AP CACULUS WORDS absolutely convergent ,adj绝对收敛antiderivative ,n不定积分binomial theorem ,n二项式定理，二项展开式chain rule ,n链规则calculus ,n微积分学conditionally convergent ,adj条件收敛continuity ,n连续converge ,v收敛definite integral ,n定积分derivative ,n导数differential coefficient ,n微分differential equation ,n微分方程directional derivative ,n方向导数diverge ,v发散divergence ,n散度gradient ,n梯度implicit differentiation ,n隐函数微分implicit function ,n隐函数improper integral ,n广义积分integrable ,adj可积的integral ,n积分integration by parts ,n部分积分法left-hand limit ,n左极限limit ,n极限local maximum ,n极大值local minimum ,n极小值method of lagrange multipliers ,n拉格朗日乘数法multiple integral ,n多重积分partial derivative ,n偏导数polar coordinates ,n极坐标power series ,n幂级数right-hand limit ,n右极限rotation ,n旋度series ,n级数substitution rule ,n替代法则table of integrals ,n积分表taylor’s formula ,n泰勒公式three-dimensional analytic geometry ,n空间解析几何total differential ,n全微分trigonometric substitution ,n三角替代法absolutely convergent绝对收敛absolute value绝对值algebraic function代数函数analytic geometry解析几何antiderivative不定积分approximate integration近似积分approximation近似法、逼近法arbitrary constant任意常数arithmetic series/progression (AP)算数级数asymptotes (vertical and horizontal)(垂直/水平)渐近线average rate of change平均变化率base基数binomial theorem二项式定理，二项展开式Cartesian coordinates笛卡儿坐标(一般指直角坐标) Cartesian coordinates system笛卡儿坐标系Cauch’s Mean Value Theorem柯西均值定理chain rule链式求导法则calculus微积分学closed interval integral闭区间积分coefficient系数conchoid蚌线continuity (函数的)连续性concavity (函数的)凹凸性conditionally convergent有条件收敛continuity连续性critical point临界点cubic function三次函数cylindrical coordinates圆柱坐标decreasing function递减函数decreasing sequence递减数列definite integral定积分derivative导数determinant行列式differential coefficient微分系数differential equation微分方程directional derivative方向导数discontinuity不连续性discriminant (二次函数)判别式disk method圆盘法divergence散度divergent发散的domain定义域dot product点积double integral二重积分ellipse椭圆ellipsoid椭圆体epicycloid外摆线Euler's method (BC)欧拉法expected valued期望值exponential function指数函数extreme value heorem极值定理factorial阶乘finite series有限级数fundamental theorem of calculus微积分基本定理geometric series/progression (GP)几何级数gradient梯度Green formula格林公式half-angle formulas半角公式harmonic series调和级数helix螺旋线higher derivative高阶导数horizontal asymptote水平渐近线horizontal line水平线hyperbola双曲线hyper boloid双曲面implicit differentiation隐函数求导implicit function隐函数improper integral广义积分、瑕积分increment增量increasing function增函数indefinite integral不定积分independent variable自变数inequality不等式ndeterminate form不定型infinite point无穷极限infinite series无穷级数infinite series无限级数inflection point (POI)拐点initial condition初始条件instaneous rate of change瞬时变化率integrable可积的integral积分integrand被积分式integration积分integration by part分部积分法intercept截距intermediate value of Theorem：中间值定理inverse function反函数irrational function无理函数iterated integral逐次积分Laplace transform拉普拉斯变换law of cosines余弦定理least upper bound最小上界left-hand derivative左导数left-hand limit左极限L'Hospital's rule洛必达法则limacon蚶线linear approximation线性近似法linear equation线性方程式linear function线性函数linearity线性linearization线性化local maximum极大值local minimum极小值logarithmic function对数函数MacLaurin series麦克劳林级数maximum最大值mean value theorem (MVT)中值定理minimum最小值method of lagrange multipliers拉格朗日乘数法modulus绝对值multiple integral多重积分multiple倍数multiplier乘子octant卦限open interval integral开区间积分optimization优化法，极值法origin原点orthogonal正交parametric equation (BC)参数方程partial derivative偏导数partial differential equation偏微分方程partial fractions部分分式piece-wise function分段函数parabola抛物线parabolic cylinder抛物柱面paraboloid：抛物面parallepiped平行六面体parallel lines并行线parameter：参数partial integration部分积分partiton：分割period：周期periodic function周期函数perpendicular lines垂直线piecewise defined function分段定义函数plane平面point of inflection反曲点point-slope form点斜式polar axis极轴polar coordinates极坐标polar equation极坐标方程pole极点polynomial多项式power series幂级数product rule积的求导法则quadrant象限quadratic functions二次函数quotient rule商的求导法则radical根式radius of convergence收敛半径range值域(related) rate of change with time (时间)变化率rational function有理函数reciprocal倒数remainder theorem余数定理Riemann sum黎曼和Riemannian geometry黎曼几何right-hand limit右极限Rolle's theorem罗尔(中值)定理root根rotation旋转secant line割线second derivative二阶导数second derivative test二阶导数试验法second partial derivative二阶偏导数series级数shell method (积分)圆筒法sine function正弦函数singularity奇点slant母线slant asymptote斜渐近线slope斜率slope-intercept equation of a line直线的斜截式smooth curve平滑曲线smooth surface平滑曲面solid of revolution旋转体symmetry对称性substitution代入法、变量代换tangent function正切函数tangent line切线tangent plane切(平)面tangent vector切矢量taylor's series泰勒级数three-dimensional analytic geometry空间解析几何total differentiation全微分trapezoid rule梯形(积分)法则。
