5 decimal places精确到5位小数degree accuracy准确度Newton-Raphson formula牛顿-拉夫森公式Root根sum of和Newton-cotes牛顿—柯特斯Coefficients系数Convergence集合sufficient and necessary condition充分必要条件iterative formula迭代公式fixed point bisection method固定点的二分法fixed point iteration固定点迭代法integration积分法linear system线性方程组triangular factorization三角分解Gauss-Seidel iteration高斯-赛德尔迭代Gaussian elimination高斯消去法，高斯消元;Jacobi method雅可比法the clamped cubic spline夹紧的三次样条the first derivative一阶导数curve fitting曲线拟合the least-squares line coefficient最小二乘线系数function函数Polynomial多项式node结点of degree n度degree of precision精密度interpolation插值approximate逼近，近似error term误差项tend to倾向于cubic spline Taylor interpolation三次样条函数的泰勒插值Hermite interpolation埃尔米特插值high-degree polynomials高阶多项式quadrature formula求积分公式constant Simpson’s rule常数辛普森规则Trapezoidal’s rule composite Simpson rule 组合梯形公式和辛普森公式Integral积分the initial value problem初始值问题Euler’s method欧拉方法spectral radius谱半径norm interval规范区间Chebyshev polynomial切比雪夫多项式strengths and weaknesses长处和短处definite integral定积分quadratic Lagrange interpolation二次拉格朗日插值divided-difference table 差分表compute计算三角分解插值切比雪夫三次样条代数精度Gauss_Seidel, Jocabi, Euler，插值型求积公式。

带重节点的牛顿插值法牛顿插值法是一种在给定数据点的情况下通过插值函数来逼近真实函数的方法。

它属于插值法中的一种，是一种非常有用和广泛使用的数值计算方法。

牛顿插值法使用一个多项式函数来逼近真实函数，该函数使用给定的数据点来确定多项式系数。

带重节点的牛顿插值法是一种牛顿插值法的扩展形式，可以在数据点重复的情况下使用。

在牛顿插值法中，我们首先将给定的数据点按照节点值从小到大排序。

然后我们需要计算每一个节点上的差商，通过差商可以得到一个多项式函数。

差商的定义如下：$f[x_0,x_1]=\frac {f(x_1)-f(x_0)}{x_1-x_0}$以此类推，差商的递归计算可以用以下公式表示：$f[x_i,x_{i+1},\dots,x_{i+j}]=\frac{f[x_{i+1},x_{i+2},\dots,x_{i+j}]-f[x_i,x_{i+1},\dots,x_{i+j-1}]}{x_{i+j}-x_i} $使用差商的定义和递归公式，我们可以得到一个多项式函数：$P_n(x)=f[x_0]+f[x_0,x_1](x-x_0)+f[x_0,x_1,x_2](x-x_0)(x-x_1)+\dots+f[x_0,x_1, \dots,x_n](x-x_0)(x-x_1)\dots(x-x_{n-1})$其中，$f[x_0,x_1,\dots,x_n]$表示一个$n$阶的差商。

但是，如果在给定的数据点中有重复的节点，那么上述算法将不再适用。

为了使用带重节点的牛顿插值法，我们需要使用多重差商（divided difference）来计算插值函数。

在插值点为$x_0,x_1,\dots,x_n$且有$m+1$个插值点重复的情况下，$m+1$重差商（divided difference）定义为：对于$m+1$个插值点重复的情况，用多重差商计算插值函数的公式如下：其中，$f(x_0,x_0,\dots,x_0,x_i)$是$i+1$重差商，$\prod_{j=0}^{i-1}(x-x_j)$是拉格朗日基函数。

UNIT1分层跟踪检测(二)DiscoveringUsefulStructures&ListeningandTalkingA级必备知识基础练Ⅰ.单句语法填空1.What fine weather! What about (go) to have a picnic this afternoon?2.If you follow my advice,you can know how (make) a fire in the wild.3.The (edit) unwillingly published the article as it had originally been written.4.Tom joined the adventure camp because he wanted to learn some (survive) skills.5.I f you’re looking for a unique (adventurous),the Space and Aviation Center is the place.6.Biologists are working together to study the (behave) of this family of birds.7.The 40-minute film about (young) and dreams got nearly 70 million views on a video website.8.After being trained for some time,the children became expert holding their breath under water.Ⅱ.单句写作1.I am very pleased to have this opportunity to stand here and (给你们演讲).2.Parents should talk to their children but(同时) they should lend an ear to what their children have to say.3.We went to the seaside during the summer holiday and we all (玩得很愉快) there.4.Adam (参加……选拔) the school basketball team,but was refused by the coach.5.A famous professor from Shandong University will give us a talk on how to (提高英语口语).6.Mary wants to (与……交朋友) Jane because both of them like playing the piano.Ⅲ.请写出画线部分属于什么短语及其所作的成分1.He is a very careful worker.属于;在句中作。

模式识别中距离方法名称及算法流程1.最常见的距离方法是欧氏距离，它是通过两个点之间的直线距离来计算它们之间的相似性。

The most common distance method is Euclidean distance, which calculates the similarity between two points by the straight-line distance between them.2.切比雪夫距离是通过两个点之间的最大差值来表示它们之间的不相似度。

Chebyshev distance represents the dissimilarity between two points by the maximum difference between them.3.曼哈顿距离是通过两个点在各个维度上的差值的绝对值之和来计算它们之间的距离。

Manhattan distance calculates the distance between two points by the sum of the absolute differences in each dimension.4.闵可夫斯基距离是欧氏距离和曼哈顿距离的一般化表示形式，具有一个参数p用于调节计算过程。

Minkowski distance is a generalization of Euclidean distance and Manhattan distance with a parameter p to adjust the calculation process.5.马氏距离考虑了各个维度之间的相关性，通过协方差矩阵的逆来调整欧氏距离的计算结果。

Mahalanobis distance takes into account the correlation between dimensions and adjusts the calculation of Euclidean distance using the inverse of the covariance matrix.6.汉明距离是用来衡量两个等长字符串之间的不同之处的度量，即它们在相应位置上的不同字符的个数。