spss单样本t检验Analyze----compare Means----one sample T test输入方式实验数据121212123456495直接输入数据Sig=0.000 差异显着独立样本t检验（两组数据）Analyze-----compare Means----Independent-samples T test 输入方式试验分组实验数据1 121 131 121 121111222222222两组数据个数可以不同成组数据t检验Analyze----compare Means-----paired-samples T test 单因素方差分析Analyze---compare means----one-way ANOVA(analyze of variance)Factor （因素）1 1 1 1 1 2 2 2 2 2 2 3 3 3 3(分组)Dependent List 试验数据polynomial linescontrast---polynomial---Degree---linearpost Hoc Multiple comparisons-----LSD(Duncan 邓肯检验) 先选方差齐性在结果中判断Sig值？＜0.05（差异显着）若不齐则进行数据转化。
数据输入分组试验数据1 121 131 1311222222333333444444双因素方差分析Analyze-----General linear Model-----univariateDependent Variable(因变因素)因别的数字变化而变化Fixed Factor （固定因素）Random Factors(随机因素)Model-----custom-----Build Term---Interaction(交互作用)----Main effects （主因素）Contrast--- simple---first----changePlot Hoc----LSD (Duncan)Univariate Options----Homogeneity tests(方差齐性分析)Display Means for （协方差使用）钙镁增重1 1 1 1 1 1 12 1 2 1 2 13 1 3 1 3 14 1 41 42 2 2 2 2 2 2 2 2 2相关性分析Anlyze---correlation----bivariate输入格式Pearson----皮尔逊检验Two-tailed 双尾Pearson correlation 相关系数=0.433 表明相关性不大Sig（2-tailed）双尾p值>0.05 差异不显着一般p>0.6 sig<0.05时两组数据显着相关（不同专业可能要求不同）回归分析Anlyze----regression---curve estimation(曲线)Dependent---因变量Independent---自变量（独立—不依靠别的数据自己变化）Linear—直线型Quadratic---二次型Compound---复合函数Growth—生长曲线Logarithmic—对数函数Cubic---三次函数S---s型曲线Exponential----指数函数Inverse 倒数函数Power---幂函数Logistic 逻辑函数直线在y轴上的截距不能是负值，因为到时候代入试验数据时会出现负值单变量协方差分析Anlyze—General Linear Model—univariateModel—custom 主变量与协变量分别以main effects选入Contrast---simple---first 点击changeOption中选择分析变量放入display means for 然后选择compare main effects Display中选择homogeneity test（方差齐性分析）Sig=0.125>0.05 方差齐性初重表示选择的初始个体中的初重差异性大（0.039<0.05）Factor中的数据已经出去了差异显着的数据LSD检验OriginA表示x自变量B表示y因变量Analysis---fitting---Nonlinear curve fit（ctrl+y）Function selection—方程选择Category 分类Function方程Code 方程一般表达式Parameters 参数（当a为定值时在fixed中打钩然后填a值若无则可不填一般给初始值1）若方程没有可自己设置Category中选择user defined Function—new写好后fit（参数形式一定要一样）。
高一英语数学建模案例分析单选题30道1. In the math modeling process of collecting data about students' grades, which of the following methods is NOT appropriate?A. Conducting a questionnaire surveyB. Randomly sampling from the class listC. Collecting data from only the top studentsD. Observing students' performance in class答案：C。
本题考查数据收集方法的合理性。
选项A，问卷调查可以获取广泛的信息；选项B，随机抽样能保证样本的代表性；选项D，课堂观察能直接了解学生表现。
而选项C 只收集顶尖学生的数据会导致样本偏差，不能全面反映整体情况。
2. When collecting data for a math modeling project about the sales of a product, which of the following should be considered first?A. The price of the productB. The location of the storeC. The target customersD. The competitors答案：C。
在进行数据收集时，首先要明确目标客户，这样才能有针对性地收集相关数据。
选项A 产品价格是重要因素，但不是首要考虑的；选项B 店铺位置也有影响，但相对次要；选项D 竞争对手是后续分析的一部分，并非首要考虑。
3. In a math modeling study about traffic flow, which data collectionmethod is the most effective?A. Asking pedestrians for their opinionsB. Installing cameras to monitorC. Reading related research papersD. Guessing based on personal experience答案：B。
数学英语专有名词一般词汇数学mathematics, maths(BrE), math(AmE) 公理axiom定理theorem均值定理mean value theorem临界点定律Critical Point Theorem极坐标polar coordinate计算calculation运算operation证明prove假设hypothesis, hypotheses(pl.)命题proposition算术arithmetic加plus(prep.), add(v.), addition(n.)被加数augend, summand加数addend和sum减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend减数subtrahend差remainder乘times(prep.), multiply(v.), multiplication(n.) 被乘数multiplicand, faciend乘数multiplicator积product除divided by(prep.), divide(v.), division(n.) 被除数dividend除数divisor商quotient等于equals, is equal to, is equivalent to大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator四则运算Four Arithmetic Operations数字digit数number自然数natural number整数integer小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null, zero, nought, nil十进制decimal system二进制binary system十六进制hexadecimal system权weight, significance进位carry截尾truncation四舍五入round下舍入round down上舍入round up有效数字significant digit无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial多项式polynomial, multinomial系数coefficient未知数unknown, x-factor, y-factor, z-factor等式，方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation二阶微分方程Second Order Differential Equations 不等式inequation阶乘factorial对数logarithm指数，幂exponent乘方power二次方，平方square三次方，立方cube四次方the power of four, the fourth powern次方the power of n, the nth power开方evolution, extraction二次方根，平方根square root三次方根，立方根cube root四次方根the root of four, the fourth rootn次方根the root of n, the nth root集合aggregate元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function反函数Inverse Functions周期函数Periodic functions幂函数power function基本初等函数Basic Elementary Functions指数函数Exponential Function对数函数Logarithmic Function显函数explicit function符号函数sign function（缩写sgn）最大整数函数greatest integer function绝对值函数absolute value function特殊函数Special Functions复合函数Composite Function三角函数Trigonometric Functions反三角函数Inverse Trigonometric Functions 双曲线函数Hyperbolic Functions反双曲线函数Inverse Hyperbolic Functions多项式函数polynomial function定义域domain, field of definition值域range奇数odd number偶数even number连续continuous;可导Differentiable可微的differential拐点inflection point驻点stationary临界点(尖点) Critical point切线tangent line最大值global max极大值local max上凹concave up下凹concave down常量constant变量variable近似值Approximation单调性monotonicity奇偶性parity周期性periodicity图象image数列，级数series微积分calculus微分differential隐函数微分,隐微分法Implicit Differentiation积分Integrals多重积分Multiple Integrals导数derivative偏导数partial derivative单边导数One-Sided derivative一阶导数First Derivative二阶导数Second Derivative高阶导数Higher-order Derivatives参数方程的导数Derivative of parametric equation极大极小Maxima and Minima最大值Maxima最小值Maxima极限limit无穷极限Infinite limits单边极限One-sided limits唯一性;单值性Uniqueness 唯一性;单值性局部有界性Local boundedness 局部有界性局部有界性水平渐近线Horizontal asymptote垂直渐近线Vertical Asymptote无穷大infinite(a.) infinity(n.)无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral有理数rational number无理数irrational number实数real number虚数imaginary number复数complex number矩阵matrix行列式determinant几何geometry向量和空间几何Vectors and the Geometry of Space 点point线line面plane体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角perigon底base边side高height三角形triangle锐角三角形acute triangle直角三角形right triangle直角边leg斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle等腰三角形isosceles triangle等边三角形equilateral triangle四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width菱形rhomb, rhombus, rhombi(pl.), diamond正方形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid 五边形pentagon六边形hexagon七边形heptagon八边形octagon九边形enneagon十边形decagon十一边形hendecagon十二边形dodecagon多边形polygon正多边形equilateral polygon 圆circle圆心centre(BrE), center(AmE) 半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference周长perimeter面积area轨迹locus, loca(pl.)相似similar全等congruent四面体tetrahedron五面体pentahedron六面体hexahedron平行六面体parallelepiped立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron十二面体dodecahedron二十面体icosahedron多面体polyhedron棱锥pyramid棱柱prism棱台frustum of a prism旋转rotation轴axis圆锥cone圆柱cylinder圆台frustum of a cone球sphere半球hemisphere底面undersurface表面积surface area体积volume空间space坐标系coordinates坐标轴x-axis, y-axis, z-axis横坐标x-coordinate纵坐标y-coordinate原点origin双曲线hyperbola抛物线parabola三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arc sine反余弦arc cosine反正切arc tangent反余切arc cotangent反正割arc secant反余割arc cosecant相位phase周期period振幅amplitude内心incentre(BrE), incenter(AmE)外心excentre(BrE), excenter(AmE)旁心escentre(BrE), escenter(AmE)垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆inscribed circle外切圆circumcircle统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-square deviation, standard deviation 比例propotion百分比percent百分点percentage百分位数percentile排列permutation组合combination概率，或然率probability分布distribution正态分布normal distribution非正态分布abnormal distribution图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图 pie diagram。
